List of top Questions asked in JEE Main

The number of five-digit numbers, greater than 40000 and divis ible by 5, which can be formed using the digits 0, 1, 3, 5, 7, and 9 without repetition, is equal to:

All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the serial number of the word PUBLIC is:

The number of ways of giving 20 distinct oranges to 3 children such that each child gets at least one orange is______

The number of triplets $ (x, y, z) $, where $ x, y, z $ are distinct non-negative integers satisfying $ x + y + z = 15 $, is:

In an examination, 5 students have been allotted their seats as per their roll numbers. The number of ways, in which none of the students sit on the allotted seat, is:

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 the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{7}=1$ and the hyperbola $\frac{x^2}{144}-\frac{y^2}{\alpha}=\frac{1}{25}$ coincide Then the length of the latus rectum of the hyperbola is:-

A parabola with focus (3, 0) and directrix x = –3. Points P and Q lie on the parabola and their ordinates are in the ratio 3 : 1. The point of intersection of tangents drawn at points P and Q lies on the parabola

The set of all values of $a^2$ for which the line $x+y=0$ bisects two distinct chords drawn from a point $P \left(\frac{1+a}{2}, \frac{1-a}{2}\right)$ on the circle $2 x^2+2 y^2-(1+a) x-(1-a) y=0$, is equal to :

If the tangent at a point 𝑃 on the parabola $𝑦^2=3𝑥$ is parallel to the line $𝑥+2𝑦=1$ and the tangents at the points 𝑄 and 𝑅 on the ellipse $\frac{𝑥^2}{ 4} +\frac{𝑦^2}{ 1} =1$ are perpendicular to the line 𝑥−𝑦=2, then the area of the triangle PQR is :

Let the tangent to the parabola $y^2 = 12x$ at the point (3, α) be perpendicular to the line 2x + 2y = 3. Then the square of distance of the point (6, – 4) from the normal to the hyperbola $α^2 x^2 – 9y^2 = 9α^2$ at its point (α– 1, α + 2) is equal to__

Consider ellipse $ E_k : \frac{x^2}{k} + \frac{y^2}{k} = 1 $, for $ k = 1, 2, \dots, 20 $. Let $ C_k $ be the circle which touches the four chords joining the end points (one on the minor axis and another on the major axis) of the ellipse $ E_k $. If $ r_k $ is the radius of the circle $ C_k $, then the value of $ \sum_{k=1}^{20} r_k^2 $ is:

Let $ H_n : \frac{x^2}{1 + n} + \frac{y^2}{3 + n} = 1, n \in \mathbb{N} $. Let $ k $ be the smallest even value of $ n $ such that the eccentricity of $ H_n $ is a rational number. If $ l $ is the length of the latus rectum of $ H_k $, then 21 $ l $ 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________

Let the equation of the plane passing through the line $x-2 y-z-5=0=x+y+3 z-5$ and parallel to the line $x+y+2 z-7=0=2 x+3 y+z-2$ be $a x+b y+c z=65$ Then the distance of the point $(a, b, c)$ from the plane $2 x+2 y-z+16=0$ is _______

The complex number $z=\frac{i-1}{\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}}$ is equal to :

If $a ≠ ±b$ and are purely real, z ϵ complex number, $Re(az^{2}+bz)=a$ and $Re(bz^{2}+az)=b$ then number of value of z possible is

Let $ z = 1 + i $ and $ z_1 = \frac{1 + \bar{z}}{z(1 - z) + 1} $, where $ \bar{z} $ denotes the conjugate of $ z $. Then$\frac{12}{\pi} \arg(z_1)$ is equal to:

Let $α=8−14𝑖$, $𝐴=\{z∈C:\frac {αz−\bar α\bar z}{z^2−(\bar z)^2−112i }=1\}$ and $𝐵={𝑧∈C:|𝑧+3𝑖|=4}$. Then $∑_{𝑧∈𝐴∩𝐵 }(\text {𝑅𝑒}\ ⁡𝑧−\text {𝐼𝑚⁡}\ 𝑧)$ is equal to _____ .

For $a∈ C, let A = {z∈C : Re (a + z ) > Im ( a + z)}$ and $B = {z∈C : Re (a + z ) < Im ( a + z)}.$ Then among the two statements:
(S₁) : If $Re (a), Im (a) > 0$, then the set A contains all the real numbers
(S₂): If $Re (a), Im (a) < 0,$ then the set B contains all the real numbers

Let S = $\{z \in C-\{i,2i\}:\frac{z^2+8iz-15}{z^2-3iz-2}\in R\}$ if $\alpha-\frac{13}{11}i\in S, a \in R-{0}$, then $242\alpha^2$ is equal to ____.

Let $S=\left\{z∈C : \bar{z}=i(z^2+Re(\bar{z}))\right\}$. Then $\sum\limits_{z∈S}|z|^2$ is equal to

Let [α] denote the greatest integer ≤ α. Then $[\sqrt1] + [ \sqrt 2 ] + [ \sqrt3 ] + . . . + [ \sqrt120 ] [\sqrt1 ] + [ \sqrt2 ] + [ \sqrt3 ] + . . . + [ 120 ]$ is equal to

Let $ w_1 $ be the point obtained by the rotation of $ z_1 = 5 + 4i $ about the origin through a right angle in the anticlockwise direction, and $ w_2 $ be the point obtained by the rotation of $ z_2 = 3 + 5i $ about the origin through a right angle in the clockwise direction. Then the principal argument of $ w_1 - w_2 $ is equal to:

If 5f ( x+y ) = f(x).f(y) and f(3) = 320, then the value of f(1) is