List of top Questions asked in JEE Main

Let f(x) = min {1, 1 + x sin x}, 0 ≤ x ≤ 2π. If m is the number of points, where f is not differentiable, and n is the number of points, where f is not continuous, then the ordered pair (m, n) is equal to

Let $α, β$ be the roots of the equation $x^2-\sqrt{2}x+\sqrt{6}=0$ and$ \frac{1}{α^2}+1$,$\frac {1}{β^2}+1$ be the roots of the equation $x^2 + ax + b = 0$ . Then the roots of the equation $x^2 – (a + b – 2)x + (a + b + 2) = 0$ are

If the charge on a capacitor is increased by 2 C, the energy stored in it increases by 44%. The original charge on the capacitor is (in C)

Two electric dipoles of dipole moments 1.2 × 10^–30 C-m and 2.4 × 10^–30 C-m are placed in two different uniform electric fields of strength 5 × 10⁴ NC^–1 and 15 × 10⁴NC^–1 respectively. The ratio of maximum torque experienced by the electric dipoles will be 1:x. The value of x is _______

Let a function ƒ : N →N be defined by
$f(n) = \left\{ \begin{array}{ll} 2n & n = 2,4,6,8,\ldots \\ n - 1 & n = 3,7,11,15,\ldots \\ \frac{n+1}{2} & n = 1,5,9,13 \end{array} \right.$
then, ƒ is

If $f(x)=\begin{cases} x+a, & x \leq 0 \\ |x-4|, & x\gt0\end{cases}$ and
$g(x)= \begin{cases}x+1 & , x\lt0 \\ (x-4)^2+b, & x \geq 0\end{cases}$
are continuous on $R$, then $(gof) (2)+(fog)(-2)$ is equal to:

Let $\alpha, \beta$ and $\gamma$ be three positive real numbers Let $f ( x )=\alpha x ^5+\beta x ^3+\gamma x , x \in R$ and $g: R \rightarrow R$ be such that $g(f(x))=x$ for all $x \in R$ If $a_1, a_2, a_3, \ldots, a_n$ be in arithmetic progression with mean zero, then the value of $f\left(g\left(\frac{1}{n} \displaystyle\sum_{i=1}^n f\left(a_i\right)\right)\right)$is equal to :

A 1 m long wire is broken into two unequal parts X and Y. The X part of the wire is stretched into another wire W. Length of W is twice the length of X and the resistance of W is twice that of Y. Find the ratio of length of X and Y.

If O₂ gas is bubbled through water at 303 K, the number of millimoles of O₂ gas that dissolve in 1 litre of water is_______. (Nearest integer)
(Given : Henry’s Law constant for O₂ at 303 K is 46.82 k bar and partial pressure of O₂ = 0.920 bar)
(Assume solubility of O₂ in water is too small, nearly negligible)

Let A and B be two $3 × 3$ non-zero real matrices such that AB is a zero matrix. Then

1L aqueous solution of $H_2SO_4$ contains 0.02 m mol $H_2SO_4$. 50% of this solution is diluted with deionized water to give 1L solution (A). In solution (A), 0.01 m mol of $H_2SO_4$ are added. Total m mols of $H_2SO_4$ in the final solution is ______ $× 10^3$ m mols.

For k ∈ R, let the solution of the equation
$\cos\left(\sin^{-1}\left(x \cot\left(\tan^{-1}\left(\cos\left(\sin^{-1}\right)\right)\right)\right)\right) = k, \quad 0 < |x| < \frac{1}{\sqrt{2}}$
Inverse trigonometric functions take only principal values. If the solutions of the equation x² – bx – 5 = 0 are
$\frac{1}{α^2}+\frac{1}{β^2} $and $\frac{α}{β}$
, then b/k2 is equal to_____.

Consider the reaction
$4\text{HNO}_3(\text{l}) + 3\text{KCl}(\text{s}) \rightarrow \text{Cl}_2(\text{g}) + \text{NOCl}(\text{g}) + 2\text{H}_2\text{O}(\text{g}) + 3\text{KNO}_3(\text{s})$
The amount of HNO₃ required to produce 110.0 g of KNO₃ is
(Given : Atomic masses of H, O, N and K are 1, 16, 14 and 39 respectively.)

The correct order of melting points of hydrides of group 16 elements is:

A ball of mass m is thrown vertically upward. Another ball of mass 2 m is thrown at an angle θ with the vertical. Both the balls stay in air for the same period of time. The ratio of the heights attained by the two balls respectively is 1/x. The value of x is _______.

Statement-I: An alloy of lithium and magnesium is used to make aircraft plates.

Statement-II: The magnesium ions are important for cell-membrane integrity.

In the light of the above statements, choose the correct answer from the options given below:

Let the minimum value v₀ of
v = |z|²+|z-3|²+|z-6i|²,z∈C
is attained at z = z₀. Then
$|2z^2_0-\overline{z}^3_0+3|^2+v^2_0$
is equal to

Match List-I with List-II.

	List - I		List - II
A.	Moment of inertia of solid sphere of Radius R about any tangent	i.	$\frac{5}{3}MR^2$
B.	Moment of inertia of hollow sphere of radius (R) about any tangent	ii.	$\frac{7}{5}MR^2$
C.	Moment of inertia of circular ring of radius (R) about its diameter	iii.	$\frac{1}{4}MR^2$
D.	Moment of inertia of circular disc of radius (R) about any diameter	iv.	$\frac{1}{2}MR^2$

Choose the correct answer from the options given below.

A uniform electric field E = (8m/e) V/m is created between two parallel plates of length 1 m as shown in figure, (where m = mass of electron and e = charge of electron). An electron enters the field symmetrically between the plates with a speed of 2 m/s. The angle of the deviation (θ) of the path of the electron as it comes out of the field will be_______.

Considering the reaction sequence given below, the correct statement(s) is(are)

In the given reaction,

$ \begin{array}{l}X+Y+3Z\rightleftharpoons XYZ_3\end{array}$

if one mole of each of X and Y with 0.05 mol of Z gives compound XYZ₃. (Given : Atomic masses of X, Y and Z are 10, 20 and 30 amu, respectively.) the yield of XYZ₃ is _______ g. (Nearest integer)

Two vectors $\overrightarrow{A}+\overrightarrow{B}$ have equal magnitudes. If magnitude of $\overrightarrow{A}+\overrightarrow{B}$ is equal to two times the magnitude of $\overrightarrow{A}-\overrightarrow{B}$ then the angle between vec A and $\overrightarrow{B}$ will be

Boiling point of a 2% aqueous solution of a non-volatile solute A is equal to the boiling point of 8% aqueous solution of a non-volatile solute B. The relation between molecular weights of A and B is

Consider a cylindrical tank of radius $1 m$ is filled with water. The top surface of water is at $15 m$ from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of $5 m$ from the bottom. A force of $5 × 10^5 N$ is applied on the top surface of water using a piston. The speed of efflux from the hole will be:

(Given atmosphere pressure $P_A = 1.01 × 10^5 Pa$, density of water $ρ_w 1000 Kg/m^3$ and gravitational acceleration $g = 10 m/s^2$)

$\begin{array}{l}\displaystyle \lim_{ x\to 0}\left(\frac{(x+2\cos x)^3 + 2(x+2\cos x)^2 + 3 \sin(x+2\cos x)}{(x+2)^3+2(x+2)^2+3\sin(x+2)}\right)^{\frac{100}{x}} \end{array}$

is equal to _________.