Practice Questions

Q70.In a game two players A and B take turns in throwing a pair of fair dice starting with player A and total of scores on the two dice, in each throw is noted. A wins the game if he throws a total of 6 before B throws a total of 7 and B wins the game if he throws a total of 7 before A throws a total of six. The game stops as soon as either of the players wins. The probability of A winning the game is : (1) 5 (2) 31 31 61 (3) 5 (4) 30 6 61

Q71.The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the hill is found to be 45°. After walking a distance of 80 meters towards the top, up a slope inclined at angle of 30° to the horizontal plane the angle of elevation of the top of the hill becomes 75°. Then the height of the hill (in meters) is _____.

Q72.Let A = {a, b, c} and B = {1, 2, 3, 4}. Then the number of elements in the set C = {f : A →B ∣2 ∈f(A) and f is not one-one } is …

Q72.If Cr ≡25Cr and C0 + 5 ∙C1 + 9 ∙C2 + … + (101) ∙C25 = 225 ∙k, then k is equal to ____________.

Q73.If y = ∑6k=1 k cos−1{ 53 cos kx −45 sin kx} then dxdy at x = 0 is

Q73. sin( x1 ) + 5x2 , x < 0 ⎧ x5 Let f : R →R be defined as f(x) = 0 , x = 0 . The value of λ for which f ′′(0) exists, ⎨ 1 ) + λx2 , x > 0 ⎩x5 cos( x is___.

Q73.Suppose a differentiable function f(x) satisfies the identity f(x + y) = f(x) + f(y) + xy2 + x2y, for all real x and y. If lim f(x)x = 1, then f ′(3) is equal to : x→0

Q73.If the variance of the following frequency distribution: JEE Main 2020 (04 Sep Shift 2) JEE Main Previous Year Paper Class: 10 −20 20 −30 30 −40 Frequency: 2 x 2 is 50, then x is equal to _______

Q74.Let f(x) = x ⋅[ x2 ], for −10 < x < 10, where [t] denotes the greatest integer function. Then the number of points of discontinuity of f(x) is equal to

Q74.Let a line y = mx(m > 0), intersect the parabola, y2 = x, at a point P, other than the origin. Let the tangent to it a P , meet the x-axis at the point Q. If area (ΔOPQ) = 4 square unit, then m is equal to

Q74.Let {x} and [x] denote the fractional part of x and the greatest integer ≤x respectively of a real number x. if n > 1) are three consecutive terms of a G.P. then n is equal ∫n0 {x}dx, ∫n0 [x]dx and 10(n2 −n), (n ∈N, to__ 2 2 2 , is equal to : + ˆj × × + ˆk × ×

Q74.The number of all 3 × 3 matrices A, with entries from the set {−1, 0, 1} such that the sum of the diagonal elements of AAT is 3, is ___________.

Q74.Let [t] denote the greatest integer less than or equal to t. Then the value of ∫21 |2x −[3x]|dx is

Q74.If the vectors, p = (a + 1)ˆi + aˆj + aˆk,→q = aˆi + (a + 1)ˆj + aˆk and →r= aˆi + aˆj + (a + 1)ˆk(a ∈R) are 2 2 coplanar and q = 0 , then the value of λ is ________ 3(→p.→q) −λ→r×→

Q75.Let a plane P contain two lines →r= ˆi + λ(ˆi ˆj), λ ∈R and→r= −ˆj + μ(ˆj −ˆk), the foot of the perpendicular drawn from the point M(1, 0, 1) to P, then 3(α + β + γ) equals ....... JEE Main 2020 (03 Sep Shift 2) JEE Main Previous Year Paper

Q75.In a bombing attack, there is 50% chance that a bomb will hit the target. At least two independent hits are required to destroy the target completely. Then the minimum number of bombs, that must be dropped to ensure that there is at least 99% chance of completely destroying the target, is . . . . . JEE Main 2020 (05 Sep Shift 2) JEE Main Previous Year Paper

Q75.Let f(x), be a polynomial of degree 3 , such that f(−1) = 10, f(1) = −6, f(x), has a critical point at x = −1 and f′(x), has a critical point at x = 1. Then f(x), has local minima at x = JEE Main 2020 (08 Jan Shift 2) JEE Main Previous Year Paper

Q75.Let S be the set of points where the function , f(x) = |2 −|x −3|, x ∈R, is not differentiable. Then ∑x∈S f(f(x)) is equal to JEE Main 2020 (07 Jan Shift 1) JEE Main Previous Year Paper

Q75.If the distance between the plane, 23x −10y −2z + 48 = 0 and the plane containing the lines x+1 2 = y−34 = z+13 and x+32 = y+26 = z−1λ (λ ∈R) is equal to √633k , then k is equal to ____________. JEE Main 2020 (09 Jan Shift 2) JEE Main Previous Year Paper

Q1. Let L, R, C and V represent inductance, resistance, capacitance and voltage, respectively. The dimension of L in SI units will be: RCV (1) [LTA] (2) [A−1] (3) [LT 2] (4) [LA−2]

Q2. A ball is thrown upward with an initial velocity V0 from the surface of the earth. The motion of the ball is affected by a drag force equal to mγv2 (where m is mass of the ball, v is its instantaneous velocity and γ is a constant). Time taken by the ball to rise to its zenith is: (1) 1 (2) 1 g √γg ln(1 + √γg V0) √γg tan−1(√γ V0) (3) 1 (4) 1 g g √γg sin−1(√γ V0) √2γg tan−1(√2γ V0)

Q3. A body is projected at t = 0 with a velocity 10 ms−1 at an angle of 60∘ with the horizontal. The radius of curvature of its trajectory at t = 1 s is R. Neglecting air resistance and taking acceleration due to gravity g = 10 ms−2 , the value of R is: (1) 10.3 m (2) 2.8 m (3) 2.5 m (4) 5.1 m

Q3. A simple pendulum, made of a string of length l and a bob of mass m, is released from a small angle θ0. It strikes a block of mass M, kept on horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle θ1. Then M is given by: (1) m( θ0−θ1θ0+θ1 ) (2) m( θ0−θ1θ0+θ1 ) (3) m θ0+θ1 (4) m θ0−θ1 2 ( θ0−θ1 ) 2 ( θ0+θ1 )

Q3. In a car race on straight road, car A takes a time t less than car B at the finish and passes finishing point with a speed v more than that of car B. Both the cars start from rest and travel with constant acceleration a1 and a2 respectively. Then v is equal to: (1) 2a1a2 t (2) a1+a2 t a1+a2 2 (3) √a1a2t (4) √2a1a2t

Q4. A body of mass 1 kg falls freely from a height of 100 m, on a platform of mass 3 kg which is mounted on a spring having spring constant k = 1.25 × 106 N/m. The bodysticks to the platform and the spring's maximum compression is found to be x. Given that g = 10 ms−2, the value of x will be close to : (1) 40 cm (2) 4 cm (3) 80 cm (4) 8 cm −−−Q5. → → → A slab is subjected to two forces F1 and F2 of same magnitude F as shown in the figure. Force F2 is in XY- plane while force F1 acts along z -axis at the point (2→i + 3→j). The moment of these forces about point O will be: (1) (3^i −2^j + 3^k) F (2) (3^i −2^j −3^k)F (3) (3^i + 2^j −3^k)F (4) (3^i + 2^j + 3^k)F