Practice Questions

Q86.Let y = y(x) be the solution of the differential equation dxdy + 2y = f(x), where x ∈[0, 1] f(x) = {1,0, otherwise If y(0) = 0, then y ( 23 ) is (1) e2−1 (2) e2−1 2e3 e3 (3) 1 (4) e2+1 2e 2e4 →

Q86.Let →a = ˆi + ˆj + ˆk, →c= ˆj −ˆk and a vector b be such that →a× b =→cand →a⋅ b = 3. Then b equals (1) 11 (2) 11 3 √3 (3) √113 (4) √113

Q86.Let y = y(x) be the solution of the differential equation sin x dxdy + y cos x = 4x, x ∈(0, π). If y( π2 ) = 0, then y( π6 ) is equal to (1) −49 π2 (2) 9√34 π2 (3) −8 π2 (4) −89 π2 9√3 → → →

Q86.Let y = y(x) be the solution of the differential equation dx {1,0, otherwisex ∈[0, 1] y(0) = 0, then y ( 23 ) is JEE Main 2018 (15 Apr) JEE Main Previous Year Paper (1) e2−1 (2) 1 e3 2e (3) e2+1 (4) e2−1 2e4 2e3 → →

Q86.The curve satisfying the differential equation, (x2 −y2)dx + 2xydy = 0 and passing through the point (1, 1) is (1) a circle of radius two (2) a circle of radius one (3) a hyperbola (4) an ellipse

Q87.If →a,→b, and→care unit vectors such that →a + 2→b + 2→c = 0 , then |→a ×→c| is equal to (1) 1 (2) √15 4 4 (3) 15 (4) √15 16 16

Q87.The sum of the intercepts on the coordinate axes of the plane passing through the point (–2, –2, 2) and containing the line joining the points (1, –1, 2) and (1, 1, 1) is JEE Main 2018 (16 Apr Online) JEE Main Previous Year Paper (1) 4 (2) 12 (3) −8 (4) −4

Q87.If →a, b, →care unit vectors such that →a+ 2 b + 2→c=→0, then →a×→c is equal to : (1) 1 (2) 15 4 16 (3) √15 (4) √15 4 16

Q87.If the position vectors of the vertices A, B and C of a △ABC are respectively 4^i + 7^j + 8^k, 2^i + 3^j + 4^k and 2^i + 5^j + 7^k , then the position vector of the point, where the bisector of ∠A meets BC is (1) 1 2 (4^i + 8^j + 11^k) (2) 13 (6^i + 13^j + 18^k) (3) 1 4 (8^i + 14^j + 9^k) (4) 13 (6^i + 11^j + 15^k)

Q87.Let u be a vector coplanar with the vectors →a = 2ˆi + 3ˆj −ˆk and b = ˆj + ˆk . If u is perpendicular to →a and → → → 2 u ⋅ b = 24, then u is equal to: (1) 84 (2) 336 (3) 315 (4) 256

Q88.If the angle between the lines x 2 = 2y = 1z and 5−x−2 = 7y−14P = z−34 is cos−1( 32 ), then P is equal to (1) 2 (2) 7 7 2 (3) −47 (4) −74

Q88.If L1 is the line of intersection of the planes 2x −2y + 3z −2 = 0, x −y + z + 1 = 0 and L2 is the line of intersection of the planes x + 2y −z −3 = 0, 3x −y + 2z −1 = 0, then the distance of the origin from the plane, containing the lines L1 and L2 is (1) 1 (2) 1 √2 4√2 (3) 1 (4) 1 3√2 2√2

Q88.A variable plane passes through a fixed point (3, 2, 1) and meets x, y and z-axes at A, B & C respectively. A plane is drawn parallel to the yz– plane through A , a second plane is drawn parallel to the zx− plane through B and a third plane is drawn parallel to the xy- plane through C . Then the locus of the point of intersection of these three planes, is (1) x 3 + 2y + 1z = 1 (2) x1 + 1y + 1z = 116 (3) x + y + z = 6 (4) x3 + 2y + 1z = 1

Q88.A variable plane passes through a fixed point ( 3 , 2, 1) and meets x, y and z axes at A, B and C respectively. A plane is drawn parallel to yz - plane through A , a second plane is drawn parallel zx plane through B and a third plane is drawn parallel to xy - plane through C . Then the locus of the point of intersection of these three planes, is (1) (x + y + z = 6) (2) x3 + 2y + 1z = 1 (3) x 3 + 2y + 1z = 1 (4) x1 + 1y + 1z = 116

Q88.An angle between the lines whose direction cosines are given by the equations, l + 3m + 5n = 0 and 5lm −2mn + 6nl = 0, is (1) cos−1 ( 81 ) (2) cos−1 ( 61 ) (3) cos−1 ( 31 ) (4) cos−1 ( 41 )

Q89.A plane bisects the line segment joining the points (1, 2, 3) and (−3, 4, 5) at right angles. Then this plane also passes through the point. (1) (−3, 2, 1) (2) (3, 2, 1) (3) (1, 2, −3) (4) (−1, 2, 3) JEE Main 2018 (15 Apr Shift 2 Online) JEE Main Previous Year Paper

Q89.The length of the projection of the line segment joining the points (5, −1, 4) and (4, −1, 3) on the plane, x + y + z = 7 is (1) √23 (2) √32 (3) 2 (4) 1 3 3

Q89.An angle between the plane x + y + z = 5 and the line of intersection of the planes, 3x + 4y + z −1 = 0 and 5x + 8y + 2z + 14 = 0 is 3 ) √17 17 (1) cos−1(√3 ) (2) cos−1( 17 (3) sin−1( √173 ) (4) sin−1(√3 )

Q89.An angle between the plane, x + y + z = 5 and the line of intersection of the planes, 3x + 4y + z −1 = 0 and 5x + 8y + 2z + 14 = 0 , is (1) cos−1 3 (2) cos−1 17 ( √17 ) (√3 ) 3 (4) (3) sin−1 sin−1 17 ( √17 ) (√3 )

Q89.Two different families A and B are blessed with equal number of children. There are 3 tickets to be distributed amongst the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to the children of the family B is 1 , then the number of children in each family is 12 (1) 6 (2) 5 (3) 3 (4) 4 ¯

Q90.A box ' A ' contanis 2 white, 3 red and 2 black balls. Another box ' B′ contains 4 white, 2 red and 3 black balls. If two balls are drawn at random, without replacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box ' B′ is (1) 7 (2) 9 16 32 (3) 87 (4) 169 JEE Main 2018 (15 Apr Shift 1 Online) JEE Main Previous Year Paper

Q90.Let A, B and C be three events, which are pair-wise independent and E denotes the complement of an event is equal to¯E . If P(A ∩B ∩C) = 0 and P(C) > 0, then P[(A ∩B) C] ¯¯¯(1) P(A) −P(B) (2) P(A) −P(B) + P(A) +¯¯¯(3) P(A) P(B) (4) P(B) JEE Main 2018 (16 Apr Online) JEE Main Previous Year Paper

Q90.A box A contains 2 white, 3 red and 2 black balls. Another box B contains 4 white, 2 red and 3 black balls. If two balls are drawn at random, without replacement from a randomly, selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box B is : (1) 7 (2) 9 8 16 (3) 7 (4) 9 16 32 JEE Main 2018 (15 Apr) JEE Main Previous Year Paper

Q90.A player X has a biased coin whose probability of showing heads is p and a player Y has a fair coin. They start playing a game with their own coins and play alternately. The player who throws a head first is a winner. If X starts the game, and the probability of winning the game by both the players is equal, then the value of ' p ' is (1) 1 (2) 1 3 5 (3) 1 (4) 2 4 5 JEE Main 2018 (15 Apr Shift 2 Online) JEE Main Previous Year Paper

Q90.A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its color is observed and this ball along with two additional balls of the same color are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is: (1) 3 (2) 3 4 10 (3) 2 (4) 1 5 5 JEE Main 2018 (08 Apr) JEE Main Previous Year Paper