List of top Questions asked in JEE Main- 2025

In a group of 3 girls and 4 boys, there are two boys \( B_1 \) and \( B_2 \). The number of ways in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but \( B_1 \) and \( B_2 \) are not adjacent to each other, is:
The value of \( (\sin 70^\circ)(\cot 10^\circ \cot 70^\circ - 1) \) is:
Let P be the parabola, whose focus is $ (-2, 1) $ and directrix is $ 2x + y + 2 = 0 $. Then the sum of the ordinates of the points on P, whose abscissa is -2, is:
Let \( A = [a_{ij}] \) be a square matrix of order 2 with entries either 0 or 1. Let \( E \) be the event that \( A \) is an invertible matrix. Then the probability \( P(E) \) is:
A and B alternately throw a pair of dice. A wins if he throws a sum of 5 before B throws a sum of 8, and B wins if he throws a sum of 8 before A throws a sum of 5. The probability that A wins if A makes the first throw is:
Let \( A = \{1, 2, 3, \dots, 10\} \) and \( B = \left\{ \frac{m}{n} : m, n \in A, m <n \text{ and } \gcd(m, n) = 1 \right\} \). Then \( n(B) \) is equal to :
Let \( \vec{a} = \hat{i} + 2\hat{j} + \hat{k} \) and \( \vec{b} = 2\hat{i} + 7\hat{j} + 3\hat{k} \). Let \( L_1 : \vec{r} = (-\hat{i} + 2\hat{j} + \hat{k}) + \lambda \vec{a}, \lambda \in {R} \) and \( L_2 : \vec{r} = (\hat{j} + \hat{k}) + \mu \vec{b}, \mu \in \mathbb{R} \) be two lines. If the line \( L_3 \) passes through the point of intersection of \( L_1 \) and \( L_2 \), and is parallel to \( \vec{a} + \vec{b} \), then \( L_3 \) passes through the point:
Two equal sides of an isosceles triangle are along \( -x + 2y = 4 \) and \( x + y = 4 \). If \( m \) is the slope of its third side, then the sum of all possible distinct values of \( m \) is:
If the image of the point \( (4, 4, 3) \) in the line \( \frac{x-1}{2} = \frac{y-2}{1} = \frac{z-1}{3} \) is \( (a, \beta, \gamma) \), then \( a + \beta + \gamma \) is equal to:
Let {an}n=0∞ be a sequence such that a0=a1=0 and an+2=3an+1−2an+1,∀ n≥0. Then a25a23−2a25a22−2a23a24+4a22a24  is equal to
Let P be the foot of the perpendicular from the point \( (1, 2, 2) \) on the line \[ \frac{x-1}{1} = \frac{y + 1}{-1} = \frac{z - 2}{2} \] Let the line \( \mathbf{r} = (-\hat{i} + \hat{j} - 2\hat{k}) + \lambda (\hat{i} - \hat{j} + \hat{k})\), \( \lambda \in \mathbb{R} \), intersect the line \(L\) at \(Q\). Then \( 2(PQ)^2 \) is equal to:
The number of integral terms in the binomial expansion of \[ \left(11^{\frac{1}{2}} + 17^{\frac{1}{8}}\right)^{1024} \] is:

If \[ f(x) = \int \frac{1}{x^{1/4} (1 + x^{1/4})} \, dx, \quad f(0) = -6 \], then f(1)  is equal to:

If \( z_1, z_2, z_3 \in \mathbb{C} \) are the vertices of an equilateral triangle, whose centroid is \( z_0 \), then \( \sum_{k=1}^{3} (z_k - z_0)^2 \) is equal to
Let the line passing through the points \( (-1, 2, 1) \) and parallel to the line \[ \frac{x - 1}{2} = \frac{y + 1}{3} = \frac{z}{4} \] intersect the line \[ \frac{x + 2}{3} = \frac{y - 3}{2} = \frac{z - 4}{1} \] at the point P. Then the distance of P from the point Q(4, -5, 1) is:
The sum of all rational numbers in \( (2 + \sqrt{3})^8 \) is:
Evaluate the following limit: \[ \lim_{x \to \infty} \frac{(2x^2 - 3x + 5) \left( 3x - 1 \right)^{x/2}}{(3x^2 + 5x + 4) \sqrt{(3x + 2)^x}}. \] The value of the limit is:

For a statistical data \( x_1, x_2, \dots, x_{10} \) of 10 values, a student obtained the mean as 5.5 and \[ \sum_{i=1}^{10} x_i^2 = 371. \] He later found that he had noted two values in the data incorrectly as 4 and 5, instead of the correct values 6 and 8, respectively. 
The variance of the corrected data is:

Let a curve \( y = f(x) \) pass through the points \( (0,5) \) and \( (\log 2, k) \). If the curve satisfies the differential equation: \[ 2(3+y)e^{2x}dx - (7+e^{2x})dy = 0, \] then \( k \) is equal to:
The sum 1 + 3 + 11 + 25 + 45 + 71 + ... upto 20 terms, is equal to

Let  R = {(1, 2), (2, 3), (3, 3)}} be a relation defined on the set \( \{1, 2, 3, 4\} \). Then the minimum number of elements needed to be added in \( R \) so that \( R \) becomes an equivalence relation, is:

Let ABCD be a trapezium whose vertices lie on the parabola \( y^2 = 4x \). Let the sides AD and BC of the trapezium be parallel to the y-axis. If the diagonal AC is of length \( \frac{25}{4} \) and it passes through the point \( (1, 0) \), then the area of ABCD is:
A line passing through the point $ P(a, 0) $ makes an acute angle $ \alpha $ with the positive $ x $-axis. Let this line be rotated about the point $ P $ through an angle $ \frac{\alpha}{2} $ in the clock-wise direction. If in the new position, the slope of the line is $ 2 - \sqrt{3} $ and its distance from the origin is $ \frac{1}{\sqrt{2}} $, then the value of $ 3a^2 \tan^2 \alpha - 2\sqrt{3} $ is

If the system of equations \[ (\lambda - 1)x + (\lambda - 4)y + \lambda z = 5 \] \[ \lambda x + (\lambda - 1)y + (\lambda - 4)z = 7 \] \[ (\lambda + 1)x + (\lambda + 2)y - (\lambda + 2)z = 9 \] has infinitely many solutions, then \( \lambda^2 + \lambda \) is equal to:

Let $ ABC $ be the triangle such that the equations of lines $ AB $ and $ AC $ are: $ 3y - x = 2 \quad \text{and} \quad x + y = 2, $ respectively, and the points $ B $ and $ C $ lie on the x-axis. If $ P $ is the orthocentre of the triangle $ ABC $, then the area of the triangle $ PBC $ is equal to: