# NTS Aptitude Test MCQs Online With Answers

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## NTS Aptitude MCQs With Answers Online Solved

1. How many ways the letter ‘SOLVING’ can be rearranged to make 7 letter words such that none of the letters repeat?
(A) 49
(B) 7C7
(C) 5040
(D) None of the above

2.Which one of the following numbers is the largest?

(A) (2+2+2)^2

(B) (2+2)^2)^2

(C) (2 x 2 x 2)^2

(D) 2 + 2^2 + (2^2)^2

3. The average age of a group of 5 students was 10. The average age increased by 4 years when 2 new students joined the group. What is the average age of the two new students who joined the group?
(A) 15
(B) 20
(C) 22
(D) 24

4. A number increases from 20 to 30 and then decreases from 30 to 20. Compare the percent of increase from 20 to 30 and that of the decrease from 30 to 20. From the following which of the following statement is true
(A) Percent decrease is less than the percent increase
(B) Percent decrease is more than the percent increase
(C) Percent increase is less than the percent increase
(D) None of the above

5. If you unscramble the letters YKANE, you will get the name of a
(A) Mountain pass
(B) Warrior
(C) Flower
(D) Country

6. 3 is 80% of what number?
(A) 2.50
(B) 3.00
(C) 3.75
(D) 3.50

7. There are twenty four students in a certain class. For every nine girls there are three boys. How many girls and how many boys are there in the class?
(A) 19 and 5
(B) 18 and 6
(C) 15 and 9
(D) 14 and 10

8. If Simran’s job is to recruit, develop and manage staff in her organization, which among the following is her designation?
(A) Personal Manager
(B) Personnal Manager
(C) Personnel Manager
(D) Personality Manager

9. Five teams from Delhi’s Schools are participating in a Summer School Football League. If each team plays the other teams 2 times, the total number of games the League will play is
(A) 10
(B) 20
(C) 30
(D) 40

10. In an equation, √96 ÷ √k = 2√6; what value of k will satisfy the equation?
(A) 2
(B) 4
(C) 6
(D) 8

11. To the correct number of significant figures, (5.0 x 10^-5) ÷ (2.00 x 10^-2) is?
(A) 2.5 x 10^-7
(B) 2.5 x 10^-3
(C) 2.50 x 10^-3
(D) None of these

12. Sonam invested Rs.120, 000 for buying 1000 BNB shares which were sold at a premium of 20%. What is the face value of the share?
(A) 100
(B) 120
(C) 144
(D) 96

13. The product of 3×2 matrix and 2×3 matrix will result in what order matrix?
(A) 3 x 2
(B) 2 x 2
(C) 2 x 3
(D) 3 x 3

14. Tutu pays 60% of his salary as house rent, 15% of salary as loan instalment and he still saves Rs. 900 after spending Rs. 1,800 on other household goods. What is his salary in Rs?
(A) 2,700
(B) 8,100
(C) 10,800
(D) 13,500

15. An investor owns 49% of the shares in a multinational company who declared 30% dividend on its stock for the fiscal year 2007. If the company’s face value of the share is Rs. 100 and the company’s stock consists of 100,000 shares, what would be the dividend income for the investor?
(A) Rs. 3.47 million
(B) Rs. 2.47 million
(C) Rs. 1.47 million
(D) Rs. 0.47 million

16. When a die is rolled, the probability of landing with 2 is?
(A) 3/6
(B) 1/6
(C) 2/6
(D) 5/6

17. In a box containing 8 marbles having equal number of black and white marbles, a black marble has been drawn in the first roun(D) The probability of drawing a white marble in the second round is?
(A) 1/7
(B) 3/7
(C) 5/7
(D) 4/7

18. Sin (90° – x) equals?
(A) Sin x
(B) 1 – Sin x
(C) Cos x
(D) Cosec x

19. The angle ‘x’ at which the values of Sin x and Cos x becomes equal is?
(A) 90°
(B) 60°
(C) 45°
(D) 30°

20. In a right triangle with vertices at (0, 0), (1, 0) and (1, 2), the angle extended from the x-axis is?
(A) 60°
(B) 62°
(C) 63.43°
(D) 64°

21. Six times a number reduced by ten equals 50. What is the number?
(A) 8
(B) 9
(C) 10
(D) 11

22. The second derivative (y”) of the function, y = 2x^5 + 4x^3 + x – 5 is?
(A) 10x^4 + 12x^2
(B) 40x^3 + 24x^2
(C) 40x^2 + 24x
(D) 80x + 24

23. 40% of 210 is same as one third of?
(A) 840
(B) 280
(C) 252
(D) 84

24. If p, q and r are the three consecutive odd integers, which of the following statements is NOT true?
(A) p + q is an even integer
(B) p + q + r is an odd integer
(C) (p + r)/2 is an even integer
(D) (p + q)/2 is an even integer

25. The point of intersection of lines, x + 3y = 8 and 3x = 2 + 2y is
(A) (0, 0)
(B) (8, 0)
(C) (2, 2)
(D) (2/3, 0)

26. The cardinal number of the set of letters in the word BHUTANESE
(A) 6
(B) 7
(C) 8
(D) 9

27. Find the ratio of a dozen and a score
(A) 3:5
(B) 4:5
(C) 3:6
(D) 4:6

28. What is the scale of a drawing if a line 3cm long on it represents 6m of the original?
(A) 1:2
(B) 1:20
(C) 1:200
(D) 1:2000

29. Mr. Gado, Mr. Kado and Mr. Nado purchased a big plot at Delhi. Mr. Gado has three- fifths of that plot while Mr. Kado has twice as much as plot belonging to Mr. Nado. What fraction of the plot belongs to Mr. Nado.
(A) 1/15
(B) 2/15
(C) 3/15
(D) 4/15

30. Find the area of a triangle whose vertices are A(-2,-3), B(3,2) and C(-1,-8)
(A) 10
(B) 15
(C) 20
(D) 25

31. In a simultaneous throw of two dice, the probability of getting a total of 7 is
(A) 4/6
(B) 3/6
(C) 2/6
(D) 1/6

32. If half of five is three, what would a third of ten be?
(A) 3
(B) 4
(C) 5
(D) 6

33. Two sides of a triangle have lengths a and b and the angle between them is θ. What value of θ will maximize the area of the triangle?
(A) π
(B) π /2
(C) π /3
(D) π / 4

34. Which of the following is NOT a Surd?
(A) √7
(B) (-32)^1/5
(C) √100
(D) (27)^1/3

35. Which of the following equations represent a circle of radius is 8 and centre at (-4,-6)
(A) (X-4)^2 + (y-6)^2 = 64
(B) (X+4)^2 + (y+6)^2 = 64
(C) (X-4)^2 + (y-6)^2 = 8
(D) (x+4)^2 + (y+6)^2 = 8

36. What is the relation between Standard Deviation and Variance?
(A) Standard Deviation is equal to Variance
(B) Standard Deviation is the square of Variance
(C) Standard Deviation is the square root of Variance
(D) Standard Deviation is twice Variance

37. If 2Sinθ -1 = 0, the value of θ in degrees, where θ is an acute angle
(A) 30 degree
(B) 45 degree
(C) 60 degree
(D) 90 degree

38. What is the arithmetic mean of all the multiples of two from 2 to 16 inclusive?
(A) 2
(B) 7
(C) 9
(D) 14

39. A wooden cube weighs 4 gms. If the same wood is used to make another cube with sides twice as long, how much will the cube weigh?
(A) 48 gms
(B) 32 gms
(C) 24 gms
(D) 18 gms

40. What is the area of a circle which as 6 by 8 rectangles inscribed in it?
(A) 64 π
(B) 48 π
(C) 36 π
(D) 25 π

41. The price of petrol was reduced by 2 per cent in the month of July. If the new price is further reduced by 5 per cent in July, The total reduction in the price of petrol in the two months equals to
(A) 6.9%
(B) 7 %
(C) 10 %
(D) 11.5%

42. If a^2 = b^2 – 1, b > 0, then which of the following is true A=a^4 and B=b^4+1
(A) A is greater
(B) B is greater
(C) A is equal to B
(D) None of the above

43. A mixture of 90 liters contains milk and water in the ratio 2: 1. If this ratio is to be changed to 1: 3, then quantity of water that should be further added is
(A) 90 liters
(B) 120 liters
(C) 150 liters
(D) 180 liters

44. 20 children took a dip in a water pool which is 10 m long and 50 m broad. If each child displaces 2 m3 of water on an average, then the rise in the water level in the pool will be
(A) 8 cm
(B) 10 cm
(C) 12.5 cm
(D) 14 cm

45. The value of log 28 is
(A) 64
(B) 16
(C) 4
(D) 3

46. For an amount of money deposited in the bank, the simple interest on it for period of 3 years at 6% per annum is Rs. 90. For the same amount, what is the amount of compound interest at the same interest rate and same time?
(A) Rs. 90
(B) Rs. 90.5
(C) Rs. 95
(D) Rs. 95.5

47. A wall clock gains 2 seconds in every 1 minute. Assuming that it was set right at 8 am and if in the evening of the same day when the wall clock indicated half past 8 o’clock, the correct time is
(A) 8:25 pm
(B) 8:05 pm
(C) 7:25 pm
(D) 7:00 pm

48. If a shopkeeper mixes 10 kg of apples costing Rs. 30 per kg with 20 kg of apples costing Rs. 60 per kg and sells the mixture at Rs. 60 per kg. His profit percent is
(A) No profit, no loss
(B) 10%
(C) 15%
(D) 20%

49. Assuming that PR = RS = QR, and angle b= 30 degrees, the value of angle a is

(A) 45 degrees
(B) 50 degrees
(C) 55 degrees
(D) 60 degrees

50. Karna can do a piece of work in 6 hours; Dorbi and Sonal together can do it in 2 hours, while Karna and Sonal together can do it in 3 hours. How long will Dorbi alone take to do it?
(A) 1 hour
(B) 2 hour
(C) 3 hour
(D) 4 hour

51. Find the value of following determinant

(A) 47
(B) – 40
(C) 2
(D) -7

52. Evaluate sin (cos^-1(3/5))
(A) 3/5
(B) 5/3
(C) 4/5
(D) 1

53. Noni can paint a room in 60 minutes, Karna can paint it in 30 minutes, and Raka can paint it in 20 minutes. How much time will they take to paint the same together?
(A) 5 minutes
(B) 10 minutes
(C) 24 minutes
(D) 36 minutes

54. Evaluate ∫ cos 2x dx
(A) ½ Cosx +c
(B) ½ Sinx +c
(C) ½ Cos2x +c
(D) ½ Sin2x +c

55. Ashima spends 25% of her salary on housing, 25% on food, 10% on clothing, 20% on fuel and rest on miscellaneous items. If she spends Rs. 2500 on miscellaneous items, her salary is
(A) Rs. 10,500
(B) Rs. 11,500
(C) Rs. 12,500
(D) Rs. 13,500

56. Using the word “BHUTAN”, how many words can be formed if all words must begin with the letter “U”?
(A) 720
(B) 540
(C) 120
(D) 60

57. Which of the following fractions is less than 3/4 ?
(A) 2/3
(B) 5/6
(C) 7/8
(D) 8/9

58. A worker is paid at a rate of Rs. 10 per hour and ½ the rate for any hours worked over 7 hours in a day. If the consultant started working at 9:00 (A)M. and left work at 8:18 P.M with 30 minutes lunch break in between. How much will he get paid for that day?
(A) Rs. 87
(B) Rs. 89
(C) Rs. 100
(D) Rs. 110

59. A toy store sold 560 toys on 1st day and 800 toys on 2nd day. What is the percent increase in the number of toys sold by the store?
(A) 30%
(B) 43%
(C) 70%
(D) 143%

60. Factor and solve 2x^2-5x+3 = 0
(A) (x=5, x=3)
(B) (x=1, x=3/2)
(C) (x= -1, x= -3)
(D) (x= -2, x= -3/2)

61. Convert 135 degrees into radians
(A) 2π
(B) 3π/4
(C) 4π/3
(D) π/2

62. The volume of a cylinder with a radius of 3 cm and height of 4 cm is
(A) 36 cm3
(B) 75.36 cm3
(C) 113.11 cm3
(D) 150.72 cm3

63. A wire is bent to form a square and the area of a square is 100 cm sq, if the same wire is then used to form a circle, the radius of the circle will be
(A) 4.5 cm
(B) 5.6 cm
(C) 6.4 cm
(D) 10 cm

64. Anikate is 8 years older than her sister, if he is 29 years in 2023, in which year was his sister born.
(A) 1984
(B) 1992
(C) 1994
(D) 2005

65. Find the area of the shaded region

(A) 30 cm sq
(B) 48 cm sq
(C) 63 cm sq
(D) 72 cm sq

66. The value of tan^-1(1) + cos^-1 (-1/2)+ sin^-1 (-1/2) is
(A) π/2
(B) 3π /4
(C) 2π/3
(D) π

67. Five teams from Kolkata’s Schools are participating in a Summer School Football League. If each team plays the other teams 2 times, the total number of games the League will play is ……..
(A) 10
(B) 20
(C) 30
(D) 40

68. Ravi pays 50% of his monthly income as house rent and 25% as loan repayment. He spends Rs. 2,000 on food and drinks. He still saves Rs. 5,000 per month and deposits into his saving account. What is Ravi’s monthly income?
(A) Rs. 35,000
(B) Rs. 33,000
(C) Rs. 30,000
(D) Rs. 28,000

69. In a classroom of 125 students, 75 are male students. What percent of the classroom is female?
(A) 60%
(B) 40%
(C) 0.6%
(D) 0.4%

70. Sonal and Prerna were given an apple pie each. Sonal ate 2/3 of the pie and Prerna ate 3/4 . What portion of the pie did they eat altogether?
(A) More than one pie
(B) Less than half a pie
(C) Three sixth of a pie
(D) The relationship cannot be determined from the information given.

71. The price of a commodity increased 8 points, then decreased 13 points, and then increased 9 points. If the commodity price before the changes was x points, which of the following was the commodity price, in points, after the changes?
(A) x-5
(B) x-4
(C) x+5
(D) x+4

72. Which number should be in next series?
1-1-2-3-5-8-13
(A) 21
(B) 26
(C) 31
(D) 41

73. Prem, who is sixteen years old, is four times as old as her brother Ajay. How old will Prem be when Prem is twice as old as her brother Ajay?
(A) 20
(B) 24
(C) 26
(D) 28

74. Choose the number that is 1/4 of half of 1/5 of 200?
(A) 40
(B) 20
(C) 10
(D) 5

75. If you arrange the letters “LNGEDNA” you have the name of a (n)
(A) Mountain
(B) Country
(C) Ocean
(D) Continent

76. You as a Professor have to be at college by 8.00. Assume it takes you 15 minutes to get dressed, 20 minutes to eat and 35 minutes to walk to school. What time should you get up every morning to get to school on time?
(A) 7:50 am
(B) 5:30 am
(C) 6:00 am
(D) 6:50 am

77. If you start with a one digit integer, multiply by 3, add 8, divide by 2 and subtract 6, you will get the integer back. Is the integer
(A) 3
(B) 5
(C) 4
(D) 2

78. If 7 cats can catch 7 rats in 7 minutes. How many cats does it take to catch 140 rats in 140 minutes?
(A) 20 cats
(B) 15 cats
(C) 10 cats
(D) 7 cats

79. You are the sports custodians in your school and you have to arrange a tennis match for 16 players for the monsoon season. If there can be no draws how many games must be played if each player can be eliminated by one loss?
(A) 12 games
(B) 14 games
(C) 16 games
(D) 15 games

80. Your boss asks you for a word that he/she can use in place of “change”. Which of the following would you give?
(A) allure
(B) altar
(C) allude
(D) alter

81. On her first birthday, her mom gifted Sandra with Rs. 100. On each birthday after that she doubled her previous gift. By the day after Sandra’s seventh birthday, what was the total amount that her mom had given her?
(A) 12,000
(B) 800
(C) 12,700
(D) 1,600

82. What is the missing number? 83-17 = 56 + ?
(A) 15
(B) 10
(C) 20
(D) 12

83. Rita’s father is four times as old as her. In 20 years, he will be only twice as old as her. How old is her father and how old she is?
(A) 32 and 8
(B) 40 and 10
(C) 36 and 9
(D) 60 and 15

84. If you were asked to list down all the numbers between 1 to 100. How many times would you write the number 2?
(A) 20 times
(B) 18 times
(C) 19 times
(D) 21 times

85. If you unscramble the letters ECEATHR, you will get the name of
(A) country
(B) Ocean
(C) profession
(D) flower

86. David spent 1/3 of his birthday money. Then he lost ½ of the rest. He now has only Rs. 100 left. How much did he get for his birthday?
(A) 200
(B) 300
(C) 350
(D) 600

87. A student had an average of exactly 84 marks after taking three tests. On the fourth test, he scored 96%. The average for all four tests is
(A) 84
(B) 86
(C) 87
(D) 82

88. There are 20 chickens, 4 dogs and 8 horses on a farm. How many legs are there?
(A) 88
(B) 98
(C) 78
(D) 108

89. If the time in city A is three hours ahead of the time in city B, what time would it be in city A if a city B clock one hour behind the time shows 4 o’clock?
(A) 1 o’clock
(B) 6 o’clock
(C) 7 o’clock
(D) 8 o’clock

90. Suppose two boys can read three books in four days. At the same rate, how long will it take eight boys to read a dozen books?
(A) 2 days
(B) 5 days
(C) 4 days
(D) 3 days

91. π/3 radians is same as
(A) 60 °
(B) 270 °
(C) 45 °
(D) 90 °

92. The mean of 100 observations is 50. If the observation 50 is replaced by 150, the resulting new mean is
(A) 57
(B) 151
(C) 101
(D) 51

93. The radius and the height of a cylinder are in ratio 2:3. If the volume of the cylinder is 1617cm^3, then the radius of the base of the cylinder will be
(A) 3.5cm
(B) 4cm
(C) 11cm
(D) 7cm

94. The pass percentage of your school stands at 91% with 455 students passing the annual examinations. How many students in your school would have to pass to raise the pass percentage to 95%?
(A) 20 students
(B) 25 students
(C) 50 students
(D) 55 students

95. In your school, the first period starts at 9:00 am and the school ends at 4:00 pm which includes 10 minutes class cleaning time. There is a morning and evening break for 10 minutes each and a 40 minute lunch break. How long will each class period be if you have to plan for 7 periods a day?
(A) 40 minutes
(B) 45 minutes
(C) 50 minutes
(D) 55 minutes

96. Sonam’s age is one third the age of his mother and half the age of his brother Dorji. Together their age totals to 66. How old is Sonam?
(A) 11
(B) 13
(C) 15
(D) 20

97. Palden spends a total of three hours of his time every day walking to school in the morning and back home in the evening. If he has to be in school by 8:30 am and the time he takes to travel is the same both ways, at what time should he leave home?
(A) 5:30 am
(B) 6:30 am
(C) 7:00 am
(D) 7:30 am

98. Your student is writing a letter of invitation. Which of the following words would you recommend for him to replace the underlined word in the following sentence? “The programme will begin at 9:00 am
(A) seize
(B) starts
(C) begun
(D) commence

99. You have 36 students in your class. You have planned for them to work in groups of equal numbers. 6 of your students are unwell and cannot participate. How many groups can you get?
(A) 2 groups of 20
(B) 3 groups of 10
(C) 7 groups of 5
(D) 10 groups of 4

100. 96÷ (4×3) + 8 ÷ 2─ 2 =?
(A) 10
(B) 12
(C) 6
(D) 0

1. Roman says: