List of top Questions asked in JEE Main

Match List I with List II :

	List I		List II
A	3 Translational degrees of freedom	I	Monoatomic gases
B	3 Translational, 2 rotational degrees of freedoms	II	Polyatomic gases
C	3 Translational, 2 rotational and 1 vibrational degrees of freedom	III	Rigid diatomic gases
D	3 Translational, 3 rotational and more than one vibrational degrees of freedom	IV	Nonrigid diatomic gases

Choose the correct answer from the options given below:

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 $f(x)= \begin{vmatrix} 1+\sin ^2 x & \cos ^2 x & \sin 2 x \\ \sin ^2 x & 1+\cos ^2 x & \sin 2 x \\ \sin ^2 x & \cos ^2 x & 1+\sin 2 x\end{vmatrix}, x \in\left[\frac{\pi}{6}, \frac{\pi}{3}\right] $ If $\alpha$ and $\beta$ respectively are the maximum and the minimum values of $f$, then

Let $x=\sin \left(2 \tan ^{-1} \alpha\right)$ and $y=\sin \left(\frac{1}{2} \tan ^{-1} \frac{4}{3}\right)$ If $S =\left\{\alpha \in R : y ^2=1- x \right\}$, then $\displaystyle\sum_{\alpha \in S } 16 \alpha^3$ is equal to ______

Magnetic flux (in weber) in a closed circuit of resistance $20 \,\Omega$ varies with time $t ( s )$ as $\phi=8 t^2-9 t+5$. The magnitude of the induced current at $t =0.25\, s$ will be ______$mA$

A particle of mass 100 g is projected at time $𝑡=0$ with a speed $20\,ms^{−1}$ at an angle $45°$ to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time $𝑡=2 s$ is found to be $\sqrt{K}\ kgm^2/s.$ The value of $K$ is ________. (Take $g=10$ $ms^{−2}$)

A point source of $100 \,W$ emits light with $5 \%$ efficiency At a distance of $5\, m$ from the source, the intensity produced by the electric field component is:

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+....+ a_n=$\frac{n^2+3n}{ (n+1 ) (n+2)}$. If $28∑^{10}_{k=1}\frac{1}{a_k} =$ P₁P₂P₃ . . . P_m , where p1, p2, …..p_m 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

7 boys and 5 girls are to be seated around a circular table such that no two girls sit together is?

The distance of the point $(7,-3,-4)$ from the plane passing through the points $(2,-3,1),(-1,1,-2)$ and $(3,-4,2)$ is :

The value of $\left(\frac{1+\sin \frac{2 \pi}{9}+i \cos \frac{2 \pi}{9}}{1+\sin \frac{2 \pi}{9}-i \cos \frac{2 \pi}{9}}\right)^3$ is

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

The set of all a∈ R for which the equation x|x-1|+|x-2|+a=0 has exactly one real root is

Let $\overrightarrow 𝑎 =4\hat 𝑖+3\hat 𝑗ˆ$ and $\overrightarrow 𝑏 =3\hat 𝑖−4\hat 𝑗$+$5\hat 𝑘$. If $\overrightarrow 𝑐$ is a vector such that $\overrightarrow 𝑐 ⋅(\overrightarrow 𝑎 ×\overrightarrow𝑏⃗ )+25=0$, $\overrightarrow𝑐 ⋅(\hat𝑖+\hat𝑗+ \hat𝑘)=4$, and projection of $\overrightarrow𝑐$ on $\overrightarrow𝑎$ is $1$ , then the projection of $\overrightarrow 𝑐$ on $\overrightarrow 𝑏$ equals

Let $f(\theta)=3[sin^4(\frac{3\pi}{2}-\theta)+sin^4(3\pi+θ)]-2(1-sin^22\theta)$ and $S=\{\theta∈[0,\pi]:f'(\theta)=-\frac{\sqrt3}{2}\}$. If $4\beta \sum_{\theta∈S}\theta$, then $f(\beta)$ is equal to

Let A = {1, 2, 3, 4, 5} and B = {1, 2, 3, 4, 5, 6). Then the number of functions f: A→B satisfying f(1) + f(2) = f(4)-1 is equal to _________ .

What is the correct order of acidity of the protons marked A-D in the given compounds?

A in the above reaction is:

Let $y=f(x)$ represent a parabola with focus $\left(-\frac{1}{2}, 0\right)$ and directrix $y=-\frac{1}{2}$ Then $S=\left\{x \in R : \tan ^{-1}(\sqrt{f(x)})+\sin ^{-1}(\sqrt{f(x)+1})=\frac{\pi}{2}\right\}$ :

If the radius of the largest circle with centre (2, 0) inscribed in the ellipse $x^2 + 4y^2 = 36$ is r, then $12r^2$ is equal to

$\displaystyle\sum_{k=0}^6{ }^{51-k} C_3$ is equal to

Let a common tangent to the curves y² = 4x and (x – 4)² + y² = 16 touch the curves at the points P and Q. Then (PQ)² is equal to ________.