List of top Questions asked in JEE Main

A spring mass system (mass \(m\), spring constant \(k\) and natural length \(l\)) rest in equilibrium on a horizontal disc. The free end of the spring is fixed at the centre of the disc. If the disc together with spring mass system, rotates about it's axis with an angular velocity \(\omega\), (\(k \gg m\omega^2\)) the relative change in the length of the spring is best given by the option :

Starting at temperature 300 K, one mole of an ideal diatomic gas (\(\gamma = 1.4\)) is first compressed adiabatically from volume \(V_1\) to \(V_2 = \frac{V_1}{16}\). It is then allowed to expand isobarically to volume \(2V_2\). If all the processes are the quasi-static then the final temperature of the gas (in \(^o\)K) is (to the nearest integer) _____.

Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is 1 : 4, the ratio of their diameters is:

A particle starts from the origin at \(t = 0\) with an initial velocity of \(3.0\,\hat{i}\) m/s and moves in the x-y plane with a constant acceleration \(\left(6\hat{i} + 4\hat{j}\right)\) m/s\(^2\). The x-coordinate of the particle at the instant when its y-coordinate is 32 m is \(D\) meters. The value of \(D\) is :-

A small circular loop of conducting wire has radius \(a\) and carries current \(I\). It is placed in a uniform magnetic field \(B\) perpendicular to its plane such that when rotated slightly about its diameter and released, it starts performing simple harmonic motion of time period \(T\). If the mass of the loop is \(m\) then :

For the four sets of three measured physical quantities as given below. Which of the following options is correct ?
(i) \(A_1 = 24.36,\ B_1 = 0.0724,\ C_1 = 256.2\)
(ii) \(A_2 = 24.44,\ B_2 = 16.082,\ C_2 = 240.2\)
(iii) \(A_3 = 25.2,\ B_3 = 19.2812,\ C_3 = 236.183\)
(iv) \(A_4 = 25,\ B_4 = 236.191,\ C_4 = 19.5\)

There is a small source of light at some depth below the surface of water (refractive index = \(\frac{4}{3}\)) in a tank of large cross sectional surface area. Neglecting any reflection from the bottom and absorption by water, percentage of light that emerges out of surface is (nearly) :
[Use the fact that surface area of a spherical cap of height h and radius of curvature r is \(2\pi rh\)]:

An electron of mass m and magnitude of charge \(|e|\) initially at rest gets accelerated by a constant electric field E. The rate of change of de-Broglie wavelength of this electron at time t ignoring relativistic effects is :

If the distance between the plane, \(23x - 10y - 2z + 48 = 0\) and the plane containing the lines
\(\frac{x + 1}{2} = \frac{y - 3}{4} = \frac{z + 1}{3}\)
and
\(\frac{x + 3}{2} = \frac{y + 2}{6} = \frac{z - 1}{\lambda}\) \((\lambda \in R)\)
is equal to \(\frac{k}{\sqrt{633}}\), then k is equal to ______.

If the curves, \(x^2 - 6x + y^2 + 8 = 0\) and \(x^2 - 8y + y^2 + 16 - k = 0\), \((k \gt 0)\) touch each other at a point, then the largest value of k is ______.

If \(C_r \equiv {}^{25}C_r\) and \(C_0 + 5 \cdot C_1 + 9 \cdot C_2 + \ldots + (101) \cdot C_{25} = 2^{25} \cdot k\), then k is equal to ______.

Let \(\vec{a}\), \(\vec{b}\) and \(\vec{c}\) be three vectors such that \(|\vec{a}| = \sqrt{3}\), \(|\vec{b}| = 5\), \(\vec{b} \cdot \vec{c} = 10\) and the angle between \(\vec{b}\) and \(\vec{c}\) is \(\frac{\pi}{3}\). If \(\vec{a}\) is perpendicular to the vector \(\vec{b} \times \vec{c}\), then \(|\vec{a} \times (\vec{b} \times \vec{c})|\) is equal to ______.

If \(A = \{x \in \mathbb{R} : |x| \lt 2\}\) and \(B = \{x \in \mathbb{R} : |x - 2| \ge 3\}\); then :

If \(p \rightarrow (p \wedge \sim q)\) is false, then the truth values of p and q are respectively :

The number of terms common to the two A.P.'s \(3, 7, 11, \ldots, 407\) and \(2, 9, 16, \ldots, 709\) is ______.

The length of the minor axis (along y-axis) of an ellipse in the standard form is \(\frac{4}{\sqrt{3}}\). If this ellipse touches the line, \(x + 6y = 8\); then its eccentricity is :

Given : \(f(x) = \begin{cases} x, & 0 \le x \lt \frac{1}{2} \\ \frac{1}{2}, & x = \frac{1}{2} \\ 1 - x, & \frac{1}{2} \lt x \le 1 \end{cases}\) and \(g(x) = \left(x - \frac{1}{2}\right)^2,\ x \in R\).
Then the area (in sq. units) of the region bounded by the curves, \(y = f(x)\) and \(y = g(x)\) between the lines, \(2x = 1\) and \(2x = \sqrt{3}\), is :

A random variable X has the following probability distribution :

X:	1	2	3	4	5
P(X):	\(K^2\)	\(2K\)	\(K\)	\(2K\)	\(5K^2\)

Then \(P(X \gt 2)\) is equal to :

If \(x = 2\sin\theta - \sin 2\theta\) and \(y = 2\cos\theta - \cos 2\theta\), \(\theta \in [0, 2\pi]\), then \(\frac{d^2y}{dx^2}\) at \(\theta = \pi\) is :

If \(x = \sum_{n=0}^{\infty} (-1)^n \tan^{2n}\theta\) and \(y = \sum_{n=0}^{\infty} \cos^{2n}\theta\) for \(0 \lt \theta \lt \frac{\pi}{4}\), then :

If \(\int \frac{d\theta}{\cos^2\theta\,(\tan 2\theta + \sec 2\theta)} = \lambda \tan\theta + 2\log_e |f(\theta)| + C\) where C is a constant of integration, then the ordered pair \((\lambda, f(\theta))\) is equal to :

Let [t] denote the greatest integer \(\le t\) and \(\lim_{x \to 0} x\left[\frac{4}{x}\right] = A\).
Then the function, \(f(x) = [x^2]\sin(\pi x)\) is discontinuous, when x is equal to :

Let f and g be differentiable functions on R such that fog is the identity function. If for some a, b \(\in\) R, \(g'(a) = 5\) and \(g(a) = b\), then \(f'(b)\) is equal to :

Let \(a - 2b + c = 1\).
If \(f(x) = \begin{vmatrix} x + a & x + 2 & x + 1 \\ x + b & x + 3 & x + 2 \\ x + c & x + 4 & x + 3 \end{vmatrix}\), then:

The following system of linear equations
\(7x + 6y - 2z = 0\)
\(3x + 4y + 2z = 0\)
\(x - 2y - 6z = 0\), has