List of top Mathematics Questions asked in JEE Main

Let \( P = \begin{bmatrix} 3 & -1 & -2 \\ 2 & 0 & \alpha \\ 3 & -5 & 0 \end{bmatrix} \), where \( \alpha \in \mathbb{R} \). Suppose \( Q = [q_{ij}] \) is a matrix satisfying \( PQ = k I_3 \) for some non-zero \( k \in \mathbb{R} \). If \( q_{23} = -\dfrac{k}{8} \) and \( |Q| = \dfrac{k^3}{2} \), then \( \alpha^2 + k^2 \) is equal to __________.
Let \(M\) be any \(3\times3\) matrix with entries from the set {0, 1, 2}. The maximum number of such matrices, for which the sum of diagonal elements of \(M^T M\) is seven, is __________.
Let \(A = \{n \in N : n \text{ is a 3-digit number}\}\), \(B = \{9k + 2 : k \in N\}\) and \(C = \{9k + l : k \in N\}\) for some \(l\) (0<l<9) If the sum of all the elements of the set \(A \cap (B \cup C)\) is \(274 \times 400\), then \(l\) is equal to __________
The minimum value of \(\alpha\) for which the equation \(\frac{4}{\sin x} + \frac{1}{1 - \sin x} = \alpha\) has at least one solution in \((0, \frac{\pi}{2})\) is ____________
If \(\int_{-a}^{a} (|x| + |x-2|) dx = 22, (a>2)\) and \([x]\) denotes the greatest integer \(\le x\), then \(\int_{a}^{-a} (x + [x]) dx\) is equal to ______
If one of the diameters of the circle \(x^2 + y^2 - 2x - 6y + 6 = 0\) is a chord of another circle 'C', whose center is at (2, 1), then its radius is ________
Let three vectors \(\vec{a}, \vec{b}\) and \(\vec{c}\) be such that \(\vec{c}\) is coplanar with \(\vec{a}\) and \(\vec{b}, \vec{a} \cdot \vec{c} = 7\) and \(\vec{b}\) is perpendicular to \(\vec{c}\), where \(\vec{a} = -\hat{i} + \hat{j} + \hat{k}\) and \(\vec{b} = 2\hat{i} + \hat{k}\), then the value of \(|2\vec{a} + \vec{b} + \vec{c}|^2\) is __________
\(\lim_{n \to \infty} \tan \left\{ \sum_{r=1}^{n} \tan^{-1} \left( \frac{1}{1 + r + r^2} \right) \right\}\) is equal to __________.
If 15 sin⁴ α + 10 cos⁴ α = 6, for some α ∈ R, then the value of 27 sec⁶ α + 8 cosec⁶ α is equal to :
If P and Q are two statements, then which of the following compound statement is a tautology ?
A pole stands vertically inside a triangular park ABC. Let the angle of elevation of the top of the pole from each corner of the park be π/3. If the radius of the circumcircle of ΔABC is 2, then the height of the pole is equal to :
Let in a series of 2n observations, half of them are equal to a and remaining half are equal to -a. Also by adding a constant b in each of these observations, the mean and standard deviation of new set become 5 and 20, respectively. Then the value of a² + b² is equal to :
Let in a Binomial distribution, consisting of 5 independent trials, probabilities of exactly 1 and 2 successes be 0.4096 and 0.2048 respectively. Then the probability of getting exactly 3 successes is equal to :
Let y = y(x) be the solution of the differential equation dy/dx = (y + 1) ((y + 1)e^{x²/2 - x} - 1), 0<x<2.1, with y(2) = 0. Then the value of dy/dx at x=1 is equal to :
Let g(x) = ∫₀ˣ f(t) dt, where f is continuous function in [0, 3] such that 1/3 ≤ f(t) ≤ 1 for all t ∈ [0, 1] and 0 ≤ f(t) ≤ 1/2 for all t ∈ (1, 3]. The largest possible interval in which g(3) lies is :
Let S1 be the sum of first 2n terms of an arithmetic progression. Let S2 be the sum of first 4n terms of the same arithmetic progression. If (S2 - S1) is 1000, then the sum of the first 6n terms of the arithmetic progression is equal to :
Let S1 : x² + y² = 9 and S2 : (x - 2)² + y² = 1. Then the locus of center of a variable circle S which touches S1 internally and S2 externally always passes through the points :
Let f : R - {3} → R - {1} be defined by f(x) = (x - 2)/(x - 3). Let g : R → R be given as g(x) = 2x - 3. Then, the sum of all the values of x for which f⁻¹(x) + g⁻¹(x) = 13/2 is equal to.
If f(x) and g(x) are two polynomials such that the polynomial P(x) = f(x³) + x · g(x³) is divisible by x² + x + 1, then P(1) is equal to ________.
Let I be an identity matrix of order 2 × 2 and P = [2 -1; 5 -3]. Then the value of n ∈ N for which Pⁿ = 5I - 8P is equal to ________.
The term independent of x in the expansion of [ (x + 1)/(x^{2/3} - x^{1/3} + 1) - (x - 1)/(x - x^{1/2}) ]¹⁰, x ≠ 1, is equal to ________.
If ∑_{r=1}^{10} r! (r³ + 6r² + 2r + 5) = α (11!), then the value of α is equal to ________.
Let P(x) be a real polynomial of degree 3 which vanishes at x = -3. Let P(x) have local minima at x = 1, local maxima at x = -1 and ∫_{-1}^{1} P(x) dx = 18, then the sum of all the coefficients of the polynomial P(x) is equal to ________.
Let y=y(x) be the solution of the differential equation x dy - y dx = √(x² - y²) dx, x ≥ 1, with y(1) = 0. If the area bounded by the line x=1, x=e^{π}, y=0 and y=y(x) is α e^{2π} + β, then the value of 10(α + β) is equal to ________.
Let P be a plane containing the line (x-1)/3 = (y+6)/4 = (z+5)/2 and parallel to the line (x-3)/4 = (y-2)/(-3) = (z+5)/7. If the point (1, -1, α) lies on the plane P, then the value of |α| is equal to ________.