Practice Questions

Q83.Let f : R →R be a function such that f(2 −x) = f(2 + x) and f(4 −x) = f(4 + x), for all x ∈R and 2 50 ∫ f(x)dx = 5. Then the value of ∫ f(x)dx is 0 10 (1) 100 (2) 125 (3) 80 (4) 200

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

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 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

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 →

Q86.In a parallelogram ABCD, AB→ = a, AD→ = b & AC→ = c. DB→ ⋅AB→ has the value: (1) 1 2 (a2 + b2 + c2) (2) 14 (a2 + b2 −c2) (3) 3 1 (b2 + c2 −a2) (4) 12 (a2 −b2 + c2)

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

Q87.Let →a, b and →c be three non - zero vectors such that no two of them are collinear and × →c→a. If θ is the angle between vectors b and →c, then a value of sin θ is = 13 b (→a → → → b) ×→c (1) −2√3 (2) 2√2 3 3 (3) −√2 (4) 2 3 3

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)

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

Q88.If the points (1, 1, λ) & (−3, 0, 1), are equidistant from the plane, 3x + 4y −12z + 13 = 0, then λ satisfies the equation: (1) 3x2 + 10x + 7 = 0 (2) 3x2 + 10x −13 = 0 (3) 3x2 −10x + 7 = 0 (4) 3x2 −10x + 21 = 0 JEE Main 2015 (10 Apr Online) JEE Main Previous Year Paper

Q88.The shortest distance between the z - axis and the line x + y + 2z −3 = 0 = 2x + 3y + 4z −4, is (1) 1 (2) 2 (3) 3 (4) 4

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

Q89.If the shortest distance between the line x−1α = y+1−1 = 1z , (α ≠−1) , and x + y + z + 1 = 0 = 2x −y + z + 3 is 1 ,then value of α is : √3 (1) −1916 (2) 3219 (3) −1619 (4) 1932

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

Q90.If the lengths of the sides of a triangle are decided by the three throws of a single fair die, then the probability that the triangle is of maximum area given that it is an isosceles triangle, is: (1) 1 (2) 1 69 26 (3) 1 (4) 1 21 15 JEE Main 2015 (11 Apr Online) JEE Main Previous Year Paper

Q90.If 12 identical balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains exactly 3 balls is (1) 22( 13 )11 (2) 195 (3) 55( 32 )10 (4) 220( 31 )12 JEE Main 2015 (04 Apr) JEE Main Previous Year Paper

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

Q61.If 1 , 1 are the roots of the equation ax2 + bx + 1 = 0, (a ≠0, a, b ∈R), then the equation √α √β x(x + b3) + (a3 −3abx) = 0 has roots: 2 and β−32 (1) √αβ and αβ (2) α−3 (3) αβ 21 and α 21 β (4) α 23 and β 23

Q61.If a ∈ R and the equation −3(x − [x])2 + 2(x − [x]) + a2 = 0 (where [x] denotes the greatest integer ≤ x) has no integral solution, then all possible values of a lie in the interval (1) (−2, −1) (2) ( −∞, −2) ∪(2,∞) (3) (−1, 0) ∪(0, 1) (4) (1, 2)