List of top Mathematics Questions asked in JEE Main

If [t] denotes the greatest integer ≤ t, then the number of points, at which the function
$f(x) = 4|2x + 3| + 9\lfloor x + \frac{1}{2} \rfloor - 12\lfloor x + 20 \rfloor$
is not differentiable in the open interval (–20, 20), is ____ .

Let
$A = \begin{pmatrix} 1+i & 1 \\ -i & 0 \end{pmatrix}$ where $i=\sqrt{−1}.$
Then, the number of elements in the set
$\left\{n∈\left\{1,2,…,100\right\}:A^n=A\right\}$
is ________.

A point P moves so that the sum of squares of its distances from the points (1, 2) and (–2, 1) is 14. Let f(x, y) = 0 be the locus of P, which intersects the x-axis at the points A, B and the y-axis at the points C, D. Then the area of the quadrilateral ACBD is equal to

If $a_1, a_2, a_3$ ….. and $b_1, b_2, b_3$ ….. are A.P., and $a_1 = 2, a_{10} = 3, a_1b_1 = 1 = a_{10}b_{10}$, then $a_4b_4$ is equal to

If $\begin{array}{l} \frac{6}{3^{12}}+\frac{10}{3^{11}}+\frac{20}{3^{10}}+\frac{40}{3^9}+\cdots +\frac{10240}{3}=2^n\cdot m, \end{array}$where m is odd, then m⋅n is equal to ________.

Let
$\begin{array}{l}f\left(x\right) = min \{\left[x – 1\right], \left[x – 2\right], …., \left[x – 10\right]\}\end{array}$
where [t] denotes the greatest integer ≤t. Then
$\begin{array}{l} \displaystyle\int\limits_{0}^{10}f\left(x\right)dx+\displaystyle\int\limits_{0}^{10}\left(f\left(x\right)\right)^2dx+\displaystyle\int\limits_{0}^{10}\left|f\left(x\right)\right|dx\end{array}$
is equal to ________.

Let y = y(x) be the solution curve of the differential equation
$\sin(2x^2) \log_e(\tan(x^2)) \,dy + (4xy - 4\sqrt{2}x\sin(x^2 - \frac{\pi}{4})) \,dx = 0, \quad 0 < x < \sqrt{\frac{\pi}{2}}$
which passes through the point $(\sqrt{\frac{π}{6}},1)$. Then $|y(\sqrt{\frac{π}{3}})|$
is equal to _______.

The value of $\cot\left(\sum_{n=1}^{50} \tan^{-1}\left(\frac{1}{1+n+n^2}\right)\right)$ is

The locus of the mid-point of the line segment joining the point (4, 3) and the points on the ellipse x² + 2y² = 4 is an ellipse with eccentricity:

The remainder when (2021)²⁰²³ is divided by 7 is

The value of the integral $∫^2_{-2}\frac{ |x^3+x|}{(e^x|x|+1)}dx$ is equal to:

If $f(x)=\begin{cases} x+a, & x \leq 0 \\ |x-4|, & x\gt0\end{cases}$ and
$g(x)= \begin{cases}x+1 & , x\lt0 \\ (x-4)^2+b, & x \geq 0\end{cases}$
are continuous on $R$, then $(gof) (2)+(fog)(-2)$ is equal to:

2sin($\frac{\pi}{22}$)sin($\frac{3\pi}{22}$)sin($\frac{5\pi}{22}$)sin($\frac{7\pi}{22}$)sin($\frac{9\pi}{22}$) is equal to

Let f : R → R be a continuous function satisfying f(x) + f(x + k) = n, for all x ∈ R where k > 0 and n is a positive integer. If
$l_1 = \int_{0}^{4nk} f(x) \, dx$ and $l_2 = \int_{-k}^{3k} f(x) \, dx$, then

Let for n = 1, 2, …, 50, S_n be the sum of the infinite geometric progression whose first term is n² and whose common ratio is
$\frac{1}{(n+1)^2}$ . Then the value of
$\frac{1}{26} + \sum_{n=1}^{50} \left(S_n+\frac{2}{n+1}-n-1 \right)$
is equal to ________.

Let
$f(x)=max\left\{|x+1|,|x+2|,……,|x+5|\right\} $
Then $\int_{-6}^{0} f(x) \, dx$
is equal to_______

Let S = {4, 6, 9} and T = {9, 10, 11, …,1000}. If A = {a1 + a2 + … +ak :k∈N, a1, a2, a3, …, ak∈S}, then the sum of all the elements in the set T – A is equal to ____________.

$\alpha = \sin 36^\circ$ is a root of which of the following equation?

A wire of length 22 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into an equilateral triangle. Then, the length of the side of the equilateral triangle, so that the combined area of the square and the equilateral triangle is minimum, is

The number of solutions of the equation $2\theta - \cos^2(\theta) + \sqrt{2} = 0$ in R is equal to ___________.

Let S be the set of all the natural numbers, for which the line
$\frac{x}{a}+\frac{y}{b}=2 $
is a tangent to the curve
$(\frac{x}{a})^n+(\frac{y}{b})^n=2 $
at the point (a, b), ab ≠ 0. Then :

The number of 5-digit natural numbers, such that the product of their digits is 36, is _____ .

Let $y = y(x)$ be the solution of the differential equation $(x + 1)y' – y = e^{3x}(x + 1)^2$, with $y(0)=\frac 13$. Then, the point $x=−\frac 43$ for the curve $y = y(x)$ is :

Let b₁b₂b₃b₄ be a 4-element permutation with b_i{1, 2, 3,…..,100} for 1≤i≤4 and b_i ≠b_j for i≠ j, such that either b₁, b₂, b₃ are consecutive integers or b₂, b₃, b₄ are consecutive integers. Then the number of such permutations b₁b₂b₃b₄ is equal to _______ .

Let Q be the foot of perpendicular drawn from the point P(1, 2, 3) to the plane x + 2y + z = 14. If R is a point on the plane such that ∠PRQ = 60°, then the area of ΔPQR is equal to :