Given below two statements :

Statement I : $ 25^{13} + 20^{13} + 8^{13} + 3^{13} $ is divisible by $ 7 $.

Statement II : The integral part of $ (7 + 4\sqrt{3})^{25} $ is an odd number.

In the light of the above statements, choose the correct answer from the options given below :

1

The sum of coefficients of $ x^{499} $ and $ x^{500} $ in

Topic: JEE Main 2026 (28 January Evening Shift)

2

Let $ A $ be the focus of the parabola $ y^2 = 8x $. Let the line $ y = mx + c $ intersect the parabola at two distinct…

Topic: JEE Main 2026 (28 January Evening Shift)

3

The probability distribution of a random variable $ X $ is given below :If $ E(X) = \frac{263}{15} $, then $ P(X < 2…

Topic: JEE Main 2026 (28 January Evening Shift)

4

Let $ f(x) = \lim_{\theta \to 0} \left( \frac{\cos \pi x - x^{(\theta)} \sin(x-1)}{1 + x^{(\theta)} (x - 1)} \right),; …

Topic: JEE Main 2026 (28 January Evening Shift)

5

Considering the principal values of inverse trigonometric functions, the value of the expression $ \tan \left( 2\sin^{-…

Topic: JEE Main 2026 (28 January Evening Shift)

6

Let the arithmetic mean of $ \frac{1}{a} $ and $ \frac{1}{b} $ be $ \frac{5}{16},; a > 2 $.If $ \alpha $ is such tha…

Topic: JEE Main 2026 (28 January Evening Shift)

7

Given below are two statements :Statement I : The function $ f : \mathbb{R} \rightarrow \mathbb{R} $ defined by$ f(x) =…

Topic: JEE Main 2026 (28 January Evening Shift)

8

An ellipse has center at $ (1,-2) $, one focus at $ (3,-2) $ and one vertex at $ (5,-2) $. Then the length of its latus…

Topic: JEE Main 2026 (28 January Evening Shift)

9

Let the ellipse $ E: \frac{x^2}{144} + \frac{y^2}{169} = 1 $ and the hyperbola$ H: \frac{x^2}{16} - \frac{y^2}{\lambda^…

Topic: JEE Main 2026 (28 January Evening Shift)

10

Let $ P_1 : y = 4x^2 $ and $ P_2 : y = x^2 + 27 $ be two parabolas. If the area of the bounded region enclosed between …

Topic: JEE Main 2026 (28 January Evening Shift)