List of top Mathematics Questions asked in JEE Main

Let $y=y(x)$ be the solution of the differential equation $\frac{d y}{d x}=\frac{4 y^3+2 y x^2}{3 x y^2+x^3}, y(1)=1$ If for some $n \in N , y (2) \in[ n -1, n )$, then $n$ is equal to ______
The value of $\displaystyle\sum_{r=0}^{22}{ }^{22} C_r{ }^{23} C_r$ is
The straight lines l1 and l2 pass through the origin and trisect the line segment of the line L: 9x + 5y = 45 between the axes. If m1 and m2 are the slopes of the lines l1 and l2, then the point of intersection of the line y = (m1 + m2)x with L lies on
Let m1 and m2 be the slopes of the tangents drawn from the point P(4,1) to the hyperbola H : \(\frac{y^2}{25} − \frac{x^2}{16 }\)= 1. If Q is the point from which the tangents drawn to H have slopes |m1| and |m2| and they make positive intercepts α and β on the x-axis, then  \(\frac{( P Q ) ^2}{ α β}\) α β is equal to _____.
Let S = {\( x∈(−\frac{ π}{ 2} , \frac{π}{2} )\) : 91−tan2 x + 9tan2 x=10 } and \(β=∑_{ x∈s} t a n ^2 (\frac{ x}{ 3} )\) , then \(\frac{1}{6}\) ( β − 14 )2  is equal to

Let \(P(x_0, y_0)\) be the point on the hyperbola \(3x^2 - 4y^2 = 36\), which is nearest to the line \(3x + 2y = 1\). Then \(\sqrt{2}(y_0 - x_0)\) is equal to:

The shortest distance between the lines $\frac{x-2}{3}=\frac{y+1}{2}=\frac{z-6}{2}$ and $\frac{x-6}{3}=\frac{1-y}{2}=\frac{z+8}{0}$ is equal to
Rank of the word PUBLIC is?
Let 5 digit numbers be constructed using the digits $0,2,3,4,7,9$ with repetition allowed, and are arranged in ascending order with serial numbers Then the serial number of the number 42923 is

Let A be a $n \times n$ matrix such that $| A |=2$ If the determinant of the matrix$\operatorname{Adj}\left(2 \cdot \operatorname{Adj}\left(2 A ^{-1}\right)\right) \cdot$ is $2^{84}$, then $n$ is equal to ____

Let $y=f(x)=\sin ^3\left(\frac{\pi}{3}\left(\cos \left(\frac{\pi}{3 \sqrt{2}}\left(-4 x^3+5 x^2+1\right)^{\frac{3}{2}}\right)\right)\right)$ Then, at $x=1$

A light ray emits from the origin making an angle \(30\degree\) with the positive x-axis. After getting reflected by the line \(x + y = 1\), if this ray intersects x-axis at Q, then the abscissa of Q is
If the sum of the series \(\left(\frac{1}{2}-\frac{1}{3}\right) + \left(\frac{1}{2^2}-\frac{1}{2·3} + \frac{1}{3^2}\right) + \left(\frac{1}{2^2}-\frac{1}{2^2·3} + \frac{1}{2·3^2} - \frac{1}{3^3}\right) + \left(\frac{1}{2^4}-\frac{1}{2^3·3} + \frac{1}{2^2·3^2} - \frac{1}{2·3^3} + \frac{1}{3^4}\right) + ........ \)
is \(\frac{α}{β}\) , where α and β are co-prime, then α+3β is equal to ________
The remainder, when $19^{200}+23^{200}$ is divided by $49$ , is_______
Let an be the nth term of the series 5 + 8 + 14 + 23 + 35 + 50 +.... and Sn = \(\displaystyle\sum_{k=1}^{n} a_k.\) Then S30 - a40 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

If the coefficient of x7 in expansion of \((ax- \frac{1}{bx^2})^{13}\) is equal to the coefficient of x-5 in expansion of \((ax + \frac{1}{bx^2})13\), then a4b4 is ______
Let $f$ be a twice differentiable function on $R$. 
If $f ^{\prime}(0)=4$ and $f(x)+\int\limits_0^x(x-t) f^{\prime}(t) d t=\left(e^{2 x}+e^{-2 x}\right) \cos 2 x+\frac{2}{a} x,$ 
then $(2 a+1)^5 a^2$ is equal to ______.
The remainder when \((2023)^{2023}\) is divided by \(35\) is _____
Let a1, a2, a3, …. be a G.P. of increasing positive numbers. Let the sum of its 6th and 8th terms be 2 and the product of its 3rd and 5th terms be \(\frac{1}{9}\) .Then 6 (a2 + a4) (a4 + a6) is equal to
If the center and radius of the circle $\left|\frac{z-2}{z-3}\right|=2$ are respectively $(\alpha, \beta)$ and $\gamma$, then $3(\alpha+\beta+\gamma)$ is equal to
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 \( \alpha, \beta \) be the roots of the equation \( x^2 - \sqrt{2}x + 2 = 0 \), then \( \alpha^{14} + \beta^{14} \) is equal to:
Let be a sequence such that a1+a2+....+ an=\(\frac{n^2+3n}{ (n+1 ) (n+2)}\). If  \(28∑^{10}_{k=1}\frac{1}{a_k} =\) P1P2P3 . . . Pm ,  where p1, p2, …..pm are the first m prime numbers, then m is equal to
A plane $E$ is perpendicular to the two planes $2 x-2 y+z=0$ and $x-y+2 z=4$, and passes through the point $P (1,-1,1)$ If the distance of the plane $E$ from the point $Q(a, a, 2)$ is $3 \sqrt{2}$, then $( PQ )^2$ is equal to