List of top Mathematics Questions asked in JEE Main

Let $ R = \{a, b, c, d, e\} $ and $ S = \{1, 2, 3, 4\} $. Total number of onto functions $ f: R \to S $ such that $ f(a) \neq 1 $, is equal to:

$\lim\limits_{x\rightarrow0}\left(\left(\frac{1-cos^2(3x)}{cos^3(4x)}\right)\left(\frac{sin^3(4x)}{(log_e(2x+1))^5}\right)\right)$is equal to

$\displaystyle\lim _{x \rightarrow \infty} \frac{(\sqrt{3 x+1}+\sqrt{3 x-1})^6+(\sqrt{3 x+1}-\sqrt{3 x-1})^6}{\left(x+\sqrt{x^2-1}\right)^6+\left(x-\sqrt{x^2-1}\right)^6} x^3$

Let f_n = $\int\limits_0^{\pi/2}$ $\left(\displaystyle\sum_{k=1}^{n}\,sin^{k-1}x\right)\left(\displaystyle\sum_{k=1}^{n}\,(2k-1)sin^{k-1}x\right)$ cosx dx, n ∈ N. Then f₂₁ – f₂₀ is equal to____.

Let $f: R -\{2,6\} \rightarrow R$ be real valued function defined as $f(x)=\frac{x^2+2 x+1}{x^2-8 x+12}$ Then range of $f$ is

The sum $\displaystyle\sum_{n=1}^{21} \frac{3}{(4 n-1)(4 n+3)}$ is equal to

Let $S =\{1,2,3,5,7,10,11\}$ The number of non-empty subsets of $S$ that have the sum of all elements a multiple of 3 , is _____

Let the area enclosed by the lines $ x + y = 2 $, $ y = 0 $, $ x = 0 $, and the curve $ f(x) = \min \left\{ x^2 + \frac{3}{4}, 1 + [x] \right\} $, where $ [x] $ denotes the greatest integer less than or equal to $ x $, be $ A $. Then the value of $ 12A $ is ____________.

The number of bijective functions $f :\{1,3,5$, $7, \ldots \ldots 99\} \rightarrow\{2,4,6,8, \ldots \ldots , 100\}$, such that $f (3) \geq f (9) \geq f (15) \geq f (21) \geq \ldots f (99), $ is _____

A line segment AB of length λ moves such that the points A and B remain on the periphery of a circle of radius λ. Then the locus of the point, that divides the line segment AB in the ratio 2 : 3, is a circle of radius

Let B =$\begin{bmatrix} 1 & 3 & α \\ 1 & 2& 3 \\ α & α & 4 \end{bmatrix}$ , α>2 be the adjoint of a matrix A and |A| = 2, then [α - 2α α] B$\begin{bmatrix} α \\ -2α \\ α \end{bmatrix}$is equal to

The value of $\int\limits_{\frac{\pi}{3}}^{\frac{\pi}{2}} \frac{(2+3 \sin x)}{\sin x(1+\cos x)} d x$ is equal to

Suppose $\displaystyle\sum_{r=0}^{2023} r^{22023} C_r=2023 \times \alpha \times 2^{2022}$ Then the value of $\alpha$ is

If f : R $\rightarrow$ R be a continuous function satisfying $\int^{\frac{\pi}{2}}_0f(sin2x)sinxdx+\alpha\int^{\frac{\pi}{4}}_0f(cos2x)cosxdx=0$, then the value of $\alpha$ is

Let be a sequence such that a₁ + a₂ +....+ a_n=$\frac{n^2+3n}{(n+1) (n+2)}$ If $28 ∑^{10}_{k=1} \frac{1}{a_k} = P _1 P_ 2 P _3 . . . P_ m$ , where p₁, p₂, …..p_mare the first m prime numbers, then m is equal to

The range of f(x) = $4\sin^{-1}(\frac{x^2}{x^2+1})$ is

Let $A :\{1,2,3,4,5,6,7\}$. Define $B=\{T \subseteq A$ : either $1 \notin T$ or $2 \in T \}$ and $C = \{T _{\subseteq} A : T$ the sum of all the elements of $T$ is a prime number $\}$. Then the number of elements in the set $B \cup C$ is _______ .

Let the vectors $\mathbf{a}, \mathbf{b}, \mathbf{c}$ represent three coterminous edges of a parallelepiped of volume $V$. Then the volume of the parallelepiped, whose coterminous edges are represented by $\mathbf{a} + \mathbf{b} + \mathbf{c}$ and $\mathbf{a} + 2\mathbf{b} + 3\mathbf{c}$, is equal to:

If the sum of all the solutions of $\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)+\cot ^{-1}\left(\frac{1-x^2}{2 x}\right)=\frac{\pi}{3},-1 < x < 1, x \neq 0$, is $\alpha-\frac{4}{\sqrt{3}}$, then $\alpha$ is equal to ___

Let $x, y, z>1$ and $A=\begin{bmatrix}1 & \log _x y & \log _x z \\ \log _y x & 2 & \log _y z \\ \log _z x & \log _z y & 3\end{bmatrix}$ Then ∣adj(adjA2)∣ is equal to

The converse of ((~ p) ∧ q) ⇒ r is

If $a_r$ is the coefficient of $x^{10-r}$ in the Binomial expansion of $(1+x)^{10}$, then $\displaystyle\sum_{r=1}^{10} r^3\left(\frac{a_r}{a_{r-1}}\right)^2$ is equal to

The sum of the first 20 terms of the series 5 + 11 + 19 + 29 + 41 + ... is

Let g(x) = f(x) + f(1 - x) and f''(x) > 0, x ∈ (0,1). If g is decreasing in the interval (0, α) and increasing in the interval (α, 1), then tan-1 (2α) + tan^-1 ($\frac{1}{α}$) + tan^-1$(\frac{α+1}{α})$ is equal to

$I(x) = \int \frac{x^2(xsec^2x + tanx)}{(xtanx+1)^2} dx$. If $I(0)=1$ then $I(\frac{\pi}{4})$ is equal to