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Algebra Aptitude Questions & Formulas with answer


Ques 1 GATE 2025 SET-2

If Pex=Qe-x for all real values of x, which one of the following statements is true?

A

P=Q=0

B

P=Q=1

C

P=1; Q=-1

D

P/Q=0

(a) is the correct answer.

We are given the equation P·ex = Q·e-x for all real x.

Multiplying both sides by ex gives P·e2x = Q.

Since this must hold true for all real values of x, and e2x changes with x, the only way the left-hand side remains a constant equal to Q is if P = 0. Substituting P = 0 into the equation gives Q = 0.

✅ Final Answer: Option (a) — P = Q = 0.

Reason: The equation can only hold for all x if both P and Q are zero, since e2x is not constant.

Ques 2 GATE 2025

If a real variable x satisfies 3x2=27×9x then the value of 2x2/(2x)2 is:

A

2-1

B

20

C

23

D

215

(d) is the correct answer.

Ques 3 GATE 2025

The relationship between two variables x and y is given by x+py+q=0 and is shown in the figure. Find the values of p and q.
Note: The figure shown is representative

A

p=-1/2; q=2

B

p=2; q=-2

C

p=1/2;q=4

D

p=2; q=4

(a) is the correct answer.

Ques 4 GATE 2025

The ceiling function of a real number x, denoted by ce(x), is defined as the smallest integer that is greater than or equal to x. Similarly, the floor function, denoted by fl(x) is defined as the largest integer that is smaller than or equal to x. Which one of the following statements is NOT correct for all possible values of x?

A

ce(x)≥x

B

fl(x)≤x

C

ce(x)≥fl(x)

D

fl(x)

(d) is the correct answer.

Ques 5 GATE 2025

If Pex=Qe-x for all real values of x, which one of the following statements is true?

A

P=Q=0

B

P=Q=1

C

P=1; Q=-1

D

P/Q=0

(a) is the correct answer.

Ques 6 GATE 2025

If Pex=Qe-x for all real values of x, which one of the following statements is true?

A

P=Q=0

B

P=Q=1

C

P=1; Q=-1

D

P/Q=0

(a) is the correct answer.

Ques 7 GATE 2023

The coefficient of x4 in the polynomial (x-1)3(x-2)3 is equal to ________

A

33

B

-3

C

30

D

21

(b) is the correct answer.

Ques 8 GATE 2019

Ten friends planned to share equally the cost of buying a gift for their teacher. When two of them decided not to contribute, each of the other friends had to pay Rs 150 more. The cost of the gift was Rs. ___.

A

666

B

3000

C

6000

D

12000

(c) is the correct answer.

Ques 9 GATE 2018

If 𝑥2 +𝑥−1=0 what is the value of 𝑥4 + 1/ 𝑥4 ?

A

1

B

5

C

7

D

9

(c) is the correct answer.

Ques 10 Gate 2018

If pqr ≠ 0 and p-x = 1/q, q-y = 1/r , r-z = 1/p, what is the value of the product xyz ?

A

-1

B

1/ pqr

C

1

D

pqr

(Algebra) is the correct answer.

Ques 11 GATE 2016 SET-1

If q-a=1/r, r-b=1/s and s-c=1/q, the value of abc is

A

(rqs)-1

B

0

C

1

D

r+q+s

(c) is the correct answer.

Ques 12 GATE 2015

Operators □, ◊ and → are defined by:
𝑎□𝑏=(𝑎−𝑏)/(𝑎+𝑏),𝑎 ◊𝑏=(𝑎+𝑏)/(𝑎−𝑏),𝑎→𝑏=𝑎𝑏
Find the value of (66□6)→(66◊6).

A

-2

B

-1

C

1

D

2

(c) is the correct answer.

Ques 13 GATE 2013

Velocity of an object fired directly in upward direction is given by V=80-32t where t (time) is in seconds. When will the velocity be between 32 m/sec and 64 m/sec?

A

(1,3/2)

B

(1/2,1)

C

(1/2,3/2)

D

(1, 3)

(b) is the correct answer.


Question Options

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