List of top Questions asked in JEE Main- 2022

An ellipse
$E:\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$
passes through the vertices of the hyperbola
$H:\frac{x^2}{49} - \frac{y^2}{64} = -1$
Let the major and minor axes of the ellipse E coincide with the transverse and conjugate axes of the hyperbola H, respectively. Let the product of the eccentricities of E and H be 1/2. If the length of the latus rectum of the ellipse E, then the value of 113l is equal to _____.

Let y = y(x) be the solution curve of the differential equation
$\sin(2x^2) \log_e(\tan(x^2)) \,dy + (4xy - 4\sqrt{2}x\sin(x^2 - \frac{\pi}{4})) \,dx = 0, \quad 0 < x < \sqrt{\frac{\pi}{2}}$
which passes through the point $(\sqrt{\frac{π}{6}},1)$. Then $|y(\sqrt{\frac{π}{3}})|$
is equal to _______.

An object of mass 1 kg is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be
[If, g = 10 ms^–2 and radius of earth = 6400 km]

1.80 g of solute A was dissolved in 62.5 cm³ of ethanol and freezing point of the solution was found to be 155.1 K. The molar mass of solute A is ____ g mol^–1.
[Given : Freezing point of ethanol is 156.0 K, Density of ethanol is 0.80 g cm^–3, Freezing point depression constant of ethanol is 2.00 K kg mol^–1]

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

If $\frac{1}{(20-a)(40-a)} + \frac{1}{(40-a)(60-a)} + \ldots + \frac{1}{(180-a)(200-a)} = \frac{1}{256}$, then the maximum value of a is :

Let
$f(x) = 2x^2 - x - 1\ and\ S = \{ n \in \mathbb{Z} : |f(n)| \leq 800 \}$
Then, the value of ∑_n∈S f(n) is equal to ________.

For the curve
$\begin{array}{l}C : \left(x^2 + y^2 – 3\right) + \left(x^2 – y^2 – 1\right)^5 = 0, \end{array}$

$\begin{array}{l}\text{the value of}\ 3y’ – y^3y”, \text{at the point}\end{array}$

$(α, α), α > 0$, on C is equal to ________.

For a cell, $Cu(s)|Cu^{2+}(0.001M)||Ag^+(0.01M)|Ag(s)$
the cell potential is found to be $0.43 V$ at $298 K$. The magnitude of standard electrode potential for $Cu^{2+}/{Cu}$ is ____ $× 10^{–2}$ V.
[Given: $E_{Ag^+/Ag^⊖}=0.80$ V and $\frac {2.303RT}{F}=0.06 V$]

Let S be the set containing all 3 × 3 matrices with entries from {-1, 0, 1}. The total number of matrices A ∈ S such that the sum of all the diagonal elements of A^TA is 6 is ________.

The torque of a force $5\^{i}+3\^{j}−7\^{k}$ about the origin is τ. If the force acts on a particle whose position vector is$ 2\^{i}+2\^{j}+\^{k}$, then the value of τ will be

If the length of the latus rectum of the ellipse x² + 4y² + 2x + 8y – λ = 0 is 4, and l is the length of its major axis, then λ + l is equal to ________.

Which of the following matrices can NOT be obtained from the matrix $\begin{bmatrix} -1 &2 \\ 1 & -1 \end{bmatrix}$ by a single elementary row operation?

Sum of oxidation state (magnitude) and coordination number of cobalt in $Na[Co(bpy)Cl_4]$ is____ .
(Given : bpy =

)

Let
$S = \left\{z∈C : z^2+\overline{z} = 0 \right\}$. Then $∑_{z∈S}(Re(z)+Im(z))$
is equal to____.

Consider the following sulphur based oxoacids.
$H_2SO_3,H_2SO_4,H_2S_2O_8 $and $H_2S_2O_7$
Amongst these oxoacids, the number of those with peroxo (O–O) bonds is_____.

Lithium nitrate and sodium nitrate, when heated separately, respectively, give :

As shown in the figure, a potentiometer wire of resistance 20 Ω and length 300 cm is connected with resistance box (R.B.) and a standard cell of emf 4 V. For a resistance ‘R‘ of resistance box introduced into the circuit, the null point for a cell of 20 mV is found to be 60 cm. The value of ‘R ‘ is Ω.

If the system of equations
$ x + y + z = 6 $,
$ 2x + 5y + \alpha z = \beta $,
$ x + 2y + 3z = 14 $
has infinitely many solutions, then $ \alpha + \beta $ is equal to:

In following pairs, the one in which both transition metal ions are colourless is :

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
$\begin{array}{l}f\left(x\right) = min \{\left[x – 1\right], \left[x – 2\right], …., \left[x – 10\right]\}\end{array}$
where [t] denotes the greatest integer ≤t. Then
$\begin{array}{l} \displaystyle\int\limits_{0}^{10}f\left(x\right)dx+\displaystyle\int\limits_{0}^{10}\left(f\left(x\right)\right)^2dx+\displaystyle\int\limits_{0}^{10}\left|f\left(x\right)\right|dx\end{array}$
is equal to ________.

The frequency of echo will be _______ Hz if the train blowing a whistle of frequency 320 Hz is moving with a velocity of 36 km/h towards a hill from which an echo is heard by the train driver. Velocity of sound in air is 330 m/s.

The diameter of an air bubble which was initially 2 mm, rises steadily through a solution of density 1750 kg m^–3at the rate of 0.35 cms^–1. The coefficient of viscosity of the solution is _______ poise (in nearest integer). (The density of air is negligible).

A block of mass ‘m’ (as shown in figure) moving with kinetic energy E compresses a spring through a distance 25 cm when its speed is halved. The value of spring constant of used spring will be nE Nm^–1 for n = _______.