Quantitative Reasoning

Number System

Easy

The value of $\left(\frac{x}{y}\right)^{2a-3b} \times \left(\frac{x}{y}\right)^{3b-4c} \times \left(\frac{x}{y}\right)^{4c-2a}$

$\frac{x}{y}$

$\left(\frac{x}{y}\right)^{2a+3b+4c}$

✅ Correct Option: 2

Adding the exponents: $(2a-3b) + (3b-4c) + (4c-2a) = 0$ . Therefore the expression equals $\left(\frac{x}{y}\right)^0 = 1$ .

2026: 22 May Shift 2

Match List-I with List-II

List-I (Statements/Expressions etc.)	List-II (Values, etc.)
(A) Find the sum of the first 20 odd natural numbers.	(I) 285
(B) How many prime numbers are there between 100 and 200?	(II) 0
(C) Find the sum of the squares of the digits from 1 to 9.	(III) 400
(D) Find the unit's digit in the product $81 \times 82 \times 83 \times ... ... ... \times 89$ ?	(IV) 21

Choose the correct answer from the options given below:

2025: 13 May Shift 2

What is the remainder when the number $(44)^2$ is divided by 9?

2022: 17 Aug Shift 1

The value of $\frac{(8.9)^2 - (2.1)^2}{8.9 - 2.1}$

2025: 3 June Shift 2

Which one of the following is/are correct?

(A) Every irrational number is a real number.

(B) Every real number is an irrational number.

(D) The product or quotient of a non-zero rational number with an irrational number is an irrational number.

Choose the correct answer from the options given below:

2023: 24 May Shift 3

The value of $(625)^{-3/4}$ is:

2026: 21 May Shift 1

If I write down all the numbers from 1 to 100, then how many times I have written the digit 3 ?

The value of (xy)2a−3b×(xy)3b−4c×(xy)4c−2a\left(\frac{x}{y}\right)^{2a-3b} \times \left(\frac{x}{y}\right)^{3b-4c} \times \left(\frac{x}{y}\right)^{4c-2a}(yx​)2a−3b×(yx​)3b−4c×(yx​)4c−2a