JEE Main 2025 April 3 Maths Question Paper is available for download. NTA conducted JEE Main 2025 Shift 1 B.Tech Exam on 3rd April 2025 from 9:00 AM to 12:00 PM and for JEE Main 2025 B.Tech Shift 2 appearing candidates from 3:00 PM to 6:00 PM. The JEE Main 2025 3rd April B.Tech Question Paper was Moderate to Tough.
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JEE Main 2025 April 3 Shift 2 Maths Question Paper with Solutions
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JEE Main 2025 Mathematics Questions with Solutions
Let \( f : \mathbb{R} \rightarrow \mathbb{R} \) be a function defined by \( f(x) = ||x+2| - 2|x|| \). If m is the number of points of local maxima of f and n is the number of points of local minima of f, then m + n is
Each of the angles \( \beta \) and \( \gamma \) that a given line makes with the positive y- and z-axes, respectively, is half the angle that this line makes with the positive x-axis. Then the sum of all possible values of the angle \( \beta \) is
If the four distinct points \( (4, 6) \), \( (-1, 5) \), \( (0, 0) \) and \( (k, 3k) \) lie on a circle of radius \( r \), then \( 10k + r^2 \) is equal to
Let the Mean and Variance of five observations \( x_i \), \( i = 1, 2, 3, 4, 5 \) be 5 and 10 respectively. If three observations are \( x_1 = 1, x_2 = 3, x_3 = a \) and \( x_4 = 7, x_5 = b \) with \( a > b \), then the Variance of the observations \( n + x_n \) for \( n = 1, 2, 3, 4, 5 \) is
Consider the lines \( x(3\lambda + 1) + y(7\lambda + 2) = 17\lambda + 5 \). If P is the point through which all these lines pass and the distance of L from the point \( Q(3, 6) \) is \( d \), then the distance of L from the point \( (3, 6) \) is \( d \), then the value of \( d^2 \) is
Let \( A = \{-2, -1, 0, 1, 2, 3\} \). Let \( R \) be a relation on \( A \) defined by \( (x, y) \in R \) if and only if \( |x| \le |y| \). Let \( m \) be the number of reflexive elements in \( R \) and \( n \) be the minimum number of elements required to be added in \( R \) to make it reflexive and symmetric relations, respectively. Then \( l + m + n \) is equal to
Let the equation \( x(x+2) * (12-k) = 2 \) have equal roots. The distance of the point \( \left(k, \frac{k}{2}\right) \) from the line \( 3x + 4y + 5 = 0 \) is
Line L1 of slope 2 and line L2 of slope \( \frac{1}{2} \) intersect at the origin O. In the first quadrant, \( P_1, P_2, \dots, P_{12} \) are 12 points on line L1 and \( Q_1, Q_2, \dots, Q_9 \) are 9 points on line L2. Then the total number of triangles that can be formed having vertices at three of the 22 points O, \( P_1, P_2, \dots, P_{12} \), \( Q_1, Q_2, \dots, Q_9 \), is:
The integral \( \int_{0}^{\pi} \frac{8x dx}{4 \cos^2 x + \sin^2 x} \) is equal to
Let \( f \) be a function such that \( f(x) + 3f\left(\frac{24}{x}\right) = 4x \), \( x \neq 0 \). Then \( f(3) + f(8) \) is equal to
The area of the region \( \{(x, y): |x - y| \le y \le 4\sqrt{x}\} \) is
If the domain of the function \( f(x) = \log_7(1 - \log_4(x^2 - 9x + 18)) \) is \( (\alpha, \beta) \cup (\gamma, \delta) \), then \( \alpha + \beta + \gamma + \delta \) is equal to
If the probability that the random variable X takes the value x is given by \( P(X = x) = k(x + 1)3^{-x} \), \( x = 0, 1, 2, 3, \dots \), where k is a constant, then \( P(X \ge 3) \) is equal to
Let \( y = y(x) \) be the solution of the differential equation \( \frac{dy}{dx} + 3(\tan^2 x) y + 3y = \sec^2 x \), with \( y(0) = \frac{1}{3} + e^3 \). Then \( y\left(\frac{\pi}{4}\right) \) 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
The number of solutions of the equation \( (4 - \sqrt{3}) \sin x - 2\sqrt{3} \cos^2 x = \frac{-4}{1 + \sqrt{3}} \), \( x \in \left[-2\pi, \frac{5\pi}{2}\right] \) is
Let C be the circle of minimum area enclosing the ellipse E: \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) with eccentricity \( \frac{1}{2} \) and foci \( (\pm 2, 0) \). Let PQR be a variable triangle, whose vertex P is on the circle C and the side QR of length 29 is parallel to the major axis and contains the point of intersection of E with the negative y-axis. Then the maximum area of the triangle PQR is:
The shortest distance between the curves \( y^2 = 8x \) and \( x^2 + y^2 + 12y + 35 = 0 \) is:
The distance of the point (7, 10, 11) from the line \( \frac{x - 4}{1} = \frac{y - 4}{0} = \frac{z - 2}{3} \) along the line \( \frac{x - 7}{2} = \frac{y - 10}{3} = \frac{z - 11}{6} \) is
The sum \( 1 + \frac{1 + 3}{2!} + \frac{1 + 3 + 5}{3!} + \frac{1 + 3 + 5 + 7}{4!} + \dots \) upto \( \infty \) terms, is equal to
Let I be the identity matrix of order 3 × 3 and for the matrix \( A = \begin{pmatrix} \lambda & 2 & 3
4 & 5 & 6
7 & -1 & 2 \end{pmatrix} \), \( |A| = -1 \). Let B be the inverse of the matrix \( adj(A \cdot adj(A^2)) \). Then \( |(\lambda B + I)| \) is equal to ______
Let \( (1 + x + x^2)^{10} = a_0 + a_1 x + a_2 x^2 + \dots + a_{20} x^{20} \). If \( (a_1 + a_3 + a_5 + \dots + a_{19}) - 11a_2 = 121k \), then k is equal to ______
If \( \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p \), then \( 96 \log_e p \) is equal to ______
Let \( \vec{a} = \hat{i} + 2\hat{j} + \hat{k} \), \( \vec{b} = 3\hat{i} - 3\hat{j} + 3\hat{k} \), \( \vec{c} = 2\hat{i} - \hat{j} + 2\hat{k} \) and \( \vec{d} \) be a vector such that \( \vec{b} \times \vec{d} = \vec{c} \times \vec{d} \) and \( \vec{a} \cdot \vec{d} = 4 \). Then \( |\vec{a} \times \vec{d}|^2 \) is equal to ______
If the equation of the hyperbola with foci \( (4, 2) \) and \( (8, 2) \) is \( 3x^2 - y^2 - \alpha x + \beta y + \gamma = 0 \), then \( \alpha + \beta + \gamma \) is equal to ______
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