Practice Questions

Q78.The set of all values of λ for which the system of linear equations: 2x1 −2x2 + x3 = λx1 2x1 −3x2 + 2x3 = λx2 −x1 + 2x2 = λx3 has a non-trivial solution, (1) Contains more than two elements. (2) Is an empty set. (3) Is a singleton. (4) Contains two elements.

Q79. (ex−1)2 , x ≠0 x ⎧ sin ( k ) log (1+ x4 ) Let k be a non - zero real number. If f(x) = is a continuous function at x = 0 ⎨ ⎩12 , x = 0 , then the value of k is (1) 2 (2) 4 (3) 3 (4) 1

Q80.The equation of a normal to the curve, sin y = x sin( π3 + y) at x = 0, is: (1) 2x −√3 y = 0 (2) 2y −√3 x = 0 (3) 2y + √3 x = 0 (4) 2x + √3 y = 0

Q80.If f(x) = 2 tan−1 x + sin−1( 1+x22x ), x > 1, then f(5) is equal to (1) π 2 (2) tan−1( 15665 ) (3) π (4) 4 tan−1(5)

Q80.If the function g (x) = {k√xmx ++21 ,, 30 <≤xx ≤3≤5 (1) 4 (2) 2 (3) 16 (4) 10 5 3

Q81.The normal to the curve x2 + 2xy −3y2 = 0 , at (1, 1) (1) Meets the curve again in the fourth quadrant (2) Does not meet the curve again (3) Meets the curve again in the second quadrant (4) Meets the curve again in the third quadrant

Q81.If Rolle's theorem holds for the function f(x) = 2x3 + bx2 + cx, x ∈[−1, 1] at the point x = 12 , then 2b + c is equal to (1) 2 (2) 1 (3) −1 (4) −3

Q82.The distance from the origin, of the normal to the curve, x = 2 cos t + 2t sin t, y = 2 sin t −2t cos t at t = π4 , is : (1) √2 (2) 2√2 (3) 4 (4) 2

Q82.If ∫ log(t+√1+t2) dt = 2 (g(t))2 + c, where c is a constant, then g(2), is equal to √1+t2 (1) 2 + + √5) (2) log(2 √5) 1 log(2 √5 + log + (3) log(2 √5) (4) 12 (2 √5)

Q83.The integral ∫ 3dx 5 , is equal to (x+1) 4 (x−2) 4 (1) 1 1 4 + c 4( x+1x−2 ) 4 + c (2) −43 ( x+1x−2 ) (3) 1 1 4 + c 4( x−2x+1 ) 4 + c (4) −43 ( x−2x+1 )

Q83.The integral ∫ dx 3 equals to x2(x4+1) 4 4 (1) x4+1 1 1 4 (2) x4+1 + c + c −( x4 ) ( x4 ) (3) 14 (4) 41 (x4 + 1) + c −(x4 + 1) + c logx2 dx is equal to

Q84.For x > 0, let f(x) = ∫x1 log1+tt dt. Then f(x) + f( x1 ) is equal to (1) 1 (log x)2 (2) log x 2 (3) 1 4 log x2 (4) 14 (log x)2

Q84.Let f : (−1, 1) →R be a continuous function. If ∫sin0 x f(t) dt = √32 x, then f( √32 ) is equal to: (1) √3 (2) √3 2 (3) 1 (4) 2 √32

Q84.The integral ∫4 logx2+log(6−x)2 2 (1) 6 (2) 2 (3) 4 (4) 1

Q85.The area (in sq. units) of the region described by [(x, y) : y2 ≤2x and y ≥4x −1] is (1) 32 9 sq. units (2) 327 sq. units (3) 64 5 sq. units (4) 6415 sq. units

Q85.The solution of the differential equation ydx −(x + 2y2)dy = 0 is x = f(y). If f(−1) = 1, then f(1) is equal to (1) 2 (2) 3 (3) 4 (4) 1 −−−−−

Q85.The area (in square units) of the region bounded by the curves y + 2x2 = 0 and y + 3x2 = 1 , is equal to (1) 4 3 sq. units (2) 13 sq. units (3) 5 3 sq. units (4) 43 sq. units

Q86.If y (x) is the solution of the differential equation (x + 2) dxdy = x2 + 4x −9, x ≠ −2 and y(0) = 0, then y(−4) is equal to (1) −1 (2) 1 (3) 0 (4) 2 × , then 2→c is equal to:

Q86.Let y (x) be the solution of the differential equation (x log x) dxdy + y = 2x log x, (x ≥1). Then y (e) is equal to (1) 2e (2) e (3) 0 (4) 2 →

Q87.A plane containing the point (3, 2, 0) and the line x−11 = y−25 = z−34 also contains the point (1) (0, 7, −10) (2) (0, 7, 10) (3) (0, 3, 1) (4) (0, −3, 1)

Q87.Let →aand→b be two unit vectors such that →a+→b = √3. If →c=→a+ 2→b + (→a →b) (1) √51 (2) √37 (3) √43 (4) √55

Q88.The distance of the point (1, 0, 2) from the point of intersection of the line x−23 = y+14 = z−212 and the plane x −y + z =16, is (1) 13 (2) 2√14 (3) 8 (4) 3√21

Q89.If the mean and the variance of a binomial variate X are 2 & 1 respectively, then the probability that X takes a value greater than or equal to one is: (1) 1 (2) 9 16 16 (3) 3 (4) 15 4 16

Q89.The equation of the plane containing the line of intersection of 2x −5y + z = 3; x + y + 4z = 5, and parallel to the plane, x + 3y + 6z = 1, is (1) 2x + 6y + 12z = −13 (2) 2x + 6y + 12z = 13 (3) x + 3y + 6z = −7 (4) x + 3y + 6z = 7

Q90.Let X be a set containing 10 elements and P(X) be its power set. If A and B are picked up at random from P(X), with replacement, then the probability that A and B have equal number of elements is: (1) (210−1) (2) 20C10 220 220 (3) 20C10 (4) (210−1) 210 210 JEE Main 2015 (10 Apr Online) JEE Main Previous Year Paper