Algebra(Exams > Cat > Quantitaitve Aptitude ) Questions and answers for exam Preparation

Exams > Cat > Quantitaitve Aptitude

ALGEBRA MCQs

Total Questions : 240 | Page 6 of 24 pages

Question 51. If there are 10 positive real numbers n1 < n2 < n3 …… < n10…… How many triplets of these numbers (n1, n2, n3), (n2, n3, n4) …. can be generated such that in each triplet the first number is always less than the second number, and the second number is always less than the third number :(CAT 2002)

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Answer: Option C. -> 120
:
C
Ans: (c)
Step 1: select the numbers
Step 2: arrange the selected numbers according to the given condition.
Three numbers can be selected and arranged out of 10 numbers in ¹⁰C₃ ways = 120.
Now, only one arrangement can be possible as A>B>C, hence the solution will be 120.

Question 52. What is the value of fo(fog)o(gof) (x)

x
x2
2x + 3
22

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Answer: Option C. -> 2x + 3
:
C
Option (c) fo(fog)0(gof) (x)We have, fog (x) = gof (x) = xSo given expression reduces to f(x), that is, 2x + 3

Question 53. The number of common terms in the two sequences 17, 21, 25,…417 and 16, 21, 26….466 is: (CAT 2008)

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Answer: Option C. -> 20
:
C
Soln:If we have 2 AP’s and are trying to find common terms, then the common terms also form a AP with a CD of LCM of the 2 common differences.The first sequence is of the form 17 + 4aAnd the second sequence is of the form 16 + 5bBy observation we see that 21 is the first term of the new sequence and the common difference is 20 ( LCM of 4 and 5)Hence the sequence will be 21 + 20cNow substitute values of c from the answer options and check that the last term should not cross 417.Hence when we sub c=19 we see that the value is lesser than 417 and when we sub c=20 the value is 421 which is greater than 417. Hence the number of terms will be 19 + first term = 20 terms or option ( c)

Question 54. Give that a>b then the relation Ma [md (a) . mn (a, b)] = mn [a, md (Ma (a, b))] does not hold if (CAT 1994)

a < 0, b < 0,
a > 0, b > 0
a > 0, b < 0, | a | < | b |
a > 0, b < 0, | a | > | b |
22

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Answer: Option A. -> a < 0, b < 0,
:
A
Soln:(a)Ma [md (a), mn (a, b)] = mn [a, md (Ma (a, b)]Ma [2, -3] = mn [-2, md (-2)]2 = mn ( -2 , 2)2 = -2Relation does not hold for a = -2 and b = -3Or a < 0, b < 0

Question 55. Value of Ma [md (a), mn (md (b), a), mn (ab, md (ac))] where a = -2, b = -3, c = 4 is (CAT 1994)

2
6
8
-2
22

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Answer: Option B. -> 6
:
B
(b)Ma [md (a), mn (md (b), a), mn (ab, md (ac))]Ma [| - 2 |, mn ( | - 3 |, -2), mn (6, | -8 |)]Ma [2, mn (3, -2), mn (6, 8)]Ma[2, -2, 6] = 6

Question 56. A, B and C are 3 cities that form a triangle and where every city is connected to every other one by at least one direct route. There are 33 routes direct and indirect from A to C and there are 23 direct routes from B to A. How many direct routes are there from A to C ?(CAT 2000)

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Answer: Option B. -> 10
:
B
Option (b)Let the number of direct routes from A to B be x, from A to C be z and that from C to B be y. Then the total number of routes from A to C are = xy + z = 33. Since the number of direct routes from A to B are 23, x = 23. Therefore 23y + z = 33. Then y must take value 1 and then z = 10, thus answer = (b).

Question 57. One year payment to the servant is Rs. 90 plus one turban. The servant leaves after 9 months and receives Rs. 65 and a turban. Then find the price of the turban (CAT 1998)

Rs. 10
Rs. 15
Rs. 7.5
Cannot be determined

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Answer: Option A. -> Rs. 10
:
A
Option (a)Let turban be of cost Rs. X, so, payment to the servant = 90 + x for 12 monthsFor 9 month = (9/12) × (90 + x) = 65 + x → x = Rs. 10(Note:- you can also go from answer options)

Question 58. In the X – Y plane, the area of the region bounded by the graph of | x + y | + | x – y | = 4 is(2005)

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Answer: Option C. -> 16
:
C
Let x ≥ 0, y ≥ 0 and x ≥ yThen, | x + y | + | x – y | = 4→ x + y + x – y = 4 → x = 2And in case x ≥ 0, y ≥ 0, x ≤ yx + y + y – x = 4 → y = 2Area in the first quadrant is 4.By symmetry, total area 4 × 4 = 16 unit.

Question 59. P and Q are two positive integers such that PQ = 64. Which of the following cannot be the value of P+Q?

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Answer: Option D. -> 35
:
D
Option (d)
PxQ = 64 = 1 × 64 = 2 × 32 = 4 × 16 = 8 × 8.
Corresponding values of P + Q are 65, 34, 20, 16.
Therefore, P + Q cannot be equal to 35.

Question 60. Let a, b, c, d and e be integers such that a = 6b = 12c, and 2b = 9d = 12e. Then which of the following pairs contains a number that is not an integer ?(CAT 2003)

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Answer: Option D. -> | |
:
D
Option (d)AssumptionStart with e. if e=12, then c=36, d=16, b=72 and a=432Now you can eliminate answer options. All the options, other than option (d) give integral values.