is Tey Admission Test for Undergraduate Programs MCQs With Explanatory Answers yee 1) 3 PU-M / Distribution of Marks Sr. No. Section Outen | Marks [1 _| Verbal Reasoning 20 | 20% 2 | Quantitative Reasoning | 20 0% 3 | Physics 20 | 20% | 4 Chemisiry 20 20% 5 | Biology 20 | 20% Total Marks: 100 Time: 120 Minutes Weyer to) COUEIMLIE IFDogar's Unique PU-Admission Test Guide PU-M (Pre-Medical) CONTENTS @ Selection Procedure ........ # Punjab University Admission Test for Undergraduate Programs — Guidelines for Applicants... @ Eligibility Criteria ~ HEC PU-2023 ¢ Content Weightages - 2023... « @ Guidelines to Fill Bubble / Answer Sheet. 6 Utd Etre th nth het Lorn (f + Tips for Solving MCQs Correctly....... + Fully Solved Original Model Paper (PU-M) STUDY MATERIAL Criteria and Subject Division Number of Test Items (100 MCQs) VERBAL REASONINGDogar's Unique PU-Admiss* Lod lo (Ligh fe veg is ae fe. mnpcrigalfigicl -L ad Uy— Umno frasety Wh cite — ome Sta ‘ bare Atl tegen he \ foe is) ion ae] rial PUGS baseless Ssis Feo scot Fait wees ReDogar’s Unique PU-Admission Test Guide PU-M (Pre-Medical) FULLY SOLVED SAMPLE PAPER-2023 UNDERGRADUATE STUDIES ADMISSION TEST (PRE-MEDICAL) Having 12 years (Intermediate or Equivalent Education) Verbal Reasoning 20 MCQs Time: 120 Minutes Quantitative Reasoning 20 MCQs Marks: 100 Marks PU-M Subjects; 60 MCQs | Instructions: Please read the following instructions carefully before attempting the paper. i 100 MCQs are given on various topics, which camry equal marks. Each correct answer carries 1 mark, | Attempl all the questions. i. In every question, four / five options are given (A, B, C, 0, E), you have fo select only one correct option. ii, ‘Mark your choice by filing in the appropriate cirde against each i wv. Use ball point pen (black or blue) to shade { blacken the corresponding circle in the answer sheet. ¥. ‘The candidates should carefully think about thelr answer before filing the circles on the answer sheet. Vi. Erasing, Cutting or overwriting is not allowed. Once an answer has been given on the answer sheet, the candidate will not be permitied to change any of his/her answer in any way. All such answers will be treated as wrong. Vil. The candidate should not wre anything regarding answers on te quasion paper. All answers must be given on the answer sheet only. VERBAL REASONING 1. Jesus is related to Christians in the same way as Zoroaster is related to ......? {a Jews (by Parsisy” ( ‘Tribals @ Catholics | 2, ‘South is related to North-West in the same way #5 Weat is related to ...-8. f@ South-West (b) Bast ! (o) North-East™ (a) South -3, Summit is related to Apex in the same way as Summon is related to .......? f Court () ~~ Judge ¢ Witness, @ Beckon” 4. Distil is related to Whisky in the same way as Brew is related to ......? (a) Ferment ‘ ) Gin © Beer (@) Sugar 5. DDT is related to Abbreviation in the same way as LASER is related to iu? (a) Antithesis (b) — ActonymY () —_ Bpigram (pitt CEADogar's Unique FU-AGmission Test VUInis 6, STRIDENCY: @ Harshness” () Flippant re) Consistency @ Sem 7. ACUTE: (a) Curious 0 Severev a Accidental @ Rice & OFTEN: i ee (a) Quickly (C] Never @ Sometimes¥ 9, . REJECT: * @ Allow 0) Agree G) Refuse (d) Accepty” 10, Stop taking drugs lest you are caught, (A) Might be caught” (B) Will be caught i (C) May be caught (D) Wouldbe caught 11. Itis all and one to me whether he lives in Karachi or Hyderabad. (A) Alll but one. (8) Allone (C) One and the same” » (D) Alor one 12. In his lecture, he dealt about the cause of the Guif War, (A) With¥ (8) On (©) For (D) No improvement 13. It is one and quarter hours since Haris went away. (A) One and quarter (B) One and quarter hour — (C) One hours and quarter {D) One hour and a 14. — Where politics fails, economics may sometime succeed, (A) May sometimes succeeds (B) May sometime succeeds (C) Sometimes succeed (D) Sometimes succeeds 1S. He has been working off and on for several years to compile a dictionary. (A) Regularly (B) Constantly ‘onal (C) On and oft” (D) Onor off. PASSAGE % “But we do not judge a cricketer so much by the runs he gets as by the way literature as in finance, says Washington Irving, “much paper and much poverty may cricket, too many runs and much dullness may be associated, If cricket is menacecDogar’s Unique PU-Admission Test Guide PU-M (Pre-Medical) perfection was astonishing; but the soul of the game was wanting in him. There was no sunshine in his play, no swift surprise of spending unselfishness. And without these things, without gaiety, daring and. the spirit of sacrifice cricket is a dead thing. Now the Jam Sahib has the root of the matter in him. His play is as sonny as his face. He is not @ miser hoarding up runs, but a millionaire spending them, with a Splendid yet judicious prodigality. It is as though his pockets are bursting with runs that be wants to shower with his blessing upon the expectant multitude. It is not difficult to belicve that in bis litle kingdom of Nawanagar where he has the power of life and death in his hands, he is extremely popular, for it is obvious that his pleasure is in giving pleasure. : 16. What is/are true of Shrewsbury? 1. He was a cricket player, {I. His technical knowledge about cricket was poor. II. There was no spirit in his play. @ Land 0) land IY © Only t (a) ‘None of these 17. The author feels that: a (a Technical perfection is not ® He who pays cricket with required in playing an adventure and enthusiasm ‘ ‘enjoyable cricket makes it enjoyableY @ He who scores a century must - (d) Cricket is a monotonous game be a good cricketer 18. Jam Sahib: E (@ ‘Was a splendid cricket player —_ (b) Lived in Nawanagar ( Neither (A) nor (B) is rue @ Both (A) and (B) are true” 19. “In literature as in finance... much paper and much poverty may co-exist.” What does it mean? fa) Jam Sahib was rich man ashe — (b) ‘Shrewsbury was a poor man was the king of Nawanagar © ‘The cricketer who gets lot of (d) ‘None of these runs may not play ain enjoyable cricket” 20, What gives cricket its character? @ The spirit of sacrifice oe The spirit of joyous adventure rr) The gaiety daring attitude of — (d) Allof these” the player : QUANTITATIVE REASONING : 21. The chairs in the school hall can be set out in 35 equal rows or in 45 equal rows or in 10 equal rows are: . : @ oo = . * bw 400 40 ® 80 22. ‘Three bells toll after intervals of 6, 9 and 15 minutes, respectively. If they toll together 5 p.m., when will they toll together next? R a 6:30¥ ’ -b) 5:30 Q 6:45 d 3:45Dogar’s Unique PU-Admission Test Guide PU-M (Pre-Medical) 23. It takes Riaz 30 minutes to mark a paper, Razi only need 25 minutes to mark a paper. If they both start marking papers at 11; 00 AM, what is the first time they will finish marking a paper at the same time? a 12;30 by 12:48 og 1:30¥ d 12:25 24, Sonia buys two off-cuts of ribbon in a sale, One is 153 cm long. The other is 204 em long, She euts them so that she ends up with a number of pieces all the same length. What is the greatest length each piece can be? a 39 ) 6 g 17 a 5iv 25. A farmer wants 10 fence a triangular field, He plaus to put a feacing post in each corner — and place other posts at equal distance along its sides, He wants the posts to be as far apart as possible. The sides of the field are 477 feet 2412 feet and 639 feet long. How far apart will the posts be? @ 18 feet ) 9 feet” o) 27 feet D159 feet ALGEBRA AND FUNCTIONS is solid cylinder of brass t2cm high and 6cot in radius is melted aad recasted into a right circular cone of diameter 16cm. Find the height of the cone. (a) 10.1Scm (b) 20:25cm~ (©) 28.75cm (@) 26.28cm — 27. ‘The slant height £ of a cone with radius of buse r and height f is given by £ = (a) War ©) y=? © wi +r @) wr 28 Ifa, band care the measures of the sides of a triangle, then area of triangle is (a) VEGF a G+ OCF, where 25=2+ bte (0) ¥s{s—a) (55) @—<) , where s=atbtey © VG=aG-BG-0. , where 3s" a+ bie @) ¥sG@=a) 6-5) @—o) , where2s=at bie 29. 20° = {a) 360° ) 630° (©) 120% @) 3600" 30. % radians € @ us () 135° 150° 31. Inthe following triangle, 4D = si Si o%Dogar’s Unique PU-Admission Test Guide PU-M (Pre-fledical) © 3 ¢ @) xi 32° «y+ 17 =9—x, what is the value of x? (a) 2 (By) 3 (c) -2 o 3 33. = 9, what is the value of.x’ ~ $7 196 @ .191¥ 16oom @ 3M. Hat—b=c~ds, what is the value of fin terms of a, 6, c and d? @ § . @) Bey 35. Primary data and ungrouped data are: A Same B ‘Opposite “ty Not same” D’ Proportional 36, The data which have not undergone any statistical treatment are dota. A Primary” ’ B Secondary "¢ Grouped “DD None of these Y BASLIVMENT AL SaREY Iss 3, ‘A tank 30 em by 20cm by ‘em is '/, full of water. How much water is in the tank? “A 3000 em? ®) 6000 em? © 1200 cm? @) 1000em? 38. During the first year, the population of 2 town increased by 4% and during the second year it diminished by 4%. If at the end of 2nd year, its population, was 2596, in Me-beginning it was: @ 25500 (8) 2,600 © 2,400, @) 2,500¥ 39. A solution of 27 gallons of acid contains 9 gallous of pure acid, How much water, in gallons, should be added to produce a 25 per cent solution of this acid? (A) ov (8) “418 (c) 27 ~ (@) 2s 40. Ina camp, there is provision for 1,600 participants to last 60 days. If the present strength of the camp is 1,200, the provision will last bd ———_ days. (A) 6 (By 86 © BO¥ os. @) n : PHYSICS — : ; al. Anelectric charge in upiforns motion produces: A) An electric field. - a enedgar’s Unique PU-Admission Test Guide soe __ Dogars Unique PU-hamlesion Test Guide__ annua 42. 43. 45, 47. 49, Si. C) A magnetic field ) Neither magnetic nor electric fields. If‘m’ ts the mass, ‘c’ is the velocity of light and x= mc’, then dimensions of ‘x’ will bez ANILT') 8) [MLT"] QIMLT}~ D) [MLT?] For a body to be in complete equilibrium A) Linear acceleration is zero B) Angular acceleration is zero. + C) Linear acceleration is zero but angular acceleration is not zero D) Linear acceleration and angular acceleration both should be zerow’ Ifa force of magnitude 8 N acts on a body in direction making an angle 34, its x and y A)Fy=4 V3 and F,=8 B) Fy 4 V3 and F,= 47 CpFx* 8 and F, 4 V3 D)Fx=8 V3 and F,=4 The difference of a vector Band its negative vector- B is i A) A cull vector B) Equal to magnitude of vector B ©) Twice the magnitinde of vector B “ -_D) Smaller than magnimde of vector 5 Time of projectile’s flight is : ein) 2 ‘ ‘ 2 a y,sin“6 5) yjsin& © 2visin® | p) sing 8 8g 8 Two forces, 5 N and 10 N are acting ut ‘O' and ‘P’ respectively on a uniform meter rod suspended at the position of ceatre of gravity $0 cm mark as shown in the figure. a $0. P___100.cm ye ‘What is the position of ‘P” on meter rod? nee A) 80cm B)70.cm ©) cm¥ —D) 65cm An Millikan’s Method, the radius of droplet can be calculated by: a, > _ MV, , 2 ny, ony, A) r= f+ By r =——v ae TE D)r=—+ ie i 36. epee A tiny droplet of oil of density ‘p' and radias ‘falls through air under force of gravity. If viscosity of air is “y’, ho terminal velocity acqeived by Gee ll drop lgiven B= 4er’p 2gr’p Sne’p Sne'p A) vm pyre, Ce ee ay cal cath Yrs le gr ie ene ele i then fringe spacing becomes: A)Zero —,_—-—_-B) Doubles of the original value” C) One D) Half of the original value ta leon’ ntertromeer 72 rg fnges ps aco the Geldof view when63, Dogar’s Unique PU-Admission Test Guide % : movable mirror is displaced through 0.233 mm using the equation I= m= the wavelength of light used is: A) 588 nmv B)348nm . C)620am DD) 400 nm In Michelson’s Experiment, the formuls to caleulate the speed of light is: A)c=2 fd Benet ©) on 2a D)c=16 tov The information received at the other end of a fibre ean be inaccurate due to & the light signal, A) Longer wavelengths C) Intensity B) Frequency D) Dispersion or Spreading” The pressure on the other sides and everywhere inside the vessel will be according to the: A) Pascal’s Law” C) Boyle's Law B) Hook's Law D) Charles's Law ‘The value of universal; Gas Constant ‘R’ is: A) 8.314 Jmol"k" C) 1.38 Jmor'k" B) 1,38 Jmol'K? D) 8.314 Jmor'k"Y For adiabatic process, the First Law of Thermodynamics is; A)W=4U+Q B)Q=W C)Q=-W D) W=-AuY ‘The entropy of the universe always: : A) Decreases C) Remains the same B) Increases” D) Both A and B The work done in moving a unit positive charge from one point to another against th electric field Is a measure of: A) Capacitance B) Potential difference between two pointsy C) Intensity of electric field D) Resistance between two points To Millikan’s Method, the radius of droplet can be calculated by: Ayr= ayy B) pay, or=Th ae . ¥2pg 28 68 2pe The scalar product of | and kis: A) Zerow | co) B) 90° D)-! CHEMISTRY A researcher hi repared a sample of 1-bromoropane from 10bg of 1-propanol. Af purification he hog tendo 12g of product. Which of the following is percentage yllds A)60% 8B) 90% ©) $8%Y D) 50% Which one of the following has same number of molecules as present in tig of C purification’ he had made 12g of product, Whieb of the following is percentage yield: A)CH,O —_B) C)H,O Q ene ee CHO ture is due to a stability in the following structure 3 ei inthe ica 13Dogar's Unique PU-Admission Test Guide 67. 70. B) Hyderogen bonding between NHY D) weak vander Waals force group of one peptide and CO group of another pertide a While finding the relative atomic mass, which of the following standard is: weed ‘compare the atomic mass of chlorine (35.5 amu): A) Carbon - 124° C) Carbon ~ 13, B)Neon~20 * D) Nucleon number Liquid in the container have temperature 70C. What will be temperature: ia scale? 4 A)283 K O)MIKY B) 350K D) 300K Number of neutrons in $}Zn will be: A)30 B)38 .C)35— D364 The maximum number of electrons in electronic configuration can be calculated formula: A)2+1 By2w'Y —C)dn?+2 D)2n +1 ‘ Isoptic symbol of fon of sulphur -33 is 2S”, How many no of protons present If the number of electrons are 1 i A)P©(8n°1S B)p=16,n=16 C)p=t6a=17% D) p=17,n=16 Which of the following isthe correct equation to calculate relative molecular. gas: A)M=mRT/PV 4 C) M=mPR/VT. B)M=PV/Mn D) M=mPRT/V ‘The formula which shows the simplest whole number ratio for the atoms of elements in a compound is; A) ionic formula C) empirical formulay’ B) structural formula D) molecular formula ‘A) pH scale C) Hydrogen Scale” B) pOH scale » _D)pK, scale ‘The reaction which is responsible for the production of electricity A) Hydrolysis reaction C) Redox reaction” ae D) Reduction reaction ~ Glucose is converted into ethanol by the enzyme A) Urease C) Sucrase B) Invertase D) Zymasey ‘The rate of resetion involving ions can be studied by A) Dilmomerrie ; C) Optical rotation D) Electrical condDogar's Unique PU-Admission Test Guide PU-M (Pre-Medical) Energy required to remove an electron from the outermost shell of its isolated gaseous atom in the ground state is A) Electron affinity C) lonization em B) Lamticeenergy D) Crystal energy * Which of the following carbonates of alkali metals is not stable towards heat and is decomposed on heating to its oxide along with liberation of CO,? A) LiCO,¥ C)K,co, B) Mg:COy D) Na;CO; ‘The presence of calcium is essential for the normal development of plarits..An adequate supply of calcium appears to stimulate the development of which part of the plants? vo A) Leaves C) Root hairsY” B) Fruits D) Branches. Which of the following sulphates is not soluble in water? A) Sodium Sulphate C) Potassium Sulphate B) Barium Sulphate” D) Zinc Sulphate The trend in the densities of elements of Group LU-A of the Periodic Table is A) A gradual increase¥ C) First decrease then increase B) A gradual decrease D) First increase then decrease BIOLOGY Which one of the following cell eventually converts to mature sperm? (A) Spermatids (B) Secondary spermatocyte (a) SpermutogoniaY” (@) Primary spermatocytes Which one of the following movement through cell membrane requires energy? (A) Active transport (8) Pinocytosis” co Enetocyces (dD) Passi... Transport ‘The most common enzyme in the world is — 5) (A) DNA Polymerase B) — Ribulose (C) ~ Huligen (DB) Gyrase Part of the Forebrain working as # coordinating centre between Nervous system and Endocrine system is: (A) Medvila (B) — Arnyglada © HippocampusY (D) Hypothalamus ‘Which carbohydrate is required for the synthesis of ATP ta) Glucose . (B) Ribolose” © Fructose (D) Ribose is involved in the release of antidiuretic hormone (ADH) involved in water (A) Anterior pituitary 3) Adernal Gland (CQ Thyroid Gland¥ (dD) Posterior pituitry Isotopes of Were used to prove semi conservative model Of DNA-...+++++++0 (A) Ribose (B) —_Nitrogeny’ (C) Uranium (D) Phosphate (aDogar's Unique A eee naneenerenenenen _ Single rlaged pyrimidines are: __£_ Inthe structure of» protein molecole resuting from the regular ¢0 of the chais of: (A) Secondary structure” B) Tertiary structure (C) —-Quadrary structure (D) —-Prismary structure = Membranous sae surrounding the human heart Is called: (A) Myocardium (8) Epicardium (C) —Pericardium ) — Endocardiumy In the stomach, Hydrochloric acid (HCI) Is produced by: (B) ne (A) — Cesterape: (C) _. Tonoplast (D) wi onan Enzyme is used to built the new strand of DNA? (d DNA reductase {B) DNA endonucleose (© DNAtipasev i) : Unit of inheritance Is (A ee 5 © @ ne retary valve Is found pig Inferior vena cowa & right (B) Alr sue of the Lungs are also called? (A) Bronchioles (©) — Alveoli Parathormone is antagonistic to; (€) Increase Blood calcium level The substrate molecule bes complementary shape with: (Aj _ Product (8) - Cofactors - (d) : (A) Cytocines, Adenine. & (8) Thymine? i (C) Adenine & Guanine (0) ¥~ FQuantitative Reasoning j2s wcos o——oo———EEe——— = The basic mathematical skills, understanding of elementary mathematical concepts, and the ability to reason quantitatively and solve problems in a quantitative setting are measured in the quantitative part of the test, The Anowledge of arithmetic, algebra, geometry and data-analysis, which are usually essential area of study of the bigh school level are, measured in balanced questions, The questions about quantitative ability can also be asked from: M Discrete Quantitative Questions M Quantitative Comparison Questions xg Arithmetic jos mc ___ ERR eee es Chapter 1 == NUMBERS Numbers: In decimal number system, we use ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 called digits, 1 represent any number. Note: A group of figures, denoting a number i called numeral | ‘Types of Numbers : | Natural Numbers: Numbers which we use for counting the objects are known as natural numbers. It denoted by 'N. N={1,2,3,4...0,} Whole Numbers: A Nar terse th 2 a es oa ember. denoted by ‘W. W20,1,2,3, ud Integers: The set of numbers which consists of whole numbers and negative numbers fs known, integers. Itis denoted by Z. AED OO. 1.2, Sirrdh is the set of all positive integers. It is clearNegative Integers: The set {0, 1, 2, 3, }is a set of non-negative integers. P| Positive Integers: The set (0, ~1, -2, -3, ......) is the set of non-positive integers. n Numbers: Tha aber Whar chi by 2 cae Even Nunbe. E=(2,4,6, d Numbers: eee Ont ate yarns 39,1 is smatier than every positive number. (is greater than every negative number. For any integer p; p x 0 = 0, For any integer p (including 0): p + 0 = undefined. For any postive igo p 0+ 90, For every integer p; p + 0 and p-0= p, as riiad ot No Wve tignbors dl then at least one of them is 0. Properties of one: For any number p: p x 1 = =pand =p, 1 is the divisor of every integer. 1s an odd integer. 3 1is not a prime number, DT ne eae Ce 4 On een Sen = ber. mple 1: Find the factors of (i) 64 and (i) 75. ttion: () 64 = 1x64 =2x32 =4x16 =8xB factors of 64 are 1, 2,4, 8, 18, 32 and 64, (i) 75 =1x75sieatty, 06760 ja general, we halve Dividend = (Divisor x Quotient) + Remainder multiple of a Number: A muttiple of any natural number is a number obtained by multiplying that number by any natural pumber. Example: Find the multiples of () 4 ess than 30 (i) 9 less than 60 Solution: (i) 4x1=4 4 4x6=24 4x7= Bete. The multiples of 4 lesg than 30 are 4, 8, 12, 16, 20, 24 and 28. (i) 9x1=9 f 9x2=18 9x3=27 9x4=36 9x5=45 9x 6=54 etc, The multiples of 9 less than 60 are 9, 18, 27, 36, 45 and 54, Divisible of a Number: ¥ a number divides a second number without leaving any remainder, then we say that the second number is divisible by the first number. For example, since the number 2 divides 14 without leaving any pomalicer, wo Say hat VA Mibipls Chat Qustine QI. How many numbers between 200 and 500 are divisible by 13? (A) 23 @) 17 (C) 15 (0) 32 Q2.- The first five multiples of 17 ares é (A) 0,1,17,34,51 © {B) 17, 34, 51, 68, 85 (C) 38, 57, 76, 95, 114 ~ (D) None of these @. The number which s alvisible by 7 but not by 14s: (A) 21 ‘ ®) © 7 2 . None of these e. TeQt) Giaabie drinker up cab are divisible by 13 6 ofp eB ygle a8 ‘The required numbers = 38 - 15= 23 Hence, the correct answer Is choice A. Q2(8) The first five multiples of 17 are 17 x5=85 7 First five mutiples of 17 are 17, 34, 51, 68 and 85, Q3,(A) The number which is divisible by 7 but not by 14 is 21, Hae, come are A Q4(8) There is only one even prime number, namely 2. Hence, the comect answers choice The least prime number Is 2. Hence, the correct answer is choice C, eoneeneeerarrenen Chapter 2 MULTIPLICATION AND DIVISION MULTIPLICATION: Multiplication isa short method of adding the seme number repeatedly. PROPERTIES OF MULTIPLICATION: 1. Multiplication is commutative for rational numbers. Example: x “ " * winols a : aiwalepogar's Unique VAT Guide USAT-M (Pre-Medical) 3 Multiplication is distributive over addition and subtraction for rational numbers. Example The sign of the product is -ive, if there are an even number of negative factors or there are egative factors. The sign of the product is ~ive, if there are an odd number of negative factors The process of subtraction of the same number from a given number for a few times is called division (+), Le, 4 6 + 253 (2.can be subtracted 3 times from 6) IMPORTANT POINTS 3 1, Division is the inverse operation of multiplication. For example 6 + 2 = 3 means to find the number by which 2 should be multiplied so as to obtain 6. Because 3x2=6 Therefore,6 + 2=3 2. When a number is divided by another number, the first number i.e. the number which is bein divided is called the dividend, the second number which divides Is called the divisor and th number obtained as a result of division is called the quotient. In the above example, 6 is th dividend, 2 is the divisor and 3 is the quotient, > . The operation of division starts from the left whereas the operations of addition, subtractic ‘and multiplication start from the right. ‘Any number in the unit's place which is either even or zero.Dogar’s Unique USAT Guide USAT-M (Pre-Medica, ee oN The last three digits of a number is | 2125000, 135923120, 7792320, 4256" divisible by 8. or The last three digits of a | etc, number are zero, SL ee et, The sum of all the digits of a number is 33456735 :3+34+44+5+64+7 43> Givisibleby®. = 36 divisible by 9. Any number which ends with zero | 70, 789790, 7111130, 5773313570, > | 112300100 et. 4235682: Sun 1=4+3+6+2= 95 Sum 2=2+5+8=15 ‘Sum 1 = Sum 2, the number is divisible by 11, or 283712 : Sum 1 =2 +3+1=6andSum2=8+7+2= 17, their differ 17 - 6 = 11 is divisible by 1. The sum of digits at odd and even places are respectively equal or differ by a number divisible by 11. The number which is divisible by both 4 and 3. ‘The number which is divisible by both 2 and. [15 | The number which is divisible by 3 and 5._| The number whose ast 4 dgt number's hse by 16. ‘Any number which is divisible by 9 and has its last digit even (or zero). Model Examples: Qi. Multiply 63987 by 91763 is not more than 3 lines. Solution: 63987 91763" —_ 4031181 ipEaen 63. 4479 09xx 700 5S/ 1550084Dogar’s Unique USAT Guide USAT-M (Pre-Medical) = 1370 * 60 metres per hour ‘ 1370% 60%39.37 T2x3xi769 "ee Parhour = — 51,077 miles per hour Ans. (Q4. A boy when asked to multiply a number by 7/8, divided this instead, by 7/8 and found the answer i too great. Find the number and the correct answer Solution: Let the number be ‘x’ (ob -(xd) até 8 8) 14 8x 78S ay nace 7 8 #14 64x-49x 15 ; 56 14 Ix _ 15 56 14 56x15 2 =f 14x15 Comet ener 4x2 32 Ans, ; Q5. The sum of the squares of two consecutive integers is 1105, Find the integers and check your answer. Solution: Let the two consecutive positive numbers be: xx Then sum of the squares of these consecutive numbers = _ 1105 Check: Reetp = 1105 (23) + (23 + 4)? = 1105 - t+ + = 105 §29 +576 = 1105 2x + 2x-1104=0 1105 = 1105bonr ---y Dogar’s Unique USAT Guide ae HIGHEST COMMON FACTOR & LEAST COMMON MULTIPLE HIGHEST COMMON FACTOR & LEAST COMMON MULTIPLE The highest common factor of two or more numbers is the greatest number which divides each of them exactly, Methods of finding 1,C.F. () By Prime Factews. Ferre ra aten wae Fe es pie eae The product of all prime common factors is known as Model Example: Find the H.C.F. of 630, 1050 and 1260, . Solution: 630=2x3x3x5x7 1050=2x3x5x5x7 1260=2x2x3x3x5x7 2. HGF. is2x3x5%7=210. Ans.” @, By Division: Find the H.C-F. of 5133 and 3953 Step |. "ding the grea rintber by the lesser, we gel manda. Step Il. Dividing the previous divisor 3953 by 1180, we get the remainder 413. Step ill. Di the previous divisor 1180 by 413 we get the remainder 354, Step IV. ividing the previous divisor 413 by 354 we get the remainder 59. Step V. Living to ora vus cor 34 Py 2 vs 0 The last divisor 59 is the H.C.F. Note:H. also known as Greatest Common Measure LEAST COMMON MULTIPLE eM) Te aEpogar’s Unique USAT Guide USAT-M (Pre-Medical) Qt. Find the L.C.M. of 70, 80, 90. Solution: 10=2%5x7 80=24«5 90=2xHxG L.C.M. = 2'x 32x 5 x 7 = 5040 Ans. (i) With the help of H.C.F, The product of two numbers is equal to the product of their L.C.M. and HOF. L.C.M. of two numbers = Product of numbers HCF. L.C.M. and H.C.F, of Factions. ‘The L.C.M of two or more fractions is the least fraction or integer which is exactly divisible by each f them. : L.C.M. of two or more fractions _ _L.C.M. of numerators “H.C.F. of denominators H.C.F, of two or more fractions The H.C-F of two or more fractions is the highest fraction which is exactly divisible by each of the fraction. 5 _ __H.CF. of numerators 7 . L.C.M. of denominators Model Examples Q1. The H.C-F. of two numbers is 34 and their L.C.M. is 4284. If one of the numbers is 204, find the other. Solution: As product of 2 numbers = their H.C.F. x L.C.M. The other number is = SaKAEeN 204 <=7t4 Ans. a2. inate at tars ih wen rin bya numbers 6; 9, 12, 15, or 187 cM of 6, 9, ae 18= 180UDAI Dogar's Unique USAT Guide DA TM (Pro-tec, 3, Three men A, B and C go walking round a circle one mile in circumference at the rates of 4149 , and 105 yards per minute, respectively. If they all start together and walk in the same direction, Whe, will they first be together again? Solution: Circumference of the circle 44 35: = { mile or 1780 yds fC ol anes A will complete the circle in Maing bias 178, 1121.2, 2 73) Amin, 1% 21,3°% 24, 2 * B will complete the circle in 7 | 231-308—35, 1760 44 =——— = -— min, 120. 3 C will complete the circle in 1760 382 105” 21 LOM = ie, Qi. Q3. Lomot tt, 22.352 minutes. ree they will be together again first after 352 min, or § hrs, 52 min. Ans. 7392 = 738 er Uo er LG z. Aneon sign flashes every 3 seconds, another sign flashes every 5 seconds, and a bj flashes every 7 seconds. if they all flash together, how many seconds will pass be they all flash simultaneously again? (A) 15 seconds (B) 35 seconds (C) 105 seconds (0) 21 seconds The greatest number which exactly divides 1155 and 735 is: A) 2% (8) 5 () 15 (0) 105 The least number which when divided by 35, leaves remainder of 25; when divided! 45 leaves a remainder of 36 and when diyided by 55 leaves 45 as remainder, Is: (A) 3455 (8) 3465 . (C) 3475 (0) - 10 The L.C.M of 12,20,24,32 Is: ; (A) 240 : (2) 360 y (Cc) 480 (0) 600 ie How many whole bricks 6 x 12 x 24 em? willbe sufficient to construct a solld cube¢ minimum size? = oe “4 : iis 8 “ — .=3x5x7= 105 Q2. —(D)_ The required numbers the H.C.F of 1185 and 735 735 ) 1155 BS 4 420 735 42 315 )420 105) 315 315 x The greatest number required is 105, @3. (A) _ The least number which is completely divided by 35, 45 and 55, is thelr L.C.M. which ts 3465. We want to find the least number which on dividing by 35, 45 and 55 leave femainders 25, 35 and 45 respectively /.e., 10 less than the quotient in each case Hence such a number is 3465 — 10 = 3455 Q4. (C) The L.C.M, of 12, 20, 24 and 32 is Bx3x5 =32x3x5= 480 Q5. — (C) One edge of the minimum cube must be 24 cms, the least common multiple of € ‘and 24, Thus, it will have a volume of 24 x 24 x 24 cubic centimeters which is equ 8 bricks : 24% 24x24—— ooo ie 7 wumbe prime factors taken hall 9s many times as they occur in te” (i) By Division. Model Example: Find the square root of 2480625. Solution: "240625 (1575 1 25/148 125 307 | 2306 2149 3145 | 15725 1725 ae © Ans, 1975 Q2. Find the square root of 43.45 to four decimal places: Solution: 64345 (6.5916 36 125 | 7.45 : 6.25 Mote 1309} 12000 . 11781 3181 | 21900 13181 131626 | 871900 8004 ‘- As remainders more than half 65917 Ans. * i Q3. Find the value of pemcemennann i er 5 a GOD i amines outon: VB \ =a) aferVO 7 SSS a JMPORTANCE: The unitary method and chain rule have quite an importance in our daily ie. It is explained by the following model examples, Mode! Examples; Q1. Ina kilometer race A can beat B by 40 metres and B can beat C by 60 metres. How many metres can A beat C in a 500 metres race? Solution: Let A covers 1000 m. Then Becovers: 1000-40 =960m. and When B covers 1000 m. then C covers 1000-50 = 950m, When B covers 960 m. C covers (iam = = 912m. UNITARY METHOD AND CHAIN RULE ie, when A covers 1000 m. C covers = tt m = 456 m, or when A covers 500 m. race, A will beat C by = 500-456 = 44m. Q2. Divide Rs. 510 between A, B and C so that A gets 2/3 of what B gets and B gots % of what C gets. Find the share of each. Solution: Let C's share be Rs. x 1 x B's share is =— i 4 Zion x ' is Soe A's share is ae é Total amount = Rs. 510 By, =+= =610 Beri pense =510 12 12x510 a= —_ Q3, Divide Rs, 600 among A, B, and C so that Rs. 40 more than 2/5 of A's share, Rs. 20 more than 2/7 of B's share, Rs. 10 more than * Sey ere te Peers Solution: Let - 2 otAsshare + Rs. 40 2 ~ of B's share + Rs. 20 3 of C's share + RS. 10 be sy, ota share =x-40 or A's share = 5 (x40) Similarly B's share = Zoe ~20) C's share = Dee-10) As total amount = Rs. 600 ef Sx-200 , 7x-140 , 17x-170 _ 69 a 2 2 9 a abe 1800s Ge a i or 142x340 = 600 x 18 = 10800 442x= 10800 + 3400 = 14200 A's share = 3110040) =Rs. 150 B's share = ae Cs share = 2 o0-10)=Rs. 170 Qs, ‘A gartson hes enough proven fo€62 dae: ar 20 dey »vedecenent of 0 at ee and the food would then last for 24 days only, How many men were there in the garrison originally? Solution: Let there be x men in the garrison originally. After 20 days no. of men = x + 400. If these men had not joined, the provision would have lasted for 50— Rake aly Fork mon te Paige on ee aaa ‘ For 1 men the provision in last for 32"ogee USAT-M (Pre-Medical) But provision lasted for 24 days 32k 94 Sr 32x = 24x + 9600 200 men, Ans, CC er at ‘What Is the least positive integer which Is to be added to 57592910 so that the sum may bea perfect square? (A) 7588 (8) 7 c M1 (0) 15166 Arectangular field which Is twice as long as it Is broad, has an area of 14450 m?, what is oe Its perimeter? (A) 85m (8) 510m (C) 165m (0) 170m 0s. The cost of the planting sugarcane at the rate of 6 paisa per square meter Is Rs. 5840.64, What is the length of side of this square field: (A) 312m (8) 622m (C) 97344m (0) 459m os. What is the smallest number which when subtracted from 1.00060219 gives a perfect ‘square number? (A) 0.00210 () 210 (©) 0.000210 (0) 0.210 35. The product of 313 with itself is; (A) 97969 (8) 17.69 (Cc) 5536.97 (0) 195938 CLL Pie x. — (C) —_ §7592910 is greater than the square of 7588 (using calculator). ‘The next squared is the square of 7589, (7589)? = 57592921. Now 57592921 — 57592910 = 11, which is the required integer to be added. 2 Ate ng ice as og 28 with and 0s earl canbe ded io 2 ee 4450. The area ofeach Square region oan =7225m* Now longi of cosh poke, iS ;Moye! Ss UInGue VORA! VulEe — ys = 2(255) = 510m, a3. (A) Cost = Rs, 5840.64 = §84064 paisas Area = 584064 _ 97344 =312m as. es 1} 1,00060219 (1.0003 pel een 2.0003] 00060219 0009 _ 210 There are eight places after the decimal in the given number. so after subtracting 000th, from the given number the remainder would be zero, So .0000021 is the required number. Qs. (A) 313x313 =97969 eerneneneanenvenes Chapter 5 FRACTIONS & DECIMALS . : FRACTIONS: if any unit be divided into any number of equal parts, O08 OF Ne. Of aa Called a fraction of the unit. ple ; The fractions one-fourth, nota shut ae ci won e | NUMERATOR AND DENOMINATOR: : Sha, one ont wh Se tects no te cn, ‘ denominator. Terms of The Fraction: The numerator and the denominator of a fractions are called its terms.pogar's Unique USAT Guide USAT-M (Pre-Medical) In the above example denominator and the numberator have a common factor, thus is noi ts Jowest terms. If we cancel out 2 by dividing numerator and denominator by 2 we fn 3 which has no 3 common factor. hence i in ts lowest terms Proper Fraction: A proper fraction is one whose numerator is less than the denominator. [ Note: The value of proper fractions is always less than 1 IMPROPER FRACTION: Arto nee et ea ee 15 13 ' imple ; Re and are improper ractons. [[Note: The value of an improper fractions is always more than as equal to 1. Mixed Fraction: ‘When an improper fraction is changed to consist of a whole number and a fraction, it is called @ mixed fraction. 15 imple ; the improper fraction +> ® can be wren as, which sa mixed fraction. 13) 15 13 2 Compound Fraction: ‘A fractions of a fraction is called a compound fraction. DEwvle 2s a compound frac, tustotdedxges Complex Fractions: i te et ke asven M (PI Now, 3 ofa plot costs «Rs 45000. 6 45000 | 6 35 Ol the plot willcost =" 17) * 95 ample 2: A sum of money increased by is sith part amount to Rs. 56. Find the stim Solution: Let x be the amount of money, thus ; x45256> ms = 5 > x = 56. > k = 6x6. ei = BS. 4g VULGAR FRACTIONS In questons of tacos signs +, -, +, of (Of sniles mulipicaton) and brackets, are a involved. In simplifying these questions the following order must be followed: IMPORTANT POINTS. () Remove the brackets. (i) Then quantities which re connected by Of shouldbe simplified. Sof =|~-—-= ieee eed “167 3|3 46Dogar o winque USAT Guide 1_Mis {5001 af {gers} “75 -3[8 +3] 2 914 36 = 74-115, 36 2 9145 USAT-M (Pre-Medical) Solution: al- ) 35415-42 Saris 315 + pei ye +] + weleNi— 1 ainiwUSAT-M (Pre-Medicay Dogar's Unique USAT Guide The fractions of the form a + — + c+—— ert & etc. are known as continued fractions where @ b, ©, ....ssss:ss: Note: In order to simplify such fractions, we begin with the lowest part and proceed upwards, etc., are any numbers. stan cy Sep,USAT-M (Pre-Medical) —_—— EEO 53. 44 583 s=x— 2 . 38 36 342 DECIMAL FRACTION A fraction involving decimat point is called decimal fraction. Conversion of a decimal fraction into vulgar fraction: Rule. Write down the given number in the numerator omitting the decimal point and for the denominator write 1 followed by as many zeroes as there are figures on the right of the decimal point, As 46776000 100 1990083 nd 19,0083 = 1920083 5% 10000 Qi. it, and are alin lowest terms, Then how many integer, x, between 30 and 407 5 ® 4 (Cc) 2 (}) 3 (0) None ofthese 66 8 6 a2. Seq" te% ae 30m 1 1 A a / (®) . as (2) o + 1 (0) Neves 3. 11 ofa number 38, what i of hat number? 9 ® A > . Ce) 16 s ols 3Dogar's Unique USAT Guide ~--s1-m (Pre-MeAeS 1 (0) 2 © 3 5 (0) None of these ed Pad Qt. (0) xis even, then wl rte in lowest tm This is because, both x and 8 are divisible by 2. Now we take the odd number between 30 and 40, these are; 31, 33, 35, 37, 39. In Srese numbers, we see that 35 and 39 are divisible by 5 and 13, respectively. Thus only 31, 33 and Saas ee 6 6 6 Q2. (A) simpliing $x 1% fe 24°30 Welt fa 1*2*3%4*5 2 Q3. (8) marianne Therefore the ofthat number willbe 78 ee 44 of anumberis 9, tereore double of (4 x 2 i Bocas = rang be equal to 39 x 2=78, Q4, (A) ite he eae ee aed axe 26x? 2x | MN exam | 21x30 _ Axe p > SA heldEe OO Der: 1 Express 2 7 % to a fraction * Change —% toa decimal @ 4 solution: " ghag = 1% @ 7 1 = Sx Replace % 7 ia eplae%by 1) bu 140 nel 140 ff 3% = 38 een Y @ 4 ‘fo 4” 100 place % by 1 3 = —=.0075 400 Change of Fraction into Percentage: To change a fraction or a mixed numbers to a percent. a. _ Multiply the fraction or mixed number by 100 b. Reduce, if possible . Cc Affix a % sign. DEewvle : | ipit 0 Change git a percent {) Change 0.05 to a percent Solution:Dogar's Unique USAT Guide USAT-M (Pre-Medicay To express one quantity *p” as a percentage of another quantity “q’. a Write p as a fraction of q. Le., . b. Maly the fracton by 100% to convert it to a percentage, ple 3: There are 56 boys in a class of 140 students, What is the percentage of the boys Solution: Total students = q= 140 Boys = p= 56 po Fraction = 2h 140 56 Percentage = = x100% 240% Important Tip: 3 j ita salary ofa man sft increased by x and then ithas decreased, the change in its initial salary isless by hofxor ae . Note: two values ae respectively hand bk more than atid value, hen he fist is 100-2 x 100's of the the first to the second? Solution: Following the above, we have the value = 100+20 *“700+50 120 TsO = 80% «100%| Dogar’s uniquy vont wulde USAT-M (Pre-Medical) imple 5: tf Hamza's salary is 35% more than that of Osama, then how much percent is Osama's salary less than that of Hamza? Solution: Following the above rules, we have the value. 100+35 on Important Tip: if the first value is 1% less than the second value, then the second is lies =F x00} ‘more than the first value. (8) (C) decreased by 12% “(0) increased by 16% a2. If x% of yis 20, then y= rf (a) 20003 e 2 © aan oO % a3. 12isy% ‘oot woataurber? ri ‘ 8) (c) 36 (0) Klee ant twa pat of 0 (A) (8) (Cc) rh What is 10% of 30% of 40%? (A) 0.12% (C) 12%Dogar’s Unique USAT Guide USAT-M (Pre-Medical) 7 [» y~v 1% increase or decrease according as the sign +ve or -ve, respectively. try 100 | t sleemeet x= 40 and y = 20. Therefore (40)20)) [+0 20 100 100 20 - ro |x 100} [20 8)% = 12% Because sign is +ve therefore its area is increased by 12%. x Q2 (C) ¥x 799720 => W=20x100 = xy=2000 aS. Part 1 Q3. (0) Using. Whoje = Y Percent, here P= 12, W=? and Y percent="95 —=— —=Yx— < = Ww 100 W 100 —=-x— > W =31200 =3600 Q4. (0) 400% of p= 400 x p= 4p, which 1% of 4009. ~x217=21 x 32! Q1. —_ In acity 90% of the population own a car, 15% own a motorcycle, and everybody own! ‘one or the other or both. What is the percentage of motorcycle owners to who ow: cars? } (A) 15% ‘ @ % () 75% 0) 33h Concrete consists of cement, sand and screenings in the ratio of 1 : 5 : 4, what is percentage of the sand mixed? (A) 10% 8) 40% “ (C) 50% (0) 60% . Q3. “Three business partners shares have profit of Rs. 24000 in the ratio 5: 4: 3. What is’ amount of the least share? :pogar’s Unique USAT Guide USAT-M (Pre-Medical) (c) 2122 (0) 3980 Qs. If theratio of xand is +! what is the value of 2x to y? i 2 ) 6 8) 6 22 u Oo = o * y pba i. (0) _Letx stand for the percentage who own both a Car and a motorcycle. Then (The %age who own a motorcycle) + (The %age who own a car) — (The kage who ‘own one or the other or both) = 100% own one or other or both. 15% + 90% —A = 100% => 105% ~A = 100% = A= 5%q The %age of motorcycle owners to who own car is a2. (C) Ratio 5: Sum of ratio =1+5+4=10 Sand = > 100=50% 10 Q3. A) Ratio =5:4:3 ne AN Sum ofratio =5+4+3=12 - least share = 5 x24000 : ‘2 = Rs, 6000 a4. (8) Le bee numberof parsn 4 Ros : Then 16: 1280:.44:x Mest ; jb No 1280, Ves. +, Dogar’s Unique USAT Guide USAT-M (Pre-Medicay Chapter 8 AVERAGE In Mathematics, average is a representative of a number of given quantities, Average Is of several kinds. METHOD OF FINDING AVERAGE: To find average of any number of quantities of the same kind is to add all the items together and then divide the sum b ra meet __ Sum of all the ite No. of items Model Examples Example 1: ha sci dlyteprae fm @ Janaty 168 Jarry (000 CANE) Wan and that from the 10" to 17" January (inclusive) was 39.2°. Nhat yes he lrberatne 00 aaa Solution: Total temp. from 9* Jan. to 16* Jan, = 38.6 x &C = 308.850 ; 4 Since the temp. on 9* = M60 s 4 Total temp. from 10 Jan, to 16 Jan. = 308.8 - 34.6 =274.2C Total temp. from 10 to 17 Jan. = 39.2 BC aa = 313.60 Temp on 17" Jan. =313.6-274.2 = 39.40 : Example 2: A goods trainin five successive minutes from its stat runs 68 metres, ter menes, mets, 312 metres and $35 metres and ort ve mindesin maintains average speed of Fin the whole dstane covered and the average speed finn kfou, Solution: Distance covered in first five minutes. _ +127 +208 3124535 iear’s Unique USAT Guide USAT -M (Pre-Mearcey, Distance covered in next five minutes = 22%5 2 EL joy oo 4 16 44 = 4 kins, Ans. Average speed == “bmn =4 560 10. = 24 km/hr. Ans. Example 3: The average salary per head of all the workers of an institution is Rs. 60. The average salary per head of 12 officers is Rs. 400. The average salary per head of the rest is Rs. 56. Find the total no. of workers in the institute, ‘Solution: Let the total No. of workers= x Total salary drawn = 60x Shah Salary of 12 officers = 12 x 400= 4800 Rs. win the rest = (x=12)*56 Hence total salary of the workers = (x 12)56+ 4800... i) 5 Total distance covered in 10 minutes = = + 4 Equating (i) and (ii) 60x = 4800 + 56x - 672 Qt. The average of even integers from 2 to 100 inclusive is: (A) 49 (BR) s2° () 51 (0) 50 Q2.° _ Whatis the average of first hundred natural numbers? (A) 50 (8) rn (C) 49.5 (2) Q3. imotinteaeage ota anda ice y=5 e641 ay tb a ) 3 ® 3 = m4: - 4, The seg ant hf rt fe ui 25,28 30a prorat ofthe oeDogar’s Unique USAT Guide USAT-M. (Pre-Medical) Q1, (C) As sum of the first n even numbers = n(n + 1) Now, the sum of even numbers from 2 to 100 is 2444648 + csc + 100 (050 even number) = 50(50 +1) = 2550 = Sum of numbers Averag® _* Number of tems 2550 ="50 75! Q2. (8) The first 100 natural numbers are (1,2,3,......100) Now.sum ofa fist number, = 2241 Samos 00ratalrunbers = “0119041 = 5050 = Sum of numbers | Now 9° * Number of terms $050. 109 = 805 Shorteut: The average of fst natural number s+ + average = 0041 +O 505 : 3, (0) “Adding the given three equations: ; (et yt 424 (24x) 2548411 t rs 2+ 2+ 22 =24 ay . ty+z) = 24 Dividing both sides by 2 xty+z =12 No svrace 15 J xeytz 12. a3 +028 =54 a+b+84 =270 (Mating both a+ b= 186 PeeEi pogs! = USAT-M (Pre-Medical) Algebra and Functions [04 MCQs| Chapter 1 === POLYNOMIALS Polynomial: A sum of finite number of monomials 1s called @ polynomial. Each monomial is called @ term of the eu: A monomial is a variable, or a constant, or a product of constant and one or more variables, with the variables having only non-negative integer in exponents. mple ; 3x?y, —5xy, and —7xy* are monomials. The algebraic expression 4? and are not monomials, because these expressions have not non-negative integer in exponent, and cannot be written as a product of a constant and a variable with a non-negative integer exponent. Degree of Monomial: in any monomial the sum of the exponents of the variables is called the degree of monomial. ple : What are the degrees of the monomials % — Bey, Tx, -18xy? Solution: in algebraic expression -3, the dagree ofthe monomial is 3, because the exponents of x and y ere 2 respectively therefore their sum is (2 + 1 = 3), Similarly the degree of the expressions 7x*y and — Multiplication of Monomials; The process of multiplication is illustrated in the following example: ple : What isthe value of -Sxy2, when x=-2 and y = —3 448 ~Dogar’s Unique USAT Guide eons ee A sum of a finite number of monomials is called a-polynomial. Each monomial in a polynomial is Caley a term of the polynomial. Degree of a Polynomial: The degree of a polynomial is the largest degree of the terms in the polynomial. What are like terms in a Polynomial? Terms of polynomial that have exactly the same variables raised to the same powers are called lig terms. Remember: like terms in a polynomial can be combined Arithmetic Operations on Polynomials: We use usual law of arithmetic, to add subtract, multiply and divide polynomials. Addition and Subtraction: Polynomials are added or subtracted by combining like terms. ample ; (2x1 + 3x + 7+ 6) + (4x? + 3x-- 2) - (5x? + 4x) = Deb + (3x2 + dx? — 5x2) + (7x + 3x — 4x) + (6-2) = 28+ 2+ 6x44 The rules for adding like terms are: Rule 1: {fall the terms are positive in a polynomial, then add their coefficients. Pe : Find the value of 8x? + 2x? + 7x? Solution: Here we have to increase 8 like things by 2 and 7 like things of the same kind, and aggrega: is 17 of each thing. Rule 2: If al the terms in a polynomial are negative add the coefficient numerically and prefix the: mine sign to the sum. ple : what is the sum of ~4x, -x, ~3x and -7x Solution: In this example the word sum indicates the aggregate of 4 subtractive quantities of like term In this case we have to take away successively 4, 1, 3 and 7 like things, therefore the result is the sam as taking away 15(4 + 1 + 3 +7) such things in the aggregate. : 2. The sum of -4x, x, ~3x, ~7xis 7 ; Rule 3: if all the terms have not same sign, add together separately the coefficient of all the 1 terms and the coefficient of all the positive terms. Then find the diference of those two r precede by fe sign ofthe gral, wi ge he coef of fe sum requ ple : Find the sum of 12x? ~ 32+ 15x¢= 1742pogar’s Unique USAT Guide USAT-M (Pre-Medical) on index equal to the sum of the indices that letter has in the separate factors, IMpple ; What is the product of 5x2y? and —3xy? solution: (5x°y")(-3xy")_ = (5)(-3)(x? x x)(y? x y4) = - 15x95 ote: The product of a monomial by any polynomial is the algebraic sum af the partial products of each seem of the polynomial by that monomial, ‘uitiplication of two Binomials: the procedure of multiplication of two binomials is tlustrated as: 4. Multiply each term of the first binomial by each term of the second. 2. When.the terms multiplied together have like signs, prefix to the product the sign +, when unlike prefix — 3. The algebraical sum of the partial products so formed gives the complete product. « DEmple : Multiply (x #3) by (x8) Solution: (x+3)(x-5) = x{x~—5) +3(x—5) B =~ 6x43x—15 == 2-15 imple : Find the value of (x +2)(x—3) -(x+4)(x=5) Solution: First of all, multiply both pairs of binomials separately, then subtract the second result from the first. (e+ 2)(x-3) = xtx- a ct bee =xt-x-6 (x+4)(x—5) = x(x-5) +4(x-5) = Bet ax 20 =¥-x-20 Subtracting: (@-x-6)- (@-x-20)= R= x- 8-8 44420 =14 FOIL Method: Te product fhe wo ional can be compte the FHL. tod This meta illustrated in the following example Last” “First Outer Inner Outer tr )=ar+ay +be +by i1 —Dogar's Unique USAT Guide USAT-M (Pre-Med Dre + Find the produc of (2x ~3) and (4x +2) using FOIL Method First Outer inner. Last (2x = 3x + 2) = (2aylde) + (2092) + (SAX) + (-3)(2) we Ot +4x~ 120-6 = Gxt—Br~6 ; Binomial Formulas; € Following are most important binomial products, those occur frequently in algebra. 1 (x+yx-y) = R= 2 (ctype = Re dy ty? 3. (xayP = R= 2y+y? 1PIe Find each ofthe flowing product: i 2) (2a+3)2a-3) : | ) (a-BoF " ' 9 Using formula (x + yxy) = x82 Et J Here (2a + 3)(2a~3)°= (26)? (3)? da? -9 7 b) Using formula (x ~ y= x8 ~2xy +? (a— Sb)?= (a —2(aXSt) + (SOP = at 100b +250? * a ple : Given x +y = 5, and.x~ y2= 10, what s the value of x ~ y? Solution: Using the fact (+ y)lr—y) =3°—y? ” Ox-y = 10 = 10 ei £ yee 5 & a Sg kay: Se : ‘ a le: Find the vale of xy, when (xy)? 25 and x? + y?= 3. 9 Solution: We know (x+y)? =x? + Zay +y? We can write (x+ y)*= (x+y) + xy Sta eae bs abeDogar's Unique USAT Guide USAT-M (Pre-Medical) To divide a monomial by a monomial, use distributive law, the index of each letter in the quotient is obtained by subtracting the index of that lettor in the divsor from that in the divided. To the result so obtained prefix its proper sign the quotient of the divided by that of divisor. To divide a polynomial by a monomial, divide each term separately by that monomial, and take the yraic sum of the partial quotient so obtained. ; wus 1: What is the quotient when ~4x2y is divided by 2x 4x) Solution: The quotient === —2xy DErmrle 2 Dhide 123 ~ 6x? -9xby 3x 3 62 eoiston: 6x" _ 9x Evaluating a Polynomial: To evaluate a polynomial, substitute the given value(s) for the variable(s) and then perform the given operation. ‘ ple x= 3, y= —7 andz=-2, find the value of xt — 26) + 172 Solution: x2 - 26y + 172 = (32 (28-7) + 17(-2) =9+182-34= 157 FACTORISING POLYNOMIALS: Writing a polynomial as a product of polynomials of lower degree is called factoring. When each of the terms which compose a polynomial is divisible by a common factor, the polynomial may be simplified by dividing each term separately by this factor, and enclosing the quotient within brackets; the common factor being placed outside as a coefficient. ; 3 ple 1; Resolve ito factors 4x8 = 20x Solution: The terms of the polynomials 4x* - 20x have a common factor 4x; 4xt - 20x= 4x(x—-5) ple 2: Resolve into factors x* — sx + tx— st Solution: We se thatthe fist two terms contain a common factor x, andthe last two terms @ common factor t, we enclose the first two terms in one bracket, and the last in another. Thus, w= sx+ bests (2 — 5) + (test). : = ; form x? + bx +.¢ can be factorized by trial method. This is illustrated in the followin,Dogar’s Unique USAT Guide USAT-M (Pre-Medical YEmple Consider the following binomial expansion’ (x+ 5x46) = x(x +6) 4+ 5(x +6) = 46x +5x 430 xe+itxe30 = (x4 6)(x + 6) Notice at11=5+6 and 30"5x6 This result can be used to factorize trinomials? For example, to factorize the trinomial x2 + 7x + 12 we eed to find two numbers so that: Product =12 and sum=7 The two numbers are 4 and 3 4x3=12and4+3=7 2+ 7x 412 = (x4 4x +3) imple :Factorze i) = x2+7x-18 i) =m=9m+14 . Solution: : ) +7x~18 Product = 9 x (-2)=-18 Sum =9+(-2)=7 eR TK= 18 = (x + 9)(x- 2) i) = m-9m+14 Product = (-7)(-2) =14 ¥v sum "=(-7)+(-2)=-8 : : me —9m+14 = (x= TKK 2) pple : Find the value of (10001)? Solution; (10001)? = (1000+ 1)? isi Gs S = (10000)? + 2000) + (17 = 100000000 + 20000 = 100020001 Algebraic Fraction: . % ‘An expression which has a variable in the denominator, is called an algebraic expression. Algebr fractions are added and subtracted using the same method as for arithmetic fractions, The denoming must be the same before these operations can be cared out. hea 7 $*s Unique USAT Guide USAT-M (Pre-Medical) 15 a 1§ a 4 (A) © only! (8) only (C) land {l only (0) only The average of the polynomials, 2x? + Sx -6, Sx? — Sx ~ 6 and 30 ~ 7x7 is: a (a) 14 (8) 18 () 6 (0) & What Is the value of x* + 14x + 24, when x = 6547 ot (a) 1000 (8) 100,000 (c) 741,296 (0) 742398 at. aM 5 y= 235 +117 = 362 at. ©) x-y iy both equations ie., es ee 34 -¥=16 2e=50 => x= 25 => x=+25 Now, x2 +y=34 => 25+ y=34oyag yes Hence, xy = (-5)(—3) = 15 = (6)(3) and xy=(-5)(3)=—15 = (5)(-3) So correct answeris C. @ (Cc) Fst of awe fod te bun. ot he Hise ay then divide the answer by 3. Sum of the three polynomials, 22+ 5x -6 5x? - 5x-6 =e 430 c 18 F . _ Sumof he tree polyrotas Now, Averego® = Sum of the tnge 4, (C) To avoid time consuming calculation, factorize the given polynomial 0+ 14x +24 = XP + 12K + Dx + 24 = x(x + 12) + 2(x + 12) (c+ 2x 12)| Dogar’s Unique USAT Guide USAT-M (Pro-Medicas Geometry 103 Mcy Chapter 1 ———— LINES & ANGLES Jarecla lomo’ by td iepesion ois Bn Gar AEA may be rays or lines, In the diagram, an angle is shown by two lines (the arms) meeting at @ point. The meeting point or point of intersection is called the vertex. The unit of measurement of an angle is degree. | (ne ful tum is 360 degrees (380%) | ; anat(2) tums 180 degrees (180%) Se A tums 90 degrees (20). Note: 4, Ahalf tum (180%) is also called straight angle. 2. A {tum (0 is locale aright ange, Classification of Angles: Angles are classified according to their degree measures. ee 0<0 Parallel Lines: Parallel lines are always the same distance apart. They never meet, even if you make them longer. Parallel lines form no angles. —— pe ——— ‘Transversal: A straight line which cuts parallel lines is called a transversal. = Perpendicular Lines: If two lines interest in such a way that they form fight angles are calle perpendicular lines Interior Angles: ‘ In the figure below, trarsvel rec ies an so fo lr and ent areDogar’s Unique USAT Guide notes EY Corresponding Angles: Corresponding angles are two angles in corresponding positions relative to the two lines and the transversal, These corresponding angles are also equal. A pair of equal Corresponding angles Is shown below. if two lines are both perpendicular to a third line, thén the lines are parallel. ee Alternatively Ifa line is perpendicular to each of a pair of lines, then that pair of lines are parallel.Dog USAT+M (Pre-Medical) 20 (8) 220 (C) 210 (0) 190 ax In the following figure, if ! || m no 120 t Brot Then x+y? 190° (A) = (a) < () > + (04. In the following figure, what is the value of y? (A) 45° (C) 46 a Inthe fre below, is 19 moe than y, what isthe value of? 6.USAT-M (Pre-Med Dogar’s Unique USAT Guide ptara Qt. (A) The sum of the given six angles make @ straight angle, and the straight angle equal ty Thws ere eereeeese = 180° => be = 100° Q2. (C) Inthe on figure, i are ion a straight angle, hence (SB 10+70+x = 180° x= 100 Because opposite angles are equal, thus x= P=100>2=100 Similarly, 2+70+y = 180° 100+70+y = 180° (-.: 2=x= 100) => y =10 Thus, Sum of the angles x+y +2_= 100+ 10 + 100 > pa =210 Q3. (A) Because when two straight lines intersect each other, the corresponding angles are equal. This fact is shown in the adjacent figure ' Hence we=70 and -y=120 + y=120+70 => +y= 190 4, (8) Thus, ytz+w=180 5 lf we add y, 2 and w, then the sum of these angles isa straight angle which is equal to yt 2y+2y =180 ( z=wex= ‘Sa Sy =180 a| Dogar’s Unique USAT Guide USAT-M (Pre-Medical) ‘Substituting the value of x, in ()), we have 155+y = 160 > y_ = 180 ~ 155 > y #25] == Chapter 2 TRIANGLES a Triangle: A three-sided polygon is called a triangle. DEmvles Types of Triangle: Due to side Due to Angle Equilateral triangle Right angle triangle LS 60" for, An equilateral triangle has 3 equal sides. Isosceles triangle An isoscales wang eer ae " anacute angie Wang al three angles Z i “measurement are less than 90°. _|Dogar’s Unique USAT Guide ‘Angle's Sum of Triangle: In any tangle the sum ofthe measures ofthe three angles is 180e, \ x+y +z= 180° Mpe lobe fae elu, haste of 2 B c Solution: Because, the angle of a triangle add up to 180°. Therefore Se+oe+Z = 180 Z = 180°= 145° Zo oa > Erne 2 Calculate the value of x in the following figure: Solution: Because the sum of the are (180° — 3x), (180° ~ 5x) and 2x. (180° 83) + (180° — 39) +2 ‘ 360°—pogar’s Unique USAT Guide USAT-M (Pre-Medical) we know when two lines intersect each other then opposite angles are equal, therefore, the third angle ie triangle will be 6, Hence 252+ Zar ZOR = 180° + Sadan x ual, here 252° and m.Zb are pair of corresponding angles. s of Isosceles Triangle: 4. If two sides of a triangle are congruent, then the angles opposite to these sides are congruent. 2. Ifthe three angles of a triangle are congruent, then the three sides are also congruent. 3 Hf two angles of a triangle are congruent, then the sides opposite these angles are also congruent. ‘4. If three sides of a triangle are congruent, then the three angles are also congruent. ingle Properties of Triangle: 4. In every triangle the greatest angle is opposite to the longest side. 2. Inevery triangle the sum of the lengths of any two sides is always greater than the length of the third side. 3. Inevery triangle the shortest side is opposite to the smallest angle. 4. When the side of a triangle is produced the exterior angle so formed which is equal to the sum of the opposite interior angles. DEmvle: she inthe figure below _ £02 2A+ 2B . - 5. Inany right triangle, the sum of the measures of the two acute angles is Q0. ple ;Dogar’s Unique USAT Guide Solution: Since, the sum of the measures of the two acute angles is 90°, therefore xe3e = 00° (i = 90°= 36° = 554 6. An equilateral triangle has three equal sides, and three equal angles of 60°. DErple: The above triangle is an equilateral triangle. Therefore, esy=22 6 g i Right Tangle: 3 |. Pythagoras’ Theorem: i . Hponagiedineen eS hypolenae it uel oe sa two sng he ltrs i a ae! atepogar’s Unique USAT Guide USAT-M (Pre-Medical) Let x be the hypotenuse of triangle ABC, Then C, 1) The leg opposite the 30° angle is ) Le, mac be > ww y 2) The leg opposite the 60° angle is Le \V3). = ww A B Dimples 30° 30" x . y 2 83 i 2 1 x=2y3 =y3 z= 16 Note: : jnan equilateral triangle, an altitude forms a 30°-60°-90° triangle and is equal to 1 itye)V3 4. ‘The 45°-45°-90° Triangle: Let x be the hypotenuse of an isosceles right triangle, then Lene . 1) Each leg is x2 ie, mAB=mAC ‘ x 2) Hypotenuse = leg/2Dogar’s Unique USAT Guide USAT-M Pret Deel Ds What is the area of the square whose diagonal is 12? Solution: In a square, diagonal = (Side)-/2 x 252 x =5y2 rebslehed adele! _ Diagonal wre Area of Triangle: } To calculate the area of a triangle, frstlook at‘Triangle Inequality: in DABC, given below AB> BC> AC and 2C> ZA>ZB These inequalities suggest the following theorems, 1. The perpendcier Soper. fom 852 > 8 ee sce eas ee ine. 2. Triangle Inequality Theorem: The sum of the lengths of two sides of a triangle is greater than the length of the third side. DEmrvle: what isthe area and perimeter of the tangle AEC, where ABCD is @rectangula? 2 ‘ iB , — 7 7 a 7 x Solution: The area of Rectangle ABCD Is 29x 14= 126 : Now area of triangle ABE | =H14)) =48 : : . and area of triangle ADC. = Ho) 14) =63 : Total area of the triangles ABE and ADC i : i =49+63=112 = 126-112 Area of'AEC = (rea ofthe rectangle) — (Sun ofthe area ofthe triangle)Dogar’s Unique USAT Guide (AE)= (14) + (7)? =196+49=285 = AE=7V5=16 In triangle ADC (ACY = (AD)? + (8C)* = (9) + (14) = 81 +196 8.277 => AC = 17 Perimeter of (AEC =AE¥EC+CA =16+17+2=35 Qt, In the following triangle, whats the value of p? Deine (A) 83 na (C) 963 The two ie oat angle ae (a) V3 (C) 23 In the following triangle, AD =pogar's Unique USAT Guide USAT-M (Pre-Medical) ONT) ot. (8) In any tangle, the sum of the angles = 180° 45 + p + 2p = 180° > 3p = 180 ~ 45 > pee aas gp (C)_ Tofind the area, frst of al we draw a equilateral triangle ABC, in which AD is altitude 4 joe ras By, 30 — 60 Right Triangle Theorem, 12 4xV3xy3 £095" 3 = 43 Now,Base= 4/3 + 4\/3 = 8/3 and altitude = 12 Thus, Area = Base x Altitude =BY3 x 12= 96y3 i ‘ if the triangle is not right, then any number greater than 1 and less than 25 could be the length ofthe third side, Now, ifthe triangle is right, then there are only two possibilities: (i) _ If Sis the hypotenuse, then the legs are 4 and 3. (i) If 3 and 5 are two legs then hypotenuse is -/34, c p a 3 0 4 c ~ In ABC, AC= 16, BC=3 +4 =7, using Pythagorean theorem, AC? = (AB)? + BC > 162= AB? +72 = 256 = AB?+ 49 => AB? = 256 ~ 49 = 207 => AB= (207 = AB=3y23. oat Now, in ABD, AD? = AB?+ BD? => AD? = (3/23)? + (3)? = A= 920) +9 = ae => AD= 66 iA) Hee, A+ 2B+ ZC= 18> a+b+40=160->a+b= 40 : Because he gven tangle isan isosceles, fe, a= i :a Dogar’s Unique USAT Guide USAT-M (Pre-Med, Equations 103 My ’An equation is a statement that has an equal sign, The parts of an equation to the right and left sign of equality are called sides of the equation and are distinguished as the right side and left side, Highest power of the variable determines tho degree of the equation. The letters used for varsaloleg, ‘an equation are called unknown quantity, The process of frding the values of variables is called sha the equation. The value so found is called the root or solution of the equation. Linear Equation; ‘The equation in which the highest power of the varlable Is one, is called a simple or linear equzattigg the first degree, DEmle: 3x29, 24527, x-729 3 Axioms of Solving Linear Equation: The process of solving linear equation depends only upon the following axioms: 1. I we add equals in an equation on both sides, the sums are equal. 2. If from equals we take equals the remainders are equal. 3. If equals are multiplied to both sides of an equation the products are equal. 4, If equals are divided by equals then the quotients are equal. ~ . Rules of Solving Linear Equation: , 7 We use following rules to solving a linear equation, oa : Rule In a linear equation, wy i at et a Bp ° changing sign. . . ple 1: * Consider a equation s 7 ceo —Tx+ 143 -3x-18 Eat: 3 Transposing 3x+14 =7x-18 or 18414 =7x-3x weenie anca- Dogar's Unique USAT Guide USAT-M (Pre-Medical) GO) —-Bo Ge To keep this equation balance, the same operation must be carried out on both sides of the equation. The process of solving above equation is ilustrated simply in two steps as fellows: 3x-8 =16 3x-8+8 =16+8 3x43 #2443 x =8 steps for Solving Linear Equations: if the equation involves a fraction, first, if necessary, clear the fractions. Transpose all the terms containing the unknown quantity to one side of the equation, and the known quantity to the other side of the equation. Le ws 3. Collect the terms on each side. 4. Divide both sides of the coefficient of the unknown variable. 5. Compute for the result. DErpe: Solve (i) 7x-12=3x (i) a3 aes 1 ji) ——=- sitist (i l+x 2 @ 3 Solution: Check ; () Ix-12 3 Substituting x = 3 in 7x 3x = 12 equation 7x-12 =3x 4x = 12 13)-12 = 3(3) xed 21-12 29Dogar's Unique USAT Guide Sal Substituting x= 5 in My"? Perit eSte Mutiplying both sides by 2(1 +x) ach aay ii Seah Tae Stats) C2 6 etx Lewd 6-1 =1+x-1 2 2 1s pare Solution is correct ae ily Substituting a = -9 in (wy) ara 3 Check given equation Multiplying bot ses by3(3+a). 4 yy} 34-9) 3 (=$,}eermeraernapaeen (4x3)+3G+a)=3ta BrackelsDogar’s Unique USAT Guide USAT-M (Pre-Medical) yz xe y+ Z Gmple : If x= y(a +d), find ain terms of x, y and b, Solution: x =y(a+b) x _ y(a+b) y y *_b satb-b Solving Second-Degree Equation: A second-degree equation involving the variable x has the generalized form axt+bx+c =0 where a, b, and c are constants with a + 0. Second-degree equations are usually called quadratic equations. A quadratic equation in which the term containing x is missing is called a pure quadratic equation. Examples of second-degree equations are 2xt—§x+12 =0 48 =16 TR 12 = 3x45 The Index Laws: For multiplying and dividing powers, wese some es. These es are cle index avs, These rules are summarized below: Multiplying powers Dividing powers Power of a power Power of a quotient Power of a product © Special Index: Zero Index Index in fraction index inneDogar’s Unique USAT Guide Solution; Weel 272908 Take LHS, QT (GI Reet ow BEN) a Hed, | by Power of a power in Index law Now take RH.S, 7207%+%= (38)m+9 = WHOM m Qrtdee Mh (2) comparing (1) and (2) Fhed agra 3 —Ox+3 == 12418 > ~ix+12x = 18-3 &x FI xe a Substitute x = Sin gven equation QT 8A+1 = 72G2*82d art =7292 By* = Ry? o2 =F Hence the solution is correct. Systems of Linear Equations: la USAT-M oc A system of equation is two equations considered together, Ifthe equations in a ines, on 8 eld tne yn of eqn. Tn long eae te equ 8 n System of equations in two variables xty=7 gs ays 33 Simultaneous Equations: A pair of equation which has two unknown, solved together, ee rbmsores crs be eo ga a aspogar’s Unique USAT Guide USAT-M (Pre-Medical) DEmple + Solving the following system of equations using substituting method x-dy = 2 4xt+3y = 14 solution: ae-dy = 2 (1) Axe3y = 4 (2) Soiving equation (1) for x in terms of y ay+2 3x 4y= 2m Bee dy} 2x2 ‘substituting the value ot x= ig) : WF) 3) = 14 salt To get ridof friction multiply both sides of the equation (3) by 3 Ady +2)+9y = 42 => y+8+9y = 42 => ws 4 - [a Tofind the value of ‘x’ substitute y = 3 in equaton (1 of). Hee wo substi tn ean (1 Bot ce 75x—136 = 50 75x = 186 = 186 75 Te solution ofthe equation inthe fom of oder pais (5558) Elimination Method: De reco aw ui laa hee Bl oe analin H the of the unknown is eliminated or: one from the other. ee ee ee n pesos (ot range tsDogar’s Unique USAT Guide KH FQ ressall) BAY Boe) Solution: Since y terms have equal but opposite coefficient, eliminate by adding ne ® 2 ) ) (by adding)” 2x_= 24 Substitute x= 12in(1) Ut 2 => d=10 Solution sets (12,5) DErvIe nse Bet 6y = cnn) arly = 9 (2) Solution: In above system of equations, to eliminate mi roto 1 Ne eS ee 6x + 18y =Dogars Linyue von Guide USAT-M (Pre-Medical) CT Gay al. Mf 3x +9 = 18, what is the value of x +37 (A) 3 (8) 6 (c) -3 (0) % a2. it Sx + 12 = 44, what Is the value of 5x~ 127 (A) 24 (8) 32 (C) 20 (D) 22 Q3. if 3x + 17 = 9 —x, what Is the value of x? (A) 2 (8) 3 (Cc) -2 o -3 a4 If x— 5 = 9, what is the value of x? - 57 (A) 1 (8) 191 (c) 16 0) 11 as. If at— b= c—dt, what is the value of tin terms of a, b,c and d? be a ) 3x@ ® 5 £ bee ) G ) avg ends Q1. (B) .3x+9=18 5 3+3)= 18(Taking 3 common from LH.S) x+3) 3 292 -5x+3=6 (Diving bot sites by 3) Q2. (C) Given that 5x + 12 =44, subtracting -24 on both sides of the given equation, we have 5x 12-24= 44-24 => 5x=12=20 Q3. (C) 3x+17=9-x=> 3x¢x=9-17 > 4x48 - 8 S eqs Q4,.(B) x-5=9 > x-5+5=9+5 => x= 14 => x= (14) = 196 Now x5 = 196-5=>x-5=191 Q5. (D) af-b=c-dt > 7 4Dogar’s Unique USAT Guide USAT-M (Pre-Medicay Ea Statistics [03 MCQs; Miscellaneous Expected Questions for Entry Test Exams Variable 9. When statistics is applied tm Economics, it is called: A Psychometry B Econometrics SET-1 I. First-hand collected data is called: A Primarydata BB Secondary data P, ete . C Economistics D Trigonomesrics C Grouped data D eee 10. Level of satisfaction is: A A Continuous B . Discrete 2 sane uae ie ems C Population D- Qualitative A ‘Samp B_ Population i. a seavle ren C Statistic D Parameter * A Yoronen B Discrete C_ Population D Parameter ay Another name of the population is: A Experiment B Survey C. Universe D Parameter 4 Quantities which don’t yary from individual to individual are called: A Variables B Surveys C Constants D Parameters x is a quantity computed from a population when the entire population is available. 1 A Variables B Surveys C Ratio D_ Parameters 6. The arrangement of data in order of magnitude is called: A Order statistic B Parameter C Ratio D Variability — A value calculated from sample is called: 7.Tpegar’s Uniquy ~~~» ~ulde SET-Il The process of making tables or arranging data into rows and columns is called: A Classification B Tabulation C_ Information D_ Arrangement The headings for different columns are called: A. Stubs B_ Source notes Cc Column D_ Footnotes captions The headings for different rows are called: A Footnotes B Prefatory note C Stub D_ None of these The entries in different cells of columns and rows in a table are called: & A Body of the B Captions table Cc Stub D Prefatory notes The part of the table containing row captions is called: ‘A Stub B_ Row captions C Box-head D_ Row-head The part of column captions is called: A Stub B_ Body of the column C Box-head D Prefatory - Data are classified according to one characteristic, called: A One-way B Tabulation. classification no C Single classification om 10. i. 12. 13. dA. USAT-M (Pre-Medical) The difference between the upper and the lower class boundaries of a class is called: A Class interval B Class distribution C_ Prequeney D Cumulative frequency The numbers used to describe classes in a frequency distribution are called: A Classlimits B Relative frequency C Cumulative D Width of » frequency class ‘Simple bar chart is represented by: A Circular B Polygons “region C Rectangles D None of these Frequency polygon is a: A Line graph B Bar graph C. Circular D_ Rectangle graph graph Graph of time series is called: A_ Sector B Ogive diagram C Historigram D None of these In tabulation, column captions are also called: A Box-head . _B Body C Stub D_ None of these In tabulation, row captions are also called: A Stub. - B_ Box-head C Body D None of these ANSWERS, Z ri [e]a Je]. [bp] = TAT SIA rete] pals tp] 9. [A|10.[A] nl fis.[p faz. [a3.[ C14. a Tas. aDogar’s Unique USAT Guid: SET-II 1. The estimate of population mean jt is: A Arithmetic B Sample mean mean C Geometric D_ Harmonic mean mean 2 Sample mean is a: A Constant B Parameter C Variable D Statistic 3, Sample mean is denoted by: A By CER po 4 A central value is also called: A Central B Variability tendency C Population D Parameter & The sum of deviations of the values from the mean is always: A Minimum B Maximum C One D Zero 6 Mean is highty affected by: A Evenvalues B Odd values C Zerovalues D Extreme value 7. The sum of squares of the deviations of the observations from their mean is: A Minimum B Maximum C Zero D One & Geometric mean of 0, 5, 1, 4, 8 is: A 8 Bei: Ge2 D1 9 G.M becomes zero if any of the observations is: A_ Zeto C_ Similar 10. i, The most frequent value in @ set is called: A Mean B Median C Mode D Quartile 2 AM is affected 4 extreme values, / A Not B Highly | C Less D_ None of thes 13, In symmetrical distribution, Mea, median and mode are: : A Equal B Different © Zero D_None of thes 14. — If any value is zero, then ay impossible to calculate: A HM B Median Cc AM D None of t 1S. A symmetrical distribution mean equal to 4, Its mode will A Lessthan4 B Equal oe's Unique USAT Guide USAT-M (Pre-Medical) C Mean D Variance 13, The first moment about mean is deviation equal to: Most common measures of A Mean B Zero ‘ absolute variability are also called: C Median D Mode Range B Measures of 14, The measures of dispersion are spread changed by a change of: C Relative D Mean A Origin B Scale measures deviation C Algebraic D_ None of these Relative measures have no: sign $ Negative B Decimal 1S. The varlance of a constant is: values values A Constant B Zero Cc Units D Value C One D None of these Sum of absolute deviations are ANSWERS. F ninimum if computed from: [Tate [ols [ole Tals] A Mean B Median [é[el 7. je] s [cls [tio | C Mode D Range fre [eyi2.[c fis. [elie [Bl is. 18) Mean deviation is always: SET-V % A Greta ain B_ Less than S.D L The point in-time at which the C EqualtoS.D D Negative selected number was measured is referred to as the: t The positive square root af the | 4 “dex number B Base period 4 ievorceeda te a © Relative price D Weighted crusts drviaion |» he'd number re elelaed C Standard D Range ae deviation A. Decimal B Ratios % The co-ecent of eae C Percentages D Options “A” “Govind |pntne bese beret feted pie C Standard D Relative deviation dispersion 10. The co-efficient of variation expressed as a: A Unit B Percentage - C Squares D_ Square root Mean deviation about the median isDogar's Unique USAT Guide C Multi index D None of these 6 An index number calculated for more than one items is called: A Composite B Simple C Relative D None of these 2 Uf all items are given equal weight, the index number is called: A Weighted B Unweighted C Relative D Composite & In chain base method, the base period is: A Fixed B Not fixed C Constant D None of these 9 In chain base year method, the z is fixed, A Year B Price C Quantity D Price and quantity Link relatives are not directly comparable because they have: A Fixedbase § B Not fixed base C Zerovalues D None ofthese ANSWERS }1.[B]2.[c[3 [als [cts [Bl L6. | [s. [Blo [a] 10. | SET-VI 1. Most of the decisions that affect our daily lives are based upon: A Absolute B Likelihood certainty 10. C Independent D None of these 2 A well-defined collection of distinct * objects is called: A Probability B Chance C_ Element D. Aset ) 3. A set that contains no element is called: A’ Null set C Zeroset $. 10. USAT-M (Pre-Medical) A Finite set B Infinite set C Universal set D Disjoint set A set consisting.of all the elemerty of the sets under consideration ix called the: A Universal set C. Overlapping set B Disjoint set D Proper set A set containing only one element is called: A Disjointset B Singleton set C Universalset D. Proper set Probability of an event cannot be: A Positive B One C Negative D None of these When a pair of dice is rolled, the sample space consists of: A 6outcomes 8B 36 outcomes C i2outcomes D 24 outcomes When each outcome of a sample Space is as likely to occur as any other, the outcomes are called: A Mutually B Exhaustive exclusive C Equally likely D None of these If P(B) = 0, then the conditional probability is: A Leto Bl C Undefined D -1 ANSWERS ss 1. |B [2.[oT3 Taya yal s. Tay [6] B[7.[cls [pfs [alio Te} 7 | | i- pogar’s Unique voAT Guide USAT-M (Pre-Medical) stochastic 4 The sum of probabilities of events of a sample space is always: The probability distribution of a discrete random variable can be described with the help of a two: A Zero B One A Rowstable 8 Column table Cc Two D_ Infinity C Circles D Curves 4 The height of students, between 5,0 | 5, The area under the probability and 5.9 feet, is an example of: density function is: A_ Discrete B_ Continuous Al BO variable variable C Minimum D_ None of these C_ Constant D Parameter 6. The simplest form of the ‘ Recording the time (minutes) taken continuous distribution is the: by the customers to wait for its A_ Discrete uniform distribution turns in a utility store while B Probability mass function standing in a queue, is an example C_ Density function of: D Continuous uniform distribution A Discrete B Continuous 7. In continuous distribution, P(y = variable variable a) and P(y = b) is always: C Constant D Parameter A Zero B One C Undefined D Negative 8 The correct condition for continuous uniform distribution 1 L The probability distribution of a represented by fly) =(5 a) & discrete random variable is usually A b Q2. Q3. Point O12. - USAT-M (Pre-Medicay C Estimator D Population interval Q6. The statistical estimation 9 population is divided info: A Two types B Three types C Cannot D_ None of these divided Q7, An estimator is always a: A Constant B Variable C Parameter D Statistic _ Q8. A specific value of an estimator computed from the sample dat, after the sample has beeq observed is called: A Pointestimate B Statistical Inference C Statistic D Parameter When choosing an estimator of population parameter, one should consider: bs A Sufficiently B Efficiency .C Options A& D None of these: B' Qs, Q/0. If an estimator T of a population Parameter 0 is biased, then tt] amount of its bias is: ; A E(1)+0 B p+ 3 C o'+0 D AN-8 Qi1. Which of the followingpogar’s Unique USAT Guide C _Unbiasedness of the estimator D_ None of these at4. An estimator T of a population parameter @ is said to be biased ifs A E1)>0 B &A(T)<0 Cc EDe0 D A7)=6 If Tis a biased estimator, then it will tend to give estimates: ats. A Far from6 B Far from¢ C NeartoO —-D_ Equalto0 ANSWERS SET-XII A null hypothesis is always one of status quo or: A effected B_ having some difference C_ having D_nodifference alternative . hypothesis The alternative hypothesis (H)) is the opposite of: A Null 5 hypothesis Co DA The statement of the alternative hypothesis never contains a(n) sign regarding the specified value of the parameter. A equal . B- greater than C_less than D_ None of these a2. Bu Q3. USAT-M (Pre-Medical) A Population B_ Statistic parameter C Sample statistic A random variable which bas a normal distribution with mean = 30 and standard deviation o = 4 is an example of: A Nall Hypothesis C Simple Hypothesis The probability of a type I error is: A. Alpha B Beta C Powercurve D_ None of these Q8. — Rejecting a null hypothesis, when itis true, is called: A Rowscale B_ Simple . D None of these a6. B Composite Statistic D None of these Q7. C Typelerror D Type ll error Q9. The normal distribution is the appropriate distribution to use in testing hypothesis about: A proportion, when "Pa. >5 and ngy, >S 4 A faan shied sa toon eet te population is normal A mean, when gis unknown but is large All of the above Q10. Fora particular test, a = 0,05 and B= 0.10. The power of this test is: A 0.15 B 0.90 _C 0.85 D 095 Q11. For a two tailed test of hypothesis at a= 0.10, the acceptance region is the entire region: To the right of the critical value een the two critical valuesUnique USAT Guide USAT-M (Pre-Modhcay Dog: D_ To the lef of the positive critical c -\02 D +02 value Q4. If the correlation coefficient r = 9, Q12. If the critical region is located the two regression lines are: equally in both tails, of the A Parallel B Perpendicular sampling distribution of test C Coincident D Inclined at statistic, the test is called ay 45° to each A Twortailed B One-tailed test test other C Right-tailed D Left-tailed Q5. The following diagram test test represents: Q13, If H; is given by 0 <@,, we use a: Right-tailed — B One-sided left test tail test C Two-tailed D_ None of these test Q14, If H; is given by 0 > 6,, we use a: Left-tailed B One-sided test tailed test ; d C Two-tailed D_ None of these A. Positive B Negative Q165. Whi ive 8=8 pee eee a bs en = 0,, we use at a Tbenicd B” Gnesied nae Nace test ight tail test Cc No D_ None of these , correlation C One-tailed D_ None of these right tail test ie ANSWERS . variables, then two lines of [D]2. Tals. Jala [p]s. | ; x= const, y= x= const, y= c 0 p const ere aE ey oP Pe ale “Q7. If the sum of the product of SET-XIV deviations of x and y series from A x=0,y=0 B Q1. The two regression lines are their means is zero, the perpendicular to each other ift correlation coefficient will be: A r= B r=0 Al B -l Cc r=-l D_ None of these co D_ None of these Q2, The two regression lines are Q8, If =1 or -1, the regression lines identical if: are: hehe? Boantyey A Parti sie atte C.re-1 D_ A,BandC The equations of regresion lines— pogar’s Unique USAT Guide If the equations of regression lines are y=0Sx+a,x= 05 +b and ¥ = 10, ¥ = 12, them the values of a and b are respectively: 7,4 B 4, -7,-4 D_ None of these If the two regression coefficients are 0.8 and 0.2, then coefficient of correlation r is: 04 Qio. aO> ait. B -04 1.6 D None of these If r between the lines of regressions of x and y and y on x, is +1, then: Lines Lines are coincides perpendicular There is perfect correlation © between x and y D A,BandC Q13. The purpose of simple linear regression analysis is to: Replace points on a scatter diagram by a straight line Measure the degree to which two variables are linearly associated Predict one variable from another variable None of these ANSWERS Qi2. A A B c D SET-XV The process of dividing the objects into two mutually exclusive classes is called: ; ~B_ Population i Qt. USAT-M (Pre-Modical) pi re Q2, The Greek letters a, used to denote the of Ay B,C ove A Presence B Inverse C Absence D None of these Q3. If A denote that the object possesses the attribute A, then a, means: AB B Not# C Nota D NotA Qs. attributes denoted by A, B, Positive B Negative attributes: attributes Contingency iiwributes D_ None of these The degree of relationship Qs. between the two attributes is called: A. Association B_ Dichotomy C Variable D_ None of these Q6. The two attributes 4 and B are independent, if the co-efficient of association: » A Equalstoone B Equals to zero c_ Notequals!9 None of these Q7. The classes AB, aB, ete. are called: Positive p Negative classes classes Negative of Ay Contrary and B cl If no attributes are specified, then the order of the class is: AO Bl Cr D None of these Q9. The frequency of classes of the highest order are called: A c Qs.'s Unique USAT Guide USAT-M (Pre-Medioay) Dog Q10, In the study of two attributes, n= mae Cyclical A B+a B (AB) + (4B) A Secular Trend B fluctuation C AB+(aB) D (4) +(a) Seasonal (A) and (B) Q14, In the study of two attributes, (B) variation only . Q7. A set of data depending om the time is called: A Historigram B Histogram C Time serics D None of these Qa A is a line or curve thay shows the general tendency of q time series, A (Af)+(aB) BB (AB) +(AP) Cc (8)+@) D (AB) + (a8) ANSWERS Seri A. Historigam 1 Seasonal C Secular Trend D None of these Shire isa systematic | Qo, In data of birth’s and death's and sre, of variation in a time epidemics as a It of A Historigram —B- Signal advancement in medical sciemees, C Noise D_ Time period the secular trend is usually: ! Q2. The is. an irregular A pees B zero tendency component of variation in a time Sei ea | series, Cae ake D None of theng A Signal B_ Noise 4 © Response _D- Noneofthese | 210» Theseasonal variations are: 3 Q3, Which of the following would i een pee likely be a trend component of a - me ae 5 time series? cee Population A A powih B Lawsuits C Holidays D_ Recessions Q4. Which of the following would likely be a seasonal component of a time series? A Holidays B > C Lawsuits D_ None of these Q5, The graph of the time series is — “called: A Histogram C Bardiagram = D~ Q6. A time series of anni contain which of tl \ components? = Population*s Unique USAT Guide B A steel strike, delaying production for a week. C A continually increasing demand for smaller automobiles. D None of these at Time series analysis is used to analyze data: Over different time periods Across different companies. Across different companies and across different time periods. That are qualitative ANSWERS o A> SET-XVII 1 GHz equals to: A 1024Hz B_ 10'MHz Cc 10°MHz D 1024 MHz A combination of characters, numbers and symbols for specific purpose is called; A Bytes B_ Data Cc MB D_ None of these 03. Number of instructions processed in one’second is called of computer. A. Accuracy B Speed C__ Frequency D_ None of these is a measure of number of vibration per second. A Frequency B Speed C Hertz D Bytes 06. The number of pelle ae in one second is called “__- A Accuracy B Feqeary’ C Herz D Data %. The unit of frequency is: A Hertz ‘ USAT-M (Pre-Medical) Q7, The main function of « computer ‘ ins A Data storage 1 Speed . Data € processing D None of these Q8. Computer means: A Complete B Processing C Data D Calculate Q9. The CPU of a digital computer consists of: A ALU B Main memory ‘ All of the C Controlunit D above Q10. A collection of eight bits is called: A Byte B Word C Record D File Q11. Computer memory: A. Performs all calculations B_ Receives input data C_ isextremely limited D_ is better than human memory Q12. A computer stores instructions in: A English language B Octal Number System * C Binary Number System D_ Decimal Number System Q1i3. Acomputer can execute: .A aflowchart B aprogram ~ allofthe C analgorihm D aboue ssa Q14. “Pascaline” was modified . by + in 1671. “Baron Gottfried Wilhelm von Leibnitz