JEE Main 2022 July 28 Shift 2 Question Paper is available here with solutions PDF and detailed solutions for every question. NTA conducted the second shift on July 28, 2022, from 3:00 PM to 6:00 PM. The JEE Main 2022 Paper 1 (B.E./B.Tech) question paper includes the following:
90 questions in a 3-hour CBT Mode: 30 each from Mathematics, Physics and Chemistry (75 to be attempted)
Section A: 20 multiple choice questions (MCQs) per subject, all compulsory, 4 marks each
Section B: 10 numerical value questions per subject, any 5 to be attempted, 4 marks each
Marking: +4 for a correct answer, -1 for an incorrect answer, 0 for an unattempted question
Maximum marks: 300 (100 per subject)
JEE Main 2022 July 28 Shift 2 Question Paper with Solution PDF
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
The sum of the absolute maximum and absolute minimum values of the function \(\begin{array}{l} f\left(x\right)=\tan^{-1}\left(\sin x-\cos x\right) \end{array}\)in the interval\( [0, π]\) is
Let the hyperbola \(H: \frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) pass through (\(2\sqrt2,-2\sqrt2\) ). A parabola is drawn whose focus is same as the focus of H with positive abscissa and the directrix of the parabola passes through the other focus of H. If the length of the latus rectum of the parabola is e times the length of the latus rectum of H, where e is the eccentricity of H, then which of the following points lies on the parabola?
Let S be the set of all a∈ R for which the angle between the vectors\( \begin{array}{l} \overrightarrow{u}=a\left(\text{log}_e b\right)\hat{i}-6\hat{j}+3\hat{k}\end{array}\) and \(\begin{array}{l} \overrightarrow{v}=\left(\text{log}_e b\right)\hat{i}+2\hat{j}+2a\left(\text{log}_e b\right)\hat{k},\left(b>1\right)\end{array}\) is acute. Then S is equal to
Let the lines\( \begin{array}{l} \frac{x-1}{\lambda}=\frac{y-2}{1}=\frac{z-3}{2}\ \text{and}\ \frac{x+26}{-2}=\frac{y+18}{3}=\frac{z+28}{\lambda}\end{array}\)be coplanar and P be the plane containing these two lines. Then which of the following points does NOT lie on P?
A plane P is parallel to two lines whose direction rations are –2, 1, –3 and –1, 2, –2 and it contains the point (2, 2, –2). Let P intersect the co-ordinate axes at the points A, B, C making the intercepts α, β, γ. If V is the volume of the tetrahedron OABC, where O is the origin and p = α + β + γ, then the ordered pair (V, p) is equal to :
A horizontal park is in the shape of a triangle OAB with AB = 16. A vertical lamp post OP is erected at the point O such that\( \begin{array}{l}\angle PAO = \angle PBO = 15^\circ ~\text{and}~ \angle PCO = 45^\circ,\end{array}\)where C is the midpoint of AB. Then (OP)2 is equal to
Let the coefficients of the middle terms in the expansion of\(\begin{array}{l} \left(\dfrac{1}{\sqrt 6}+ \beta x\right)^4, \left(1 – 3\beta x\right)^2 \text{and}\left(1 – \dfrac{\beta}{2}x\right )^6, \beta > 0,\end{array}\)respectively form the first three terms of an A.P. If d is the common difference of this A.P., then \(\begin{array}{l} 50-\frac{2d}{\beta^2} \end{array}\)is equal to _______.
A bag contains 4 white and 6 black balls. Three balls are drawn at random from the bag. Let X be the number of white balls, among the drawn balls. If \(σ^2 \) is the variance of X, then 100 σ2 is equal to ____.
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 ______.
If\(\begin{array}{l}1 + \left(2 + ^{49}C_1 + ^{49}C_2 + … ^{49}C_{49}\right) \left(^{50}C_2 + ^{50}C_4 + … ^{50}C_{50}\right) \end{array}\)is equal to 2n. m, where m is odd, then n + m is equal to ______.
Two tangent lines l1 and l2 are drawn from the point (2, 0) to the parabola 2y2 = – x. If the lines l1 and l2 are also tangent to the circle (x – 5)2 + y2 = r, then 17r is equal to _________.
If \(\begin{array}{l} \frac{6}{3^{12}}+\frac{10}{3^{11}}+\frac{20}{3^{10}}+\frac{40}{3^9}+\cdots +\frac{10240}{3}=2^n\cdot m, \end{array}\)where m is odd, then m⋅n is equal to ________.
Let \(\begin{array}{l} S=\left[-\pi, \frac{\pi}{2}\right)-\left[-\frac{\pi}{2},-\frac{\pi}{4},-\frac{3\pi}{4},\frac{\pi}{4}\right].\end{array}\)Then the number of elements in the set \(\begin{array}{l} A=\left\{\theta\in S:\tan\theta\left(1+\sqrt{5}\tan\left(2\theta\right)\right)=\sqrt{5}-\tan\left(2\theta\right) \right\} \end{array}\)is ________.
Consider the efficiency of Carnot's engine is given by \(η=\frac {αβ}{sinθ}log_e\frac {βx}{kT}\), where \(α\) and \(β\) are constants. If \(T\) is temperature, \(k\) is Boltzman constant, \(θ\) is angular displacement and \(x\) has the dimensions of length. Then, choose the incorrect option.
(1) Dimensions of \(β\) is same as that of force.
(2) Dimension of \(α^{-1}x\) is same as that of energy.
(3) Dimension of \(η^{-1} sinθ\) is same as that of \(αβ\).
At time t = 0 a particle starts travelling from a height \(7\hat z cm\) in a plane keeping \(z\) coordinate constant. At any instant time it's position along the \(x\) and \(y\) directions are defined as \(3t\) and \(5t^3\) respectively. At \(t = 1s\) acceleration of the particle will be
A pressure-pump has a horizontal tube of cross sectional area \(10 cm^2 \) for the outflow of water at a speed of \(20 m/s\). The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, is
A uniform metal chain of mass m and length ‘\(L\)’ passes over a massless and frictionless pully. It is released from rest with a part of its length ‘\(l\)’ is hanging on one side and rest of its length '\(L – l\)' is hanging on the other side of the pully. At a certain point of time, when \(l = L/x\), the acceleration of the chain is \(g/2\). The value of \(x\) is ______.
A bullet of mass \(200 g\) having initial kinetic energy \(90 J\) is shot inside a long swimming pool as shown in the figure. If it’s kinetic energy reduces to \(40 J\) within \(1 s\), the minimum length of the pool, the bullet has to travel so that it completely comes to rest is
Assume there are two identical simple pendulum. Clock -1 is placed on the earth and Clock-2 is placed on a space station located at a height \(h\) above the earth surface. Clock-1 and Clock-2 operate at time periods \(4s\) and \(6s\) respectively. Then the value of \(h\) is -
(consider radius of earth \(R_E = 6400 km\) and \(g\) on earth \(10 m/s^2\) )
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 \(g = 10 m/s^2\))
A vessel contains \(14 g\) of nitrogen gas at a temperature of \(27°C\). The amount of heat to be transferred to the gas to double the r.m.s speed of its molecules will be:
A slab of dielectric constant K has the same cross-sectional area as the plates of a parallel plate capacitor and thickness (3/4)d, where d is the separation of the plates. The capacitance of the capacitor when the slab is inserted between the plates will be:
(Given \(C_0\) = capacitance of capacitor with air as medium between plates.)
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_______.
Statement I : A uniform wire of resistance 80 Ω is cut into four equal parts. These parts are now connected in parallel. The equivalent resistance of the combination will be 5 Ω.
Statement II : Two resistances 2R and 3R are connected in parallel in a electric circuit. The value of thermal energy developed in 3R and 2R will be in the ratio 3 : 2.
In the light of the above statements, choose the most appropriate answer from the option given below.
(1) Both statement I and statement II are correct
(2) Both statement I and statement II are incorrect
(3) Statement I is correct but statement II is incorrect
(4) Statement I is incorrect but statement II is correct
A triangular shaped wire carrying 10 A current is placed in a uniform magnetic field of 0.5 T, as shown in figure. The magnetic force on segment CD is (Given BC = CD = BD = 5 cm).
The magnetic field at the center of current carrying circular loop is \(B_1\). The magnetic field at a distance of √3 times radius of the given circular loop from the center on its axis is \(B_2\). The value of \(B_1/B_2\) will be
A transformer operating at primary voltage 8 kV and secondary voltage 160 V serves a load of 80 kW. Assuming the transformer to be ideal with purely resistive load and working on unity power factor, the loads in the primary and secondary circuit would be
Sun light falls normally on a surface of area \(36 cm^2\) and exerts an average force of \(7.2 × 10^{–9} N\) within a time period of \(20 minutes\). Considering a case of complete absorption, the energy flux of incident light is
The power of a lens (biconvex) is \(1.25 m^{–1}\) in particular medium. Refractive index of the lens is \(1.5\), and the radii of curvature are \(20 cm\) and \(40 cm\), respectively. The refractive index of surrounding medium
Two streams of photons, possessing energies equal to five and ten times the work function of metal are incident on the metal surface successively. The ratio of maximum velocities of the photoelectron emitted, in the two cases respectively, will be
A ball is thrown vertically upwards with a velocity of \(19.6 ms^{–1}\) from the top of a tower. The ball strikes the ground after \(6 s\). The height from the ground up to which the ball can rise will be \((k/5) m\). The value of k is ______ (use \(g = 9.8 m/s^2\))
The distance of centre of mass from end \(A\) of a one dimensional rod (\(AB\)) having mass density \(ρ=ρ_0(1-\frac{x^2}{L^2})kg/m\) and length L. (in meter) is \(\frac{3L}{α} m\). The value of \(α\) is......... (where \(x\) is the distance form end \(A\))
A string of area of cross-section \(4mm^2\) and length \(0.5 m\) is connected with a rigid body of mass \(2 kg\). The body is rotated in a vertical circular path of radius \(0.5 m\). The body acquires a speed of \(5 m/s\) at the bottom of the circular path. Strain produced in the string when the body is at the bottom of the circle is ______\(×10^{–5}\).
(use young’s modulus \(10^{11} N/m^2\) and \(g = 10 m/s^2\))
At a certain temperature, the degrees of freedom per molecule for gas is 8. The gas performs 150 J of work when it expands under constant pressure. The amount of heat absorbed by the gas will be ______ J.
The potential energy of a particle of mass \(4 kg\) in motion along the x-axis is given by \(U = 4(1- cos 4x) J\). The time period of the particle for small oscillation \((sin θ ≃ θ)\) is \((\frac{π}{K})\) s. The value of \(K\) is ..........
An electrical bulb rated 220 V, 100 W, is connected in series with another bulb rated 220 V, 60 W. If the voltage across combination is 220 V, the power consumed by the 100 W bulb will be about ____ W.
An object O is placed at a distance of 100 cm in front of a concave mirror of radius of curvature 200 cm as shown in the figure. The object starts moving towards the mirror at a speed 2 cm/s. The position of the image from the mirror after 10 s will be at ____ cm.
In an experiment with a convex lens, the plot of the image distance (ν′) against the object distance (μ′) measured from the focus gives a curve ν′μ′ = 225. If all the distances are measured in cm. The magnitude of the focal length of the lens is _______ cm.
In an experiment to find acceleration due to gravity (g) using simple pendulum, time period of 0.5 s is measured from time of 100 oscillations with a watch of 1 s resolution. If measured value of length is 10 cm known to 1 mm accuracy, the accuracy in the determination of g is found to be x %. The value of x is _________ .
2 L of 0.2 M \(H_2SO_4\) is reacted with 2 L of 0.1 M NaOH solution, the molarity of the resulting product \(Na_2SO_4\) in the solution is _______ millimolar. (Nearest integer)
If the wavelength for an electron emitted from H-atom is 3.3 × 10–10 m, then energy absorbed by the electron in its ground state compared to minimum energy required for its escape from the atom, is ______ times. (Nearest integer)
\(\begin{array}{l}\left[\text{Given} : h = 6.626 \times 10^{-34}~ \text{J s}\right]\\ \left[\text{Mass of electron} = 9.1 \times 10^{-31} ~\text{kg}\right]\end{array}\)
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)
The reaction occurring as above comes to equilibrium under a total pressure of 1 atm. Analysis of the system shows that 0.6 mol of oxygen are present at equilibrium. The equilibrium constant for the reaction is _______. (Nearest integer)
A sample of 0.125 g of an organic compound when analysed by Duma’s method yields 22.78 mL of nitrogen gas collected over KOH solution at 280 K and 759 mm Hg. The percentage of nitrogen in the given organic compound is____.(Nearest integer)
Given : 1. The vapour pressure of water of 280 K is 14.2 mm Hg.
On reaction with stronger oxidizing agent like KIO4, hydrogen peroxide oxidizes with the evolution of O2. The oxidation number of I in KIO4 changes to____.
Multiple Choice Questions (MCQs) + Numerical Value Questions
Subjects
Mathematics, Physics, Chemistry
Total Questions
90 questions (75 to be attempted)
Total Marks
300 marks
Marking Scheme
+4 for correct answer & -1 for incorrect MCQ and Numerical Value-based Questions
JEE Main 2022 July 28 Shift 2 Difficulty Level
The question paper was reported moderate in difficulty level. Students found Mathematics section as difficulty and lengthy, Physics as moderate and Chemistry easy. Check JEE Main 2022 July 28 Shift 2 Paper Analysis
JEE Main 2022 July 28 Shift 2 Subject-wise Memory-Based Solutions PDF
JEE Main 2022 Phase 2 Question Papers with Solution PDFs
Candidates can also check shift-wise JEE Main 2022 Phase 2 Question Papers with Solution PDFs. These shift-wise question paper PDFs for JEE Main 2022 will help candidates know the overall difficulty, topics with the highest weightage and the type of questions asked in the exam.
JEE Main 2022 Phase 1 Question Papers with Solution PDFs
Shift-wise JEE Main 2022 Phase 1 Question Papers with Solution PDFs are also available. Candidates preparing for Phase 2 of the exam can check and download JEE Main Question Paper PDFs to practice and test their exam prep level.
The solubility product constants of \(Ag_2CrO_4\) and \(AgBr\) are \(32x\) and \(4y\) respectively at 298 K. The value of}
\[
\left(\frac{\text{molarity of } Ag_2CrO_4}{\text{molarity of } AgBr}\right)
\]
can be expressed as:
Let $a_1,a_2,a_3,a_4$ be an A.P. of four terms such that each term of the A.P. and its common difference are integers. If $a_1+a_2+a_3+a_4=48$ and $a_1^2a_2a_3a_4+1^4=361$, then the largest term of the A.P. is equal to
Let $P=[p_{ij}]$ and $Q=[q_{ij}]$ be two square matrices of order $3$ such that
$q_{ij}=2^{(i+j-1)}p_{ij}$ and $\det(Q)=2^{10}$. Then the value of $\det(\operatorname{adj}(\operatorname{adj} P))$ is
The sum of all possible values of \( \theta \in [0,2\pi] \), for which the system of equations :
\[
x\cos3\theta - 8y - 12z = 0
\]
\[
x\cos2\theta + 3y + 3z = 0
\]
\[
x + y + 3z = 0
\]
has a non-trivial solution, is equal to :
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