Practice Questions

Q90.In an examination, there are 10 true-false type questions. Out of 10 , a student can guess the answer of 4 questions correctly with probability 3 4 and the remaining 6 questions correctly with probability 14 . If the JEE Main 2022 (24 Jun Shift 2) JEE Main Previous Year Paper probability that the student guesses the answers of exactly 8 questions correctly out of 10 is 27k , then k is 410 equal to JEE Main 2022 (24 Jun Shift 2) JEE Main Previous Year Paper

Q90.Let P1 :→r⋅(2ˆi + ˆj −3ˆk) (2, − 3, 2)(2, −2, −3) and (1, −4, 2). If the direction ratios of the line of intersection of P1 and P2 be 16 , α, β, then the value of α + β is equal to ______. JEE Main 2022 (29 Jun Shift 1) JEE Main Previous Year Paper

Q90.Let →a, b,→cbe three non-coplanar vectors such that →a× b = 4→c, b ×→c= 9→a and →c×→a = αb, α > 0 → If →a + b + →c = 36, then α is equal to _______. JEE Main 2022 (27 Jul Shift 2) JEE Main Previous Year Paper

Q90.Let →a = ˆi −2ˆj + 3ˆk, b = ˆi + ˆj + ˆk and →cbe a vector such that →a× ( +→c) =→0 equal to _______. JEE Main 2022 (29 Jun Shift 2) JEE Main Previous Year Paper

Q90.If the shortest distance between the lines→r= (−ˆi 3ˆk) λ(ˆi −aˆj) and →r (−ˆj 2ˆk) μ(ˆi −ˆj ˆk) is , then the integral value of a is equal to _____ √23 JEE Main 2022 (24 Jun Shift 1) JEE Main Previous Year Paper

Q90.Let S = (0, 2π) −{ π2 , 3π4 , 3π2 , 7π4 }. Let y = y(x), x ∈S , be the solution curve of the differential equation dy dx = 1+sin1 2x , y( π4 ) = 21 . If the sum of abscissas of all the points of intersection of the curve y = y(x) with the curve y = √2 sin x is kπ12 , then k is equal to _____. JEE Main 2022 (26 Jun Shift 1) JEE Main Previous Year Paper

Q90.Let Q and R be two points on the line x+1 2 = 3 = z−12 at a distance √26 from the point P(4, 2, 7). Then the square of the area of the triangle PQR is ________. JEE Main 2022 (26 Jul Shift 1) JEE Main Previous Year Paper

Q90.Let 𝑙1 be the line in 𝑥𝑦-plane with 𝑥 and 𝑦 intercepts 8 and 4√2 respectively, and 𝑙2 be the line in 𝑧𝑥-plane with 𝑥 and 𝑧 intercepts -1 and - 1 respectively. If 𝑑 is the shortest distance between the line 𝑙1 and 𝑙2, then 𝑑-2 8 6√3 is equal to _____. JEE Main 2022 (25 Jun Shift 2) JEE Main Previous Year Paper

Q90.If →a = 2ˆi + ˆj + 3ˆk, b = 3ˆi + 3ˆj + ˆk and →c= c1ˆi + c2ˆj + c3ˆk are coplanar vectors and →a⋅→c= 5, b ⊥→c, then 122(c1 + c2 + c3) is equal to ______. JEE Main 2022 (28 Jun Shift 1) JEE Main Previous Year Paper

Q90.Let the lines 𝐿1: →𝑟= 𝜆 ^𝑖+ 2 ^𝑗+ 3 ^𝑘, 𝜆∈𝑅 and 𝐿2: →𝑟= ^𝑖+ 3 ^𝑗+ ^𝑘+ 𝜇( ^𝑖+ ^𝑗+ 5 ^𝑘); 𝜇∈𝑅, intersect at the point 𝑆. If a plane 𝑎𝑥+ 𝑏𝑦- 𝑧+ 𝑑= 0 passes through 𝑆 and is parallel to the lines 𝐿1 and 𝐿2, then the value of JEE Main 2022 (25 Jun Shift 1) JEE Main Previous Year Paper 𝑎+ 𝑏+ 𝑑 is equal to ______. JEE Main 2022 (25 Jun Shift 1) JEE Main Previous Year Paper

Q90.Let 𝑃-2, - 1, 1 and 𝑄 17, 17, 17 be the vertices of the rhombus 𝑃𝑅𝑄𝑆. If the direction ratios of the diagonal 𝑅𝑆 are 𝛼, - 1, 𝛽, where both 𝛼 and $\beta$ are integers of minimum absolute values, then 𝛼2 + 𝛽2 is equal to JEE Main 2022 (28 Jul Shift 1) JEE Main Previous Year Paper

Q90.Let a line with direction ratios a, −4 a, −7 be perpendicular to the lines with direction ratios 3, −1, 2b and b, a, −2. If the point of intersection of the line x+1 = y−2 = 1z and the plane x −y + z = 0 is (α, β, γ), a2+b2 a2−b2 then α + β + γ is equal to ________. JEE Main 2022 (29 Jul Shift 1) JEE Main Previous Year Paper

Q90.Let y = y(x) be the solution of the differential equation dxdy = 4y3+2yx23xy2+x3 n ∈N, y(2) ∈[n −1, n), then n is equal to _______. JEE Main 2022 (25 Jul Shift 2) JEE Main Previous Year Paper

Q90.Let the mirror image of the point (a, b, c) with respect to the plane 3x −4y + 12z + 19 = 0 be (a −6, β, γ). If a + b + c = 5, then 7β −9γ is equal to ______. JEE Main 2022 (27 Jun Shift 1) JEE Main Previous Year Paper

Q1. The period of oscillation of a simple pendulum is T = 2π√Lg having a minimum division of 1 mm and time of one complete oscillation is 1. 95 s measured from stopwatch of 0. 01 s resolution. The percentage error in the determination of ′g′ will be: (1) 1. 03% (2) 1. 33% (3) 1. 30% (4) 1. 13%

Q1. Two vectors P and Q have equal magnitudes. If the magnitude of P + Q is n times the magnitude of P − Q, → → then angle between P and Q is (1) sin−1( n−1n+1 ) (2) cos−1( n+1n−1 ) (3) sin−1( n2−1n2+1 ) (4) cos−1( n2+1n2−1 )

Q1. If the length of the pendulum in pendulum clock increases by 0. 1% , then the error in time per day is: (1) 43. 2 s (2) 8. 64 s (3) 86. 4 s (4) 4. 32 s → → →

Q1. If e is the electronic charge, c is the speed of light in free space and h is Planck's constant, the quantity hc 4πε0 has dimensions of : (1) [MLT0] (2) [M0 L0 T0] (3) [MLT−1] (4) [LC−1]

Q1. In a typical combustion engine the workdone by a gas molecule is given by W = α2βe −βx2k T , where x is the displacement, k is the Boltzmann constant and T is the temperature. If α and β are constants, dimensions of α will be: (1) [MLT−2] (2) [M2 LT−2] (3) [MLT−1] (4) [M0 LT0]

Q1. A wire of 1 Ω has a length of 1 m. It is stretched till its length increases by 25%. The percentage change in resistance to the nearest integer is : (1) 12. 5% (2) 76% (3) 25% (4) 56%

Q1. Assertion A : If A, B, C, D are four points on a semi-circular arc with a centre at O such that −−−−−−−−−→ → → → → → → → → AB = BC = CD . Then, AB + AC + AD = 4AO + OB + OC −−−−−→ → → → → Reason R : Polygon law of vector addition yields AB + BC + CD + AD = 2AO In the light of the above statements, choose the most appropriate answer from the options given below. (1) A is correct but R is not correct. (2) A is not correct but R is correct. (3) Both A and R are correct and R is the correct (4) Both A and R are correct but R is not the correct explanation of A. explanation of A.

Q1. Match List- (I) with List- (II). List- (I) List- (II) a RH (Rydberg constant) i kg m−1 s−1 b h (Planck's constant) ii kg m2 s−1 c μB (Magnetic field energy density) iii m−1 d η (coefficient of viscosity) iv kg m−1 s−2 Choose the most appropriate answer from the options given below: (1) (a) -( iv ), (b )-( ii ), (c )-( i ), (d )-( iii) (2) (a) −(ii), (b) −(iii), (c) −(iv), (d) −(i) (3) (a) −(iii), (b) −(ii), (c) −(iv), (d) −(i) (4) (a) −(iii), (b) −(ii), (c) −(i), (d) −(iv)

Q1. Statement I: If three forces →𝐹1, →𝐹2 and →𝐹3 are represented by three sides of a triangle and →𝐹1 + →𝐹2 = - →𝐹3, then these three forces are concurrent forces and satisfy the condition for equilibrium. Statement II: A triangle made up of three forces →𝐹1, →𝐹2 and →𝐹3 as its sides were taken in the same order, satisfies the condition for translatory equilibrium. In the light of the above statements, choose the most appropriate answer from the options given below: (1) Both Statement I and Statement II are true. (2) Statement I is true but Statement II is false. (3) Both Statement I and Statement II are false. (4) Statement I is false but Statement II is true.

Q1. A physical quantity y is represented by the formula y = m2r−4 gxl−32 If the percentage errors found in y, m, r, l and g are 18, 1, 0. 5, 4 and p respectively, then find the value of x and p. (1) 5 and ±2 (2) 4 and ±3 (3) 16 3 and ± 23 (4) 8 and ±2

Q1. The work done by a gas molecule in an isolated system is given by, 𝑊= 𝛼𝛽2𝑒- 𝛼𝑘 𝑇, where 𝑥 is the displacement, 𝑘 is the Boltzmann constant and 𝑇 is the temperature. 𝛼 and 𝛽 are constants. Then the dimensions of 𝛽 will be: (1) M2 L T2 (2) ML2 T-2 (3) MLT-2 (4) M0 L T0