List of top Questions asked in JEE Main

The number of solutions of |cos x| = sinx, such that –4π ≤ x ≤ 4π is :

A line, with a slope greater than one, passes through point A(4, 3) and intersects the line x – y – 2 = 0 at the point B. If the length of the line segment AB is $\frac{\sqrt{29}}{3}$ then B also lies on the line :

The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, is

If $t = \sqrt{x} + 4$, then $\left.\frac{dx}{dt}\right|_{t=4}$ is

The correct order of melting point is

Let m₁, m₂ be the slopes of two adjacent sides of a square of side a such that $a^2 + 11a + 3(m_1^2 + m_2^2) = 220$. If one vertex of the square is $(10(\cos \alpha - \sin \alpha), 10(\sin \alpha + \cos \alpha))$, where $\alpha \in \left(0, \frac{\pi}{2}\right)$and the equation of one diagonal is $(\cos \alpha - \sin \alpha)x + (\sin \alpha + \cos \alpha)y = 10$, then $72(\sin^4 \alpha + \cos^4 \alpha) + a^2 - 3a + 13$ is equal to :

A circle C₁ passes through the origin O and has diameter 4 on the positive x-axis. The line y = 2x gives a chord OA of circle C₁. Let C₂ be the circle with OA as a diameter. If the tangent to C₂ at the point A meets the x-axis at P and y-axis at Q, then QA :AP is equal to

Two identical thin biconvex lenses of focal length 15 cm and refractive index 1.5 are in contact with each other. The space between the lenses is filled with a liquid of refractive index 1.25. The focal length of the combination is ___ cm.

Class XII students were asked to prepare one litre of buffer solution of pH $8.26$ by their Chemistry teacher. The amount of ammonium chloride to be dissolved by the student in $0.2$ M ammonia solution to make one litre of the buffer is (Given : $pK_b$ $(NH_3)$ = $4.74$, Molar mass of $NH_3$ = $17$ g $mol^{–1}$, Molar mass of $NH_4Cl$ = $53.5$ $g$ $mol^{–1}$)

A body of mass 8 kg and another of mass 2 kg are moving with equal kinetic energy. The ratio of their respective momenta will be

Let the lines$ \begin{array}{l} \frac{x-1}{\lambda}=\frac{y-2}{1}=\frac{z-3}{2}\ \text{and}\ \frac{x+26}{-2}=\frac{y+18}{3}=\frac{z+28}{\lambda}\end{array}$be coplanar and P be the plane containing these two lines. Then which of the following points does NOT lie on P?

A resistance of 40 Ω is connected to a source of alternating current rated 220 V, 50 Hz. Find the time taken by the current to change from its maximum value to the rms value :

[A] → [B]
Reactant Product
If formation of compound [B] follows the first order of kinetics and after 70 minutes the concentration of [A] was found to be half of its initial concentration. Then the rate constant of the reaction is x × 10^–6 s^–1. The value of x is _________. (Nearest Integer).

Let $\alpha, \beta$ be the roots of the equation $x^2 - 4\lambda x + 5 = 0$ and α, γ be the roots of the equation $x^2 - (3\sqrt{2} + 2\sqrt{3})x + 7 + 3\lambda\sqrt{3} = 0$. If $\beta + \gamma = 3\sqrt{2}$ then $(\alpha + 2\beta + \gamma)^2$ is equal to _______.

If the sum of all the roots of the equation $e^{2x} - 11e^x - 45e^{-x} + \frac{81}{2} = 0$
is log_eP, then p is equal to _____.

The line y = x + 1 meets the ellipse $\frac{x^2}{4}+\frac{y^2}{2}=1$ at two points P and Q. If r is the radius of the circle with PQ as diameter then (3r)² is equal to

A ray of light passing through the point P(2, 3) reflects on the x-axis at point A and the reflected ray passes through the point Q(5, 4). Let R be the point that divides the line segment AQ internally into the ratio 2:1. Let the co-ordinates of the foot of the perpendicular M from R on the bisector of the angle PAQ be (α, β). Then, the value of $7α + 3β$ is equal to ________ .

If the equation of the parabola, whose vertex is at $(5, 4)$ and the directrix is $3x + y – 29 = 0$, is $x^2 + ay^2 + bxy + cx + dy + k = 0$, then $a + b + c + d + k$ is equal to

If the circle
x²+y²-2gx+6y-19c = 0,g,c∈R
passes through the point (6, 1) and its centre lies on the line x – 2cy = 8, then the length of intercept made by the circle on x-axis is

A mass 0.9 kg, attached a horizontal spring, executes SHM with an amplitude A₁. When this mass passes through its mean position, then a smaller mass of 124 g is placed over it and both masses move together with amplitude A₂. If the ratio A₁/A₂ is α/(α – 1), then the value of α will be _____.

According to MO theory, number of species/ions from the following having identical bond order is ___.
CN-, NO+, O2, O+2, O2+2

The number of real solutions of the equation e^4x + 4e^3x - 58e^2x + 4ex + 1 = 0 is _____.

A ball of mass 100 g is dropped from a height h =10 cm on a platform fixed at the top of a vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance $\frac{ℎ}{2}$.The spring constant is ______ Nm^–1. (Use g = 10 ms^-2)

A car is moving with speed of 150 km/h and after applying the break it will move 27 m before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after travelling ___ m distance.

The number of points, where the function $f: \mathbb{R} \to \mathbb{R}$, $$ f(x) = |x - 1|\cos|x - 2|\sin|x - 1| + (x - 3)|x^2 - 5x + 4|, $$ is NOT differentiable, is