List of top Questions asked in JEE Main

There are 5 black and 3 white balls in the bag. A die is rolled, we need to pick the number of balls appearing on the die. The probability that the balls are white is?

Which one of the following statements is correct for electrolysis of brine solution?

A cubic solid is made up of two elements $X$ and $Y$ Atoms of $X$ are present on every alternate corner and one at the center of cube $Y$ is at $\frac{1}{3} rd$ of the total faces. The empirical formula of the compound is

Match items of Row I with those of Row II

The following circuit contains diodes with forward bias having resistance $25Ω$, and reverse bias having infinite resistance. The ratio of $\frac{I_{1}}{I_{2}}$ is equal to

The orbital angular momentum of a satellite is L, when it is revolving in a circular orbit at height h from earth surface. If the distance of satellite from the earth centre is increased by eight times to its initial value, then the new angular momentum will be

Which of the following is not ambidentate ligand

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason $R$
Assertion A: Efficiency of a reversible heat engine will be highest at $-273^{\circ} C$ temperature of cold reservoir
Reason R: The efficiency of Carnot's engine depends not only on temperature of cold reservoir but it depends on the temperature of hot reservoir too and is given as $n =\left(1-\frac{T_2}{T_1}\right)$
In the light of the above statements, choose the correct answer from the options given below

Pressure for polytropic process P varies with volume V as P=av-3, find out the bulk modulus.

Let $ (\alpha, \beta) $ be the centroid of the triangle formed by the lines $ 15x - y = 82 $, $ 6x - 5y = -4 $, and $ 9x + 4y = 17 $. Then $ \alpha + 2\beta $ and $ 2\alpha - \beta $ are the roots of the equation:

If the CFSE of $\left[ Ti \left( H _2 O \right)_6\right]^{3+}$ is $-960 kJ / mol$, this complex will absorb maximum at wavelength ___$nm$ (nearest integer) Assume Planck's constant $( h )=64 \times 10^{-34} Js$, Speed of light $( c )=30 \times 10^8 m / s$ and Avogadro's Constant $\left( N _{ A }\right)=6 \times 10^{23} / mol$

A body cools from $60\degree C$ to $40\degree C$ in 6 minutes. If, temperature of surroundings is $10\degree C$. Then, after the next 6 minutes, its temperature will be ______$\degree C$.

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

A particle is moving with constant speed in a circular path. When the particle turns by an angle $90\degree$ , the ratio of instantaneous velocity to its average velocity is $π : x\sqrt2$. The value of x will be -

An aluminium rod with Young's modulus Y=7.0×10¹⁰ N/m² undergoes elastic strain of 0.04%. The energy per unit volume stored in the rod in SI unit 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 straight lines l₁ and l₂ pass through the origin and trisect the line segment of the line L: 9x + 5y = 45 between the axes. If m₁ and m₂ are the slopes of the lines l₁ and l_2, then the point of intersection of the line y = (m₁ + m₂)x with L lies on

Let m1 and m2 be the slopes of the tangents drawn from the point P(4,1) to the hyperbola H : $\frac{y^2}{25} − \frac{x^2}{16 }$= 1. If Q is the point from which the tangents drawn to H have slopes |m₁| and |m₂| and they make positive intercepts α and β on the x-axis, then $\frac{( P Q ) ^2}{ α β}$ α β is equal to _____.

Let S = {$ x∈(−\frac{ π}{ 2} , \frac{π}{2} )$ : 9^1−tan2 x + 9^tan2 x=10 } and $β=∑_{ x∈s} t a n ^2 (\frac{ x}{ 3} )$ , then $\frac{1}{6}$ ( β − 14 )² is equal to

Let $P(x_0, y_0)$ be the point on the hyperbola $3x^2 - 4y^2 = 36$, which is nearest to the line $3x + 2y = 1$. Then $\sqrt{2}(y_0 - x_0)$ is equal to:

The work functions of Aluminium and Gold are 4.1 eV and 5.1 eV respectively. The ratio of the slope of the stopping potential versus frequency plot for Gold to that of Aluminium 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

For the given YDSE setup. Find the number of fringes by which the central maxima gets shifted from point O.
(Given d = 1 mm D = 1 m λ = 5000 Å)