List of top Questions asked in JEE Main

If a point $P (\alpha, \beta, \gamma)$ satisfying $(\alpha\,\, \beta\,\, \gamma) \begin{pmatrix} 2 & 10 & 8 \\9 & 3 & 8 \\8 & 4 & 8\end{pmatrix}=(0\,\,0\,\,0) $ lies on the plane $2 x+4 y+3 z=5$, then $6 \alpha+9 \beta+7 \gamma$ is equal to :

The locus of the mid points of the chords of the circle $C_1:(x-4)^2+(y-5)^2=4$ which subtend an angle $\theta_i$ at the centre of the circle $C_1$, is a circle of radius $r_i$ If $\theta_1=\frac{\pi}{3}, \theta_3=\frac{2 \pi}{3}$ and $r_1^2=r_2^2+r_3^2$, then $\theta_2$ is equal to

Let $y=y(x)$ be the solution of the differential equation $x^3 d y+(x y-1) d x=0, x>0$, $y\left(\frac{1}{2}\right)=3- e$ Then $y(1)$ is equal to

The number of solutions of cos4θ – 2cos2θ + 3sin6θ + 1 = 0 in [0, 2π] is

Area bounded by larger part in I quadrant by x = 4y² , x = 2 and y = x is A then 3A equals

Let $x = 2$ be a root of the equation $x^2 + px + q = 0$ and $f(x)=\begin{cases}\frac{1-cos(x^2-4px+q^2+8q+16)}{(x-2p)^4} & x≠2p\\0 & x=2p\end{cases}$.
Then $lim_{x \rightarrow 2p}[f(x)]$, where [·] denotes greatest integer function, is

Let B and C be the two points on the line $y + x = 0$ such that B and C are symmetric with respect to the origin. Suppose A is a point on $y – 2x = 2$ such that $\Delta ABC$ is an equilateral triangle. Then, the area of the $\Delta ABC$ is

Let sets A and B have 5 elements each. Let mean of the elements in sets A and B be 5 and 8 respectively and the variance of the elements in sets A and B be 12 and 20 respectively. A new set C of 10 elements is formed by subtracting 3 from each element of A and adding 2 to each element of B. Then the sum of the mean and variance of the elements of C is:

The compound statement $(-(P \wedge Q)) \vee((-P) \wedge Q) \Rightarrow((-P) \wedge(-Q))$ is equivalent to

Plane P₃ is passing through (1,1,1) and line of intersection of P₁ and P₂ where $P_{1}: 2x - y + z = 5$ and $P_{2}: x + 3y + 2z + 2 = 0$. Then distance of (1,1,10) from P₃ is:

The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48, is

Let the first term a and the common ratio r of a geometric progression be positive integers. If the sum of its squares of first three terms is 33033, then the sum of these three terms is equal to

If $P$ is a $3 \times 3$ real matrix such that $P^T=a P+(a-1) I$, where $a>$, then

Let P = $\left[\begin{matrix} \frac{\sqrt3}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt3}{2} \end{matrix}\right]$ A = $\left[\begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}\right]$ and Q = PAP^T. If P^TQ²⁰⁰⁷P = $\left[\begin{matrix} a & b \\ c & d \end{matrix}\right]$, then 2a+b-3c-4d equal to

The slope of tangent at any point (x, y) on a curve y = y(x) is $\frac{x^2+y^2}{2xy},x>0$ If y(2) = 0, then a value of y(8) is

if $2x^y+3y^x=20$ then $\frac{dy}{dx}$ at (2,2) is equal to:

Let$ S={x∈R:0<x<1 and\ 2 tan−1\frac{(1+x)}{(1−x)}=cos^{−1}\frac{(1-x^2)}{(1+x^2)}}$. If n(S) denotes the number of elements in S then :

The number of real solutions of the equation $3\left(x^2+\frac{1}{x^2}\right)-2\left(x+\frac{1}{x}\right)+5=0$, is

Let the plane containing the line of intersection of the planes $P 1: x+(\lambda+4) y+z=1$ and $P 2: 2 x+$ $y+z=2$ pass through the points $(0,1,0)$ and $(1,0,1)$ Then the distance of the point $(2 \lambda, \lambda,-\lambda)$ from the plane $P 2$ is

The number of integers, greater than $7000$ that can be formed, using the digits $3,5,6,7,8$ without repetition, is

For the system of linear equations
$x+y+z=6$
$\alpha x+\beta y+7 z=3$
$x+2 y+3 z=14$.
which of the following is NOT true ?

Among the relations
$S=\left\{(a, b): a, b \in R -\{0\}, 2+\frac{a}{b}>\right\}$
and $T=\left\{(a, b): a, b \in R , a^2-b^2 \in Z\right\}$,

Let $ (\alpha, \beta) $ be the centroid of the triangle formed by the lines $ 15x - y = 82 $, $ 6x - 5y = -4 $, and $ 9x + 4y = 17 $. Then $ \alpha + 2\beta $ and $ 2\alpha - \beta $ are the roots of the equation:

If the set $\left( Re \left( \frac{z-\bar{z}+z\bar{z}}{2-3z+5\bar{z}}\right) : z ∈ C, Re(z)=3 \right)$ is equal to the interval (α,β), then 24(β-α) is equal to

Let the solution curve y = y(x) of the differential equation$\frac{dy}{dx} - \frac{3x^5 \tan^{-1}(x^3)}{(1 + x^6)^{3/2}} y = 2x \exp\left(x^3 - \frac{\tan^{-1}(x^3)}{1 + x}\right)^6$pass through the origin. Then y(1) is equal to: