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EQUATIONS
Basics

2𝑥+5 3𝑥+10
1. 10
+ 15 = 5, then value of x
(a) 10.58 (b) 9.58
(c) 9.5 (d) none of these

2. The roots of the equation 𝑥 2 − 7𝑥 + 10 = 0 are:

(a) -2 and -5 (b) 2 and 5
(c) 2 and -5 (d) -2and 5

3. If one root of the equation 𝑥 2 − 3𝑥 + 𝑘 = 0 is 2, then value of k will be

(a) -10 (b) 0
(c) 2 (d) 10

Nature of Roots

4. The equation 𝑥 2 − (𝑃 + 4)𝑥 + 2𝑃 + 5 = 0 has equal roots. The value of p is

(a) 2 (b) -2
(c) ±2 (d) 3

5. The roots of the quadratic equation 𝑥 2 − 4𝑥 + 𝑘 = 0 are coincident if

(a) k = 4 (b) k = 3
(c) k = 2 (d) k = 1

6. The roots of the equation 𝑥 2 − 𝑥 + 1 = 0 are

(a) Imaginary and unequal (b) Real and unequal
(c) Real and equal (d) Imaginary and equal

7. If the roots of (𝑘 − 4)𝑥 2 − 2𝑘𝑥 + (𝑘 + 5) = 0 are coincident. Then the value of k?

(a) 14 (b) 20
(c) 18 (d) 22

Useful Factors
𝛼2 𝛽2
8. Let α and β be the roots of equation 𝑥 2 + 7𝑥 + 12 = 0. Then the value of ( 𝛽 + ) will be
𝛼
49 144 7 12
(a) (144 + ) (b) (12 + )
49 7
91
(c) (− 12) (d) none of these

9. If roots of equation 𝑥 2 + 𝑥 + 𝑟 = 0 are α and β and ∝3 + 𝛽 3 = −6. Find the value of ‘r’
(a) -5/3 (b) 7/3
(c) -4/3 (d) 1

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2 −1 −1
10. Roots of the equation 2𝑥 + 3𝑥 + 7 = 0 are α and β then the value of 𝛼𝛽 + 𝛽𝛼 is
(a) 2 (b) 3/7
(c) 7/2 (d) -19/14

Formation of Equations

11. Find the quadratic equation given that 5 + √3 is one root

(a) 𝑥 2 − 10𝑥 + 22 = 0 (b) 𝑥 2 + 10𝑥 − 22 = 0
(c) 𝑥 2 − 10𝑥 − 22 = 0 (d) −𝑥 2 − 10𝑥 + 22 = 0

12. If α and β are the roots of the equation 𝑥 2 + 7𝑥 + 12 = 0, then the equation whose roots
(𝛼 + 𝛽)2 and (𝛼 − 𝛽)2 will be
(a) 𝑥 2 − 14𝑥 + 49 = 0 (b) 𝑥 2 − 24𝑥 + 144 = 0
(c) 𝑥 2 − 50𝑥 + 49 = 0 (d) 𝑥 2 − 19𝑥 + 49 = 0

13. If arithmetic mean between roots of a quadratic equation is 8 and the geometric mean
between them is 5, the equation is _____
(a) 𝑥 2 − 16𝑥 − 25 = 0 (b) 𝑥 2 − 16𝑥 + 25 = 0
(c) 𝑥 2 + 16𝑥 + 25 = 0 (d) none of these

Variables Questions

14. If the ratio of the roots of the Equation 4𝑥 2 − 6𝑥 + 𝑝 = 0 is 1: 2 then the value of p is:
(a) 1 (b) 2
(c) -2 (d) -1

15. Roots of the equation 3𝑥 2 − 14𝑥 + 𝑘 = 0 will be reciprocal of each other if:
(a) k = -3 (b) k = 0
(c) k = 3 (d) k = 14

16. The equation 3𝑥 2 + 𝑚𝑥 + 𝑛 = 0 has roots that are double that of the equation
𝑥 2 + 10𝑥 + 12 = 0. What is the value of m + n?
(a) 104 (b) 204
(c) 102 (d) 202

Word Problems

17. The age of a person is twice the sum of the ages of his two sons and five years ago his age
was thrice the sum of their ages. Find his present age.
(a) 60 years (b) 52 years
(c) 51 years (d) 50 years

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18. 5 chairs and 3 tables cost of Rs.350 and 3 chairs and 5 tables cost Rs.370. What is the cost
of the table and two chairs?
(a) Rs.130 (b) Rs.120
(c) Rs.150 (d) Rs.140

19. A man wants to cut three lengths from a single piece of board of length 91cm. The Second
length is to be 3cm longer than the shortest and third length is to be twice as the shortest.
What is the possible length for the shortest piece?
(a) 22 (b) 20
(c) 15 (d) 18

20. X and Y have their present ages in the ratio 6: 7. 14 years ago, the ratio of the ages of the two
was 4: 5. What will be the ratio of their ages 21 years from now?
(a) 7: 11 (b) 9: 10
(c) 8: 11 (d) 11: 13

Cubic Equations
21. The roots of the equation 𝑥 3 + 𝑥 2 − 20𝑥 = 0
(a) 0, 4, 5 (b) 0, -4, 5
(c) 0, 4, -5 (d) 0, -4, -5

Misc

22. If 𝑥 = 51/3 + 5−1/3 , 5𝑥 3 − 15𝑥 is given by

(a) 25 (b) 26
(c) 27 (d) 30

23. The value of √6 + √6 + √6+. . . . . . . . . ∞ is

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

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MATHEMATICS OF FINANCE
Simple Interest
24. A person deposited a sum of Rs.10,000 in a bank. After 2 years, he withdrew Rs.4,000 and
at the end of 5 years, he received an amount of Rs.7,900; then the rate of simple interest is:
(a) 6% (b) 5%
(c) 10% (d) none of these

25. Certain sum of money borrowed at simple interest amount to Rs.2688 in three years and to
Rs.2784 in four years at the rate per annum equal to
(a) 7% (b) 6%
(c) 5% (d) 4%

26. A sum of Rs.46,875 was lent out at simple interest and at the end of 1 year 8 months the
total amount was Rs.50,000. Find the rate of interest percent per annum.
(a) 5% (b) 6%
(c) 4% (d) 8%

27. Rs.8,000 becomes Rs.10,000 in two years at simple interest. The amount that will become
Rs.6,875 in 3 years at the same rate of interest is:
(a) Rs.4,850 (b) Rs.5,000
(c) Rs.5,500 (d) Rs.5,275

28. If a simple interest on a sum of money at 6% p.a. for 7 tears is equal to twice of simple
interest on another sum for 9 years at 5% p.a. The ratio will be
(a) 2 : 15 (b) 7 : 15
(c) 15 : 7 (d) 1 : 7

29. How much time would the simple interest on a certain sum be 0.125 times the principal at
10% per annum
1 3
(a) 1 4 𝑦𝑒𝑎𝑟𝑠 (b) 1 4 𝑦𝑒𝑎𝑟𝑠
1 3
(c) 2 4 𝑦𝑒𝑎𝑟𝑠 (d) 2 4 𝑦𝑒𝑎𝑟𝑠

30. The rate of interest for the first 2 year is 3% per annum, for next 3 years is 8% per annum
and for the period beyond 5 years, 10% per annum. If a man gets Rs.1520 as a simple
interest for 6 years; how much money did he deposit?
(a) Rs.3800 (b) Rs.3000
(c) Rs.4000 (d) None of these

31. In Simple interest if the principal is Rs.2,000 and the rate and time are roots of the equation
𝑥 2 − 11𝑥 + 30 = 0
(a) Rs.500 (b) Rs.600
(c) Rs.700 (d) Rs.800

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32. A certain sum of money was put at S.I. for 2.5 years at a certain rate of S.I. p.a. Had it been
put at 4% higher rate; it would have fetched Rs.500 more. Find the sum of money.
(a) Rs.4000 (b) Rs.5000
(c) Rs.6000 (d) None

33. Miss Liza lent Rs.4,000 in such a way that some amount was given to Mr. A at 3% p.a. S.I.
and rest amount to was given to B at 5% p.a. S.I., the annual interest from both is Rs.144, Find
the amount lent to Mr. A
(a) Rs.2,800 (b) Rs.1,200
(c) Rs.2,500 (d) None

Compound Interest

34. The time in which a sum of money will be doubled at 6% compound interest compounded
interest compounded interest compounded annually approximately.
(a) 10 years (b) 12 years
(c) 13 years (d) 14 years

35. The compound interest on a certain sum is Rs.209 simple interest is Rs.200 for 2 years. What
is the rate per cent for 2 years? What is the rate percent?
(a) 9% (b) 18%
(c) 4.5% (d) 10%

36. Rs.10,000 is invested at annual rate of interest of 10% p.a. The amount after two years at
annual compounding is
(a) Rs.21100 (b) Rs.12100
(c) Rs.12110 (d) None of these

37. The difference between the simple and compound interest on a certain sum for 3 years
at 5% p.a is Rs.228.75. The compound interest on the sum for 2 years at 5% p.a is:
(a) Rs.3,175 (b) Rs.3,075
(c) Rs.3,275 (d) Rs.2,975

38. A person borrows Rs.5,000 for 2 years at 4% p.a. simple interest. He immediately lends to
1
another person at 6 4 % p.a. for 2 years. Find his gain in the transaction per year:
(a) Rs.112.50 (b) Rs.125
(c) Rs.225 (d) Rs.167.50

39. If A person invests Rs.5,000 in a three years investment that pays you 12% per annum.
Calculate the future value of the investment.
(a) Rs.7024.64 (b) Rs.7124.78
(c) Rs.7324.48 (d) Rs.7526.48

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40. What will be population after 3 years when present population is 25,000 and population
increase at the rate of 3% in first year, at 4% in second year and at 5% in third year?
(a) 28,119 (b) 29,118
(c) 30,100 (d) 27,100

41. A sum amount to Rs.1331 at a principal of Rs.1000 at 10% compounded annually. Find the
time
(a) 3.31 years (b) 4 years
(c) 3 years (d) 2 years

42. The nominal rate of growth is 17% and inflation is 9% for the five years. Let P be the Gross
Domestic Product (GDP) amount at the present year then the projected real GDP after 6
years is
(a) 1.587P (b) 1.921P
(c) 1.403P (d) 2.51P

43. How long will it take for a principal to double if money is worth 12% compounded monthly?
(a) 4.25 years (b) 5.81 years
(c) 6 years (d) none of these

Effective Rate

44. Nominal rate of interest 9.9% p.a. If interest is compounded monthly. What will be the
4033 12
effective rate of interest? (given (4000) = 1.1036)
(a) 10.36% (b) 9.36%
(c) 11.36% (d) 9.9%

45. If the effective rate of interest is 12% per annum and the interest is compounded quarterly,
the nominal rate of interest per annum
(a) 11.78% (b) 11.21%
(c) 11.89% (d) 11.49%

Depreciation

46. A Maruti Zen cost Rs.3,60,000. Its price depreciates at the rate of 10% of a year during the
first two years and at the rate of 20% in third year. Find the total depreciation.
(a) Rs.1,26,720 (b) Rs.1,15,620
(c) Rs.1,25,000 (d) Rs.1,10,520

47. A machine worth of Rs.4,90,740 is depreciated at 15% on its opening value each year. When
its value reduce to Rs.2,00,000
(a) 5 years 6 months (b) 5 years 7 months
(c) 5 years 5 months (d) none

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Present Value

48. Find the present value of an ordinary annuity of 8 quarterly payments of Rs.500 each, the
rate of interest being 8% p.a. compound quarterly
(a) 4275.00 (b) 4725.00
(c) 3662.50 (d) 3266.50

49. The present value of an annuity of Rs.80 for 20 years at 5% p.a is [𝐺𝑖𝑣𝑒𝑛 (1.05)20 = 2.6533]
(a) Rs.997 (appx.) (b) Rs.900
(c) Rs.1,000 (d) none of these

50. Shoba borrows Rs.50,00,000 to buy a house. If he pays equal installments for 20 years and
10% interest on outstanding balance, what will be the equal annual installment?
(a) Rs.687298.4 (b) Rs.685298.4
(c) Rs.585298.4 (d) Rs.587298.4

51. Suppose your father decides to gift you Rs.5,000 every year starts from today for the next
four years. You deposit the amount is a bank as and when you receive and get 10% per
annum interest rate compound annually. The present value of this annuity
(a) Rs.17,434.25 (b) Rs.17,344.25
(c) Rs.17434.52 (d) Rs.17,344.52

52. An overdraft of Rs.50,000 to be paid back in equal annual installments over a period of 20
years. Find the value of installment, if interest is compounded annually at 14% per annum.
(a) Rs.9550.50 (b) Rs.7549.30
(c) Rs.8559.50 (d) Rs.6560.50

53. Arun purchased a vacuum cleaner by giving Rs.1700 as cash down payment, which will be
followed by five EMIs of Rs.480 each. The vacuum cleaner can also be bought by paying
Rs.3900 cash. What is the approx. rate of interest p.a. (at simple interest) under this
installment plan?
(a) 18% (b) 19%
(c) 22% (d) 20%

54. Paul borrows Rs.20,000 on condition to repay it with compound interest at 5% p.a. in annual
instalment of Rs.2,000 each. Find the number of years in which the debt would be paid off.
(a) 10 years (b) 12 years
(c) 14 years (d) 15 years

55. Assuming that the discount rate is 7% per annum, how much would you pay to receive
Rs.50, growing at 5% annually forever?
(a) 2,600 (b) 2,000
(c) 2,500 (d) 3,000

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Future Value

56. How much money is to be invested every year so too accumulate Rs.3,00,000 at the end of
10 years if interest is compounded annually at 10% [A(10,0.1)=15.9374]
(a) Rs.18823.65 (b) Rs.18833.64
(c) Rs.18223.60 (d) Rs.16823.65

57. Rajesh deposits Rs.3,000 at the start of each quarter in his savings account. If the account
earns interest 5.75% per annum compounded quarterly, how much money (in Rs) while he
have at the end of 4 years? [Given that (1.014375)16 = 1.25654]
(a) Rs.54,308.6 (b) Rs.58,553.6
(c) Rs.68,353.6 (d) Rs.63,624.4

58. Rajesh invests Rs.20,000 per year in a stock index fund, with earns 9% per year, for the next
ten years. What would be closest value of accumulated investment upon payment of the last
installment? [Given: (1.09)10 = 2.36736]
(a) Rs.3,88,764.968 (b) Rs.3,03,858.564
(c) Rs.2,68,728.484 (d) Rs.4,08,718.364

59. Raju invests Rs.20,000 every year in a deposit scheme starting from today for next 12 years.
Assuming that interest rate on this deposit is 7% per annum compounded annually. What
will be the future value of this annuity?
(a) Rs.540,576 (b) Rs.382,813
(c) Rs.643,483 (d) Rs.357,769

60. A company establishes a sinking fund to provide for the payment of Rs.2,00,000 debt
maturing in 20 years. Contributions to the fund are to be made at the end of every year. Find
the amount of each annual deposit if interest is 5% per annum:
(a) Rs.6,142 (b) Rs.6,049
(c) Rs.6,052 (d) Rs.6,159

61. At six months intervals A deposited of Rs.1000 in a savings account which credit interest at
10% p.a., compounded semi-annually. The first deposit was made when A’s son was 6
months old and last deposit was made when his son was 8 years old. The money remained
in the account and was presented to the son on his 10𝑡ℎ birthday. How much did he receive?
(a) Rs.25740 (b) Rs.23740
(c) Rs.25860 (d) Rs.25760

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Application of TVM

62. A machine can be purchased for Rs.50,000. Machine will contribute Rs.12,000 per year for
the next five years. Assume borrowing cost is 10% per annum compounded annually.
Determine whether machine would be purchased or not?
(a) Purchased (b) Not purchased
(c) Profitable (d) None of the above

63. A company is considering proposal of purchasing a machine either by making full payment
of Rs.4000 or by leasing it for four years at an annual rate of Rs.1250. Which course of action
is preferable if the company can borrow money at 14% compounded annually?
(a) leasing is not preferable (b) leasing is preferable
(c) cannot be determined (d) none of these

64. Let the operating profit of a manufacturer for five years is given as
Year 1 2 3 4 5 6
Operating profit (in lakh Rs.) 90 100 106.4 107.14 120.24 157.35
Calculate Compound Annual Growth Rate (CAGR)
(a) 9% (b) 12%
(c) 11% (d) 13%

65. A Rs.1000 bond paying annual dividends at 8.5% will be redeemed at par at the end of 10
years. Find the purchase price of this bond if the investor wishes a yield rate of 8%
(a) Rs.907.135 (b) Rs.1033.54
(c) Rs.945.67 (d) none of these

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SEQUENCE & SERIES

Sequence & Series

66. The Sum of First n terms of an A.P is 5𝑛2 + 7𝑛. The 10𝑡ℎ term is
(a) 101 (b) 96
(c) 84 (d) 102

67. Find the sum to n terms of the series: 7 + 77 + 777 + ……. to n terms;
7 7𝑛 7 7𝑛
(a) 9 (10𝑛+1 − 10) − 9
(b) 9 (10𝑛+1 − 10) + 9
7 7𝑛 7 7𝑛
(c) 81 (10𝑛+1 − 10) − 9 (d) 81 (10𝑛+1 − 10) + 9

68. If the sum of n terms of an A.P. is (3𝑛2 − 𝑛) and its common difference is 6, then its third term is:
(a) 10 (b) 12
(c) 14 (d) 16

69. If the sum of n terms of an A.P be 𝟐𝒏𝟐 + 𝟓𝒏, then its ‘n’ term is:
(a) 4n – 2 (b) 3n – 4
(c) 4n + 3 (d) 3n + 4

70. Find the sum of the series. 243 + 324 + 432 + ⋯ … … … … … …. to n terms
4𝑛 4𝑛
(a) 36 ( − 1) (b) 34 ( − 1)
3𝑛 3𝑛
3 𝑛
(c) 36 ( − 1) (d) None of these
4

Arithmetic Progression

71. If 6𝑡ℎ 𝑎𝑛𝑑 13𝑡ℎ term of an A.P are 15 and 36 respectively the A.P is
(a) 2, 5, 8, 11 (b) 1, 4, 6, 8
(c) -4, -1, 2, 5 (d) 0, 3, 6, 9

72. The two-arithmetic means between 4 and 13 are

(a) 7,10 (b) 3,14
(c) 5,12 (d) 6,11

73. The first and the last term of an AP are -4 and 146. The sum of the terms is 7171. The number of
terms is
(a) 101 (b) 100
(c) 99 (d) none of these

𝑛
74. Find the sum of first twenty-five terms of A.P. series whose 𝑛𝑡ℎ term is (5 + 2).
(a) 105 (b) 115
(c) 125 (d) 135

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Geometric Progression

75. The sum of the infinite series 1 + 2/3 + 4/9+. . . . . . . .. is

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

76. In a GP if fourth term is 3 then the product of first seven terms is

(a) 35 (b) 37
(c) 36 (d) 38

2 2
77. In a G.P if the third term of a GP is 3 𝑎𝑛𝑑 6𝑡ℎ term is 81, then the first term is
(a) 6 (b) 1/3
(c) 9 (d) 2

Miscellaneous
78. If a, b, c are in AP and x, y, z are in GP, then the value of 𝑥 (𝑏−𝑐) . 𝑥 (𝑐−𝑎) . 𝑥 (𝑎−𝑏) is
(a) 1 (b) 0
(c) b (c – a) (d) none

79. The ratio of sum of first n natural numbers to that of sum of cubes of first n natural numbers is
(a) 3: 16 (b) n(n+1)/2
(c) 2/n(n+1) (d) none of the above

80. Sum lying from 100 to 300 which is divisible by 4 and 5 is

(a) 2000 (b) 2100
(c) 2200 (d) 2300

81. If the 𝑝𝑡ℎ term of an A.P. is ‘q’ and the 𝑞 𝑡ℎ term is ‘p’, then its 𝑟 𝑡ℎ term is:
(a) p + q + r (b) p + q – r
(c) p – q – r (d) p + q

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PERMUTATION & COMBINATION

Problems on Word
82. In how many ways can the letters of words “ACCOUNTANT” be arranged if vowels always occur
together?
(a) 7560 (b) 7650
(c) 7660 (d) 7550

Problems on Number

83. The sum of all the 4 digits numbers that can be formed with the digits 3, 4, 5, 5 is
(a) 18887 (b) 33333
(c) 38887 (d) 56661

84. Find the number of even numbers greater than 100 that can be formed with the digits 0,1,2,3?
(a) 10 (b) 15
(c) 20 (d) None of these

85. How many numbers can be formed with the help of 2,3,4,5,6,1 which is not divisible by 5, given that
it is a five-digit number and digits are not repeating?
(a) 1200 (b) 400
(c) 600 (d) 1400

Problems on Geometry
86. There are 12 points in a plane which are collinear no three points is a straight lie, number of
triangular that can be formed with the vertices as there points are:
(a) 216 (b) 220
(c) 110 (d) 108

87. The number of diagonals in a polygon of 6 sides

(a) 9 (b) 8
(c) 6 (d) 12

Miscellaneous
88. A man has 5 friends. In how many ways can be invite one or more of his friends to dinner?
(a) 30 (b) 31
(c) 32 (d) 10

89. The number of ways in which 8 examination paper be arranged so that the best and worst papers
never come together.
(a) 8! – 2 × 7! (b) 8! – 7!
(c) 8! (d) 7!

90. In how many ways can a committee of 3 ladies and four gents be chosen from 8 ladies and 7 gents?
(a) 1950 (b) 1920
(c) 1940 (d) 1960

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91. An examination paper with 10 questions consists of 6 questions in Algebra and 4 questions in
Geometry. At least one question from each section is to be attempted. In how many ways can this
be done?
(a) 945 (b) 100
(c) 1000 (d) none of these

92. In an election the number of candidates is one more than the number of members to be elected. If
a voter can vote in 254 different ways; find the number of candidates.
(a) 8 (b) 10
(c) 7 (d) none of these

93. The number of ways of arranging 6 boys and 4 girls in a row so that all 4 girls are together is:
(a) 6!. 4! (b) 2(7! 4!)
(c) 7! 4! (d) 2(6! 4!)

94. In how many ways can a party of 4 men and 4 women be seated at a circular table, so that no two
women are adjacent?
(a) 164 (b) 174
(c) 144 (d) 154

95. There are 5 books on English, 4 Books on Tamil and 3 books on Hindi. In how many ways can these
books be placed on a shelf if the books on the same subjects are to be together?
(a) 1,36,800 (b) 1,83,600
(c) 1,03,680 (d) 1,63,800

96. The number of ways that 12 prizes can be divided among 4 students so that each may have 3 prizes
is:
(a) 15,400 (b) 15,000
(c) 14,400 (d) 369600

97. How many ways can 5 different trophies can be arranged on a shelf if one particular trophy must
always be in the middle?
(a) 24 (b) 120
(c) 48 (d) 144

Algebra Based
𝑛
98. 𝑃𝑟 = 720 𝑎𝑛𝑑 𝑛𝐶𝑟 = 120 then value of r is
(a) 4 (b) 5
(c) 3 (d) 6

99. If 20𝐶𝑟 = 20
𝐶𝑟+6. Then the value of r is
(a) 10 (b) 7
(c) 11 (d) None of these

1 1 𝑁
100. The value of N in 7! + 8! = 9! is
(a) 81 (b) 78
(c) 89 (d) 64

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Space for Rough

Maths – Super 100 Questions