List of top Questions asked in JEE Main- 2022

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 \(NH_4Cl\) = \(53.5\) \(g\) \(mol^{–1}\))

If the line x – 1 = 0 is a directrix of the hyperbola kx² – y² = 6, then the hyperbola passes through the point

Let Q and R be two points on the line
\(\frac{x+1}{2}=\frac{y+2}{3}=\frac{z−1}{2}\) at a distance \(\sqrt{26}\)
from the point P(4, 2, 7). Then the square of the area of the triangle PQR is _______ .

Let f: ℝ → ℝ be defined as
\(f(x) = \left\{ \begin{array}{ll} [e^x] & x < 0 \\ [a e^x + [x-1]] & 0 \leq x < 1 \\ [b + [\sin(\pi x)]] & 1 \leq x < 2 \\ [[e^{-x}] - c] & x \geq 2 \\ \end{array} \right.\)
Where a, b, c ∈ ℝ and [t] denotes greatest integer less than or equal to t.
Then, which of the following statements is true?

A √(34) m long ladder weighing 10 kg leans on a frictionless wall. Its feet rest on the floor 3 m away from the wall as shown in the figure. If F_f and F_w are the reaction forces of the floor and the wall, then ratio of F_w/F_f will be:
(Use g = 10 m/s²)

A wire of length 30 cm, stretched between rigid supports, has it’s n^th and (n + 1)^th harmonics at 400 Hz and 450 Hz, respectively. If tension in the string is 2700 N, its linear mass density is _____ kg/m.

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).

A gaseous mixture of two substances A and B, under a total pressure of 0.8 atm is in equilibrium with an ideal liquid solution. The mole fraction of substance A is 0.5 in the vapour phase and 0.2 in the liquid phase. The vapour pressure of pure liquid A is ______ atm. (Nearest integer)

Let\( A(1, 1), B(-4, 3) \)and \(C(-2, -5)\) be vertices of a triangle ABC, P be a point on side BC, and \(Δ1\) and \(Δ2\) be the areas of triangles APB and ABC, respectively. If \(Δ1 : Δ2 = 4 : 7\), then the area enclosed by the lines AP, AC and the x-axis is

A uniform disc with mass M = 4 kg and radius R = 10 cm is mounted on a fixed horizontal axle as shown in figure.

A block with mass m = 2 kg hangs from a massless cord that is wrapped around the rim of the disc. During the fall of the block, the cord does not slip and there is no friction at the axle. The tension in the cord is _____ N. (Take g = 10 ms^–2)

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 :

Sand is being dropped from a stationary dropper at a rate of 0.5 kgs^–1 on a conveyor belt moving with a velocity of 5 ms^–l. The power needed to keep the belt moving with the same velocity will be

If
\(\sum_{k=1}^{10} \frac{k}{k^4 + k^2 + 1} = \frac{m}{n}\)
where m and n are co-prime, then m + n is equal to

In an isosceles triangle ABC, the vertex A is \((6, 1)\) and the equation of the base BC is \(2x + y = 4\). Let the point B lie on the line \(x + 3y = 7\). If \((α, β)\) is the centroid of ΔABC, then \(15(α + β)\) is equal to :

Let a triangle be bounded by the lines L₁ : 2x + 5y = 10; L₂ : –4x + 3y = 12 and the line L₃, which passes through the point P(2, 3), intersects L₂ at A and L₁ at B. If the point P divides the line-segment AB, internally in the ratio 1 : 3, then the area of the triangle is equal to

Water falls from a 40 m high dam at the rate of 9 × 10⁴ kg per hour. Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydro electric energy number of 100 W lamps, that can be lit, is :
(Take g = 10 ms^–2)

If z ≠ 0 be a complex number such that\(|z-\frac{1}{z}|=2\), then the maximum value of |z| is

2.4 g coal is burnt in a bomb calorimeter in excess of oxygen at 298 K and 1 atm pressure. The temperature of the calorimeter rises from 298 K to 300 K. The enthalpy change during the combustion of coal is –x kJ mol^–1. The value of x is ______.(Nearest integer)
(Given : Heat capacity of bomb calorimeter is 20.0 kJ K^–1. Assume coal to be pure carbon)

A body of mass 10 kg is projected at an angle of 45° with the horizontal. The trajectory of the body is observed to pass through a point (20, 10). If T is the time of flight, then its momentum vector, at time t = T/√2, is _________.
[Take g = 10m/s²]

If z² + z + 1 = 0,
\(z ∈ C\), then \(\left| \sum_{n=1}^{15} \left( z_n + (-1)^n \frac{1}{z_n} \right)^2 \right|\)
is equal to ________.

Let M and N be the number of points on the curve y⁵ – 9xy + 2x = 0, where the tangents to the curve are parallel to x-axis and y-axis, respectively. Then the value of M + N equals ________.

When 600 mL of 0.2 M HNO₃ is mixed with 400 mL of 0.1 M NaOH solution in a flask, the rise in temperature of the flask is ________ × 10^–2°C.
(Enthalpy of neutralisation = 57 kJ mol^–1 and Specific heat of water = 4.2 JK^–1 g^–1)
(Neglect heat capacity of flask)

If the length of a wire is made double and radius is halved of its respective values. Then, the Young’s modulus of the material of the wire will :

An AC source is connected to an inductance of 100 mH, a capacitance of 100 μF and a resistance of 120 Ω as shown in the figure. The time in which the resistance having a thermal capacity 2 J/°C will get heated by 16°C is ___ s.

The value of the integral \(∫^{ \frac{π}{2}}_{ \frac{-π}{2}} \frac{dx}{(1+e^x)(sin^6x+cos^6x)}\) is equal to

List of top Questions asked in JEE Main- 2022

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