List of top Questions asked in JEE Main

In the arrangement shown in figure a₁, a₂, a₃ and a₄ are the accelerations of masses m₁, m₂, m₃ and m₄ respectively. Which of the following relation is true for this arrangement

Let S={z=x+iy:|z–1+i|≥|z|,|z|<2,|z+i|=|z–1|}.
Then the set of all values of x, for which w = 2x + iy ∈ S for some y ∈ R is

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 __________.

The number of points of intersection of $|z - (4 + 3i)| = 2$ and $|z| + |z - 4| = 6$, $z \in \mathbb{C}$, is

Let $S ={ (\begin{matrix} -1 & 0 \\ a & b \end{matrix}), a,b, ∈(1,2,3,.....100)}$ and
let $T_n = {A ∈ S : A^{n(n + 1)} = I}. $
Then the number of elements in $\bigcap_{n=1}^{100}$ $T_n $ is

The value of the integral
$\frac{48}{\pi^4} \int_{0}^{\pi}(\frac{3\pi x^2}{2} - x^3) \frac{ \sin(x)}{1 + \cos^2x} \, dx$
is equal to ________

What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of 5 times its mass? (Assume the collision to be head-on elastic collision)

Let A = {n∈N : H.C.F. (n, 45) = 1} and
Let B = {2k :k∈ {1, 2, …,100}}. Then the sum of all the elements of $A∩B$ is ___________

While performing a thermodynamics experiment, a student made the following observations.
HCl + NaOH $\rightarrow$ NaCl + H₂O; ΔH = – 57.3 kJ mol^–1
CH₃COOH + NaOH $\rightarrow$ CH₃COONa + H₂O; ΔH = –55.3 kJ mol^–1
The enthalpy of ionization of CH₃COOH, as calculated by the student, is ______ kJ mol^–1. [nearest integer]

At 600 K, 2 mol of NO are mixed with 1 mol of $O_2$.

$\begin{array}{l}2NO\left(g\right)+O_2\left(g\right)\rightleftharpoons 2NO_2\left(g\right)\end{array} $

The reaction occurring as above comes to equilibrium under a total pressure of 1 atm. Analysis of the system shows that 0.6 mol of oxygen are present at equilibrium. The equilibrium constant for the reaction is _______. (Nearest integer)

The number of matrices
$A=\begin{pmatrix} a & b \\ c & d \\ \end{pmatrix}$, where a,b,c,d ∈−1,0,1,2,3,…..,10
such that A = A^-1, is ______.

If the sum of solutions of the system of equations 2sin²θ – cos2θ = 0 and 2cos²θ + 3sinθ = 0 in the interval [0, 2π] is kπ, then k is equal to _______.

Let
$A = \{z \in \mathbb{C} : |\frac{z+1}{z-1}| < 1\}$
and
$B = \{z \in \mathbb{C} : \text{arg}(\frac{z-1}{z+1}) = \frac{2\pi}{3}\}$
Then $A∩B$ is :

0.01 M KMnO₄ solution was added to 20.0 mL of 0.05 M Mohr’s salt solution through a burette. The initial reading of 50 mL burette is zero. The volume of KMnO₄ solution left in burette after the end point is _____ml. [nearest integer]

In an experiment to find out the diameter of the wire using a screw gauge, the following observations were noted:
(A) Screw moves 0.5 mm on main scale in one complete rotation
(B) Total divisions on circular scale = 50
(C) Main scale reading is 2.5 mm
(D) 45^th division of circular scale is in the pitch line
(E) Instrument has 0.03 mm negative error
Then the diameter of wire is :

The number of functions f, from the set
$A = {x∈N: x^2-10x+9≤0} $to the set $B = {n62:n∈N}$
such that
$f(x)≤(x-3)^2+1$, for every $x∈A,$
is ______.

A gas (Molar mass = 280 g mol^–1) was burnt in excess O₂ in a constant volume calorimeter and during combustion the temperature of calorimeter increased from 298.0 K to 298.45 K. If the heat capacity of calorimeter is 2.5 kJ K^–1 and enthalpy of combustion of gas is 9 kJ mol^–1 then amount of gas burnt is __________g. (Nearest Integer).

Let
$\begin{array}{l} f\left(x\right)=3^{\left(x^2-2\right)^3+4},x\in \mathbb{R}.\end{array}$
Then which of the following statements are true?
P : x = 0 is a point of local minima of f
Q : x = √2 is a point of inflection of f
R : f ′ is increasing for x > √2

If two vectors P = $\hat{i} $+2m$\hat{j}$+m$\hat{k}$ & Q = 4$\hat{i}$-2$\hat{j}$+m$\hat{k}$ are perpendicular to each other, then the value of m will be:

A fighter jet is flying horizontally at a certain altitude with a speed of 200 ms^–1. When it passes directly overhead an anti-aircraft gun, a bullet is fired from the gun, at an angle θ with the horizontal, to hit the jet. If the bullet speed is 400 m/s, the value of θ will be ____°

If $\lim_{{x \to 0}} \frac{\alpha e^x + \beta e^{-x} + \gamma \sin x}{x \sin^2 x} = \frac{2}{3}$, where $\alpha, \beta, \gamma \in \mathbb{R}$ then which of the following is NOT correct?

A system of two blocks of masses m = 2 kg and M = 8 kg is placed on a smooth table as shown in the figure. The coefficient of static friction between two blocks is 0.5. The maximum horizontal force F that can be applied to the block of mass M so that the blocks move together will be

Let the abscissae of the two points P and Q on a circle be the roots of x² – 4x – 6 = 0 and the ordinates of P and Q be the roots of y² + 2y – 7 = 0. If PQ is a diameter of the circle x² + y² + 2ax + 2by + c = 0, then the value of (a + b – c) is

A radioactive element has a half life of 200 days. The percentage of original activity remaining after 83 days is ________. (Nearest integer) (Given : antilog 0.125 = 1.333, antilog 0.693 = 4.93)

Let $x_1, x_2, x_3, …, x_{20}$ be in geometric progression with $x_1 = 3$ and the common ratio 1/2. A new data is constructed replacing each $x_i $ by $(x_i – i)^2$. If $x̄$ is the mean of new data, then the greatest integer less than or equal to $x̄$ is _________