List of top Questions asked in JEE Main

A body starts from rest on a long inclined plane of slope \(45^\circ\). The coefficient of friction between the body and the plane varies as \(\mu=0.3x\), where \(x\) is distance travelled down the plane. The body will have maximum speed (for \(g=10\ \mathrm{m/s^2}\)) when \(x=\)

The change in the value of acceleration of earth towards sun, when the moon comes from the position of solar eclipse to the position on the other side of earth in line with sun is: (mass of the moon \(=7.36\times10^{22}\) kg, radius of the moon's orbit \(=3.8\times10^{8}\) m ).

Given that 1 g of water in liquid phase has volume 1 cm\(^3\) and in vapour phase 1671 cm\(^3\) at atmospheric pressure and the latent heat of vaporization of water is 2256 J/g; the change in the internal energy in joules for 1 g of water at 373 K when it changes from liquid phase to vapour phase at the same temperature is :

A certain amount of gas is taken through a cyclic process (A B C D A) that has two isobars, one isochore and one isothermal. The cycle can be represented on a \(P-V\) indicator diagram as :

Given two independent events, if the probability that exactly one of them occurs is \(\frac{26}{49}\) and the probability that none of them occurs is \(\frac{15}{49}\), then the probability of more probable of the two events is :

A ball projected from ground at an angle of \(45^\circ\) just clears a wall in front. If point of projection is 4 m from the foot of wall and ball strikes the ground at a distance of 6 m on the other side of the wall, the height of the wall is :

If \(\hat a,\ \hat b\) and \(\hat c\) are unit vectors satisfying \(\hat a-\sqrt3\,\hat b+\hat c=\vec 0\), then the angle between the vectors \(\hat a\) and \(\hat c\) is :

Let Q be the foot of perpendicular from the origin to the plane \(4x-3y+z+13=0\) and R be a point \((-1,-6)\) on the plane. Then length QR is :

The integral \(\int_{7\pi/4}^{7\pi/3}\sqrt{\tan^2x}\,dx\) is equal to :

The area of the region (in sq. units), in the first quadrant bounded by the parabola \(y=9x^2\) and the lines \(x=0,\ y=1\) and \(y=4\), is :

Consider the differential equation :
\(\frac{dy}{dx}=\frac{y^3}{2(xy^2-x^2)}\)
Statement-1: The substitution \(z=y^2\) transforms the above equation into a first order homogenous differential equation.
Statement-2: The solution of this differential equation is \(y^2e^{-y^2}/x=C\).

Statement-1: The function \(x^2(e^x+e^{-x})\) is increasing for all \(x \gt 0\).
Statement-2: The functions \(x^2e^x\) and \(x^2e^{-x}\) are increasing for all \(x \gt 0\) and the sum of two increasing functions in any interval \((a,b)\) is an increasing function in \((a,b)\).

For \(a \gt 0,\ t \in \left(0, \dfrac{\pi}{2}\right)\), let \(x = \sqrt{a^{\sin^{-1}t}}\) and \(y = \sqrt{a^{\cos^{-1}t}}\), Then, \(1 + \left(\dfrac{dy}{dx}\right)^2\) equals :

If the system of linear equations :
\(x_1 + 2x_2 + 3x_3 = 6\)
\(x_1 + 3x_2 + 5x_3 = 9\)
\(2x_1 + 5x_2 + ax_3 = b\)
is consistent and has infinite number of solutions, then :

If \(\int \frac{x^2-x+1}{x^2+1}\,e^{\cot^{-1}x}\,dx = A(x)\,e^{\cot^{-1}x}+C\), then \(A(x)\) is equal to :

If \(p, q, r\) are 3 real numbers satisfying the matrix equation, \([p\ q\ r]\begin{bmatrix}3&4&1\\3&2&3\\2&0&2\end{bmatrix} = [3\ \ 0\ \ 1]\) then \(2p + q - r\) equals :

Let \(f(x) = -1 + |x - 2|\), and \(g(x) = 1 - |x|\); then the set of all points where \(f\!og\) is discontinuous is :

Mean of 5 observations is 7 . If four of these observations are 6, 7, 8, 10 and one is missing then the variance of all the five observations is :

The acute angle between two lines such that the direction cosines \(l, m, n\), of each of them satisfy the equations \(l + m + n = 0\) and \(l^2 + m^2 - n^2 = 0\) is :

Statement-1: The number of common solutions of the trigonometric equations \(2\sin^2\theta - \cos 2\theta = 0\) and \(2\cos^2\theta - 3\sin\theta = 0\) in the interval \([0, 2\pi]\) is two.
Statement-2: The number of solutions of the equation, \(2\cos^2\theta - 3\sin\theta = 0\) in the interval \([0, \pi]\) is two.

The number of solutions of the equation, \(\sin^{-1}x = 2\tan^{-1}x\) (in principal values) is :

If the 7th term in the binomial expansion of \(\left(\dfrac{3}{\sqrt[3]{84}} + \sqrt{3}\ln x\right)^9\), \(x \gt 0\), is equal to 729 , then \(x\) can be:

The statement \(p \to (q \to p)\) is equivalent to :

The sum \(\dfrac{3}{1^2} + \dfrac{5}{1^2+2^2} + \dfrac{7}{1^2+2^2+3^2} + \cdots\) upto 11-terms is :

Given sum of the first \(n\) terms of an A.P. is \(2n + 3n^2\). Another A.P. is formed with the same first term and double of the common difference, the sum of \(n\) terms of the new A.P. is :