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Table of Contents
Sr. Particulars Page
No Number
1 Ratio and Proportion, Indices, Logarithms 1.1 - 1.14
2 Equations 2.1 - 2.8
3 Linear Inequalities 3.1 - 3.8
4 Mathematics of Finance 4.1 - 4.28
5 Basic Concepts of Permutation & Combinations 5.1 - 5.10
6 Sequence & Series: Arithmetic & Geometric Progressions 6.1 - 6.8
7 Sets, Relations and Functions, Basics of Limits & Continuity Functions 7.1 - 7.8
8 Basic Application of Differential and Integral Calculus in Business and
Economics
8.1 Differential Calculus 8.1.1 - 8.1.5
8.2 Integral Calculus 8.2.1 - 8.2.4
9 Number Series, Coding and Decoding and Odd man Out 9.1 - 9.11
10 Direction Tests 10.1 - 10.11
11 Seating Arrangements 11.1 - 11.13
12 Blood Relations 12.1 - 12.12
13.1 Statistical Description of Data 13.1.1 - 13.1.9
13.2 Sampling 13.2.1 - 13.2.1
14 Measures of Central Tendancy and Dispersion
14.1 Measures of Central Tendancy 14.1.1 - 14.1.12
14.2 Dispersion 14.2.1 - 14.2.20
15 Probability 15.1 - 15.16
16 Theoretical Distributions 16.1 - 16.12
17 Correlation and Regression 17.1 - 17.13
18 Index Numbers 18.1 - 18.11
 1-1

Chapter 1
Ratio and Propotion, Indices, Logarithms

1. If x = 2 +√𝟑 and y = 2 -√𝟑 then value of 𝒙𝟐 + 𝒚𝟐 =……………. (MTP 1 Mark Dec’23)

(a) 14 (b) 4
(c) 2 (d) 6
Answer: (a)

2. If (𝟐𝟓)𝟏𝟓𝟎 = (𝟐𝟓𝒙)𝟓𝟎, then the value of x will be: (MTP 1 Mark Dec’23, May’23, Jun’22)
(a) 53 (b) 54
(c) 52 (d) 5
Answer: (b)

3. On solving the equation log t + log (t-3) = 1 we get the value of t as (MTP 1 Mark Dec’23)
(a) 5 (b) 2
(c) 3 (d) 0
Answer: (a)

4. If log 2 = 0.3010 and log 3 = 0.4771, then the value of log 24 is : (MTP 1 Mark Dec’23)
(a) 1.0791 (b) 1.7323
(c) 1.3801 (d) 1.8301
Answer: (c)

𝟏 𝟏 𝟏 𝟏
5. If four numbers , , , are proportional then x =………. (MTP 1 Mark Dec’23)
𝟐 𝟑 𝟓 𝒙
6 5
(a) (b)
5 6
15 (d) none
(c) 2
Answer: (c)

6. A box contains 276 coins of 5 rupees, 2 rupees and 1 rupee. The value of each kind of coins are in
the ratio 2:3:5 respectively. The number of 2 rupees coin is (MTP 1 Mark Dec’23)
(a) 52 (b) 60
(c) 76 (d) 85
Answer: (b)

7. What must be added to each term of the ratio 49 : 68, so that it becomes 3 : 4 ?
(MTP 1 Mark Dec’23)
(a) 3 (b) 5
(c) 8 (d) 9
Answer: (c)

8. The students in three classes are in the ratio 2 : 3 : 5. If 40 students are increased in each class the
ratio changes to 4 : 5 : 7. Originally the total number of students was (MTP 1 Mark, Apr’24)
(a) 180 (b) 400
(c) 100 (d) 200
Answer: (d)

9. A bag contains coins of denominations 1 rupee, 2 rupee and 5 rupees . Their numbers are in the
ratio 4:3:2 .If bag has total of Rs. 1800 then find the number of 2 rupee coins? (MTP 1 Mark, Apr’24)
(a) 270 (b) 230
(c) 180 (d) 210
Answer: (d)

Chapter 1 Ratio and Propotion, Indices, Logarithms

 1-2

10. The ages of two persons are in the ratio 5:7. Eighteen years ago their ages were in the ratio of 8:13,
their present ages (in years) are : (MTP 1 Mark, Apr’24)
(a) 50, 70 (b) 70, 50
(c) 40, 56 (d) None of these
Answer: (a)

11. A box contains ₹ 56 in the form of coins of one rupee, 50 paise and 25 paise. The number of 50 paise
coin is double the number of 25 paise coins and four times the numbers of one rupee coins. The
numbers of 50 paise coins in the box is (MTP 1 Mark, Apr’24)
(a) 64 (b) 32
(c) 16 (d) 14
Answer: (a)

12. A man starts his job with a certain monthly salary and earns a fixed increment every year. If his
salary was ₹ 1,500 after 4 years of service and ₹ 1,800 after 10 years of service, what was his starting
salary and what is the annual increment in rupees? (MTP 1 Mark, Apr’24)
(a) ₹ 1,300, ₹ 50 (b) ₹ 1,100, ₹ 50
(c) ₹ 1,500, ₹ 30 (d) None
Answer: (a)

13. If 𝐥𝐨𝐠 𝟒 (𝐱 𝟐 + x) – 𝐥𝐨𝐠 𝟒 (x + 1) = 2 then the value of x is (MTP 1 Mark, Apr’24)

(a) 2 (b) 3
(c) 16 (d) 8
Answer: (c)

14. The expenditues and savings of a person are in the ratio 4:1. If his savings are increased by 25% of
his income , then what is the new ratio of his expenditure and savings ? (MTP 1 Mark, May’24)
(a) 11:9 (b) 8:5
(c) 7:5 (d) 7:4
Answer: (a)

𝐚−𝐛 𝟏
15. If log = 𝟐 (log a + log b), the value of 𝒂𝟐 + 𝒃𝟐 is (MTP 1 Mark, May’24)
𝟐
(a) 6ab (b) 8ab
(c) 6𝑎2 62 (d) None of these
Answer: (a)

𝐩+𝐪 𝐩
16. What is the value of 𝐩−𝐪 if 𝐪 = 7 (MTP 1 Mark, Nov’23)
(a) 4/3 (b) 2/3
(c) 2/6 (d) 7/8
Answer: (a)

17. If x/2 = y/3 = z/7, then the value of (2x – 5y + 4z)/2y is (MTP 1 Mark, Nov’23)
(a) 6/23 (b) 23/6
(c) 3/2 (d) 17/6
Answer: (d)

18. If x : y = 3 : 4, the value of 𝒙𝟐 y + 𝒙𝒚𝟐 : 𝒙𝟑 + 𝒚𝟑 is (MTP 1 Mark, Nov’23)

(a) 13 : 12 (b) 12 : 13
(c) 21 : 31 (d) none of these
Answer: (b)

19. If 𝒂𝒙 = b, 𝐛 𝐲= c, 𝐜 𝐳 = a, then xyz is (MTP 1 Mark, Nov’23)

Chapter 1 Ratio and Propotion, Indices, Logarithms
 1-3

(a) 1 (b) 2
(c) 3 (d) none of these
Answer: (a)

20. Given that 𝐥𝐨𝐠 𝟏𝟎 2 = x and 𝐥𝐨𝐠 𝟏𝟎 3 = y, the value of 𝐥𝐨𝐠 𝟏𝟎 120 is expressed as (MTP 1 Mark, Nov’23)
(a) 2x – y + 1 (b) 2x + y + 1
(c) 2x – y – 1 (d) none of these
Answer: (b)

𝟏
21. The simplified value of 2 𝐥𝐨𝐠 𝟏𝟎 𝟓 + 𝐥𝐨𝐠 𝟏𝟎 𝟖 - 𝟐 𝐥𝐨𝐠 𝟏𝟎 𝟒 is (MTP 1 Mark, Nov’23)
(a) 1/2 (b) 4
(c) 2 (d) none of these
Answer: (b)

𝐚+𝐛 𝟏 𝐚 𝐛
22. If log ( 𝟒
) = 𝟐 (log a + log b) then 𝐛 + 𝐚 (MTP 1 Mark, Nov’23)
(a) 12 (b) 14
(c) 16 (d) 8
Answer: (b)

√𝐱+𝟓 + √𝐱−𝟏𝟔 𝟕
23. If = 𝟑 then x equals (MTP 1 Mark, Nov’23)
√𝐱+𝟓 − √𝐱−𝟏𝟔
(a) 10 (b) 20
(c) 30 (d) 40
Answer: (b)

𝟏 𝟏 𝟏 𝟏
24. If x = 𝟑𝟒 = 𝟑− 𝟒 and y = 𝟑𝟒 - 𝟑− 𝟒 then the value 3(𝒙𝟐 + 𝒚𝟐 )𝟐 will be (MTP 1 Mark, Nov’23)
(a) 12 (b) 18
(c) 46 (d) 64
Answer: (d)

25. The monthly incomes of A& B are in the ratio 4 : 5 and their monthly expenditures are in the ratio
5 :7 If each saves ₹ 150 per month, find their monthly incomes. (MTP 1 Mark, May’23)
(a) (40; 50) (b) (50; 40)
(c) (400; 500) (d) None of the these
Answer: (c)

26. Two vessels containing water and milk in the ratio 2 : 3 and 4 : 5 are mixed in the ratio 1 :2. The ratio
of milk and water in the resulting mixture. (MTP 1 Mark, May’23)
(a) 58 : 77 (b) 77 : 58
(c) 68 : 77 (d) None of these
Answer: (b)

27. If (x – 9): (3x + 6) is the duplicate ratio of 4: 9, find the value of x (MTP 1 Mark, May’23)
(a) x= 9 (b) x=16
(c) x= 36 (d) x= 25
Answer: (d)

𝟏 𝟏 𝟏
28. Value of (𝒂𝟏/𝟖 + 𝒂−𝟏/𝟖 )(𝒂𝟏/𝟖 − 𝒂−𝟖 )(𝒂𝟒 + 𝒂−𝟒 ) (𝒂𝟏/𝟐 + 𝒂−𝟏/𝟐 ) (MTP 1 Mark, May’23)
1 1
(a) a+a (b) a-a
1 1
(c) 𝑎2 + (d) 𝑎2 -
𝑎2 𝑎2
Answer: (b)

Chapter 1 Ratio and Propotion, Indices, Logarithms

 1-4

𝟏𝟔 𝟐𝟓 𝟖𝟏
29. 7log (𝟏𝟓) + 5log (𝟐𝟒) + 3log (𝟖𝟎) is equal to (MTP 1 Mark, May’23)
(a) 0 (b) 1
(c) Log 2 (d) Log 3
Answer: (c)

30. 𝐥𝐨𝐠 𝟒 (𝐱 𝟐 + 𝐱) - 𝐥𝐨𝐠 𝟒 (x+1) = 2. Find x (MTP 1 Mark, May’23)

(a) 16 (b) 0
(c) -1 (d) None of these
Answer: (a)

31. Given log 2 = 0.3010 and log3 = 0.4771 then the value of log 24 (MTP 1 Mark, May’23)
(a) 1.3081 (b) 1.1038
(c) 1.3801 (d) 1.830
Answer: (a)

𝟔𝟒(𝐛𝟒 𝐚𝟑 )𝟔
32. The value of [𝟒(𝐚𝟑𝐛)𝟐 ×(𝐚𝐛)𝟐] (MTP 1 Mark, Apr’23)
10 20
(a) 16 a b (b) 4 a20 b10
(c) 8 a10 b20 (d) 4 a10 b20
Answer: (a)

33. Four persons A, B, C, D wish to share a sum in the ratio of 5:4:2:3. If D gets `1000 less than C, then
the share of B ? (MTP 1 Mark, Apr’23)
(a) 2000 (b) 1200
(c) 2400 (d) 3000
Answer: (a)

34. The mean proportional between 12𝒙𝟐 and 27𝒚𝟐 (MTP 1 Mark, Apr’23)
(a) 18 xy (b) 81 xy
(c) 8xy (d) 9xy
Answer: (a)

35. If 𝐥𝐨𝐠 𝟑 4. 𝐥𝐨𝐠 𝟒 5. 𝐥𝐨𝐠 𝟓 6. 𝐥𝐨𝐠 𝟔 7. 𝐥𝐨𝐠 𝟕 8. 𝐥𝐨𝐠 𝟖 9 = x, then find the value of x (MTP 1 Mark, Apr’23)
(a) 4 (b) 3
(c) 2 (d) 1
Answer: (b)

36. if ½ 𝒍𝒐𝒈𝟏𝟎𝟒 = y and if ½ 𝒍𝒐𝒈𝟏𝟎𝟗 = x, then the value of 𝒍𝒐𝒈𝟏𝟎𝟏𝟓 (MTP 1 Mark, Apr’23)
(a) x-y+1 (b) x+y-1
(c) x+y+1 (d) y-x+1
Answer: (a)

37. In a hostel ration stocked for 400 students upto 31 days. After 28 days 280 students were vacated
the hostel. Find the number of days for which the remaining ratio will be sufficient for the remaining
students. (MTP 1 Mark, Apr’23)
(a) 5 (b) 4
(c) 7 (d) 10
Answer: (d)

𝟓/𝟐 𝟕/𝟐
√𝟑 𝟗
38. ( 𝟗 ) (𝟑 ) (MTP 1 Mark, Nov’22)
√𝟑
(a) 1 (b) √3
3
(c) 3√3 (d) 9√3
Chapter 1 Ratio and Propotion, Indices, Logarithms
 1-5

Answer: (a)

𝐩 𝟐 𝟐𝐩+𝐪
39. If 𝐪 = 𝟑 then the value of 𝟐𝐩−𝐪 is (MTP 1 Mark, Nov’22)
1 1
(a) 7
(b) −7
(c) 1 (d) 7
Answer: (d)

𝟏
40. 𝒍𝒐𝒈𝒂 √𝟑 = 𝟔 , find the value of a (MTP 1 Mark, Nov’22)
(a) 9 (b) 81
(c) 27 (d) 3
Answer: (c)

𝐩𝟐 𝐪𝟐 𝐫𝟐
41. log 𝐪𝐫 + log 𝐩𝐫 + log 𝐩𝐪 = (MTP 1 Mark, Nov’22)
(a) pqr 1
(b) pqr
(c) 1 (d) 0
Answer: (d)

𝟑𝐭 −𝟏
42. Find the value of 𝟏 (MTP 1 Mark, Nov’22)
−
𝐭 𝟑
3 3
(a) 2 (b) 3
t3 t2
3 3
(c) 1 (d) t2
t3
Answer: (a)

43. A bag conatind 25 paise, 10 paise and 5 paise are in the ratio 3:2:1. The total value of ₹40, the
number of 5 paise coins is (MTP 1 Mark, Nov’22)
(a) 45 (b) 48
(c) 40 (d) 20
Answer: (c)

44. The ratio of two numbers are 3 : 4. The difference of their squares is 28 .Greater number is:
(MTP 1 Mark, Nov’22)
(a) 8 (b) 12
(c) 24 (d) 64
Answer: (a)

45. The price of scooter and moped are in the ratio 7 : 9. The price of moped is ₹1600 more than that of
scooter. Then the price of moped is: (MTP 1 Mark, Nov’22)
(e) ₹7200 (f) ₹5600
(g) ₹800 (h) ₹700
Answer: (a)

46. 𝐥𝐨𝐠 𝟎.𝟎𝟏10,000 = ? (MTP 1 Mark, Nov’22)

(a) 2 (b) -2
(c) 4 (d) -4
Answer: (b)

𝟏
𝟏
𝐧+ √𝟑.𝟑𝐧 𝐧
47. Value of [𝟗 𝟒 . ] (MTP 1 Mark, Nov’22)
𝟑.√𝟑−𝐧
(a) 9 (b) 27
(c) 81 (d) 3
Chapter 1 Ratio and Propotion, Indices, Logarithms
 1-6

Answer: (b)

48. If x: y = 2:3, then (5x+2y): (3x-y) = (MTP 1 Mark, Jun’22)

(a) 19:3 (b) 16:3
(c) 7:2 (d) 7:3
Answer: (b)

𝟐 𝟐 𝒃𝟐 +𝒃𝒄+𝒄𝟐 𝟐 𝟐
𝒚𝒂 𝒂 +𝒂𝒃+𝒃 𝒚𝒃 𝒚𝒄 𝒄 +𝒄𝒂+𝒂
49. The value of (𝒚𝒃 ) × ( 𝒚𝒄 ) × (𝒚𝒂 ) is equal to (MTP 1 Mark, Jun’22)
(a) y (b) -1
(c) 1 (d) None of these
Answer: (c)

50. If x = 𝐥𝐨𝐠 𝟐𝟒 12, y = 𝐥𝐨𝐠 𝟑𝟔 24, z = 𝐥𝐨𝐠 𝟒𝟖 36, then xyz + 1 = (MTP 1 Mark, Jun’22)
(a) 2xy (b) 2xz
(c) 2yz (d) 2
Answer: (c)

51. A person has asset worth of ₹1,48,200. He wish to divide it amongst his wife, son and daughter in
the ratio 3:2:1 respectively. From this assets share of his wife son will be :
(MTP 1 Mark, Jun’22)
(a) ₹24,700 (b) ₹49.400
(c) ₹74,100 (d) ₹37,050
Answer: (b)

52. X, Y, Z together starts a business, if X invests 3 times as much as Y invests and Y invests two third of
what Z invests, then the ratio of capitals of X, Y, Z is (MTP 1 Mark, Jun’22)
(a) 3:9:2 (b) 6:3:2
(c) 3:6:2 (d) 6:2:3
Answer: (b)

53. If 𝟐𝐱+𝐲 = 𝟐𝟐𝐱+𝐲 = √𝟖 then the respective values of x and y are __________.
(MTP 1 Mark, Jun’22)
(a) 1, ½ (b) ½, 1
(c) ½, ½ (d) None of these
Answer: (a)

54. Find the value of [𝐥𝐨𝐠 𝟏𝟎 √𝟐𝟓 − 𝐥𝐨𝐠 𝟏𝟎 (𝟐𝟑 ) + 𝐥𝐨𝐠 𝟏𝟎 (𝟒)𝟐 ] (MTP 1 Mark, Mar’22)
(a) x (b) 10
(c) 1 (d) None
Answer: (c)

55. If A: B = 2:5, then (10A + 3B): (5A + 2B) is equal to (MTP 1 Mark, Mar’22)
(a) 7:4 (b) 7:3
(c) 6:5 (d) 7:9
Answer: (a)

56. The ratio compounded of 4:5 and sub-duplicate of a:9 is 8:15. Then value of “a” is
(MTP 1 Mark, Mar’22)
(a) 2 (b) 3
(c) 4 (d) 5
Answer: (c)

Chapter 1 Ratio and Propotion, Indices, Logarithms

 1-7

57. If ½ , 1/3 ,1/5 and 1/x are in proportion , then the value of x will be (MTP 1 Mark, Mar’22)
(a) 15/2 (b) 6/5
(c) 10/3 (d) 5/6
Answer: (a)

58. If P = 𝐱 𝟏/𝟑 + 𝐱 −𝟏/𝟑 then find value of 3𝐩𝟑 – 9p (MTP 1 Mark, Mar’22)
(a) 3 (b) ½(x+1/x)
(c) (x+1/x)) (d) 2((x+1/x))
Answer: (c)

59. Fourth proportional to x, 2x, (x+1) is: (MTP 1 Mark, Mar’22)

(a) (x+2) (b) (x-2)
(c) (2x+2) (d) (2x-2)
Answer: (c)

𝟑𝐧+𝟏 +𝟑𝐧
60. The value of 𝟑𝐧+𝟑−𝟑𝐧+𝟏 is equal to (MTP 1 Mark, Mar’22)
(a) 1/5 (b) 1/6
(c) 1/4 (d) 1/9
Answer: (b)

𝐱 𝟐 −(𝐲−𝐳)𝟐 𝐲 𝟐 −(𝐱−𝐳)𝟐 𝐳 𝟐 −(𝐱−𝐲)𝟐

61. The value of (𝐱+𝐳)𝟐−𝐲𝟐 + (𝐱+𝐲)𝟐−𝐳𝟐 + (𝐲+𝐳)𝟐−𝐱𝟐 (MTP 1 Mark, Mar’22)
(a) 0 (b) 1
(c) -1 (d) ∞
Answer: (b)

𝟏 𝟏 𝟏
62. If abc = 2 then the value of + 𝟏 + is (MTP 1 Mark, Mar’22)
𝟏+𝐚+𝟐𝐛 −𝟏 𝟏+ 𝐛+𝐜 −𝟏 𝟏+𝐜+𝐚−𝟏
𝟐
(a) 1 (b) 2
(c) 3 (d) ½
Answer: (a)

𝟑𝐱−𝟐
63. If 𝟓𝐱−𝟔 is the duplicate ratio of 2/3 then the value of ‘x’ is (MTP 1 Mark, Mar’22)
(a) 2 (b) 6
(c) 5 (d) 9
Answer: (b)

64. If , then x is equal to: (MTP 1 Mark, Nov’21)

(a) 1 (b) 3
(c) 5 (d) 10
Answer: (b)

𝐱+𝐲 𝐳+𝐲 𝐱+𝐳

65. If xy + yz + zx = -1, then the value of (𝟏+𝐱𝐲 + 𝟏+𝐳𝐲 + 𝟏+𝐳𝐱) is (MTP 1 Mark, Nov’21)
(a) xyz 1
(b) - yz
1 1
(c) xyz
(d) 𝑥+𝑦+𝑧
Answer: (c)

66. The salaries of A, B and C are of ratio 2:3:5. if the increments of 15 %, 10% and 20% are done their
respective salaries, then find new salaries. (MTP 1 Mark, Nov’21)
(a) 23: 33: 60 (b) 33: 23: 60
(c) 23: 60: 33 (d) 33: 60: 23
Answer: (a)
Chapter 1 Ratio and Propotion, Indices, Logarithms
 1-8

67. If A: B = 5:3, B:C = 6:7 and C: D = 14:9 then the value of A: B:C:D (MTP 1 Mark, Nov’21)
(a) 20:14:12:9 (b) 20:9:12:14
(c) 20:9:14:12 (d) 20:12:14:9
Answer: (d)

68. The salary of P is 25% lower than that of Q and the salary of R is 20% higher than Q , the ratio of
salary of R and P will be : (MTP 1 Mark, Nov’21)
(a) 5:8 (b) 8:5
(c) 5:3 (d) 3:5
Answer: (b)

69. The cab bill is partly fixed and partly varies on the distance covered. For 456 km the bill is Rs.8252,
for 484 km the bill is Rs. 8728. What will the bill be for 500km? (MTP 1 Mark, Nov’21)
(a) Rs. 8876 (b) Rs.9156
(c) Rs. 9472 (d) Rs.9000
Answer: (d)

𝟏 𝟏 𝟏 𝟏
70. If x: y = 3:5, then find ( + ): ( − ) (MTP 1 Mark, Oct’21)
𝐱 𝐲 𝐱 𝐲
(a) 2 (b) 4
(c) 6 (d) 8
Answer: (b)

71. if A: B = 3:5 and B:C= 5:4 , C:D = 2:3 and D is 50% more than E, find the ratio between A and E
(MTP 1 Mark, Oct’21)
(a) 2:3 (b) 3:4
(c) 3:5 (d) 4:5
Answer: (b)

𝟒 𝟖
72. Find the value of √𝟔𝟓𝟔𝟏 + √𝟔𝟓𝟔𝟏 + √𝟔𝟓𝟔𝟏 (MTP 1 Mark, Oct’21)
(a) 81 (b) 93
(c) 121 (d) 243
Answer: (b)

𝐱𝐧 𝐲𝐧 𝐳𝐧
73. Find the value of log 𝐲𝐧 + log 𝐳 𝐧 + log 𝐱 𝐧 (MTP 1 Mark, Oct’21)
(a) -1 (b) 0
(c) 1 (d) 2
Answer: (b)

𝟖𝒏 ×𝟐𝟑 ×𝟏𝟔𝟎𝟏 𝟏
74. If = then the value of n (MTP 1 Mark, Oct’21)
𝟐𝒏 ×𝟒𝟐 𝟒
(a) 1 (b) 3
3 2
(c) 2
(d) 3
Answer: (c)

75. The ratio of the number of boys and girls in a school is 2:5. if there are 280 students in the school,
find number of girls in the school (MTP 1 Mark, Apr’21)

(a) 200 (b) 250

(c) 150 (d) 100
Answer: (a)

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76. The third proportional to 9 and 25 (MTP 1 Mark, Apr’21)

(a) 80/3 (b) 80
(c) 80/7 (d) None of these
Answer: (d)

𝟓/𝟐 𝟕/𝟐
√𝟑 𝟗
77. ( 𝟗 ) (𝟑 ) × 9 is equal to (MTP 1 Mark, Apr’21)
√𝟑
(a) 1 (b) √3
3 3
(c) √3 (d) 9
√3
Answer: (a)

𝐥𝐨𝐠 𝟑 𝟖
78. The value 𝐥𝐨𝐠 is: (MTP 1 Mark, Apr’21)
𝟗 𝟏𝟔.𝐥𝐨𝐠 𝟒 𝟏𝟎
(a) 3 log10 2 (b) 7 log10 3
(c) 3 log e z (d) None
Answer: (a)

𝐩 𝟐 𝟐𝐪+𝐪
79. 𝐪
= - 𝟑 then the value of 𝟐𝐩−𝐪
is: (MTP 1 Mark, Apr’21)
(a) 1 (b) -1/7
(c) 1/7 (d) 7
Answer: (c)

80. Two numbers are in the ratio 7: 8 if 3 is added to each of them, their ratio becomes 8:9, the
numbers are (MTP 1 Mark, Mar’21)
(a) 14/16 (b) 24/27
(c) 21/24 (d) 16/18
Answer: (c)

81. Which of the numbers are not in proportions? (MTP 1 Mark, Mar’21)
(a) 6,8,5,7 (b) 7.3,14,6
(c) 18,27,12,18 (d) 8,6,12, 9
Answer: (a)

𝟏
82. If 𝐱 𝟐 + 𝐲 𝟐 = 7xy, then log (x + y) = then x is (MTP 1 Mark, Mar’21)
𝟑
(a) (log x + log y) (b) 1/2(log x + log y)
(c) 1/3(log x + log y) (d) 3(log x / log y)
Answer: (b)

𝟐𝒏 +𝟐𝒏−𝟏
83. The value of is (MTP 1 Mark, Mar’21)
𝟐𝒏+𝟏 −𝟐𝒏
(a) 1/2 (b) 3/2
(c) 2/3 (d) 2
Answer: (b)

84. If 𝟑𝐱 = 𝟓𝐲 = 𝟕𝟓𝐳 then (MTP 1 Mark, Mar’21)

(a) x + y – z = 0 2 1 1
(b) x
+y= z
1 2 1 2 1 1
(c) +y= z (d) x
+𝑧=𝑦
x
Answer: (c)

85. The value of √𝟔 + √𝟔 + √𝟔 +. . … ∞ is (MTP 1 Mark, Mar’21)

(a) -3 (b) 2
(c) 3 (d) 4
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Answer: (c)

86. If x: y = 2: 3, then find (5x+2y): (3x-y) (MTP 1 Mark, Oct’20)

(a) 13/3 (b) 16/3
(c) 19/3 (d) 7/3
Answer: (b)

87. A bag contains ₹187 in the form 1 rupee, 50 paise and 10 paise coins in the ratio 3:4:5. Find the
number of each type of coins. (MTP 1 Mark, Oct’20)
(a) 102, 136, 170 (b) 136,102, 170
(c) 170, 102, 136 (d) none
Answer: (a)

88. 𝐥𝐨𝐠 𝐞x + log(1+x) = 0 is equivalent to (MTP 1 Mark, Oct’20)

(a) x 2 + x + e = 0 (b) x 2 + x - e = 0
2
(c) x + x + 1 = 0 (d) x 2 + x - 1 = 0
Answer: (d)

89. The ratio of the speed of the two trains is 2: 5. If the distances they travel are in the ratio 5: 9, find
the ratio of times taken by them. (MTP 1 Mark, Oct’20)
(a) 2:9 (b) 18:25
(c) 25:18 (d) 10:45
Answer: (c)

90. If x = 𝟑𝟏/𝟒 + 𝟑−𝟏/𝟒 and y = 𝟑−𝟏/𝟒 , then the value of 3 (𝐱 𝟐 + 𝐲 𝟐 )𝟐 will be (MTP 1 Mark, Oct’20)
(a) 12 (b) 18
(c) 46 (d) 64
Answer: (d)

𝐲 𝐱 𝐲 𝐱 𝟏
91. Find the value of (x+y), if (𝐱 + 𝐱 𝟐) – (𝐲 + 𝐱) + (𝐲𝟐 + 𝐲) = 𝟑 (MTP 1 Mark, Oct’20)
(a) 1/3 (b) 3
(c) 1/2 (d) 2
Answer: (b)

92. The ratio of the prices of two houses was 16: 23. Two years later when the price of the first has
increased by 10% and that of the second by Rs. 477, the ratio of the prices becomes 11: 20. Find the
original prices of the two houses. (MTP 1 Mark, May’20)
(a) Rs. 848, Rs. 1,219. (b) Rs. 838, Rs. 1,119.
(c) Rs. 828, Rs. 1,219. (d) Rs. 848 Rs. 1,229.
Answer: (a)

93. If a: b = 3: 4, the value of (2a+3b): (3a+4b) is (MTP 1 Mark, May’20)

(a) 54:25 (b) 8:25
(c) 17:24 (d) 18:25
Answer: (d)

94. 𝟓𝟏𝟔 + 𝟏𝟐𝟓𝟓 is divisible by which of the following (MTP 1 Mark, May’20)
(a) 5 (b) 6
(c) 8 (d) 9
Answer: (b)
95. Given that log 𝟏𝟎𝟐 = x and 𝐥𝐨𝐠 𝟏𝟎𝟑 = y, the value of 𝐥𝐨𝐠 𝟏𝟎𝟔𝟎 is expressed as (MTP 1 Mark, May’20)
(a) 5 (b) 6
(c) 8 (d) 9
Answer: (b)

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96. If pqr = 𝐚𝐱 , qrs = 𝐚𝐲 and rsp = 𝐚𝐳 , then find the value of (𝐩𝐪𝐫𝐬)𝟏/𝟐 (MTP 1 Mark, May’20)
(a) 𝐚𝐱+𝐲+𝐳 (b) a√x + y + z
(c) a 4√𝑥 + 𝑦 + 𝑧 (d) (𝑎 𝑥+𝑦+𝑧 )1/4
Answer: (d)

97. The sum of two numbers is 62 and their product is 960. The sum of their reciprocals is
(MTP 1 Mark, May’20)
5 29
(a) (b) 480
480
61 41
(c) 960
(d) 960
Answer: (a)

98. The ratio of the earnings of two persons 3:2. If each saves 1/5th of their earnings, the ratio of their
savings. (MTP 1 Mark, Oct’19)
(a) 2:3 (b) 3:2
(c) 4:5 (d) 5:4
Answer: (b)

99. The Third Proportional to 15 and 20 is (MTP 1 Mark, Oct’19)

(a) 80/3 (b) 80
(c) 80/7 (d) 120
Answer: (a)

𝟑
100. If 𝐥𝐨𝐠 𝟗 𝐱 + 𝐥𝐨𝐠 𝟑 𝐱 = then x is (MTP 1 Mark, Oct’19)
𝟐
(a) 0 (b) 1
9 (d) 3
(c) 4
Answer: (b)

101. If x+y, y+z, z+x are in the ratio 6:7:8 and x + y + z =14 then the value of x is (MTP 1 Mark, Oct’19)
(a) 6 (b) 7
(c) 8 (d) 10
Answer: (b)

1 1
102. If 𝟐𝐱 = 𝟑𝐲 = 𝟔𝐳 then x
+ y = (MTP 1 Mark, Oct’19)
1 1 1
(a) 𝑧
(b) 𝑧
-x
1 1 (d) 0
(c) 𝑧
+x
Answer: (a)

103. If x:y:z = 2: 3:5 if x+ y+ z = 60 ,then the value of z (MTP 1 Mark, Apr’19)

(a) 30 (b) 15
(c) 9 (d) 12
Answer: (a)

104. The ratio of two numbers is 15:19. If a certain number is added to each term of the ratio it become
8: 9. What is the number added to each of the ratio? (MTP 1 Mark, Apr’19)
(a) 6 (b) 15
(c) 17 (d) 23
Answer: (c)
𝐚 𝐛 𝒄 𝟐𝐚+𝟑𝐛+𝟐𝐜
105. If 𝟑 = 𝟒 = 𝟓 then 𝟒𝐚−𝐛+𝟐𝐜
is (MTP 1 Mark, Apr’19)
11 17
(a) (b)
19 9
19 19
(c) 9
(d) 7
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Answer: (c)

𝟐𝒏 +𝟐𝒏−𝟏
106. Simplify 𝟐𝒏+𝟏+𝟐𝒏 = (MTP 1 Mark, Apr’19)
(a) 2n+2 (b) 2n
(c) 2 1
(d)
2
Answer: (d)

𝟏 𝟏
107. If 𝟐𝐚 = 𝟑𝐛 = 𝟏𝟐𝐜 then 𝐚 + 𝐛 = (MTP 1 Mark, Apr’19)
1 1 1
(a) c
(b) c
-a
1 (d) 0
(c) -c
Answer: (b)

108. The value of 𝐥𝐨𝐠 𝟔𝟒 512 is (MTP 1 Mark, Apr’19)

(a) 9 (b) 9/2
(c) 9/4 (d) 3/2
Answer: (d)

109. The value of (𝐥𝐨𝐠 𝐛 𝐚 𝐥𝐨𝐠 𝐜 𝐛 𝐥𝐨𝐠 𝐚 𝐜)𝟑 = (MTP 1 Mark, Apr’19)
(a) 1 (b) 3
(c) (log b C)3 (d) (log c b)3
Answer: (a)

110. The ratio compounded of 2:3, 9:4, 5:6 and 8: 10 is (MTP 1 Mark, Mar’19)
(a) 1: 1 (b) 1:5
(c) 3: 8 (d) none of these
Answer: (a)

111. The sub-triplicate ratio of 8: 27 (MTP 1 Mark, Mar’19)

(a) 27: 8 (b) 24: 81
(c) 2: 3 (d) none of these
Answer: (c)
𝐩 𝐫 𝐩−𝐫
112. If 𝐪 = 𝐬 = 𝐪−𝐬 , the process is called (MTP 1 Mark, Mar’19)
(a) Subtrahendo (b) Componendoc
(c) Alternendo (d) None of these
Answer: (a)
𝟐 𝟐 (𝒃𝟐 +𝒃𝒄+𝒄𝟐 ) 𝟐 𝟐
𝑿 (𝒂 +𝒂𝒃+𝒃 ) 𝑿𝒃 𝑿𝒄 (𝒄 +𝒄𝒂+𝒂 )
113. The value of (𝑿𝒂𝒃 ) x ( 𝑿𝒄 ) x (𝑿𝒂 ) (MTP 1 Mark, Mar’19)
(a) 1 (b) 0
(c) -1 (d) None of these
Answer: (a)

114. If a = 𝐥𝐨𝐠 𝟏𝟐 24 , b = 𝐥𝐨𝐠 𝟑𝟔 24 , b = 𝐥𝐨𝐠 𝟒𝟖 36 then prove that 1 + abc = (MTP 1 Mark, Mar’19)
(a) 2bc (b) 2ca
(c) 2ba (d) 3bc
Answer: (a)

115. If x = 𝟓𝟏/𝟑 + 𝟓−𝟏/𝟑 , 𝟓𝟑 - 15x is given by (MTP 1 Mark, Mar’19)

(a) 25 (b) 26
(c) 27 (d) 30
Answer: (b)
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116. Ten years ago the age of a father was four times his son. Ten years hence the age of the father will
be twice that of his son. The present age of the father and the son are (MTP 1 Mark, Mar’19)
(a) (50, 20) (b) (60, 20)
(c) (55, 25) (d) none of these
Answer: (a)

117. For a, b, c > 0 the value of each ratio is

𝐚 𝐛 𝐜
𝐛+𝐜
= 𝐜+𝐚 = 𝐚+𝐛 , then find the value of each ratio if a + b+ c ≠ 0 (MTP 1 Mark, Oct’18)
(a) 1/2 (b) 1/3
(c) 1/4 (d) 1
Answer: (a)
𝐱 𝐲 𝐳
118. If 𝐛+𝐜−𝐚 = 𝐜+𝐚−𝐛 = 𝐚+𝐛−𝐜 , then find the value of (b - c) x + (c - a)y + (a - b)z = (MTP 1 Mark, Oct’18)
(a) 0 (b) -1
(c) +1 (d) 1/2
Answer: (a)

119. x:y:z = 2:3:5 . If x+y+z = 60 then the value of z is (MTP 1 Mark, Oct’18)
(a) 30 (b) 15
(c) 9 (d) 12
Answer: (a)

120. Simplify 𝐥𝐨𝐠 𝟐 𝟑 𝐥𝐨𝐠 𝟑 𝟒 𝐥𝐨𝐠 𝟒 𝟓 𝐥𝐨𝐠 𝟓 𝟔 𝐥𝐨𝐠 𝟔 𝟕 𝐥𝐨𝐠 𝟕 𝟖 (MTP 1 Mark, Oct’18)
(a) 2 (b) 3
(c) 4 (d) 3/2
Answer: (b)

121. For p, q, r, s > 0 the value of each ratio is (MTP 1 Mark, Aug’18)
𝐩 𝐪 𝐫 𝐬
- -
𝐪+𝐫 𝐫+𝐬 𝐬+𝐩 𝐩+𝐪
-
(a) 1/2 (b) 1/3
(c) 1/4 (d) 1
Answer: (a)

𝐱+𝐲+𝐳
122. Let x, y and z are three positive numbers and P = 𝟐
; if (p-x) : (p-y) : (p-z) = 3:5:7 then the ratio of
x:y:z is (MTP 1 Mark, Aug’18)
(a) 4:5:6 (b) 6:5:4
(c) 3:5:7 (d) 7:5:3
Answer: (b)

123. If x = √√𝟔 + 𝟔 + (√𝟕 + 𝟐√𝟔) - √𝟔 then the value (MTP 1 Mark, Aug’18)
(a) 1 (b) 2
(c) 3 (d) 6
Answer: (a)

124. If 𝐥𝐨𝐠 𝟕 𝐥𝐨𝐠 𝟓 (√𝒙 + 𝟓 + √𝒙 = 0, the value of x is (MTP 1 Mark, Aug’18)

(a) 0 (b) 1
(c) 1/4 (d) 4
Answer: (d)

125. P, Q and R three cities. The ratio of average temperature between P and Q is 11: 12 and that
between P and R is 9:8. The ratio between the average temperature Q and R (MTP 1 Mark, Mar’18)

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(a) 22.27 (b) 27.22

(c) 32.33 (d) none
Answer: (b)

126. The third proportional between (𝒂𝟐 −𝒂𝟐 ) and (𝐚 + 𝐛)𝟐 is: (MTP 1 Mark, Mar’18)
a+b a−b
(a) a−b
(b) a+b
(a−b)2 (a+b)2
(c) a+b
(d) a−b
Answer: (d)

127. The value of 𝐥𝐨𝐠 𝟎.𝟏 0.001 = (MTP 1 Mark, Mar’18)

(a) 3 (b) 2
(c) 4 (d) 1/3
Answer: (a)

128. if 𝐥𝐨𝐠 𝟒 x = -3/2. Then x is (MTP 1 Mark, Mar’18)

(a) 1/8 (b) 1/4
(c) 1/2 (d) 1/3
Answer: (a)

Chapter 1 Ratio and Propotion, Indices, Logarithms