Mathematics (Solved Paper 2024 – II) (01 to 50)

Total Questions: 50

1. Let X be a matrix of order 3 × 3 Y be a matrix of order 2 × 3 and Z be a matrix of order 3 × 2 Which of the following statements are correct?

A. (ZY)X is defined and is a square matrix of order 3.

B. Y(XZ) is defined and is a square matrix of order 2.

C. X(YZ) is not defined.

Select the answer using the code given below.

Correct Answer: (d) A, B and C
Solution:

2. Consider the following statements :

A. The set of all irrational numbers between √12 and √15 is an infinite set.

B. The set of all odd integers less than 1000 is a finite set.

Which of the statements given above is/are correct?

Correct Answer: (a) A only
Solution:Since between any two irrational numbers, infinite number of irrational numbers are there. Hence, the set of all irrational numbers between √12 and √15 is having infinite number of elements.

Set of all odd integers less than 1000 is {____-5,-3, 1, 3, ___999} which is an infinite set.

3. How many 4-digit numbers are there having all digits as odd?

Correct Answer: (a) 625
Solution:

4. If ω≠1 is a cube root of unity, then what is

(1 + ω - ω²)¹⁰⁰ + (1 - ω + ω²)¹⁰⁰ equal to?

Correct Answer: (d) - 2¹⁰⁰
Solution:

5. Let A and B be two square matrices of same order. If AB is a null matrix, then which one of the following is correct?

Correct Answer: (c) B is a null matrix if A is a non-singular matrix
Solution:

Comparing both sides, we have

ap + br = 0     ...(i)

aq + bs = 0     ...(ii)

cp + dr = 0      ...(iii)

cq + ds = 0      ...(iv)

Solving equation (i) and (iii), we get (ad - bc) p = 0 and (ad - bc) r = 0 Solving equation (ii) amd (iv), we get (ad - bc)q = 0 and (ad - bc)s = 0

Now, If A is non-singular ad - bc ≠ 0.

So, we get, p = q = r = s = 0

So, B is a null matrix.

6. In the expansion of (1 + x)ᵖ (1 + x)q if the coefficient of x³ is 35, then what is the value of (p + q)

Correct Answer: (c) 7
Solution:

7. If p times the pᵗʰ term of an AP is equal to q times the qᵗʰ tem (p≠q), then what is the (p + q)ᵗʰ term equal to?

Correct Answer: (a) 0
Solution:

8. Let p = In(x), q = ln(x³) and r = ln(x⁵), where x > 1. Which of the following statements is/are correct?

A. p, q and r are in AP.

B. p, q and r can never be in GP.

Select the answer using the code given below:

Correct Answer: (c) Both A and B
Solution:

9. what is modulus of Z equal to?

Correct Answer: (b) √2
Solution:

10. What is the value of the sum ?

where i = √-1 ?

Correct Answer: (b) 0
Solution: