List of top Questions asked in JEE Main

$\frac{dy}{dx}$ + $\frac{5}{x(1+x^5)}$y = $\frac{(1+x^5)^2}{x^7}$ If y(1) = 2, then the value of y(2) is:

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 $y=y(x)$ be the solution of the differential equation $\frac{d y}{d x}=\frac{4 y^3+2 y x^2}{3 x y^2+x^3}, y(1)=1$ If for some $n \in N , y (2) \in[ n -1, n )$, then $n$ is equal to ______

The value of $\displaystyle\sum_{r=0}^{22}{ }^{22} C_r{ }^{23} C_r$ is

The shortest distance between the lines $\frac{x-2}{3}=\frac{y+1}{2}=\frac{z-6}{2}$ and $\frac{x-6}{3}=\frac{1-y}{2}=\frac{z+8}{0}$ is equal to

The length of a seconds pendulum at a height h=2R from earth surface will be :
(Given : R= Radius of earth and acceleration due to gravity at the surface of earth g=π²ms⁻²)

Let 5 digit numbers be constructed using the digits $0,2,3,4,7,9$ with repetition allowed, and are arranged in ascending order with serial numbers Then the serial number of the number 42923 is

600 mL of 0.01M HCl is mixed with 400 mL of 0.01 M H₂SO₄.The pH of the mixture is ______ × 10^-2(Nearest integer)
[Given log 2 =0.30 , log 3 =0.48 log 5 =0.69 log 7 -0.84 log 11 =1.04 ]

Match List I with List II

List I (Complex)		List II (Hybridization)
A.	Ni(CO)₄	I.	sp³
B.	[Cu(NH₃)₄]²⁺	II.	dsp²
C.	[Fe(NH₃)₆]²⁺	III.	sp³d²
D.	[Fe(H₂O)₆]²⁺	IV.	d²sp³

Choose the correct answer from the options given below:

What is the center of gravity of a semi-circular disc of radius (R)?

A $100\, m$ long wire having cross-sectional area $625 \times 10^{-4} \, m ^2$ and Young's modulus is $10^{10} Nm ^{-2}$ is subjected to a load of $250 \, N$, then the elongation in the wire will be:

A block is fastened to a horizontal spring. The block is pulled to a distance $x=10\ cm$ from its equilibrium position (at $x=0$ ) on a frictionless surface from rest. The energy of the block at $x=5$ $cm$ is $025 J$. The spring constant of the spring is _____$Nm ^{-1}$.

The primary and secondary valencies of cobalt respectively in $[ Co(NH_3)_5Cl]Cl_2$ are :

Let $f$ be a twice differentiable function on $R$.
If $f ^{\prime}(0)=4$ and $f(x)+\int\limits_0^x(x-t) f^{\prime}(t) d t=\left(e^{2 x}+e^{-2 x}\right) \cos 2 x+\frac{2}{a} x,$
then $(2 a+1)^5 a^2$ is equal to ______.

On a temperature scale X, the boiling point of water is 65° X and the freezing point is 15° X. Assume that the X scale is linear. The equivalent temperature corresponding to 95° X on the Fahrenheit scale would be:

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$
Assertion A: Steel is used in the construction of buildings and bridges.
Reason R: Steel is more elastic and its elastic limit is high.
In the light of above statements, choose the most appropriate 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 $ \alpha, \beta $ be the roots of the equation $ x^2 - \sqrt{2}x + 2 = 0 $, then $ \alpha^{14} + \beta^{14} $ 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 :

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

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

Solid fuel used in rocket is a mixture of Fe₂O₃ and Al (in ratio 1 : 2) the heat evolved (KJ) per gram of the mixture is ______ (Nearest integer)
Given $\Delta H_f^{\circ}(Al_2O_3) = -1700 \, \text{KJ mol}^{-1}$
$\Delta H_f^{\circ}(Fe_2O_3) = -840 \, \text{KJ mol}^{-1}$ }