List of top Mathematics Questions asked in JEE Main

Let $x=\sin \left(2 \tan ^{-1} \alpha\right)$ and $y=\sin \left(\frac{1}{2} \tan ^{-1} \frac{4}{3}\right)$ If $S =\left\{\alpha \in R : y ^2=1- x \right\}$, then $\displaystyle\sum_{\alpha \in S } 16 \alpha^3$ is equal to ______

Let $\vec{a}=\hat{i}+2 \hat{j}+\lambda \hat{k}, \vec{b}=3 \hat{i}-5 \hat{j}-\lambda \hat{k}, \vec{a} \cdot \vec{c}=7,2 \vec{b} \cdot \vec{c}+43=0, \vec{a} \times \vec{c}=\vec{b} \times \vec{c}$. Then $|\vec{a} \cdot \vec{b}|$ is equal to

Let
$A=\{(x,y) ∈R^2:y≥0,2x≤y≤\sqrt{4-(x-1)^2} \}$
and
$B=\{(x,y) ∈R\times R:0≤y≤min \{2x,\sqrt{4-(x-1)^2}\}\}$
Then the ratio of the area of A to the area of B is

If the tangents at the points P and Q on the circle x² + y²– 2x + y = 5 meet at the point R $( \frac{9}{4},2 ) $then the area of the triangle PQR is

The value of $\displaystyle\sum_{r=0}^{22}{ }^{22} C_r{ }^{23} C_r$ is

The area of the region enclosed by the curve y = x³ and its tangent at the point (-1, -1) 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 _____

Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three non zero vectors such that $\vec{b} \cdot \vec{c}=0$ and $\vec{a} \times(\vec{b} \times \vec{c})=\frac{\vec{b}-\vec{c}}{2}$ If $\vec{d}$ be a vector such that $\vec{b} \cdot \vec{d}=\vec{a} \cdot \vec{b}$, then $(\vec{a} \times \vec{b}) \cdot(\vec{c} \times \vec{d})$ is equal to

The coefficient of x and x$^2$ in (1 + x)$^p$ (1 – x)$^q$ are 4 and – 5, then 2p + 3q is

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

Let $ \alpha, \beta $ be the roots of the equation $ x^2 - \sqrt{2}x + 2 = 0 $, then $ \alpha^{14} + \beta^{14} $ is equal to:

Let S = {1, 2, 3, 4, 5, 6}. Then the number of one-one functions $f : S → P(S)$, where $P(S)$ denotes the power set of S, such that $f(n) ⊂ f(m)$ where $n < m,$ is:

The integral $\int \left(\frac{x}{2}\right)^x + \left(\frac{2}{x}\right)^x \log x \, dx$ is equal to:

Let $A$ be a $3 \times 3$ matrix such that $|\operatorname{adj}(\operatorname{adj}(\operatorname{adj} A ))|=12^4$ Then $\mid A ^{-1}$ adj $A \mid$ is equal to

Let $S=\{\theta \in[0,2 \pi): \tan (\pi \cos \theta)+\tan (\pi \sin \theta)=0\}$ Then $\displaystyle\sum_{\theta \in s } \sin ^2\left(\theta+\frac{\pi}{4}\right)$ is equal to _______

If the function $f(x)=\begin{cases}(1+|\cos x|) \frac{\lambda}{|\cos x|} & , 0 < x < \frac{\pi}{2} \\\mu & , \quad x=\frac{\pi}{2} \\\frac{\cot 6 x}{e^{\cot 4 x}} & \frac{\pi}{2}< x< \pi\end{cases}$is continuous at $x=\frac{\pi}{2}, then 9 \lambda+6 \log _{ e } \mu+\mu^6- e ^{6 \lambda}$ is equal to

Let awards in event A is 48 and awards in event B is 25 and awards in event C is 18 and also n(A ∪ B ∪ C) = 60, n(A ⋂ B ⋂ C) = 5, then how many got exactly two awards is?

The domain of the function f(x) = $\frac{1}{\sqrt{[x]^2-3[x]-10}}$ is (where [x] denotes the greatest integer less than or equal to x)

Let $f^1(x)=\frac{3 x+2}{2 x+3}, x \in R -\left\{\frac{-3}{2}\right\}$ For $n \geq 2$, define $f^{ n }(x)=f^1 o f^{ n -1}(x)$ if $f^5(x)=\frac{ a x+ b }{ b x+ a }, \operatorname{gcd}( a , b )=1$, then $a + b$ is equal to ______ .

The absolute minimum value, of the function $f(x)=\left|x^2-x+1\right|+\left[x^2-x+1\right]$, where $[t]$ denotes the greatest integer function, in the interval $[-1,2]$, is:

Let A = {1, 2, 3, 4} and R be a relation on the set AxA defined by R = {((a, b), (c, d)): 2a+3b = 4c +5d}. Then the number of elements in R is

The sum of roots of |x² - 8x + 15| - 2x + 7 = 0 is:

Let $A=\begin{pmatrix}1 & 0 & 0 \\ 0 & 4 & -1 \\ 0 & 12 & -3\end{pmatrix}$ Then the sum of the diagonal elements of the matrix $(A+I)^{11}$ is equal to :

Let $M$ be the maximum value of the product of two positive integers when their sum is 66. Let the sample space $S =\left\{x \in Z : x(66-x) \geq \frac{5}{9} M\right\}$ and the event $A =\{x \in S : x$ is a multiple of 3$\}$. Then $P ( A )$ is equal to

If $f(x)=x^3-x^2 f^{\prime}(1)+x f^{\prime \prime}(2)-f^{\prime \prime \prime}(3), x \in R$, then