UGEE 2019 SUPR

Question 1: A pipe open at both ends and a pipe closed at one end have same length. The ratio of
frequencies of their P overtone is
Options:
 +1
(a)
2
 +1
(b)
2 + 1
2 (  + 1)
(c)
2 + 1

(d)
2 + 1

Question 2: Glass has reflective index μ with respect to air and the critical angle for a ray of light
going from glass to air is 0. If a ray of light is incident from air on the glass with angle of incidence
 , corresponding angle of refraction is
Options:
(a) sin −1 (  )
 1 
(b) sin −1  2 
 
 1 
(c) sin −1 
  
 
1
(d) sin −1  


Question 3: Maximum kinetic energy gained by the charged particle in the cyclotron is
independent of
Options:
(a) Radius of the dees
(b) Charge
(c) Mass
(d) Frequency of revolution

Question 4: The magnifying power of a telescope is nine. When it is adjusted for parallel rays, the
distance between the objective and eyepiece is 20 cm. The focal length of objective and eyepiece
are respectively
Options:
(a) 10 cm, 10 cm
(b) 18 cm, 2 cm
(c) 15 cm, 5 cm
(d) 11 cm, 9 cm

Question 5: The SI unit and dimensions of Stefan’s constant  in case of Stefan’s law of radiation
is
Options:
J
(a) 3 4 ,  M 1 L0T −3 
ms
J
(b) 2 4 ,  M 1L0T −3 K 3 
ms K
J
(c) 3 4 4 ,  M 1 L0T −3 K 4 
ms K
J
(d) 2 4 ,  M 1L0T −3 K −4 
m sK

Question 6: In a hydrogen atom, an electron of charge  revolves in a orbit of radius r with speed
v. Ther, magnetic moment associated with electron is
Options:
 vr
(a)
2
(b) 2 vr
(c)  vr
 vr
(d)
3

Question 7: V-I characterstics of LED is shown correctly by graph

Options:
(a)

(b)
(c)

(d)

Question 8: The stopping potential of the photoelectrons, from a photo cell is

Options:
(a) Directly proportional to intensity of incident light
(b) Directly proportional to frequency of incident light
(c) Inversely proportional to frequency of incident light
(d) Inversely proportional to intensity of incident light

Question 9: The refractive index of the material of crystal is 1.68 and that of castor oil is 1.2.
When a ray of light passes from oil to glass, its velocity will change by a factor
Options:
2
(a)
3
3
(b)
4
5
(c)
6
5
(d)
7
Question 10: Consider a particle of mass m suspended by a string at the equator. Let R and M
denote radius and mass of the earth. If ω is the angular velocity of rotation of the earth about its
own axis, then the tension on the string will be (cos0o = 1)
Options:
GMm
(a)
R2
GMm
(b)
2R2
GMm
(c) 2
+ m 2 R
2R
GMm
(d) 2
− m 2 R
R

Question 11: Six very long insulated copper wires are bound together to form a cable. The currents
carried by the wires are l1 = +10 A , l2 = −13 A , l3 = +10 A , l4 = +7 A , l5 = −12 A and l6 = +18 A .
The magnetic induction at a perpendicular distance of 10 cm from the cable is
( 0 = 4 10−7Wb / A − m )
Options:
(a) 40 μT
(b) 375 μT
(c) 30 μT
(d) 35 μT

Question 12: The fundamental frequency of sonometer wire increases by 9 Hz, if its tension is
increased by 69%, keeping the length constant. The frequency of the wire is
Options:
(a) 42 Hz
(b) 24 Hz
(c) 30 Hz
(d) 36 Hz

Question 13: In case of dimensions of electric field and electric dipole moment the power of mass
is respectively.
Options:
(a) 1, 1
(b) 1, 0
(c) 0, 1
(d) 0, 0

Question 14: A potentiometer wire has length L. For given cell of emf E, the balancing length is
L
from the positive end of the wire. If the length of potentiometer wire is increased by 50%, then
3
for the same cell, the balance point is obtained at length
Options:
 L
(a) from positive end
2
L
(b) from positive end
5
L
(c) from positive end
3
L
(d) from positive end
4

Question 15: For homogeneous isotropic material, which one of the following cannot be the value
of Poison’s ratio?
Options:
(a) 0, 1
(b) -1
(c) 0.5
(d) 0.8

Question 16: A mass is whirled in a circular path with constant angular velocity and its linear
velocity is v. If the string is now halved keeping the angular momentum same, the linear velocity
is
Options:
(a) 2v
v
(b)
2
(c) v
(d) v 2

Question 17: A circular coil and a square coil is prepared from two identical metal wires and a
current is passed through it. Ratio of magnetic dipole moment associated with circular coil to that
of square coil is
Options:
2
(a)


(b)
2
(c) π
4
(d)


Question 18: In Young’s double slit experiment fifth dark fringe is formed opposite to one of the
slit. If D is the distance between the slits and the screen and d is the separation between the slits,
then the wavelength of light used is
Options:
 d2
(a)
5D
d2
(b)
9D
d2
(c)
6D
d2
(d)
15 D

Question 19: Figure show the circular coil carrying current l kept very close but not touching at a
point A on a straight conductor carrying the same current l. The magnitude of magnetic induction
at the centre of the circular coil will be

Options:
 J 1
(a) 0 1 + 
2r   
l
(b) 0
2 r
0l
(c)
2r
(d) Zero

( ) () (
Question 20: The vector equation of the plane t = 2iˆ − kˆ +  iˆ +  iˆ + 2 ˆj − 3kˆ ) in scalar

( )
product form is r − 3iˆ + 2kˆ =  then α = ….
Options:
(a) 2
(b) 3
(c) 1
(d) 0

Question 21: Area of the region bounded by y = cosx, x = 0, x = π and X-axis is _____ sq. units.
Options:
(a) 3
(b) 1
(c) 2
(d) 4
 18 4
Question 22: The length of the latusrectum of an ellipse is and eccentricity is , then equation
5 5
of the ellipse______
Options:
x2 y 2
(a) − =1
25 8
x2 y 2
(b) + =1
25 9
x2 y 2
(c) + =1
25 16
x2 y 2
(d) + =1
16 9

Question 23: Let a :~ ( p  −r )  ( ~ q  s ) and b : ( p  s )  ( q  r ) . If the truth values of p and q

are true and that of r and s are false, then the truth values of a and b are respectively _____
Options:
(a) F, F
(b) T, T
(c) T, F
(d) F, T

Question 24: “If two triangles are congruent, then their areas are equal” is the given statement
then the contrapositive of, the inverse of the given statement is
Options:
(a) If areas of two triangles are not equal then they are congruent
(b) If two triangles are not congruent then their areas are equal
(c) It two triangles are not congruent then their areas are not equal
(d) If areas of two triangles are equal then they are congruent

−2
Question 25:  log x  log ( ex )  dx = ….
Options:
x
(a) +c
1 − log x
(b) x (1 − log x ) + c
(c) x (1 + log x ) + c
x
(d) +c
1 − log x

 x + x 2 + 25 
Question 26: If y = log   then _______
 x 2 + 25 − x 
Options:
 1
(a)
x 2 + 25
2
(b)
x 2 + 25
−1
(c)
x 2 + 25
−2
(d)
x 2 + 25

Question 27: If the scalar triple product of the vectors −3iˆ + 7 ˆj − 3kˆ,3iˆ − 7 ˆj +  kˆ and 7iˆ − 5 ˆj − 3kˆ
is 272 then  = _______
Options:
(a) 9
(b) 11
(c) 8
(d) 10

Question 28: The edge of a cube is decreasing at the rate of 0.04 cm/sec. If the edge of the cube
is 10 cms, then rate of decrease of surface area of the cube is …..
Options:
(a) 4.8 cm2/sec
(b) 4.08 cm2/sec
(c) 48 cm2/sec
(d) 4.008 cm2/sec

Question 29: The joint equation of lines passing through origin and having slopes 1 + 2 and ( )
−1
is _______
1+ 2
Options:
(a) x2 + 2 xy − y 2 = 0
(b) x 2 − 2 2 xy − y 2 = 0
(c) x 2 − 2 2 xy + y 2 = 0
(d) x2 + 2 xy + y 2 = 0

Question 30: If r is the radius of spherical balloon at time t and the surface area of balloon changes
at a constant rate K, then _____
Options:
Kt 2
(a) 4 r 2 = +c
2
(b) 8 r 2 = Kt + c
 Kt 2
(c)  r 2 = +c
2
(d) 4 r 2 = Kt + c


Question 31: 0
2
cos  + sin 2  d = _____
Options:
−20
(a)
21
−8
(b)
21
20
(c)
21
8
(d)
21

 0 0
Question 32: If ω is a complex cube root of unity and A =  0  2 0  then A-1 = _____
 0 0 1 
Options:
 2 0 0 
 
(a)  0  0 
 0 0 1
 
1 0 0 
(b) 0 1 0 
0 0 1 
1 0 0 
(c)  0  2 0 
 0 0  
0 0  
(d)  0  2 0 
1 0 0 

Question 33: If A and B are square matrices of order 3 such that |A| = 2, |B| = 4, then |A(adj B)| =
______
Options:
(a) 16
(b) 8
(c) 64
(d) 32

1
Question 34: If  1 − cot x dx = Ax + B log sin x − cos x + c then A + B = ______
Options:
(a) 1
(b) -1
(c) 0
(d) -2

 
Question 35: The polar co-ordinates of P are  2,  . If Q is the image of P about the X-axis then
 6
the polar co-ordinates of Q are ______
Options:
 5 
(a)  2, 
 6 
 
(b)  2, 
 6
 
(c)  2, 
 3
 11 
(d)  2, 
 6 

Question 36: a and b are non-collinear vectors. If c = (x – 2)a + b and d = (2x + 1)a – b are collinear
vectors, then the value of x = ______
Options:
1
(a)
2
1
(b)
4
1
(c)
5
1
(d)
3

Question 37: Let X be the number of successes in ‘n’ independent Bernoulli trials with probability
3
of success p = . The least value of ‘n’ so that P ( X  1)  0.9375 is ______
4
Options:
(a) 2
(b) 1
(c) 4
(d) 3

1
Question 38: The slope of normal to the curve x = t and y = t − at t = 4 is ______
t
Options:
−17
(a)
4
4
(b)
17
−4
(c)
17
17
(d)
4

Question 39: What is the shape and magnetic nature of permanganate ion?
Options:
(a) Pyramidal diamagnetic
(b) Tetrahedral, diamagnetic
(c) Tetrahedral, paramagnetic
(d) Planar, paramagnetic

Question 40: Which of the following oxides can act both as an oxidising agent as well as reducing
agent?
Options:
(a) N2O
(b) SO2
(c) SO3
(d) P2O5

Question 41: “The mass and energy both are conserved in an isolated system”, is the statement of
Options:
(a) Second law of thermodynamics
(b) Third law of thermodynamics
(c) Modified first law of thermodynamics
(d) First law of thermodynamics

Question 42: Which among the following is correct for electrolysis of brine solution?
Options:
(a) O2 gas is liberated at cathode
(b) Sodium metal is collected at anode
(c) H2 gas is liberated at cathode
(d) Cl2 gas is liberated at cathode

Question 43: The number of pi-bonds present in benz acid molecule are
Options:
(a) 5
(b) 4
(c) 3
(d) 6

Question 44: The elevation in boiling point of 0.25 mol aqueous solution of a substance is
(Kb = 0.52 K kg mol-1)
Options:
(a) 0.15 K
(b) 0.50 K
(c) 0.13 K
(d) 2.0 K

Question 45: The combining ratios of hydrogen and oxygen in water and hydrogen peroxide are
1 : 8 and 1 : 16. Which law is illustrated in this exampl
Options:
(a) Law of definite proportions
(b) Law of conservation of mass
(c) Gay Lussac’s law of combining volumes of gases
(d) Law of multiple proportions

Question 46: If a metal crystallises in bcc structure with edge length of unit cell 4.29 × 10-8 cm
the radius of metal atom is
Options:
(a) 3.2 × 10-7 cm
(b) 1.86 × 10-8 cm
(c) 1.07 × 10-7 cm
(d) 1.07 × 10-8 cm

Question 47: The temperature of 32oC is equivalent to

Options:
(a) 89.6oF
(b) 85.6oF
(c) 70oF
(d) 69oF

Question 48: The element which does not belong to group 15 is

Options:
(a) As
(b) P
(c) Bi
(d) Se
 UGEE 2019 REAP

Question 1: A five digit number is formed using the digits 1,3,5,7 and 9 without repeating any of
them. What is the sum of all such possible five digit numbers?
Options:
(a) 6666660
(b) 6666600
(c) 6666666
(d) 6666606

2
 1  2 1
Question 2: If  z +  = 98 , compute z + 2 
 z  z 

Question 3: The roots of ax2 + bx + c = 0 are real and positive a, b and c are real.
Then ax2 + b|x| + c = 0 has
Options:
(a) No roots
(b) 2 real roots
(c) 3 real roots
(d) 4 real roots

Question 4: Round-trip tickets to a tourist destination are eligible for a discount of 10% on the
total fare. In addition, groups of 4 or more get a discount of 5% on the total fare. It the one way
single person fare is Rs.100, a group of 5 tourists purchasing round trip tickets will be charged Rs.
_______

Question 5: In a survey 300 respondents were asked whether they own a vehicle or not. If yes,
they wore further asked to mention whether they own a car or scooter or both. Their responses are
tabulated below. What percent of respondents do not own a scooter.
Man Women
Car 40 34
Own Vehicle Scooter 30 20
Both 60 46
Do not own Vehicle 20 50
When a point inside of a tetrahedron (a solid with four triangular surfaces) is connected by straight
lines to corners, how many (new) internal planes are created with these lines? _____

Question 6: What is the average of all multiples of 10 from 2 to 1987

Options:
(a) 90
(b) 100
(c) 110
(d) 120
Question 7: The value of 12 + 12 + 12 + is
Options:
(a) 3.464
(b) 3.932
(c) 4.000
(d) 4.444

Question 8: If x is real and |x2 – 2x + 3| = 11, then possible values of |-x3 + x2 – x| include
Options:
(a) 2, 4
(b) 2, 14
(c) 4, 52
(d) 14, 52

Question 9: The ratio of male to female students in a college for five years is plotted in the
following line graph. If the number of female students doubled in 2009, by what percent did the
number of male students increase in 2009?

Question 10: At what time between 6 a.m. and 7 a.m. will the minute hand and hour hand of a
clock make an angle closest to 60o?
Options:
(a) 6:22 a.m.
(b) 6:27 a.m.
(c) 6:38 a.m.
(d) 6:45 a.m.

Question 11: Which number does not belong in the series below?
2, 5, 10, 17, 26, 37, 50, 64
Options:
(a) 17
(b) 37
(c) 64
(d) 26

Question 12: The table below has question wise data on the performance of students in an
examination. The marks for each question are also listed. There is no negative or partial marking
in the examination.
 Q. No Marks Answered Answered Not
Correctly Wrongly Attempted
1 2 21 17 6
2 3 15 27 2
3 2 23 18 3
What is the average of the marks obtained by the class in the examination?
Options:
(a) 1.34
(b) 1.74
(c) 3.02
(d) 3.91

Question 13: Find the odd one in the following group. ALRVX, EPVZB, lTZDF, OYElK
Options:
(a) ALRVX
(b) EPVZB
(c) lTZDF
(d) OYElK

Question 14: Anuj, Bhola, Chandan, Dilip, Eswar and Faisal live on different floors in a six-
storeyed building (the ground floor is numbered 1, the floor above it 2, and so on) Anuj lives on
an even-numbered floor Bhola does not live on an odd numbered floor Chandan does not live on
any of the floors below Faisal’s floor Dilip does not live on floor number 2 Eswar does not live on
a floor immediately above or immediately below Bhola Faisal lives three floors above Dilip.
Which of the following floor person combination is correct?
Options:
(a) Anuj – 6, Bhola – 2, Chandan – 5, Dilip – 1, Eswar – 3, Faisal – 4
(b) Anuj – 2, Bhola – 6, Chandan – 5, Dilip – 1, Eswar – 3, Faisal – 4
(c) Anuj – 4, Bhola – 2, Chandan – 6, Dilip – 3, Eswar – 1, Faisal – 5
(d) Anuj – 2, Bhola – 4, Chandan – 6, Dilip – 1, Eswar – 3, Faisal – 5

Question 15: The smallest angle of a triangle is equal to two thirds of the smallest angle of a
quadrilateral. The ratio between the angles of the quadrilateral is 3 4 5:6. The largest angle of the
triangle is twice its smallest angle. What is the sum, in degrees, of the second largest angle of the
triangle and the largest angle of the quadrilateral?

Question 16: One percent of the people of country X are taller than 6 ft. Two percent of the people
of country Y are taller than 6 ft. There are thrice as many people in country X as in country Y.
Taking both countries together. What is the percentage of people taller than 6 ft?
Options:
(a) 3.0
(b) 2.5
(c) 1.5
(d) 1.25
Question 17: The monthly rainfall chart based on 50 years of rainfall in Agra is shown in the
following figure. Which of the followings are true? (k percentile is the value such that k percent
of the data fall below that value)

(i) On average, it rains more in July than in December

(ii) Every year, the amount of rainfall in August is more than that in January
(iii) July rainfall can be estimated with better confidence than February rainfall
(iv) In August, there is at least 500 mm of rainfall
Options:
(a) (i) and (ii)
(b) (i) and (iii)
(c) (ii) and (iii)
(d) (iii) and (iv)

Question 18: In any given year probability of an earthquake greater than Magnitude 6 occurring
in the Garhwal Himalayas is 0.04. The average time between successive occurrences of such
earthquakes is ______ years.

Question 19: The population of a new city is 5 million and is growing at 20% annually. How many
years would it take to double at this growth rat?
Options:
(a) 3-4 years
(b) 4-5 years
(c) 5-6 years
(d) 6-7 years

Question 20: In a group of four children, Som is younger to Riaz, Shiv is elder to Ansu. Ansu is
youngest in the group. Which of the following statements is/are required to find the eldest child in
the group?
Statements
1. Shiv is younger to Riaz.
2. Shiv elder to Som.
Options:
(a) Statement 1 by itself determines the eldest child
(b) Statement 2 by itself determines the eldest child
(c) Statements 1 and 2 are both required to determine the eldest child
(d) Statements 1 and 2 are not sufficient to determine the eldest child.

Question 21: The total exports and revenues from the exports of a country are given in the two
pie charts below. The pie chart for exports shows the quantity of each item as a percentage of the
total quantity of exports. The pie chart for the revenues shows the percentage of the total revenue
generated through export of each item. The total quantity of exports of all the items is 5 lakh tonnes
and the total revenues are 250 crore rupees. What is the ratio of the revenue generated through
export of item 1 per kilogram to the revenue generated through export of item 4 per kilogram?

Options:
(a) 1 : 2
(b) 2 : 1
(c) 1 : 4
(d) 4 : 1

Question 22: x is 1 km northeast of Y.Y is 1 km southeast of Z. W is 1 km west of Z. P is 1 km

south of W. Q is 1 km east of P. What is the distance between X and Q is km?
Options:
(a) 1
(b) 2
(c) 3
(d) 2

Question 23: 10% ofthe population in a town is HIV+. A new diagnostic kit for HIV detection is
available, this lot correctly identifies HIV+ individuals 95% of the time and HIV- individuals 89%
of the time. A particular patient is tested using this kit and is found to be positive. The probability
that the individual is actually positive is _____

Question 24: If ROAD is written as URDG, then SWAN should be written as

Options:
(a) VXDQ
(b) VZDQ
(c) VZDP
(d) UXDQ

Question 25: A function f(x) is linear and has a value of 29 at x = -2 and 39 at x = 3. Find its value
at x = 5.
Options:
(a) 59
(b) 45
(c) 43
(d) 35

Question 26: The exports and imports (in crores of Rs.) of a country from the year 2000 to 2007
are given in the following bar chart. In which year is the combined percentage increase in imports
and exports the highest?

Question 27: Choose the most appropriate equation for the function drawn as a thick line, in the
plot below:

Options:
(a) x = y - lyt
(b) x = -(y – lyt)
(c) x = y + lyt
(d) x = -(y + lyt)

Question 28: Four cards are randomly selected from a pack of 52 cards. If the first two cards are
kings, what is the probability that the third card is a king?
Options:
 4
(a)
52
2
(b)
50
 1   1 
(c)     
 52   52 
 1  1  1 
(d)        
 52   51   50 

Question 29: Mr.Vivek walks 6 meters North-East, then turns and walks 6 meters South-East,
both at 60 degrees to East. He further moves 2 meters South and 4 meters West. What is the straight
distance in meters between the point he started from and the point he finally reached?
Options:
(a) 2 2
(b) 2
(c) 2
1
(d)
2

Question 30: Read the following table given sales data of five types of batteries for years 2006 to
2012
Year Type I Type II Type II Type IV Type V
2006 75 144 114 102 108
2007 90 126 102 84 126
2008 96 114 75 105 135
2009 105 90 150 90 75
2010 90 75 135 75 90
2011 105 60 165 45 120
2012 115 65 160 100 145
Out of following, which type of battery achieved highest growth between the years 2006 and 2012?
Options:
(a) Type V
(b) Type III
(c) Type II
(d) Type I

Question 31: How many four digit numbers can be formed with the 10 digits 0, 1, 2, ……..9 if
no number can start with 0 and if repetitions are not allow?

Question 32: The given question is followed by two statements; select; select the most
appropriate option that solves the question
Capacity of a solution tank A is 70% of the capacity of tank B. How many gallons of solution are
in tank A and tank B?
Statements:
I. Tank A is 80% full and tank B is 40% full.
II. Tank A if full contains 14,000 gallons of solution
Options:
(a) Statement I alone is sufficient
(b) Statement II alone is sufficient
(c) Either statement I or II alone is sufficient
(d) Both the statements I and II together are sufficient

Question 33: There are 16 teachers who can teach Thermodynamics (TD). 11 who can teach
Electrical Sciences (ES) and 5 who can teach both TD and Engineering Mechanics (EM). There
are a total of 40 teachers. 6 cannot teach any of the three subjects, i.e. EM. ES or TD. 6 can teach
only ES. 4 can teach all three subjects, i.e. EM, ES and TD. 4 can teach ES and TD. How many
can teach both ES and EM but not TD?
Options:
(a) 1
(b) 2
(c) 3
(d) 4

Question 34: Consider a function f ( x ) = 1 − x on −1  x  1 . The value of x at which the function

attains a maximum, and the maximum value of the function are:
Options:
(a) 0, -1
(b) -1, 0
(c) 0, 1
(d) -1, 2
Answers of UGEE 2019 SUPR

1. (c) 2. (b) 3. (d) 4. (b) 5. (d) 6. (a) 7. (b) 8. (b) 9. (d) 10. (d)
11. (a) 12. (d) 13. (b) 14. (a) 15. (d) 16. (a) 17. (d) 18. (b) 19. * 20. (a)
21. (c) 22. (b) 23. (a) 24. (b) 25. (a) 26. (d) 27. (b) 28. (a) 29. (a) 30. (d)
31. (d) 32. (a) 33. (d) 34. (a) 35. (d) 36. (d) 37. (a) 38. (c) 39. (b) 40. (b)
41. (c) 42. (c) 43. (b) 44. (c) 45. (d) 46. (b) 47. (a) 48. (d)

Answer of UGEE 2019 REAP

1. (b) 2. 96 3. (d) 4. 850 5. 48 6. (b) 7. (c) 8. (d) 9. 140 10. (a)

11. (c) 12. (c) 13. (d) 14. (b) 15. 180 16. (d) 17. (b) 18. 25 19. (a) 20. (a)
21. (d) 22. (c) 23. 0.4896 24. (b) 25. (c) 26. 4.54 27. (b) 28. (b) 29. (a) 30. (d)
31. 4536 32. (d) 33. (a) 34. (c)