List of top Questions asked in JEE Main

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
If the image of point P(1, 2, 3) about the plane 2x - y + 3z = 2 is Q, then the area of triangle PQR, where coordinates of R is (4, 10, 12)
Using the number 1, 2, 3 ... 7, total numbers of 7 digit number which does not contain string 154 or 2367 is (Repetition is not allowed)

The mean and variance of the marks obtained by the students in a test are 10 and 4 respectively Later, the marks of one of the students is increased from 8 to 12 If the new mean of the marks is $10.2$, then their new variance is equal to :

If the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ meets the line $\frac{x}{7}+\frac{y}{2 \sqrt{6}}=1$ on the $x$-axis and the line $\frac{x}{7}-\frac{y}{2 \sqrt{6}}=1$ on the $y$-axis, then the eccentricity of the ellipse is
The foot of perpendicular of the point $(2,0,5)$ on the line $\frac{x+1}{2}=\frac{y-1}{5}-\frac{z+1}{-1}$ is $(a, \beta, \gamma)$. Then which of the following is NOT correct?
\(y=f(x)\) is a quadratic function passing through (โ€“1, 0) and tangent to it at (1, 1) is \(y=x\). Find x intercept by normal at point (๐›‚, ๐›‚ + 1), (๐›‚ > 0)
Let \(\vec{a}=-\hat{i}-\hat{j}+\hat{k}, \vec{a} \cdot \vec{b}=1\) and \(\vec{a} \times \vec{b}=\hat{i}-\hat{j}\). Then \(\vec{a}-6 \vec{b}\) is equal to

A has 5 elements and B has 2 elements. The number of subsets of A ร— B such that the number of elements in subset is more than or equal to 3 and less than 6, is?

Let A,B,C be 3ร—3 matrices such that A is symmetric and B and C are skew symmetric. Consider the statements:
(S1) A13B26 โˆ’ B26A13 is symmetric.
(S2) A26C13 โˆ’ C13A26 is symmetric.Then:
Let \(z\) be a complex number such that \(\left|\frac{z-2 i}{z+i}\right|=2 z \neq-i\) Then \(z\) lies on the circle of radius 2 and centre
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
Consider the following statements : $P$ : Ramu is intelligent $Q: $ Ramu is rich $R$ : Ramu is not honest The negation of the statement "Ramu is intelligent and honest if and only if Ramu is not rich" can be expressed as :
Let $[t]$ denote the greatest integer less than or equal to t Then the value of the integral $\int\limits_{-3}^{101}\left([\sin (\pi x)]+e^{[\cos (2 \pi x)]}\right) d x$ is equal to
The shortest distance between the lines $\frac{x+7}{-6}=\frac{y-6}{7}=z$ and $\frac{7-x}{2}=y-2=z-6$ is

Let $f:(0,1) \rightarrow R$ be a function defined by

$f(x)=\frac{1}{1-e^{-x}}$, and $g(x)=(f(-x)-f(x))$ Consider two statements

(I) $g$ is an increasing function in $(0,1)$

(II) $g$ is one-one in $(0,1)$Then,

The equations of two sides of a variable triangle are \(x-0\) and \(y=3\), and its third side is a tangent to the parabola \(y^2=6 x\). The locus of its circumcentre is:
Let $T$ and $C$ respectively be the transverse and conjugate axes of the hyperbola $16 x^2-y^2+64 x+4 y$ $+44=0$. Then the area of the region above the parabola $x^2=y+4$, below the transverse axis $T$ and on the right of the coujugate axis $C$ is:
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
The number of solutions of cos4ฮธ โ€“ 2cos2ฮธ + 3sin6ฮธ + 1 = 0 in [0, 2ฯ€] is
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 โˆช B โˆช C) = 60, n(A โ‹‚ B โ‹‚ C) = 5, then how many got exactly two awards is?
Positive numbers a1, a2, .... a5 are in geometric progression. Their mean and variance are \(\frac{31}{10}\) and \(\frac{m}{n}\) respectively. The mean of the reciprocals is \(\frac{31}{40}\), then m + n is?
An object is placed Infront of a plane mirror 12 cm away from it. The object is kept fixed while the plane mirror is shifted towards the object by a distance of 4 cm. The length of shift in the position of image is equal to ___________ cm.
let Dk=\(\begin{vmatrix} 1 & 2k& 2k-1\\ n & n^2+n+2 & n^2\\ n & n^2+n & n^2+n+2 \end{vmatrix}\) if \(โˆ‘^n_{ k=1}\) Dk=96, Then n is equal to
Let $z=1+i$ and $z_1=\frac{1+i \bar{z}}{\bar{z}(1-z)+\frac{1}{z}}$ Then $\frac{12}{\pi} \arg \left(z_1\right)$ is equal to________