CAT Practice Test: Week 15 - CAT MCQ

The composition of f and g is given by f(g(x)) which is equal to 2(3x + 4) + 1.

Since f (128) = 4, we can see that the product of f (256). f (0.5) = f (256 × 0.5) = f (128) = 4.
Similarly, the products f (1). f (128) = f (2). f (64)
= f (4). f (32) = f (8). f (16) = 4.
Thus, M = 4 × 4 × 4 × 4 × 4 = 1024.
Option (d) is the correct answer.

f(0) = 1, f(1) = 2 and f(2) = 4
Hence, they are in G.P.

(x + 3)³ would be shifted 3 units to the left and hence (x + 3)³ + 1 would shift 3 units to the left
and 1 unit up. Option (c) is correct.

(x² + loge x) would be neither odd nor even since it obeys neither of the rules for even function
(f(x) = f(–x)) nor for odd functions (f(x) = –f(–x)).

y = e^x
fi log_e y = x.
fi f ^–1(x) = log_e x.

If you differentiate each function with respect to x, and equate it to 0 you would see that for none
of the three options will get you a value of x = –3 as its solution. Thus, option (d) viz. None of
these is correct.

The given function would become h[ 11, 80, 1] = 2640.

The given function would become f[3, 3, 3] = 27.

The number of g’s and f’s should be equal on the LHS and RHS since both these functions are
essentially inverse of each other.
Option (c) is correct.

Father's wife → mother. Hence, the daughter of the mother means sister and sister's younger brother means brother. Therefore, the boy is the brother of Deepak.

The only daughter of the father of A's mother' means the mother of A.

Hence, A is the child of the lady in the photograph.

He is the son.

∴ The answer is son.

Ashok is the only brother of Sudeep and Veena is the sister-in-law of Ashok. Hence Veena is the wife of Sudeep. Kalyani is the mother-in-law of Veena. Kalyani is the mother of Ashok.

P x Q → P is the wife of Q

Q % R → Q is the father of R

R - T → R is the brother of T

T + S → T is the sister of S.

Therefore, T is the daughter of P.

Daughter of Abhijit's brother → niece of Abhijit. Thus the granddaughter of the woman is Abhijit's niece.

Hence, the woman is the mother of Abhijit.

Grandson of Amit’s brother means Son of Amit in this situation. Then the girl is the wife of Amit’s Son that makes Ami the Father-in-law of the Girl.

A and B are children of D.
From (1), C is the brother B and son of E.
Since, the sex of D and E are not known. Hence (1) is not sufficient to answer the question.
From (2). F is the mother of B. Hence, F is also the mother of A. Hence D is the father of A.
Thus, (2) is sufficient to answer the question.

Only daughter of my mother → myself.

Hence, the woman is the mother of the man.

A is the mother of B, B is the brother of C and C is the daughter of D. Hence, D is the father.

Brother of mother means maternal uncle. Hence only nephew of Aamir's maternal uncle means Aamir himself. Therefore Sonia is the wife of Aamir.