CDS Questions

Equations L1

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.

Equations L1

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

Equations L1

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

Equations L1

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

Equations L1

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

Quant Quadratic L1

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

Quant Quadratic L1

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

Quant Quadratic L1

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

Quant Quadratic L1

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

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

Quant Quadratic L1

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

Quant Quadratic L1

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.

Quant Quadratic L1

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

Quant Quadratic L1

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

Quant Quadratic L1

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

Quant Quadratic L1

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

Logarithms

Log (402 - 202) is equal to

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

Logarithms

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)

Logarithms

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

Logarithms

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

Numbers L1

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

Numbers L1

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

Numbers L1

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

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

Numbers L1

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

Numbers L1

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

Numbers L1

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

Numbers L1

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

Numbers L1

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

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

Numbers L1

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

Numbers L1

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

Numbers L1

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

Numbers L1

The number of prime numbers which are less than 100 is

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

Numbers L1

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

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

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.

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.

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.

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.

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.

Ordering of Words

The multi sourcing of

  • P: financial mess with
  • Q: coins led to a
  • R: using their own mix of
  • S: different mints

metals and alloys.

  1. SQRP
  2. QPSR
  3. RPQS
  4. PSRQ

Ordering of Words

In paliopathology

  • P: would be to obtain
  • Q: the fundamental objective
  • R: background information
  • S: as much

on the skeleton as possible.

  1. PRQS
  2. QPSR
  3. SRQP
  4. RPSQ

Ordering of Words

The national unity of a free people

  • P: to make it impracticable
  • Q: for there to be an arbitrary administration
  • R: depends upon a sufficiently even balance of political power
  • S: against a revolutionary opposition that is irreconcilably opposed to it
  1. QRPS
  2. RSPQ
  3. QRSP
  4. RPQS

Ordering of Words

It is very easy

  • P: a great deal more than one realises
  • Q: may mean
  • R: that a phrase that one does not quite understand
  • S: to persuade oneself
  1. SPQR
  2. RSQP
  3. RQPS
  4. SRQP

Ordering of Words

These positive effects vary from genetic changes that

  • P: to other related infections,
  • Q: make us more resistant to the diseases responsible
  • R: for epidemics and
  • S: which have effects on human that are

hard to pin down and quantify.

  1. QRPS
  2. SQPR
  3. PRSQ
  4. RPQS

Ordering of Words

All such students

  • P: get success
  • Q: who are honest and hard-working
  • R: and recognition
  • S: in very walk of life
  1. PSRQ
  2. SPRQ
  3. PRQS
  4. QPRS

Ordering of Words

He was so kind and generous that

  • P: he not only
  • Q: made others do so
  • R: but also
  • S: helped them himself
  1. SPQR
  2. PRSQ
  3. QPRS
  4. PSRQ

Ordering of Words

We must read

  • P: if we want to absorb the fruits of great literature
  • Q: but with concentration
  • R: them not as we do cricket stories
  • S: undefined
  1. QPSR
  2. PRQS
  3. PSQR
  4. PRSQ

Ordering of Words

It has been established that

  • P: Einstein was
  • Q: although a great scientist
  • R: weak in arithmetic
  • S: right from his school days
  1. SRPQ
  2. QPRS
  3. RQPS
  4. QPSR

Ordering of Words

Education is

  • P: of the proper sense of responsibilities
  • Q: the first need
  • R: in a citizen
  • S: for the development
  1. SQPR
  2. QSRP
  3. QSPR
  4. PQRS

Para Jumbles

The first line (S1) is fixed. Arrange the other four lines P, Q, R and S in a logical sequence.

  • S1: The beginning of the universe had, of course, been discussed for a long time.
  • P: One argument of such a beginning was the feeling that it was necessary to have a first cause to explain the existence of the universe.
  • Q: He pointed out that civilization is progressing, and we remember who performed this deed or developed that technique;
  • R: According to a number of early cosmologies in the Jewish/Christian/Muslim tradition, the universe started at a finite and not very distant time in the past.
  • S: Another argument was put forward by St. Augustine in his book, The City of God.
  1. QRSP
  2. RPSQ
  3. PSQR
  4. SQPR

Para Jumbles

The first line (S1) is fixed. Arrange the other four lines P, Q, R and S in a logical sequence.

  • S1: I was so eager not to disappoint my parents that I ran errands for anyone.
  • P: On the way a boy on a bicycle crashed into me and my left shoulder hurt so much that my eyes watered.
  • Q: Only then did I cry
  • R: But I still went and bought the maize, took it to my neighbours and then went home.
  • S: One day my neighbours asked me to buy some maize for them from the bazaar.
  1. SPRQ
  2. PQSR
  3. QRPS
  4. RSQP