NTA JEE Main 2025 April 8th Shift 2

Let the area of the bounded region $$\{(x, y) : 0 \le 9x \le y^2, y \ge 3x - 6\}$$ be A. Then 6A is equal to _____.

Let the domain of the function $$f(x) = \cos^{-1}\left(\frac{4x+5}{3x-7}\right)$$ be $$[\alpha, \beta]$$ and the domain of $$g(x) = \log_2(2 - 6\log_{27}(2x+5))$$ be $$(\gamma, \delta)$$. Then $$|7(\alpha + \beta) + 4(\gamma + \delta)|$$ is equal to _____.

Let the area of the triangle formed by the lines $$x + 2 = y - 1 = z$$, $$\frac{x-3}{5} = \frac{y}{-1} = \frac{z-1}{1}$$ and $$\frac{x}{-3} = \frac{y-3}{3} = \frac{z-2}{1}$$ be A. Then $$A^2$$ is equal to _____.

The product of the last two digits of $$(1919)^{1919}$$ is _____.

Let r be the radius of the circle, which touches the x-axis at point $$(a, 0)$$, $$a < 0$$ and the parabola $$y^2 = 9x$$ at the point $$(4, 6)$$. Then r is equal to _____.

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : Work done in moving a test charge between two points inside a uniformly charged spherical shell is zero, no matter which path is chosen.
Reason R : Electrostatic potential inside a uniformly charged spherical shell is constant and is same as that on the surface of the shell.
Choose the correct answer :

A rod of linear mass density '$$\lambda$$' and length 'L' is bent to form a ring of radius 'R'. Moment of inertia of ring about any of its diameter is :

A 3 m long wire of radius 3 mm shows an extension of 0.1 mm when loaded vertically by a mass of 50 kg in an experiment to determine Young's modulus. The value of Young's modulus of the wire is $$P \times 10^{11}$$ Nm$$^{-2}$$, where P is : (Take $$g = 3\pi$$ m/s$$^2$$)

Electric charge is transferred to an irregular metallic disk as shown in figure. If $$\sigma_1$$, $$\sigma_2$$, $$\sigma_3$$ and $$\sigma_4$$ are charge densities at given points then, choose the correct answer from the options given below :

Water falls from a height of 200 m into a pool. Calculate the rise in temperature of the water assuming no heat dissipation from the water in the pool. (Take $$g = 10$$ m/s$$^2$$, specific heat of water = 4200 J/(kg K))