List of top Mathematics Questions asked in JEE Main

The value of the integral, ∫ from 1 to 3 of [x² - 2x - 2] dx, where [x] denotes the greatest integer less than or equal to x, is :
The negation of the statement ~p ∧ (p ∨ q) is :
Let A and B be 3 × 3 real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the system of linear equations (A²B² - B²A²) X = O, where X is a 3 × 1 column matrix of unknown variables and O is a 3 × 1 null matrix, has :
Let f(x) be a differentiable function defined on [0, 2] such that f'(x) = f'(2-x) for all x ∈ (0, 2), f(0) = 1 and f(2) = e². Then the value of ∫ from 0 to 2 f(x) dx is :
If the curve y = ax² + bx + c passes through (1, 2) and the tangent at origin is y = x, then a, b, c are :
If n ≥ 2 is a positive integer, then the sum of the series $^{n+1}C_2 + 2( ^2C_2 + ^3C_2 + ^4C_2 + ....... + ^nC_2 )$ is :
Let f(x) = -55x (x<-5), 2x³ - 3x² - 120x (-5 ≤ x ≤ 4), 2x³ - 3x² - 36x - 336 (x>4). Let A = {x ∈ ℝ : f is increasing}. Then A is equal to :
A possible value of \( \tan\!\left(\frac{1}{4}\sin^{-1}\!\left(\frac{\sqrt{63}}{8}\right)\right) \) is :
The angle of elevation of a jet plane from a point A on the ground is 60°. After 20 s at speed 432 km/h, the angle changes to 30°. If the jet plane is at constant height, then its height is :
The vector equation of the plane passing through the intersection of r · (i + j + k) = 1 and r · (i - 2j) = -2, and the point (1, 0, 2) is :
The area of the region : R = {(x, y) : 5x² ≤ y ≤ 2x² + 9} is :
If the variance of 10 natural numbers 1, 1, 1, ......., 1, k is less than 10, then the maximum possible value of k is ______
Let a point P be such that its distance from the point (5, 0) is thrice the distance of P from the point (-5, 0). If the locus of the point P is a circle of radius r, then 4r² is equal to ________
If the area of the triangle formed by the positive x-axis, the normal and the tangent to the circle \( (x-2)^2 + (y-3)^2 = 25 \) at the point \( (5, 7) \) is \( A \), then \( 24A \) is equal to _______
Let i = √-1. If $\frac{(-1 + i\sqrt{3})^{21}}{(1 - i)^{24}} + \frac{(1 + i\sqrt{3})^{21}}{(1 + i)^{24}} = k$, and $n = \lfloor |k| \rfloor$. Then $\sum_{j=0}^{n+5} (j + 5)^2 - \sum_{j=0}^{n+5} (j + 5)$ is equal to __________.
The students S1, S2, ......., S10 are to be divided into 3 groups A, B and C such that each group has at least one student and the group C has at most 3 students. Then the total number of possibilities of forming such groups is _________
The maximum value of k for which the sum $\sum_{i=0}^k \binom{10}{i} \binom{15}{k-i} + \sum_{i=0}^{k+1} \binom{12}{i} \binom{13}{k+1-i}$ exists, is equal to __________.
If a + α = 1, b + β = 2 and a f(x) + α f(1/x) = b x + β / x, then [f(x) + f(1/x)] / [x + 1/x] is ________
If the shortest distance between x - λ = 2y - 1 = -2z and x = y + 2λ = z - λ is √7 / 2√2, then |λ| is _______
If the sum of all possible 4 digit numbers formed using digits 1, 2, 3, 4 without repetition, is \(1111 \mathrm{k}\), then \(\mathrm{k}\) is equal to ________.
Let the function \(f: \mathrm{N} \rightarrow \mathrm{R}\) satisfy \(f(x+y)=f(x) \cdot f(y)\) for all \(x, y \in \mathrm{N}\) and \(f(1)=2\). If \(\sum_{\mathrm{k}=1}^{50} f(4+\mathrm{k})=\lambda\left(2^{\beta}-1\right)\), then \(\lambda+\beta\) is equal to ________.
If \(y=y(x)\) is a solution of the differential equation, \(x\frac{dy}{dx}=y(2-3xy),\ x>0\) with \(y(1)=1\), then \(y\left(\frac{1}{4}\right)\) is equal to ________.
If \(x=\operatorname{cosec} \theta-\sin \theta\) and \(y=\operatorname{cosec}^{5} \theta-\sin ^{5} \theta, 0<\theta<\frac{\pi}{2}\), then \(\left(x^{2}+4\right)\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)^{2}-25 y^{2}\) is equal to ________.
Let the circle, \((x-\mathrm{a})^{2}+(y-\mathrm{b})^{2}=8\) and the parabola, \(y^{2}=4 x\) have a common tangent at the point \(\mathrm{P}(1,2)\). If \(\mathrm{C}\) is the centre of the circle and \(\mathrm{S}\) is the focus of the parabola, then the area (in sq. units) of \(\triangle \mathrm{CPS}\) is equal to ________.
A six faced biased dice is so loaded that in any of its toss getting any of even scores is equally likely and the probability of getting an even score is three times the probability of getting an odd score. This dice is tossed repeatedly until a six is obtained. If X denotes the number of tosses required, then \(\mathrm{P}(\mathrm{X}<4)\) is :