List of top Questions asked in JEE Main- 2025

A wire of length $ 25 \, \text{m} $ and cross-sectional area $ 5 \, \text{mm}^2 $ having resistivity $ 2 \times 10^{-6} \, \Omega \cdot \text{m} $ is bent into a complete circle. The resistance between diametrically opposite points will be:
Choose the figure that will correctly replace the question mark \((?)\) in the given series.
The question figure shows the 3D view of an object. Identify the correct view when looking in the direction of the arrow.
A cube having a side of 10 cm with unknown mass and 200 gm mass were hung at two ends of an uniform rigid rod of 27 cm long. The rod along with masses was placed on a wedge keeping the distance between wedge point and 200 gm weight as 25 cm. Initially the masses were not at balance. A beaker is placed beneath the unknown mass and water is added slowly to it. At given point the masses were in balance and half volume of the unknown mass was inside the water. (Take the density of the unknown mass is more than that of the water, the mass did not absorb water and water density is 1 gm/cm$^3$.) The unknown mass is ______ kg.

A square Lamina OABC of length 10 cm is pivoted at \( O \). Forces act at Lamina as shown in figure. If Lamina remains stationary, then the magnitude of \( F \) is:

Displacement of a wave is expressed as $$ x(t) = 5 \cos \left( 628t + \frac{\pi}{2} \right) \, \text{m}. $$ The wavelength of the wave when its velocity is 300 m/s is:
Moment of inertia of a rod of mass \( M \) and length \( L \) about an axis passing through its center and normal to its length is \( \alpha \). Now the rod is cut into two equal parts and these parts are joined symmetrically to form a cross shape. Moment of inertia of cross about an axis passing through its center and normal to the plane containing cross is:

Considering Bohr’s atomic model for hydrogen atom :
(A) the energy of H atom in ground state is same as energy of He+ ion in its first excited state. 
(B) the energy of H atom in ground state is same as that for Li++ ion in its second excited state. 
(C) the energy of H atom in its ground state is same as that of He+ ion for its ground state. 
(D) the energy of He+ ion in its first excited state is same as that for Li++ ion in its ground state.

Liquid A and B form an ideal solution. The vapour pressure of pure liquids A and B are 350 and 750 mm Hg respectively at the same temperature. If $ x_A $ and $ x_B $ are the mole fraction of A and B in solution while $ y_A $ and $ y_B $ are the mole fraction of A and B in vapour phase then :
The roots of the quadratic equation \( 3x^2 - px + q = 0 \) are the 10th and 11th terms of an arithmetic progression with common difference \( \frac{3}{2} \). If the sum of the first 11 terms of this arithmetic progression is 88, then \( q - 2q \) is equal to:
Let \( f(x) = \frac{2^{x+2} + 16}{2^{2x+1} + 2^{x+4} + 32} \). Then the value of \[ 8 \left( f\left( \frac{1}{15} \right) + f\left( \frac{2}{15} \right) + \dots + f\left( \frac{59}{15} \right) \right) \] is equal to:
If $ \sum_{r=1}^{9} \left( \frac{r+3}{2^r} \right) \cdot {^9C_r} = \alpha \left( \frac{3}{2} \right)^9 - \beta $, $ \alpha, \beta \in \mathbb{N} $, then $ (\alpha + \beta)^2 $ is equal to
A circle touches the parabola $ y^2 = 9x $ at $ (4, 6) $ and the positive x-axis. Find the radius of the circle.
Let P be the set of seven-digit numbers with the sum of their digits equal to 11. If the numbers in P are formed by using the digits 1, 2, and 3 only, then the number of elements in the set P is:
If the function \( f(x) = 2x^3 - 9ax^2 + 12a^2x + 1 \), where \( a>0 \), attains its local maximum and minimum at \( p \) and \( q \), respectively, such that \( p^2 = q \), then \( f(3) \) is equal to:
The sum of all local minimum values of the function \( f(x) \) as defined below is:
\[ f(x) = \begin{cases} 1 - 2x & \text{if } x < -1, \\[10pt] \frac{1}{3}(7 + 2|x|) & \text{if } -1 \leq x \leq 2, \\[10pt] \frac{11}{18}(x-4)(x-5) & \text{if } x > 2. \end{cases} \]
There are 5 boys and 4 girls. The sum of the number of ways to sit them such that all boys sit together and the number of ways such that no boys sit together is equal to:
The area of the region enclosed by the curves \( y = e^x \), \( y = |e^x - 1| \), and the y-axis is:
Let \( L_1: \frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{4} \) and \( L_2: \frac{x-2}{3} = \frac{y-4}{4} = \frac{z-5}{5} \) be two lines. Then which of the following points lies on the line of the shortest distance between \( L_1 \) and \( L_2 \)?
Find the value of the integral \( \int_0^{\frac{\pi}{2}} \sin^2(x) \, dx \).
Let \( D = \{a, b, c\} \). How many distinct ways can \( D \) be partitioned into non-empty subsets, representing equivalence relations?
Let for two distinct values of $ p $, the lines $ y = x + p $ touch the ellipse $ E: \frac{x^2}{4} + \frac{y^2}{9} = 1 $ at the points $ A $ and $ B $. Let the line $ y = x $ intersect $ E $ at the points $ C $ and $ D $. Then the area of the quadrilateral $ ABCD $ is equal to:
For some \( a, b \), let \( f(x) = \left| \begin{matrix} a + \frac{\sin x}{x} & 1 & b \\ a & 1 + \frac{\sin x}{x} & b \\ a & 1 & b + \frac{\sin x}{x} \end{matrix} \right| \), where \( x \neq 0 \), \( \lim_{x \to 0} f(x) = \lambda + \mu a + \nu b \). Then \( (\lambda + \mu + \nu)^2 \) is equal to:
If the locus of $ z \in \mathbb{C} $, such that $ \text{Re} \left( \frac{z - 1}{2z + i} \right) + \text{Re} \left( \frac{ \bar{z} - 1}{2 \bar{z} - i} \right) = 2, $ is a circle of radius $ r $ and center $ (a, b) $, then $ \frac{15ab}{r^2} \text{ is equal to:} $
Let \( \alpha_1 \) and \( \beta_1 \) be the distinct roots of \( 2x^2 + (\cos\theta)x - 1 = 0, \ \theta \in (0, 2\pi) \). If \( m \) and \( M \) are the minimum and the maximum values of \( \alpha_1 + \beta_1 \), then \( 16(M + m) \) equals: