List of top Questions asked in JEE Main

The distance of the Sun from Earth is \(1.5 × 10^{11}\) \(m\), and its angular diameter is \((2000)\) \(s\) when observed from the earth. The diameter of the Sun will be :

When a ball is dropped into a lake from a height 4.9 m above the water level, it hits the water with a velocity v and then sinks to the bottom with the constant velocity v. It reaches the bottom of the lake 4.0 s after it is dropped. The approximate depth of the lake is :

A stone tied to a string of length \(L\) is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed \(u\). The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is \(\sqrt{x(u^2−gL)}\). The value of \(x\) is

If two straight lines whose direction cosines are given by the relations \(l + m – n = 0\), \(3l^2 + m^2 + cnl = 0\) are parallel, then the positive value of \(c\) is :

Four spheres each of mass m form a square of side d (as shown in figure). A fifth sphere of mass M is situated at the centre of square. The total gravitational potential energy of the system is:

For a perfect gas, two pressures \(P_1\) and \(P_2\) are shown in the figure. The graph shows:

Let \(\vec a=\hat i+\hat j−\hat k\) and \(\vec c=2\hat i−3\hat j+2\hat k\). Then the number of vectors \(\vec b\) such that \(\vec b×\vec c=\vec a\) and \(|\vec b|∈{1,2,…,10}\) is :

A lead bullet penetrates into a solid object and melts. Assuming that 40% of its kinetic energy is used to heat it, the initial speed of bullet is: (Given initial temperature of the bullet = 127°C), Melting point of the bullet = 327°C, Latent heat of fusion of lead = \(2.5 × 10^4 J kg^{–1}\)Specific heat capacity of lead = 125 J/kg K)

The equation of a particle executing simple harmonic motion is given by \(x=sin\;π\bigg(t+\frac{1}{3}\bigg)m\). At \(t = 1s\), the speed of the particle will be

Metal M crystallizes into a fcc lattice with the edge length of \(4.0 × 10^{–8} cm\). The atomic mass of the metal is _______ g/mol. (Nearest integer)

(Use :\( N_A=6.02×10^{23} mol^{-1}\),density of metal , \(M = 9.03 g cm^{- 3}\))

If L, C and R are the self-inductance, capacitance and resistance, respectively, which of the following does not have the dimension of time?

On reaction with stronger oxidizing agent like KIO₄, hydrogen peroxide oxidizes with the evolution of O₂. The oxidation number of I in KIO₄ changes to____.

Three identical charged balls each of charge \(2\) \(C\) are suspended from a common point \(P\) by silk threads of \(2\) \(m\) each (as shown in figure). They form an equilateral triangle of side \(1\) \(m\). The ratio of net force on a charged ball to the force between any two charged balls will be:

Let
\(A1 = {(x,y):|x| <= y^2,|x|+2y≤8} \)
and
\(A2 = {(x,y) : |x| +|y|≤k}. \)
If 27(Area A₁) = 5(Area A₂), then k is equal to :

If the sum of the first ten terms of the series
\(\frac{1}{5} + \frac{2}{65} + \frac{3}{325} + \frac{4}{1025} + \frac{5}{2501}\)+… is \(\frac{m}{n}\),
where m and n are co-prime numbers, then m + n is equal to __________.

A rectangle R with end points of one of its sides as (1, 2) and (3, 6) is inscribed in a circle. If the equation of a diameter of the circle is 2x – y + 4 = 0, then the area of R is ________.

A circle of radius 2 unit passes through the vertex and the focus of the parabola y² = 2x and touches the parabola \(y=\left (x−\frac{1}{4}\right)^2+α,\) where \(α > 0\). Then \((4α – 8)^2\) is equal to ___________.

Among the following the number of state variables is____.

Let the mirror image of the point (a, b, c) with respect to the plane 3x – 4y + 12z + 19 = 0 be (a – 6, β, γ). If a + b + c = 5, then 7β – 9γ is equal to __________.

Let
\(\vec{a}=\hat{i} - 2\hat{j} + 3\hat{k}, \vec{b}=\hat{i} - \hat{j} + \hat{k} \) and \(\vec{c}\)
be a vector such that
\(\vec{a} + (\vec{b}×\vec{c}) = \vec{0}\) and \(\vec{b}.\vec{c} = 5.\)
Then the value of 3(\(\vec{c}.\vec{a}\)) is equal to

Let y = y(x), x > 1, be the solution of the differential equation
\((x-1)\frac{dy}{dx} + 2xy = \frac{1}{x-1}\)with \(y(2) = \frac{1+e^4}{2e^4}\). If \(y(3) = \frac{e^α + 1}{βe^α}\) ,
then the value of α + β is equal to ____.

Let 3, 6, 9, 12, … upto 78 terms and 5, 9, 13, 17, … upto 59 terms be two series. Then, the sum of terms common to both the series is equal to _____.