List of top Questions asked in JEE Main

The sum of the cubes of all the roots of the equation x⁴ – 3x³ –2x² + 3x +1 = 0 is

N>40000, where N is divisible by 5. How many such 5 digit numbers can be formed using 0,1,3,5,7,9 without repetition.

Let $A$ be the area of the region
$\left\{(x, y): y \geq x^2, y \geq(1-x)^2, y \leq 2 x(1-x)\right\}$. 
Then $540 A$ is equal to ______.

If the value of the integral \[ \int_{-1}^{1} \frac{\cos \alpha x}{1 + 3^x} \, dx = \frac{2}{\pi}, \] then a value of \( \alpha \) is:

The resistance per centimeter of a meter bridge wire is \( r \), with \( X \, \Omega \) resistance in the left gap. Balancing length from the left end is at 40 cm with 25 \( \Omega \) resistance in the right gap. Now the wire is replaced by another wire of \( 2r \) resistance per centimeter. The new balancing length for the same settings will be at:

Only \( 2 \, \text{mL} \) of \( \text{KMnO}_4 \) solution of unknown molarity is required to reach the end point of a titration of \( 20 \, \text{mL} \) of oxalic acid (\( 2 \, \text{M} \)) in acidic medium. The molarity of \( \text{KMnO}_4 \) solution should be ______ \( \text{M} \).

A cyclist starts from the point P of a circular ground of radius 2 km and travels along its circumference to the point S. The displacement of a cyclist is :

The correct nomenclature for the following compound is:

An electric field \( \vec{E} = (2x \hat{i}) \, \text{N C}^{-1} \) exists in space. A cube of side \( 2 \, \text{m} \) is placed in the space as per the figure given below. The electric flux through the cube is __________ \( \text{N m}^2/\text{C} \).

An alternating current at any instant is given by \[ i = \left[ 6 + \sqrt{56} \sin\left(100 \pi t + \frac{\pi}{3}\right) \right] \, \text{A}.\] The RMS value of the current is ______ A.

Two moles a monoatomic gas is mixed with six moles of a diatomic gas. The molar specific heat of the mixture at constant volume is :

The deflection in a moving coil galvanometer falls from 25 divisions to 5 divisions when a shunt of \( 24 \, \Omega \) is applied. The resistance of the galvanometer coil will be:

\(3, a, b, c\) are in Ap and \(3, a-1, b+1, c+9\) are in GP. Then AM of \(a, b, c\) is

Let A= {2, 3, 6, 8, 9, 11} and B = {1, 4, 5, 10, 15} Let R be a relation on A × B define by (a, b)R(c, d) if and only if 3ad – 7bc is an even integer. Then the relation R is

If $A$ is a square matrix of order 3 such that \[ \det(A) = 3 \] and \[ \det(\text{adj}(-4 \, \text{adj}(-3 \, \text{adj}(3 \, \text{adj}((2A)^{-1}))))) = 2^{m^3 n}, \] then $m + 2n$ is equal to:

A body projected vertically upwards with a certain speed from the top of a tower reaches the ground in t1. If it is projected vertically downwards from the same point with the same speed, it reaches the ground in t2. Time required to reach the ground, if it is dropped from the top of the tower, is :

Each of three blocks \( P \), \( Q \), and \( R \) shown in the figure has a mass of 3 kg. Each of the wires \( A \) and \( B \) has a cross-sectional area of 0.005 cm\(^2\) and Young's modulus \( 2 \times 10^{11} \, \text{N} \, \text{m}^{-2} \). Neglecting friction, the longitudinal strain on wire \( B \) is \( \ldots \times 10^{-4} \). (Take \( g = 10 \, \text{m/s}^2 \))

A body of mass 50 kg is lifted to a height of 20 m from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases, will be:

Given below are two statements:
Statement I:

IUPAC name of Compound A is 4-chloro-1, 3-dinitrobenzene.
Statement II:

IUPAC name of Compound B is 4-ethyl-2-methylaniline.
In the light of the above statements, choose the most appropriate answer from the options given below:

If \[ S(x) = (1 + x) + 2(1 + x)^2 + 3(1 + x)^3 + \ldots + 60(1 + x)^{60}, \, x \neq 0, \] and \[ (60)^2 S(60) = a(b)^b + b, \] where $a, b \in \mathbb{N}$, then $(a + b)$ is equal to ________.

A ball is released from a height of \(1\) \(m\) on a fixed smooth hemispherical surface as shown. Find its velocity when it is at a height of \(0.5\) \(m\) from ground. (take \(g\) = \(10\;m / s^2\))

A 1 kg mass is suspended from the ceiling by a rope of length 4m. A horizontal force 'F' is applied at the mid point of the rope so that the rope makes an angle of 45° with respect to the vertical axis as shown in figure. The magnitude of F is