CDS Questions

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?

48 m
30 m
25 m
24 m

If 2 cot θ = 3, then what is the value of

Quant Trigo

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

The value of cosec^2 67 + sec^2 57 - cot^2 33 - tan^2 23

Quant Trigo

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

2√2
2
√2
0

If tan A + cot A = 4, then tan^4 A + cot^4 A

Quant Trigo

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

The angle of elevation of the tip of a tower from a point

Quant Trigo

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?

48 m
49 m
50 m
51 m

If sin x + cos x = c, then sin^6 x + cos^6 x is equal to

Quant Trigo

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

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

What is the angle of elevation of the sun when the shadow

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?

30°
45°
60°
75°

From an aeroplane vertically above a straight horizontal road

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

(tan α + tan β) / (tan α tan β)
(tan α tan β) / (tan α + tan β)
(cot α cot β) / (cot α + cot β)
(cot α + cot β) / (cot α cot β)

From the top of a building 90 m high, the angles of depression

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?

30√3 m
90 - 30√3 m
90 + 30√3 m
60 + 30√3 m

If x = a cos θ + b sin θ and y = a sin θ – b cos θ

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?

2ab
a + b
a² + b²
a² – b²

An aeroplane flying at a height of 300 m above the ground passes

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?

100√3 m
100/√3 m
50√3 m
150(√3 + 1) m

If 7 sin^2 x + 3 cos^2 x = 4, then what is the value of tan x

Quant Trigo

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

√2
1
√3/2
1/√3

What is the value of (Quant Trigo #01)

Quant Trigo

What is equal to?

cos² A - sin² A
cos A - sin A
1
2

What is the value of (Quant Trigo #02)

Quant Trigo

What is the value of

√2
2√2
√2 tan x
0

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

Quant Trigo

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

0°
30°
45°
60°

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

Quant Trigo

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

What is the minimum value of 9 tan^2 θ + 4 cot^2 θ

Quant Trigo

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

If D is the number of degrees and R is the number of radians in an angle θ

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?

πD = 180R
πD = 90R
πR = 180D
πR = 90D

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

Quant Statistics

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

The mean of 100 values is 45. If 15 is added to each of the first forty

Quant Statistics

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

The arithmetic mean and geometric mean of two numbers

Quant Statistics

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

32/3
10
72/7
13

Ten observations are written in ascending order

Quant Statistics

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?

Which relations for the numbers 10, 7, 8, 5, 6, 8, 5, 8, 6 is correct

Quant Statistics

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

Mean = Mode
Mean = Median
Mean > Median
Mean > Mode

In histogram the width of the bars is proportional to

Quant Statistics

In histogram the width of the bars is proportional to

number of classes
class interval
cumulative frequency
frequency

What are the values of f1 and f2 respectively

Quant Statistics

Consider the following frequency distribution:

What are the values of f₁ and f₂ respectively?

10 and 17
17 and 10
11 and 16
16 and 11

An individual purchases three qualities of pencils

Quant Statistics

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?

₹10
₹30
₹40
₹60

In an asymmetrical-distribution, if the mean and median of the distribution

Quant Statistics

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

In a pie diagram, there are four slices with angles 150°, 90°, 60° and 60°

Quant Statistics

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

The largest slice has angle 150°
The smallest slice has angle 70°
The largest slice has angle 180°
The smallest slice has angle 90°

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

Quant Statistics

Consider the following distribution:

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

The mean marks obtained by 300 students in a subject are 60

Quant Statistics

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

The mean of 5 numbers is 15. If one more number is included

Quant Statistics

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?

If a + b = 5 and ab = 6, then what is the value of a^3+ b^3

Polynomials

If a + b = 5 and ab = 6, then what is the value of a³+ b³?

Log (40^2-20^2) is equal to

Logarithms

Log (40² - 20²) is equal to

log 3
log 60 + log 20
log 40 – log 20
log 20

If log25 5 = a and log25 15 = b, then the value of log25 27 is

Logarithms

If log₂₅ 5 = a and log₂₅ 15 = b, then the value of log₂₅ 27 is

3(b+a)
3(1-b-a)
3(a+b-1)
3(1-b+a)

What is the solution of the equation x log10 (10/3) + log10 3

Logarithms

What is the solution of the equation
x log₁₀ (10/3) + log₁₀ 3 = log₁₀ (2 + 3^x) + x?

If x is a real number such that log3 5 = log5 (2 + x)

Logarithms

If x is a real number such that log₃ 5 = log₅ (2 + x), then which of the following is true?

0 < x < 3
23 < x < 30
x > 30
3 < x < 23

Sometimes the messages are sent with

Selecting Words

In the following passage, at certain points you are given a choice of three words, one of which fits the meaning of the passage. Choose the best word.

Sometimes the messages are sent with 1. (a) many (b) few (c) no accompanying words and we speak in 2. (a) body (b) signal (c) foreign language alone. But what gestures make 3. (a) with body (b) up (c) into language? Most of us are 4. (a) easy (b) familiar (c) efficient with the common hand gestures. Some 5. (a) students (b) people (c) officers cannot talk without using their hands. 6. (a) We (b) Arms (c) They reach out as they explain almost 7. (a) exacting (b) shaping (c) changing their words, emphasizing and exaggerating and 8. (a) teaching (b) holding (c) punctuating their hands. Other people hardly 9. (a) adjust (b) use (c) wave their hands at all when they 10. (a) lecture (b) unite (c) talk.

One of the most interesting new books published recently

Selecting Words

In the following passage, at certain points you are given a choice of three words, one of which fits the meaning of the passage. Choose the best word.

One of the most interesting new books published recently is "Spaceship' by Prof. E.C. Walker, Our earth he says 1. (a) is (b) have been (c) will be like a spaceship, and all the 400 million people 2. (a) over (b) on (c) upon earth are passengers on it. And we are heading 3. (a) about (b) to (c) towards a disaster. The levels of atmospheric pollution 4. (a) increasing (b) arriving (c) coming in the cities and industrial areas of the world could in time change the weather patterns of the earth, raising the temperature 5. (a) in (b) of (c) for the whole planet. If this rose a few 6. (a) degrees (b) steps (c) miles the deserts of the world would expand to double their size. The polar ice caps would start inching. If the polar ice caps melted, the 7. (a) water (b) ice (c) sea level all over the world would rise 8. (a) in (b) by (c) to about 60 meters. Prof. Walker's 9. (a) idea (b) thought (c) book is not at all about gloom and doom. He admits that the 10. (a) ideas (b) changes (c) solutions he describes could take thousands of years.

I was engaged in many activities and I wanted a proper reconciliation

Selecting Words

In the following passage, at certain points you are given a choice of three words, one of which fits the meaning of the passage. Choose the best word.

I was engaged in many activities and I wanted a proper reconciliation between my activity and thought. Thought without 1. (a) wish (b) action (c) idea is undeveloped thought. Action without 2. (a) thought (b) wish (c) idea is folly. Of course we 3. (a) never (b) belatedly (c) sometimes act on some impulse or 4. (a) peaceful (b) uncontrollable (c) indisputable urge. If suddenly you through 5. (a) no (b) an (c) a brick at me and my 6. (a) hand (b) wrist (c) finger goes up in front to 7. (a) stimulate (b) rescue (c) protect myself, it is an automatic 8. (a) uncontrollable (b) instinctive (c) impulsive action and not a result 9. (a) to (b) in (c) of deliberate thought. Over living is 10. (a) made (b) conditioned (c) developed by a series of automatic 11. (a) thoughts (b) actions (c) wishes from morning till night. Anything 12. (a) we (b) I (c) they do outside that common range of 13. (a) thoughts (b) ideas (c) actions, however, has to be 14. (a) proceeded (b) preceded (c) followed by some measure of thinking. 15. (a) Some (b) If (c) The more action and thought are 16. (a) developed (b) allied (c) hostile and integrated, the more effective 17. (a) they (b) thoughts (c) we become and the happier you 18. (a) appear (b) develop (c) grow. There will then be no 19. (a) reconciliation (b) conflict (c) inflict between a wish to do something and 20. (a) inability (b) probability (c) plausibility to act.

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