Find the value of √(6 + √(6 + √(6 + √(6 + )))). Option 1: 3 Option 2: 2 Option 3: 6 Option 4: √8

Answer: 3. Solution: Let x = √(6 + √(6 + )). Then x^2 = 6 + x. x^2 - x - 6 = 0, so (x-3)(x+2) = 0. Taking the positive root, x = 3.

Quantitative Reasoning

Number System

Medium

Find the value of $\sqrt{6 + \sqrt{6 + \sqrt{6 + \sqrt{6 + \ldots}}}}$ .

$\sqrt{8}$

✅ Correct Option: 1

Let $x = \sqrt{6 + \sqrt{6 + \ldots}}$ . Then $x^2 = 6 + x$ .

$x^2 - x - 6 = 0$ , so $(x-3)(x+2) = 0$ .

Taking the positive root, $x = 3$ .

2022: 17 Aug Shift 1

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

2022: 20 Aug Shift 1

$-\sqrt{8} + \sqrt{128} - \sqrt{32}$ is equal to

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: 3 June Shift 1

Match List-I with List-II

[a, b as given in the Euclidean algorithm, quotient (q), Remainder (r)]

Remainder (r)

$a = bq + r$

Choose the correct answer from the options given below:

2024

The difference of the greatest and the smallest of the fractions $\frac{1}{2}$ , $\frac{8}{11}$ , $\frac{7}{8}$ , $\frac{7}{9}$ , $\frac{5}{6}$ is:

2026: 30 May Shift 1

Consider the following statements:

I. If a and b are composite numbers, then a + b is always composite.

II. Zero is a natural number but not a whole number.

Which of the above statements is/are correct from the options given below: