List of top Mathematics Questions asked in JEE Main

Four distinct points $ (2k, 3k), (1, 0), (0, 1) $ and $ (0, 0) $ lie on a circle for $ k $ equal to:

If $ (a, b) $ be the orthocenter of the triangle whose vertices are $ (1, 2) $, $ (2, 3) $, and $ (3, 1) $, and $ I_1 = \int_a^b x \sin(4x - x^2) dx $, $ I_2 = \int_a^b \sin(4x - x^2) dx $, then $ 36 \frac{I_1}{I_2} $ is equal to:

If $å= î+2ĵ + k, b = 3(î - ĵ + k), å · c = 3$ and $å \times č = b$, then $å·((xb)-b-č)$=

$\int^1_0\frac{1}{\sqrt{3+x}+\sqrt{1+x}}dx=a+b\sqrt2+c\sqrt3$ then $2a-3b-4c$ is equal to _____.

If $n-1C_r= (k^2-8)^nC_r+1$ Find $k$.

If $f(x)$ = $\begin {bmatrix} Cos x& -sinx & 0\\sinx & cos x& 0\\0&0&1 \end {bmatrix} $Statement I $⇒ f(x).f(y) = f(x+y)$ Statement II $⇒f(-x) =0 $ is invertible

How many times 3 comes from 1 to 1000?

10, 30, 68, 130, ___ ,350
find the missing number?

An equation of a plane parallel to the plane $x-2y+2z-5=0$ and at a unit distance from the origin is?

Let $A=\left[\begin{array}{cc}\frac{1}{\sqrt{10}} & \frac{3}{\sqrt{10}} \\ \frac{-3}{\sqrt{10}} & \frac{1}{\sqrt{10}}\end{array}\right]$ and $B=\left[\begin{array}{cc}1 & -i \\ 0 & 1\end{array}\right]$, where $i=\sqrt{-1}$ If $M = A ^{ T } B A$, then the inverse of the matrix $AM ^{2023} A ^{ T }$ is

Let $A = \begin{bmatrix} 1 & a & a \\ 0 & 1 & b \\ 0 & 0 & 1\end{bmatrix}, a , b \in R$.
If for some $n \in N , A ^{ n }=\begin{bmatrix}1 & 48 & 2160 \\ 0 & 1 & 96 \\ 0 & 0 & 1\end{bmatrix}$
then $n + a + b$ is equal to _________.

Let a and b are roots of $x^2 – 7x – 1 = 0$. The value of $\frac{(a_{21} + b_{21} + a_{17} + b_{17})}{(a_{19} + b_{19})}$ 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 a, b, c and d be positive real numbers such that a + b + c + d = 11. If the maximum value of $a^5b ^3c ^2d$ is $3750\;\beta$, then the value of $\beta$ is

If $\lim\limits_{x\rightarrow0}\frac{e^{ax}-\cos(bx)-\frac{cxe^{-ce}}{2}}{1-\cos(2x)}=17$ ,then 5a² + b² is equal to

Let $A =\left[ a _{i j}\right], a _{i j} \in Z \cap[0,4], 1 \leq i, j \leq 2$ .
The number of matrices $A$ such that the sum of all entries is a prime number $p \in(2,13)$ is _____.

If $\left({ }^{30} C _1\right)^2+2\left({ }^{30} C _2\right)^2+3\left({ }^{30} C _3\right)^2+\ldots+30\left({ }^{30} C _{30}\right)^2=\frac{\alpha 60 !}{(30 !)^2}$ then $\alpha$ is equal to :

The number of points of non-differentiability of the function f(x) = [4 + 13sinx] in (0, 2𝜋) is ____.

If $\phi(x)=\frac{1}{\sqrt{ x }} \int_{\frac{\pi}{4}}^x\left(4 \sqrt{2} \sin t-3 \phi^{\prime}(t)\right) dt , x>$, then $\emptyset^{\prime}\left(\frac{\pi}{4}\right)$ is equal to :

\[ f(x) = \log_e \left( 4x^2 + 11x + 6 \right) + \sin^{-1} \left( 4x + 3 \right) + \cos^{-1} \left( \frac{10x + 6}{3} \right) \]then $ 36|\alpha + \beta| $ is equal to:

Let $P(\frac{2√3}{√7} ,\frac{ 6}{√7} ), $Q,R and S be four points on the ellipse 9x² + 4y² = 36. Let PQ and RS be mutually perpendicular and pass through the origin. If $\frac{1}{( P Q ) ^2} + \frac{1}{( R S ) ^2} = \frac{P}{q }$, where p and q are coprime, then p + q is equal to

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