# CDS Questions

In a rare coin collection, there is one gold coin for every three non-gold coins. 10 more gold coins are added to the collection and the ratio of gold coins to non-gold coins would be 1:2. Based on the information; the total number of corns in the collection now becomes

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

The costs of two articles are in the ratio 3:5. If there is 30% loss on the first article and 20% gain on the second article, what is the overall percentage of loss or gain?

1. 2% loss
2. 2.25% gain
3. 5.25% loss
4. 1.25% gain

Two numbers are in the ratio 3:5. If 9 is subtracted from each number, then they are in the ratio of 12:23. What is the second number?

1. 44
2. 55
3. 66
4. 77

Age of X is 6 times that of Y. After 4 years, X is 4 times elder to Y. What is the present age of Y?

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

In a certain school, the ratio of boys and girls is 7 : 5. If there are 2400 students in the school, then how many girls are there?

1. 500
2. 700
3. 800
4. 1000

The rabbit population in community A increases at 25% per year while that in community B increases at 50% per year. If the present populations of A and B are equal, what will he the ratio of the number of rabbits in community B to that in community A after 2 years?

1. 1.44
2. 1.72
3. 1.90
4. 1.26

The areas of two circular fields are in the ratio 16 : 49. If the radius of the bigger field is 14 m, then what is the radius of the smaller field?

1. 4 m
2. 8 m
3. 9 m
4. 10 m

The angles of a triangle are in the ratio 2:4:3. The smallest angle of the triangle is

1. 20°
2. 40°
3. 50°
4. 60°

The ratio of two numbers is 1:5 and their product is 320. What is the difference between the squares of these two numbers?

1. 1024
2. 1256
3. 1536
4. 1640

In a class of 49 students, the ratio of girls to boys is 4:3. If 4 girls leave the class, the ratio of girls to boys would be

1. 11:7
2. 8:7
3. 6:5
4. 9:8

The cost of a diamond varies directly as the square of its weight. A diamond broke into four pieces with their weights in the ratio of 1:2:3:4. If the loss in total value of the diamond was the ₹ 70,000, what was the price of the original diamond?

1. ₹ 1,00,000
2. ₹ 1,40,000
3. ₹ 1,50,000
4. ₹ 1,75,000

A person has only Rs. 1 and Rs. 2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is Rs. 75, then the number of Rs. 1 and Rs. 2 coins are, respectively.

1. 30 and 20
2. 35 and 15
3. 25 and 25
4. 15 and 35

X paid Rs. 47 for certain cups of tea and coffee. If tea costs Rs. 5 per cup and coffee costs Rs. 8 per cup, which one of the following statements is correct?

1. He drank 8 cups of tea and coffee.
2. He drank the same number of cups of tea and coffee.
3. He drank more tea than coffee.
4. He drank more coffee than tea.

The system of equations 2x + 4y = 6 and 4x + 8y = 8 is

1. Consistent with a unique solution
2. Consistent with infinitely many solutions
3. Inconsistent
4. None of the above

Sunil wants to spend Rs.200 on two types of sweets, costing Rs.7 and Rs.10 respectively. What is the maximum number of sweets he can get so that no money is left over?

1. 25
2. 26
3. 27
4. 28

Leela got married 6 years ago. Today her age is 1¼ times her age at the time of her marriage. Her son’s age is 1/10 times her age. What is the present age of her son?

1. 1 year
2. 2 years
3. 3 years
4. 4 years

The pair of linear equations kx + 3y + 1 = 0 and 2x + y + 3 = 0 intersect each other, if

1. k = 6
2. k ≠ 6
3. k = 0
4. k ≠ 0

If the roots of the equation (a2 - bc)x2 + 2(b2 - ac)x + (c2 - ab) = 0 are equal, where b ≠ 0, then which one of the following is correct?

1. a3 + b3 + c3 = 0
2. a3 + b3 + c3 = 3abc
3. a2 + b2 + c2 = 0
4. a + b + c = abc

If α and β are the roots of the equation x2 - x - 1 = 0, then what is (α2 + β2)/((α2 - β2)(α - β))

1. 2/5
2. 4/5
3. 3/5
4. 1/5

If x2 = 6 + √(6 + √(6 + √(6 + ....∞)), then what is one of the values of x equal to?

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

The expression 2x3 + x2 - 2x - 1 = 0 is divisible by

1. 2x - 1
2. 2x + 1
3. x + 2
4. x - 2

In solving a problem, one student makes a mistake in the coefficient of the first degree term and obtains -9 and -1 for the roots. Another student makes a mistake in the constant term of the equation and obtains 8 and 2 for the roots. The correct equation was:

1. x2 + 10x + 9 = 0
2. x2 - 10x + 16 = 0
3. x2 - 10x + 9 = 0
4. x2 + 10x + 16 = 0

The sign of the quadratic polynomial ax2 + bx + c is always positive if

1. a is positive and b2 - 4ac ≤ 0.
2. a can be any real number and b2 - 4ac ≤ 0.
3. a can be any real number and b2 - 4ac ≥ 0.
4. a is positive and b2 - 4ac ≥ 0.

If a - b = 4 and a2 + b2 = 40 where a and b are positive integers, where a and b are positive integers, then a3 + b6 is equal to

1. 264
2. 280
3. 300
4. 324

If the roots of the equation Ax2 + Bx + C = 0 are -1 and 1, then which one of the following is correct?

1. A and B are both positive
2. A and C are both negative
3. A and C are of opposite sign
4. A and C are both zero

The value of x2 - 4x + 11 can never be less than

1. 7
2. 8
3. 11
4. 22

Aman and Alok attempted to solve a quadratic equation. Aman made a mistake in writing down the constant term and ended up in roots (4, 3). Alok made a mistake in writing down the coefficient of x to get roots (3, 2). The correct roots of the equation are

1. –4, –3
2. 6, 1
3. 4, 3
4. –6, –1

If α and β are the roots of the equation x2 + px + q = 0, then what is α2 + β2 equal to?

1. p2 – 2q
2. q2 – 2p
3. p2 + 2q
4. q2 – q

Log (402 - 202) is equal to

1. log 3
2. log 60 + log 20
3. log 40 – log 20
4. log 20

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

1. 3(b+a)
2. 3(1-b-a)
3. 3(a+b-1)
4. 3(1-b+a)

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

1. 10
2. 3
3. 1
4. 0

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

1. 0 < x < 3
2. 23 < x < 30
3. x > 30
4. 3 < x < 23

If n is a whole number greater than 1, then n2(n2 - 1) is always divisible by

1. 12
2. 24
3. 48
4. 60

The sum of two numbers is 10 and their product is 20. What is the sum of their reciprocals?

1. 1
2. 1/2
3. 2
4. 1/10

What is the last digit in 7402 + 3402?

1. 0
2. 2
3. 4
4. 8

The difference between the squares of two consecutive odd integers is always divisible by

1. 16
2. 8
3. 7
4. 3

If x is a positive even integer and y is a negative odd integer, then xy is

1. even integer
2. rational number
3. odd integer
4. none

A student was asked to multiply a number by 25. He instead multiplied the number by 52 and got the answer 324 more than the correct answer. The number to be multiplied was

1. 15
2. 32
3. 12
4. 25

What is the maximum value of m if the number

N = 35 × 45 × 55 × 60 × 124 × 75

is divisible by 5m?

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

If n is a natural number, then √n is

1. always a rational number
2. always a natural number
3. always an irrational number
4. either a natural number or an irrational number

The digit in the units place of the product 81×82×83×84×....×99 is

1. 0
2. 4
3. 6
4. 8

If N, N+2 and N+4 are prime numbers, then the number of possible solutions for N are

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

The sum of two numbers is 143. If the greater number is divided by the difference of the numbers, the quotient is 7. What is the difference of the two numbers?

1. 9
2. 11
3. 14
4. 15

The values of x which satisfy the equation 51+x + 51–x = 26 are

1. –1, 1
2. 0, 1
3. 1, 2
4. –1, 0

The number of prime numbers which are less than 100 is

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

What is the remainder when the number (4444)4444 is divided by 9?

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

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.

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.

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.

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.

According to a report in yesterday's newspaper 1. (a) once (b) a (c) new police dog was taken to Raj Bhavan 2. (a) at (b) next (c) on Monday. This was to trace the 3. (a) killers (b) dogs (c) police of the "very important horse" which 4. (a) has (b) were (c) was reported missing on Sunday. The dog picked 5. (a) on (b) at (c) up the scent on some traces of 6. (a) those (b) blood (c) report and ran a few yards before losing the 7. (a) bet (b) track (c) game. The police have launched a vigorous 8. (a) search (b) investigation (c) campaign into the whole affair. They have 9. (a) given up (b) requisitioned (c) report the services of a forensic expert, 10. (a) a (b) an (c) two fingerprint expert and a photographer. 11. (a) There (b) We (c) So are now fourteen horses at Raj Bhavan 12. (a) who (b) where (c) which are kept in a large shed near the gate.