List of top Questions asked in JEE Main- 2022

A square aluminium (shear modulus is 25 × 10⁹ Nm^–2) slab of side 60 cm and thickness 15 cm is subjected to a shearing force (on its narrow face) of 18.0 × 10⁴ N. The lower edge is riveted to the floor. The displacement of the upper edge is ______μm.

For the hyperbola \(H: x^2 – y^2 = 1\) and the ellipse \(E:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,a>b>0\), let the
(1) eccentricity of E be reciprocal of the eccentricity of H, and
(2) the line \(y= \sqrt\frac{5}{2} x+k\) be a common tangent of E and H.
Then \(4(a^2 + b^2)\) is equal to _______.

The equations of the sides AB, BC and CA of a triangle ABC are 2x + y = 0, x + py = 15a and x – y = 3, respectively. If its orthocentre is
\((2, a),−\frac{1}{2}<a<2 \)
then p is equal to _______.

A class contains b boys and g girls. If the number of ways of selecting 3 boys and 2 girls from the class is 168, then b + 3g is equal to ______.

If \(z = 2 + 3i\), then \(z^5 + (\overline{z})^5\) is equal to:

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

is equal to _________.

Let the circumcentre of a triangle with vertices A(a, 3), B(b, 5) and C(a, b), ab > 0 be P(1, 1). If the line AP intersects the line BC at the point Q(k₁, k₂), then k₁ + k₂ is equal to :

If the equation of the parabola, whose vertex is at \((5, 4)\) and the directrix is \(3x + y – 29 = 0\), is \(x^2 + ay^2 + bxy + cx + dy + k = 0\), then \(a + b + c + d + k\) is equal to

If a₁ (> 0), a₂, a₃, a₄, a₅ are in a G.P., a₂ + a₄ = 2a₃ + 1 and 3a₂ + a₃ = 2a₄, then a₂ + a₄ + 2a₅ is equal to _______.

Let P and Q be any points on the curves (x – 1)² + (y + 1)² = 1 and y = x², respectively. The distance between P and Q is minimum for some value of the abscissa of P in the interval

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

Which of the following pair of molecules contain odd electron molecule and an expanded octet molecule?

Sodium light of wavelengths 650 nm and 655 nm is used to study diffraction at a single slit of aperture 0.5 mm. The distance between the slit and the screen is 2.0 m. The separation between the positions of the first maxima of diffraction pattern obtained in the two cases is _____ × 10^–5 m.

A singly ionized magnesium atom (A=24) ion is accelerated to kinetic energy 5keV and is projected perpendicularly into a magnetic field B of the magnitude 0.5 T. The radius of path formed will be ________ cm.

Let O be the origin and A be the point \(z_1 = 1 + 2i\). If B is the point \(z_2, Re(z_2) < 0\), such that OAB is a right angled isosceles triangle with OB as hypotenuse, then which of the following is NOT true?

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Energy of 2s orbital of hydrogen atom is greater than that of 2s orbital of lithium.
Reason R : Energies of the orbitals in the same subshell decrease with increase in the atomic number.
In the light of the above statements, choose the correct answer from the options given below.

A body of mass 8 kg and another of mass 2 kg are moving with equal kinetic energy. The ratio of their respective momenta will be

C(s)+O₂(g)→CO₂(g)+400 kJ
C(s)+\(\frac{1}{2}\) O₂(g)→CO(s)+100 kJ
When coal of purity 60% is allowed to burn in presence of insufficient oxygen, 60% of carbon is converted into ‘CO’ and the remaining is converted into ‘CO₂’. The heat generated when 0.6 kg of coal is burnt is _______.

\(y=tan^{-1}(sec \;x^3 - tan\; x^3), \frac{π}{2} < x^3< \frac{3π}{2},\) then

The value of the integral \(\begin{array}{l} \displaystyle\int\limits_0^{\frac{\pi}{2}}60\frac{\sin\left(6x\right)}{\sin x}dx \end{array}\) is equal to ______.

The Integral
\(\int \frac{(1 - \frac{1}{\sqrt{3}})(\cos x - \sin x)}{1 + \frac{2}{\sqrt{3}}\sin2 x} \,dx\)
is equal to

A copper block of mass 5.0 kg is heated to a temperature of 500°C and is placed on a large ice block. What is the maximum amount of ice that can melt?

[Specific heat of copper 0.39 J g^–1 °C^–1 and latent heat of fusion of water : 335 J g^–1]

A water drop of radius 1 cm is broken into 729 equal droplets. If surface tension of water is 75 dyne/cm, then the gain in surface energy upto first decimal place will be :
(Given \(\pi\) = 3.14)

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

List of top Questions asked in JEE Main- 2022

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