If function (x + 296 × 298) is a perfect square, then the value of x is: Option 1: 0 Option 2: 1 Option 3: 2 Option 4: 3

Answer: 1. Solution: The expression (x + 296 x 298) needs to be a perfect square. Notice that 296 and 298 are consecutive even numbers around 297: 296 = 297 - 1 298 = 297 + 1 Using the formula (a - b)(a + b) = a^2 - b^2 with a = 297 and b = 1: 296 x 298 = (297 - 1)(297 + 1) = 297^2 - 1^2 = 297^2 - 1 Substituting back into the original expression: x + 296 x 298 = x + (297^2 - 1) = x + 297^2 - 1 = 297^2 + (x - 1) For this to be a perfect square, the simplest case is when it equals 297^2 exactly. This occurs when: x - 1 = 0 x = 1 Therefore, the value of x is 1.

Quantitative Reasoning

Number System

Medium

If function (x + 296 × 298) is a perfect square, then the value of x is:

✅ Correct Option: 2

The expression $(x + 296 \times 298)$ needs to be a perfect square.

Notice that $296$ and $298$ are consecutive even numbers around $297$ :

$296 = 297 - 1$

$298 = 297 + 1$

Using the formula $(a - b)(a + b) = a^2 - b^2$ with $a = 297$ and $b = 1$ :

$296 \times 298 = (297 - 1)(297 + 1)$

$= 297^2 - 1^2$

$= 297^2 - 1$

Substituting back into the original expression:

$x + 296 \times 298 = x + (297^2 - 1)$

$= x + 297^2 - 1$

$= 297^2 + (x - 1)$

For this to be a perfect square, the simplest case is when it equals $297^2$ exactly.

This occurs when:

$x - 1 = 0$

$x = 1$

Therefore, the value of $x$ is $1$ .

2025: 30 May Shift 2

Consider the following statements:

(A) The unit's digit in the product of (5236 x 6231) is 1.

(B) The digit in the unit's place for the product 31 x 32 x 33 x 34 x ....x 49 is 0.

(D) The sum of the place values of 3 in 3935 is 6.

Choose the correct answer from the options given below:

2022: 20 Aug Shift 1

$296 \times 296 - 204 \times 204 = ?$

2026: 12 May Shift 2

Which of the following lists of numbers is/are an Arithmetic Progression?

(A) 2, 8, 14, 20,........

(B) 0, 4, 8, 12,........

(D) 21, 17,15,........

Choose the correct answer from the options given below:

2023: 11 June Shift 2

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2026: 29 May Shift 2

Find the sum of the first n positive integers.

2023: 28 May Shift 1

The ratio of two numbers is 2:3 and their HCF is 4. Their LCM is :

If function (x + 296 × 298) is a perfect square, then the value of x is:

Solution

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