Practice Questions

Q64.A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after (1) 19 months (2) 20 months (3) 21 months (4) 18 months

Q65.The coefficient of x7 in the expansion of (1 −x −x2 + x3) 6 is (1) −132 (2) −144 (3) 132 (4) 144

Q66.If A = sin2 x + cos4 x, then for all real x (1) 13 16 ≤A ≤1 (2) 1 ≤A ≤2 (3) 3 4 ≤A ≤1316 (4) 43 ≤A ≤1 JEE Main 2011 JEE Main Previous Year Paper

Q68.The two circles x2 + y2 = ax and x2 + y2 = c2(c > 0) touch each other if (1) |a| = c (2) a = 2c (3) |a| = 2c (4) 2|a| = c

Q69.Equation of the ellipse whose axes are the axes of coordinates and which passes through the point (−3, 1) and has eccentricity is √25 (1) 5x2 + 3y2 −48 = 0 (2) 3x2 + 5y2 −15 = 0 (3) 5x2 + 3y2 −32 = 0 (4) 3x2 + 5y2 −32 = 0 Q70.$$ \lim _{x \rightarrow 2}\left(\frac{\sqrt{1-\cos \{2(x-2)\}}}{x-2}\right) (1) equals √2 (2) equals −√2 (3) equals 1 (4) does not exist √2

Q71.Consider the following statements P : Suman is brilliant Q : Suman is rich R : Suman is honest The negation of the statement "Suman is brilliant and dishonest if and only if Suman is rich" can be expressed as (1) ∼(Q ↔(P∧∼R)) (2) ∼Q ↔∼P ∧R (3) ∼(P∧∼R) ↔Q (4) ∼P ∧(Q ↔∼R)

Q73.Let R be the set of real numbers This question has Statement −1 and Statement −2. Of the four choices given after the statements, choose the one that best describes the two statements. Statement-1 : A = {(x, y) ∈R × R : y −x is an integer } is an equivalence relation on R. Statement-2 : B = {(x, y) ∈R × R : x = αy for some rational number α} is an equivalence relation on R. (1) Statement −1 is true, Statement −2 is true; (2) Statement −1 is true, Statement- 2 is false. Statement −2 is not a correct explanation for Statement −1 (3) Statement −1 is false, Statement −2 is true. (4) Statement −1 is true, Statement −2 is true; Statement −2 is a correct explanation for Statement −1 JEE Main 2011 JEE Main Previous Year Paper

Q74.Let A and B be two symmetric matrices of order 3 . This question has Statement −1 and Statement −2. Of the four choices given after the statements, choose the one that best describes the two statements. Statement −1 : A(BA) and (AB)A are symmetric matrices. Statement - 2 : AB is symmetric matrix if matrix multiplication of A and B is commutative. (1) Statement −1 is true, Statement −2 is true; (2) Statement −1 is true, Statement −2 is false. Statement −2 is not a correct explanation for Statement −1 (3) Statement −1 is false, Statement- 2 is true. (4) Statement −1 is true, Statement −2 is true; Statement −2 is a correct explanation for Statement −1

Q75.The number of values of k for which the linear equations 4x + ky + 2z = 0; kx + 4y + z = 0; 2x + 2y + z = 0 possess a non-zero solution is (1) 2 (2) 1 (3) zero (4) 3

Q78. d2x equals dy2 (1) d2y −1 dy −3 (2) d2y dy −2 −( dx2 ) ( dx ) ( dx2 )( dx ) (3) −( dx2d2y )( dxdy ) −3 (4) ( dx2d2y ) −1

Q79.The shortest distance between line y −x = 1 and curve x = y2 is (1) 3√2 (2) 8 8 3√2 (3) 4 (4) √3 √3 4 dx is

Q80.The value of ∫10 8 log(1+x)1+x2 (1) π 8 log 2 (2) π2 log 2 (3) log 2 (4) π log 2 tdt. Then f has

Q81.For x ∈(0, 5π2 ), define f(x) = ∫x0 √t sin (1) local minimum at π and 2π (2) local minimum at π and local maximum at 2π (3) local maximum at π and local minimum at 2π (4) local maximum at π and 2π

Q82.The area of the region enclosed by the curves y = x, x = e, y = x1 and the positive x-axis is JEE Main 2011 JEE Main Previous Year Paper (1) 1 square units (2) 3 square units 2 (3) 5 square units (4) 1 square units 2 2

Q87.If the angle between the line x = y−12 = 14 (√5 ) (1) 3 (2) 2 2 5 (3) 5 (4) 2 3 3

Q88.This question has Statement −1 and Statement −2. Of the four choices given after the statements, choose the one that best describes the two statements. Statement-1 : The point A(1, 0, 7) is the mirror image of the point B(1, 6, 3) in the line x1 = y−12 = z−23 . Statement-2 : The line: x1 = y−12 = z−23 bisects the line segment joining A(1, 0, 7) and B(1, 6, 3). (1) Statement −1 is true, Statement-2 is true; (2) Statement −1 is true, Statement −2 is false. Statement −2 is not a correct explanation for Statement −1 (3) Statement −1 is false, Statement −2 is true. (4) Statement −1 is true, Statement −2 is true; Statement −2 is a correct explanation for Statement −1

Q89.Consider 5 independent Bernoulli's trials each with probability of success p . If the probability of at least one failure is greater than or equal to 31 , then p lies in the interval 32 (1) ( 34 , 1112 ] (2) [0, 12 ] (3) ( 1112 , 1] (4) ( 12 , 34 ]

Q2. A particle is moving with velocity →v = K(y^i + x^j), where K is a constant. The general equation for its path is (1) y = x2+ constant (2) y2 = x+ constant (3) xy = constant (4) y2 = x2+ constant

Q3. A small particle of mass m is projected at an angle θ with the x-axis with an initial velocity v0 in the x −y plane as shown in the figure. At a time t < v0 sing θ , the angular momentum of the particle is where ^i,^j and ^k are unit vectors along x, y and z-axis respectively. (1) −mgv0 t2 cos θ^j (2) mgv0 t cos θ^k (3) −12 mgv0t2 cos θ^k (4) 21 mgv0t2 cos θ^i

Q4. Two fixed frictionless inclined plane making an angle 30∘ and 60∘ with the vertical are shown in the figure. Two block A and B are placed on the two planes. What is the relative vertical acceleration of A with respect to B ? (1) 4.9 ms−2 in horizontal direction (2) 9.8 ms−2 in vertical direction (3) zero (4) 4.9 ms−2 in vertical direction

Q5. The potential energy function for the force between two atoms in a diatomic molecule is approximately given by U(x) = a − b , where a and b are constants and x is the distance between the atoms. If the dissociation x12 x6 energy of the molecule is D = [U(x = ∞) −Uat equilbrium ], D is (1) b2 (2) b2 2a 12a (3) b2 (4) b2 4a 6a

Q6. Statement-1 : Two particles moving in the same direction do not lose all their energy in a completely inelastic collision. Statement-2 : Principle of conservation of momentum holds true for all kinds of collisions. Of the four choices given after the statements, choose the one that best describes the two statements. Of the four choices given after the statements, choose the one that best describes the two statements. JEE Main 2010 JEE Main Previous Year Paper (1) Statement-1 is true, Statement-2 is true; (2) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-2 is not the correct explanation of Statement-1. Statement1 (3) Statement-1 is false, Statement-2 is true. (4) Statement-1 is true, Statement-2 is false.

Q7. The figure shows the position - time (x −t) graph of one-dimensional motion of a body of mass 0.4 kg. The magnitude of each impulse is (1) 0.4Ns (2) 0.8Ns (3) 1.6Ns (4) 0.2Ns

Q8. A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of ' P ' is such that it sweeps out a length s = t3 + 5 , where s is in metres and t is in seconds. The radius of the path is 20 m. The acceleration of ' P ' when t = 2 s is nearly (1) 13 m/s2 (2) 12 m/s2 (3) 7.2 m/s2 (4) 14 m/s2

Q11.Two conductors have the same resistance at 0∘C but their temperature coefficients of resistance are α1 and α2 . The respective temperature coefficients of their series and parallel combinations are nearly (1) α1+α2 2 , α1 + α2 (2) α1 + α2, α1+α22 α1α2 (4) α1+α2 (3) α1 + α2, 2 , α1+α22 α1+α2