# CDS Questions

The area of a regular hexagon of side 'a' is equal to

1. √2/3 a2 square units
2. 3√3/2 a2 square units
3. 1/3 a2 square units
4. √3/2 a2 square units

Three circles each of radius 3.5 cm touch one another. The area subtended between them is

1. 6(√3π - 2) square units
2. 6(2π - √3) square units
3. 49/8 (2√3 - π) square units
4. 49/8 (√3 - π) square units 8

A ball of radius 1 cm is put into a cylindrical pipe so that it fits inside the pipe. If the length of the pipe is 14 m, what is the surface area of the pipe?

1. 2200 square cm
2. 4400 square cm
3. 8800 square cm
4. 17600 square cm

If the perimeter of a rectangle is 10 cm and the area is 4 cm2, then its length is

1. 6 cm
2. 5 cm
3. 4.5 cm
4. 4 cm

If  with 0 < θ < 90°, then what is θ equal to?

1. 30°
2. 45°
3. 60°
4. 75°

If 3 sin x + 5 cos x = 5, then what is the value of (3 cos x – 5 sin x)?

1. 0
2. 2
3. 3
4. 5

If tan (A + B) = √3 and tan A = 1, then tan (A - B) is equal to

1. 0
2. 1
3. 1/√3
4. √2

The angles of elevation of the top of a tower from two points situated at distance 36 m and 64 m from its base and in the same straight line with it are complementary. What is the height of the tower?

1. 48 m
2. 30 m
3. 25 m
4. 24 m

If 2 cot θ = 3, then what is the value of (2 cos θ - sin θ) / (2 cos θ + sin θ)?

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

The value of cosec2 67 + sec2 57 - cot2 33 - tan2 23 is

1. 2√2
2. 2
3. √2
4. 0

If tan A + cot A = 4, then tan4 A  + cot4 A is equal to

1. 194
2. 191
3. 110
4. 80

The angle of elevation of the tip of a tower from a point on the ground is 45°. Moving 21 m directly towards the base of the tower, the angle of elevation changes to 60°. What is the height of the tower, to the nearest meter?

1. 48 m
2. 49 m
3. 50 m
4. 51 m

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

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°

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)

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

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

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

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

What is equal to?

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

What is the value of

1. √2
2. 2√2
3. √2 tan x
4. 0

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

1. 30°
2. 45°
3. 60°

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

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

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

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

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

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

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

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

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

In histogram the width of the bars is proportional to

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

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

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

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

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°

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

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

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

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

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

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

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

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

What is 5% of 50% of 500?

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

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%

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

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%

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

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

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

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%