List of top Questions asked in JEE Main- 2022

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

Let a > 0, b > 0. Let e and l respectively be the eccentricity and length of the latus rectum of the hyperbola 
\(\frac{x^2}{a^2}−\frac{y^2}{b^2}=1\)
Let e′ and l′ respectively be the eccentricity and length of the latus rectum of its conjugate hyperbola. If 
\(e^2=\frac{11}{14}l\) and \((e^′)^2=\frac{11}{8}l^′\)
then the value of 77a + 44b is equal to :

Given below are two statements:
Statement I : According to the Ellingham diagram, any metal oxide with higher ΔG° is more stable than the one with lower ΔG°.
Statement II :The metal involved in the formation of oxide placed lower in the Ellingham diagram can reduce the oxide of a metal placed higher in the diagram.
In the light of the above statements, choose the most appropriate answer from the options given below

Let,
\(\vec{a}=a\hat{i}+2\hat{j}−\hat{k}\) and \(\vec{b}=−2\hat{i}+α\hat{j}+\hat{k}\)
, where α ∈ R. If the area of the parallelogram whose adjacent sides are represented by the vectors 
\(\vec{a}\) and \(\vec{b}\) is \(\sqrt{15(α^2+4)}\) , then the value of \(2|\vec{a}|^2+(\vec{a}⋅\vec{b})|\vec{b}|^2 \)
is equal to :

If vertex of a parabola is (2, –1) and the equation of its directrix is 4x – 3y = 21, then the length of its latus rectum is :
Consider the following reaction:
 \({2HSO_4^ −}_{(aq)}\xrightarrow[(2)Hydrolysis]{(1)Electrolysis}  2HSO_4^− + 2H^+ + A\)
The dihedral angle in product A in its solid phase at 110 K is :
Let the plane ax + by + cz = d pass through (2, 3, –5) and is perpendicular to the planes 2x + y – 5z = 10 and 3x + 5y – 7z = 12. If a, b, c, d are integers d > 0 and gcd (|a|, |b|, |c|, d) = 1, then the value of a + 7b + c + 20d is equal to :
The correct order of melting point is
The probability that a randomly chosen one-one function from the set {a, b, c, d} to the set {1, 2, 3, 4, 5} satisfies f(a) + 2f(b) – f(c) = f(d) is :

The value of 
\(\lim_{{n \to \infty}} 6\tan\left\{\sum_{{r=1}}^{n} \tan^{-1}\left(\frac{1}{{r^2+3r+3}}\right)\right\}\)
is equal to :

The correct order of melting points of hydrides of group 16 elements is:
A source of potential difference \(V\) is connected to the combination of two identical capacitors as shown in the figure. When key \(‘K’\) is closed, the total energy stored across the combination is \(E_1\). Now key \(‘K’\) is opened and dielectric of dielectric constant \(5\) is introduced between the plates of the capacitors. The total energy stored across the combination is now \(E_2\). The ratio \(\frac{E_1}{E_2}\) will be
A source of potential difference V is connected to the combination of two identical capacitors
Consider the following reaction: 
A + alkali → B (Major Product)
If B is an oxoacid of phosphorus with no P-H bond, then A is
Two concentric circular loops of radii \(r_1 = 30\) cm and \(r_2 = 50\) cm are placed in \(X–Y\) plane as shown in the figure. \(A\) current \(I = 7 \;A\) is flowing through them in the direction as shown in figure. The net magnetic moment of this system of two circular loops is approximately
Two concentric circular loops
A velocity selector consists of electric field \(\overrightarrow E=E\hat K\) and magnetic field \(\overrightarrow B=B\hat j\) with \(B = 12 \;mT\). The value of E required for an electron of energy \(728\) \(eV\) moving along the positive x-axis to pass undeflected is (Given, mass of electron = \(9.1 × 10^{–31}\) kg)
Polar stratospheric clouds facilitate the formation of:
Match List I with List II. 
 List-I List-II
A.
I.Br2 in CS2
B.
II.Na2CR2O7/H2SO4
C.
III.Zn
D.
IV.CHCl3/NaOH

Choose the correct answer from the options given below:
A thin circular ring of mass M and radius R is rotating with a constant angular velocity 2 rad s–1 in a horizontal plane about an axis vertical to its plane and passing through the center of the ring. If two objects each of mass m be attached gently to the opposite ends of a diameter of ring, the ring will then rotate with an angular velocity (in rad s–1)
If \(\overrightarrow A=(2\hat i+3\hat j−\hat k)m\) and \(\overrightarrow B=(\hat i+2\hat j+2\hat k)m\). The magnitude of component of vector \(\overrightarrow A\) along vector \(\overrightarrow B\) will be ______\(m\).
The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be_________m. Given the length of the rod is \(10\sqrt3\; m\).
In the given figure, the face AC of the equilateral prism is immersed in a liquid of refractive index ‘n‘. For incident angle 60° at the side AC the refracted light beam just grazes along face AC. The refractive index of the liquid n = \((\sqrt x)/4\). The value of \(x\) is _______.(Given refractive index of glass = \(1.5\))
the face AC of the equilateral prism is immersed in a liquid of refractive index ‘n‘.
Two lighter nuclei combine to from a comparatively heavier nucleus by the relation given below: \(^2_1X+^2_1X=^4_2Y\). The binding energies per nucleon for, \(^2_1X\) and \(^4_2Y\) are 1.1 MeV and 7.6 MeV respectively. The energy released in the process is ______ MeV.
A uniform heavy rod of mass \(20\) kg, cross sectional area \(0.4\) \(m^2\) and length \(20\) \(m\) is hanging from a fixed support. Neglecting the lateral contraction, the elongation in the rod due to its own weight is \(x × 10^{–9}\) \(m\). The value of \(x\) is _____(Given Young’s modulus \(Y = 2 × 10^{11} Nm^{–2}\)and g = \(10\; ms^{–2})\)
The typical transfer characteristics of a transistor in CE configuration is shown in figure. A load resistor of \(2\) \(kΩ\) is connected in the collector branch of the circuit used. The input resistance of the transistor is \(0.50\) \(kΩ\). The voltage gain of the transistor is ________.
The variation of acceleration due to gravity (g) with distance (r) from the center of the earth is correctly represented by
(Given R = radius of earth)