List of top Questions asked in JEE Main

The ratio of de-Broglie wavelength of an $\alpha$ particle and a proton accelerated from rest by the same potential is $\frac {1}{\sqrt 𝑚}$ , the value of $m$ is-

The number of following statements which are incorrect line emission

The value of $\int\limits_{\frac{\pi}{3}}^{\frac{\pi}{2}} \frac{(2+3 \sin x)}{\sin x(1+\cos x)} d x$ is equal to

Let $y=y(x)$ be the solution of the differential equation $\left(3 y^2-5 x^2\right) y d x+2 x\left(x^2-y^2\right) d y=0$ such that $y(1)=1$ Then $\left|(y(2))^3-12 y(2)\right|$ is equal to :

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 $\vec{a}$, $\vec{b}$, $\vec{c}$ are three non-zero vectors and $\hat{n}$ is a unit vector perpendicular to $\vec{c}$ such that $\vec{a}$=$\alpha \vec{b}$-$\hat{n}$, $\alpha \neq 0$ and $\vec{b}$ .$ \vec{c}$=12, then |$\vec{c} \times(\vec{a} \times \vec{b})$| is equal to:

Match List I with List II

The minimum value of the function $f(x)=\int\limits_0^2 e^{|x-t|} d t$ is :

Correct statement is:

Let $\vec{\alpha}=4 \hat{i}+3 \hat{j}+5 \hat{k}$ and $\vec{\beta}=\hat{i}+2 \hat{j}-4 \hat{k}$ Let $\vec{\beta}_1$ be parallel to $\vec{\alpha}$ and $\vec{\beta}_2$ be perpendicular to $\vec{\alpha}$ If $\vec{\beta}=\vec{\beta}_1+\vec{\beta}_2$, then the value of $5 \vec{\beta}_2 \cdot(\hat{i}+\hat{j}+\hat{k})$ is

The value of the integral:$\int\limits_{\frac{3 \sqrt{2}}{4}}^{\frac{3 \sqrt{3}}{4}} \frac{48}{\sqrt{9-4 x^2}} d x$ is equal to

Let $p$ and $q$ be two statements Then $\sim(p \wedge(p \Rightarrow \sim q))$ is equivalent to

The number of molecules from the following which contain only two lone pair of electrons is _____ .
$H_2O, N_2, CO, XeF_4, NH_3, NO, CO_2, F_2$

The number of elements in the set $\{n ∈ Z : n^2-10n+19| < 6\}$ is __.

Let f: R→R be a function such that $f(x)=\frac{x^2+2x+1}{x^2+1}$. Then

the points P and Q are respectively the circumcentre and the orthocentre of a ΔABC, then $ \overrightarrow{PA}+ \overrightarrow{PB}+ \overrightarrow{PC}$ is

If the local maximum value of the function f( x )=$(\frac{√3e}{2 sin x} )^{ sin^2x}$ ,$ x ∈ ( 0,\frac{π}{2} )$, is $\frac{k}{e}$, then $(\frac{k}{e})^8+\frac{k^8}{e^5}+k^8 $ is equal to

If $\lim\limits_{x\rightarrow0}\frac{e^{ax}-\cos(bx)-\frac{cxe^{-ce}}{2}}{1-\cos(2x)}=17$ ,then 5a² + b² is equal to

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

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

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

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

List I (Current configuration)	List II(Magnetic field at point O)
A	i	\(B_0=\frac{\mu_0I}{4\pi r}[\pi+2]\)
B	ii	\(B_0=\frac{\mu_0}{4}\frac{I}{r}\)
C	iii	\(B_0=\frac{\mu_0I}{2\pi r}[\pi-1]\)
D	iv	\(B_0=\frac{\mu_0I}{4\pi r}[\pi+1]\)