CDS Questions

Quant Trigo

If sin x + cos x = c, then sin6 x + cos6 x is equal to

  1. (1 + 6c2 - 3c4)/16
  2. (1 + 6c2 - 3c4)/4
  3. (1 + 6c2 + 3c4)/16
  4. (1 + 6c2 + 3c4)/4

Quant Trigo

What is the angle of elevation of the sun when the shadow of a pole is √3 times the length of the pole?

  1. 30°
  2. 45°
  3. 60°
  4. 75°

Quant Trigo

From an aeroplane vertically above a straight horizontal road, the angle of depression of two consecutive kilometer stones on the opposite sides of the aeroplane are found to be α and β. The height of the aeroplane above the road is

  1. (tan α + tan β) / (tan α tan β)
  2. (tan α tan β) / (tan α + tan β)
  3. (cot α cot β) / (cot α + cot β)
  4. (cot α + cot β) / (cot α cot β)

Quant Trigo

From the top of a building 90 m high, the angles of depression of the top and the bottom of a tree are 30° and 45° respectively. What is the height of the tree?

  1. 30√3 m
  2. 90 - 30√3 m
  3. 90 + 30√3 m
  4. 60 + 30√3 m

Quant Trigo

If x = a cos θ + b sin θ and y = a sin θ – b cos θ, then what is x2 + y2 equal to?

  1. 2ab
  2. a + b
  3. a2 + b2
  4. a2 – b2

Quant Trigo

An aeroplane flying at a height of 300 m above the ground passes vertically above another plane at an instant when the angles of elevation of the two planes from the same point on the ground are 60° and 45° respectively. What is the height of the lower plane from the ground?

  1. 100√3 m
  2. 100/√3 m
  3. 50√3 m
  4. 150(√3 + 1) m

Quant Trigo

If 7 sin2 x + 3 cos2 x = 4, 0 < x < 90°, then what is the value of tan x?

  1. √2
  2. 1
  3. √3/2
  4. 1/√3

Quant Trigo

What is equal to?

  1. cos2 A - sin2 A
  2. cos A - sin A
  3. 1
  4. 2

Quant Trigo

What is the value of which satisfies the equation cos θ + tan θ = 1?

  1. 30°
  2. 45°
  3. 60°

Quant Trigo

If cos θ1 + cos θ2 + cos θ3 = 3, then what is sin θ1 + sin θ2 + sin θ3 equal to?

  1. 0
  2. 1
  3. 2
  4. 3

Quant Trigo

What is the minimum value of 9 tan2 θ + 4 cot2 θ

  1. 6
  2. 9
  3. 12
  4. 13

Quant Trigo

If D is the number of degrees and R is the number of radians in an angle θ, then which one of the following is correct?

  1. πD = 180R
  2. πD = 90R
  3. πR = 180D
  4. πR = 90D

Statistics L1

The geometric mean of 32, 4, 8, X, 2 is 8. What is the value of X?

  1. 2
  2. 4
  3. 8
  4. 16

Statistics L1

The mean of 100 values is 45. If 15 is added to each of the first forty values and 5 is subtracted from each of the remaining sixty values, the new mean becomes

  1. 45
  2. 48
  3. 51
  4. 55

Statistics L1

The arithmetic mean and geometric mean of two numbers are 14 and 12 respectively. What is the harmonic mean of the numbers?

  1. 32/3
  2. 10
  3. 72/7
  4. 13

Statistics L1

Ten observations 6, 14, 15, 17, x + 1, 2x - 13, 30, 32, 34 and 43 are written in ascending order. The median of the data is 24. What is x?

  1. 15
  2. 18
  3. 20
  4. 24

Statistics L1

Which one of the following relations for the numbers 10, 7, 8, 5, 6, 8, 5, 8, 6 is correct?

  1. Mean = Mode
  2. Mean = Median
  3. Mean > Median
  4. Mean > Mode

Statistics L1

In histogram the width of the bars is proportional to

  1. number of classes
  2. class interval
  3. cumulative frequency
  4. frequency

Statistics L1

Consider the following frequency distribution:

What are the values of f1 and f2 respectively?

  1. 10 and 17
  2. 17 and 10
  3. 11 and 16
  4. 16 and 11

Statistics L1

An individual purchases three qualities of pencils. The relevant data is given below:

It is known that the average price per pencil is ₹1.25. What is the value of x?

  1. ₹10
  2. ₹30
  3. ₹40
  4. ₹60

Statistics L1

In an asymmetrical-distribution, if the mean and median of the distribution are 270 and 220 respectively, then the mode of the data is

  1. 120
  2. 220
  3. 280
  4. 370

Statistics L1

In a pie diagram, there are four slices with angles 150°, 90°, 60° and 60°. A new pie diagram is formed by deleting one of the slices having angle 60° in the given pie diagram. In the new pie diagram

  1. The largest slice has angle 150°
  2. The smallest slice has angle 70°
  3. The largest slice has angle 180°
  4. The smallest slice has angle 90°

Statistics L1

Consider the following distribution:

If the mean of the above distribution is 50, what is the value of f?

  1. 24
  2. 34
  3. 56
  4. 96

Statistics L1

The mean marks obtained by 300 students in a subject are 60. The mean of top 100 students was found to be 80 and the mean of last 100 students was found to be 50. The mean marks of the remaining 100 students are

  1. 70
  2. 65
  3. 60
  4. 50

Statistics L1

The mean of 5 numbers is 15. If one more number is included, the mean of the 6 numbers becomes 17. What is the included number?

  1. 24
  2. 25
  3. 26
  4. 27

Mixtures Alligation L1

25 kg of alloy X is mixed with 125 kg of alloy Y. If the amount of lead and tin in the alloy X is in the ratio 1:2 and the amount of lead and tin in the alloy Y is in the ratio 2:3, then what is the ratio of lead to tin in the mixture?

  1. 1:2
  2. 2:3
  3. 3:5
  4. 7:11

Percentages L1

In a group of persons, 70% of the persons are male and 30% of the persons are married. If two sevenths of males are married, what fraction of the females is single?

  1. 2/7
  2. 3/7
  3. 2/3
  4. 1/3

Percentages L1

The tank-full petrol in Arun's motor-cycle lasts for 10 days. If he starts using 25% more everyday, how many days will the tank-full petrol last?

  1. 5
  2. 6
  3. 7
  4. 8

Percentages L1

An employee is required to contribute 10% of his pay to General Provident Fund. If he gets ₹13,500 as net pay in a month, then what is the monthly General Provident Fund contribution (assuming no other deductions)?

  1. ₹ 1215
  2. ₹ 1350
  3. ₹ 1500
  4. ₹ 1650

Percentages L1

A man loses 20% of his money. After spending 25% of the remainder, he has ₹ 480 left. What is the amount of money he originally had?

  1. ₹ 600
  2. ₹ 720
  3. ₹ 800
  4. ₹ 840

Percentages L1

What is 5% of 50% of 500?

  1. 1.25
  2. 12.5
  3. 6.25
  4. 25

Percentages L1

If m% of m + n% of n = 2% of (m × n), then what percentage of m is n?

  1. 25%
  2. 50%
  3. 75%
  4. 100%

Percentages L1

The price of an article is ₹ 25. After two successive cuts by the same percentage, the price becomes ₹ 20.25. If each time the cut was x%, then

  1. x = 9
  2. x = 10
  3. x = 11
  4. x = 11.5

Percentages L1 Mensuration L1

The radius of the base of a right circular cone is increased by 15% keeping the height fixed. The volume of the cone will be increased by

  1. 34.75%
  2. 32.25%
  3. 31%
  4. 30%

Percentages L1

What is the number whose 20% is 30% of 40?

  1. 50
  2. 60
  3. 80
  4. 90

Percentages L1

In a certain year, a school had 60% boys and 40% girls as students. In the next five years the number of boys decreased by 10% and the number of girls increased by 10%. What is the change in total roll strength of the school in the five years?

  1. 3% increase
  2. 2% decrease
  3. No change
  4. 5% decrease

Percentages L1 Mensuration L1

If each of the dimensions of a rectangle is increased by 200%, the area is increased by

  1. 300%
  2. 400%
  3. 600%
  4. 800%

Percentages L1

5/9 th part of the population in a village are males. If 30% of the males are married, the percentage of unmarried females in the total population is

  1. 20 2/9
  2. 27 2/9
  3. 27 7/9
  4. 29 2/9

Percentages L1

If a% of a + b% of b = 2% of ab, then what percent of a is b?

  1. 50%
  2. 75%
  3. 100%
  4. Cannot be determined

Interests L1

The difference between compound interest and the simple interest at the same rate of interest R percent per annum on an amount of Rs. 15,000 for two years is Rs. 96. What is the value of R?

  1. 8
  2. 10
  3. 12
  4. Cannot be determined due to insufficient data

Interests L1

What is the least number of complete years in which a sum of money at 20% compound interest will be more than doubled?

  1. 4
  2. 5
  3. 6
  4. 7

Interests L1

There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest on Rs. 12,000 after 3 years at the same rate of interest?

  1. Rs. 6,240
  2. Rs. 2,160
  3. Rs. 3,972
  4. Rs. 3,120

Interests L1

A sum of money on compound interest amounts to Rs. 9680 in 2 yr and Rs. 10648 in 3 yr. What is the rate of interest per annum?

  1. 5%
  2. 10%
  3. 15%
  4. 20%

Interests L1

A sum of money becomes 3 times in 5 years at simple interest. In how many years will the same sum become 6 times at the same rate of simple interest?

  1. 10.5 years
  2. 12 years
  3. 12.5 years
  4. 10 years

Interests L1

The principal on which a simple interest of Rs. 55 will be obtained after 9 months at the rate of 3⅔% per annum is

  1. Rs. 1000
  2. Rs. 1500
  3. Rs. 2000
  4. Rs. 2500

Interests L1

A certain sum at simple interest amounts to Rs.1350 in 5 years and to Rs.1620 in 8 years. What is the sum?

  1. Rs.900
  2. Rs.800
  3. Rs.700
  4. Rs.1000

Interests L1

What is the compound interest on ₹1600 at 25% per annum of 2 year compounded annually

  1. ₹ 900
  2. ₹ 800
  3. ₹ 750
  4. ₹ 700

Interests L1

An automobile financer claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging the interest at the rate of 10%, the effective rate of interest becomes:

  1. 11%
  2. 10.75%
  3. 10.5%
  4. 10.25%

Interests L1

The difference between the simple and the compound interest on a certain sum of money at 4% per annum in 2 years is Rs. 10. What is the sum?

  1. Rs. 5,500
  2. Rs. 6,000
  3. Rs. 6,250
  4. Rs. 7,500