List of top Mathematics Questions asked in JEE Main

Out of $60 \%$ female and $40 \%$ male candidates appearing in an exam, $60 \%$ candidates qualify it The number of females qualifying the exam is twice the number of males qualifying it A candidate is randomly chosen from the qualified candidates The probability, that the chosen candidate is a female, is :

If $a = \lim_{{n \to \infty}} \sum_{{k=1}}^{n} \frac{2n}{{n^2 + k^2}}$and
$f(x) = \sqrt{\frac{1 - \cos x}{1 + \cos x}}, \quad x \in (0, 1)$ then

16 sin(20°) sin(40°) sin(80°) is equal to :

The area bounded by the curves y = |x² – 1| and y = 1 is

If $y = y ( x ), x \in\left(0, \frac{\pi}{2}\right)$ be the solution curve of the differential equation$ \left(\sin ^2 2 x\right) \frac{d y}{d x}+\left(8 \sin ^2 2 x+2 \sin 4 x\right) y$ $ =2 e^{-4 x}(2 \sin 2 x+\cos 2 x), \text { with } y\left(\frac{\pi}{4}\right)=e^{-\pi},$ then $y\left(\frac{\pi}{6}\right)$ is equal to:

If
$n(2n+1)\int_{0}^{1}(1−xn)^{2n}dx=1177\int_{0}^{1}(1−x^n)^{2n+1}dx$
,then n ∈ N is equal to ______.

Let the coefficients of the middle terms in the expansion of$\begin{array}{l} \left(\dfrac{1}{\sqrt 6}+ \beta x\right)^4, \left(1 – 3\beta x\right)^2 \text{and}\left(1 – \dfrac{\beta}{2}x\right )^6, \beta > 0,\end{array}$respectively form the first three terms of an A.P. If d is the common difference of this A.P., then $\begin{array}{l} 50-\frac{2d}{\beta^2} \end{array}$is equal to _______.

Let A, B, C be three points whose position vectors respectively are
$\vec{a} = \hat{i} + 4\hat{j} + 3\hat{k}$
$\vec{b} = 2\hat{i} + α\hat{j} + 4\hat{k}, α ∈ R$
$\vec{c} = 3\hat{i} - 2\hat{j} + 5\hat{k}$
If α is the smallest positive integer for which$\vec{a},\vec{b},\vec{c}$
are non collinear, then the length of the median, in ΔABC, through A is:

Let a vector $\vec{a}$ has a magnitude 9. Let a vector $\vec{b}$ be such that for every $(x, y) \in R \times R-\{(0,0)\}$, the vector $(x \vec{a}+y \vec{b})$ is perpendicular to the vector $(6 y \vec{a}-18 x \vec{b})$. Then the value of $|\vec{a} \times \vec{b}|$ is equal to:

Let $\vec{a} = 3\hat{i} + \hat{j}$ and $\vec{b} = \hat{i} + 2\hat{j} + \hat{k}$.
Let $\vec{c}$ be a vector satisfying $\vec{a} \times (\vec{b} \times \vec{c}) = \vec{b} + \lambda \vec{c}$
If $\vec{b}$ and $\vec{c}$ are non-parallel, then the value of $λ$ is

Let S = {E₁, E₂, ……………., E₈} be a sample space of a random experiment such that $P(E_n) = \frac{n}{36}$ for every n = 1, 2, ………, 8. Then the number of elements in the set$\{ A \subseteq S : P(A) \geq \frac{4}{5} \}$ is_________.

Let P(–2, –1, 1) and Q(56/17, 43/17, 111/17) be the vertices of the rhombus PRQS. If the direction ratios of the diagonal RS are $α, –1, β,$ where both $α$ and $β$ are integers of minimum absolute values, then $α^2 + β^2$ is equal to ___________.

The largest value of a, for which the perpendicular distance of the plane containing the lines
$ \vec{r} (\hat{i}+\hat{j})+λ(\hat{i}+a\hat{j}−\hat{k})\ and\ \vec{r}=(\hat{i}+\hat{j})+μ(−\hat{i}+\hat{j}−a\hat{k}) $
from the point (2, 1, 4) is √3, is _____________.

The number of matrices of order 3 × 3, whose entries are either 0 or 1 and the sum of all the entries is a prime number, is _________.

Let the lines$ \begin{array}{l} \frac{x-1}{\lambda}=\frac{y-2}{1}=\frac{z-3}{2}\ \text{and}\ \frac{x+26}{-2}=\frac{y+18}{3}=\frac{z+28}{\lambda}\end{array}$be coplanar and P be the plane containing these two lines. Then which of the following points does NOT lie on P?

If the tangent to the curve y = x³ – x² + x at the point (a, b) is also tangent to the curve y = 5x² + 2x – 25 at the point (2, –1), then |2a + 9b| is equal to _____ .

Let the tangent drawn to the parabola y² = 24x at the point (α, β) is perpendicular to the line 2x + 2y = 5. Then the normal to the hyperbola
$\frac{x^2}{α^2}−\frac{y^2}{β^2}=1$
at the point (α + 4, β + 4) does NOT pass through the point

The length of the perpendicular from the point $(1,-2,5)$ on the line passing through $(1,2,4)$ and parallel to the line $x+y-z=0=x-2 y+3 z-5$ is :

Two tangent lines l₁ and l₂ are drawn from the point (2, 0) to the parabola 2y² = – x. If the lines l₁ and l₂ are also tangent to the circle (x – 5)² + y² = r, then 17r is equal to _________.

Let a curve y = y(x) pass through the point (3, 3) and the area of the region under this curve, above the x-axis and between the abscissae 3 and
$x(>3)\ be\ (\frac{y}{x})^3$
. If this curve also passes through the point (α,6√10) in the first quadrant, then α is equal to _______.

The value of the integral $\begin{array}{l} \displaystyle\int\limits_0^{\frac{\pi}{2}}60\frac{\sin\left(6x\right)}{\sin x}dx \end{array}$ is equal to ______.

Let
$\begin{array}{l} \vec{a},\vec{b},\vec{c}\ \text{be three non-coplanar vectors such that}\end{array}$
$\begin{array}{l} \overrightarrow{a}\times\vec{b}=4\vec{c},\vec{b}\times\vec{c}=9\vec{a}\ \text{and}\ \vec{c}\times\vec{a}=\alpha\vec{b},\alpha>0.\end{array}$

If
$\begin{array}{l} \left|\overrightarrow{a}\right|+\left|\overrightarrow{b}\right|+\left|\overrightarrow{c}\right|=\frac{1}{36}\end{array}, $

then $α$ is equal to___.

Let $x(t)=2\sqrt2costsin\sqrt2t $ and $y(t)=2\sqrt2sintsin\sqrt2t$ ,$t ∈(0,\frac{π}{2})$

Then $\frac{1+(\frac{dy}{dx})^2}{\frac{d^2y}{dx^2}}$ at $t=\frac{π}{4}$ is equal to

Let M and N be the number of points on the curve y⁵ – 9xy + 2x = 0, where the tangents to the curve are parallel to x-axis and y-axis, respectively. Then the value of M + N equals ________.

If n arithmetic means are inserted between a and 100 such that the ratio of the first mean to the last mean is 1 : 7 and a + n = 33, then the value of n is: