Practice Questions

Q81.If the curves y2 = 6x, 9x2 + by2 = 16 intersect each other at right angles, then the value of b is: (1) 9 (2) 6 2 (3) 7 (4) 4 2

Q81.Let M and m be respectively the absolute maximum and the absolute minimum values of the function, f(x) = 2x3 −9x2 + 12x + 5 in the interval [0, 3] . Then M −m is equal to (1) 9 (2) 4 (3) 1 (4) 5 + C , ( C is a constant of integration), then the ordered pair

Q81.If f(x) is a quadratic expression such that f(1) + f (2) = 0, and −1 is a root of f(x) = 0, then the other root of f(x) = 0 is (1) −58 (2) −85 (3) 5 (4) 8 8 5

Q81.If x2 + y2 + sin y = 4 , then the value of d2y at the point (−2, 0) is : dx2 (1) −34 (2) 4 (3) −2 (4) −32

Q81.If x2 + y2 + sin y = 4, then the value of d2y at the point (−2, 0) is dx2 (1) −34 (2) −32 (3) −2 (4) 4

Q82.Let f(x) = x2 + x21 and g(x) = x −1x , x ∈R −{−1, 0, 1}. If h(x) = f(x)g(x) , then the local minimum value of h(x) is: (1) 2√2 (2) 3 (3) −3 (4) −2√2

Q82.Let f(x) be a polynomial of degree 4 having extreme values at x = 1 and x = 2. If limx→0 f(x)x2 + = 3 ( 1) then f(−1) is equal to (1) 1 (2) 3 2 2 (3) 5 (4) 9 2 2

Q82.If a right circularcone having maximum volume, is inscribed in a sphere of radius 3 cm, then the curved surface area (in cm2 ) of this cone is (1) 8√3π (2) 6√2π (3) 6√3π (4) 8√2π

Q82.If ∫ 1+tantanx+tan2x x dx = x − √AK tan−1( K tan√Ax+1 ) (K, A) is equal to (1) (2, 1) (2) (2, 3) (3) (−2, 1) (4) (−2, 3) x −sin t)dt, then

Q82.If a right circular cone, having maximum volume, is inscribed in a sphere of radius 3 cm, then the curved surface area (in cm2 ) of this cone is : (1) 8√2π (2) 6√2π (3) 8√3π (4) 6√3π

Q83.The integral ∫ sin2 x cos2 x dx, is equal to (sin5 x+cos3 x sin2 x+sin3 x cos2 x+cos5 x)2 (where C is the constant of integration). (1) −1 + C (2) 1 + C 1+cot3 x 3(1+tan3 x) (3) −1 + C (4) 1 + C 3(1+tan3 x) 1+cot3 x π 2 sin2x dx is

Q83. dx = A√7 −6x −x2 + B sin−1 + C ( 4 ) ∫ √7 2x−6x+ 5−x2 x + 3 (where C is a constant of integration), then the ordered pair (A, B) is equal to (1) (−2, −1) (2) (2, −1) (3) (−2, 1) (4) (2, 1) 3π dx is

Q83.If f( x+2x−4 ) = 2x + 1, (x ∈R −{1, −2}), then ∫f(x)dx is equal to (1) 12 ln|1 −x| −3x + C (2) −12 ln|1 −x| −3x + C (3) 12 ln|1 −x| + 3x + C (4) −12 ln|1 −x| + 3x + C π 2 2+sin x is

Q83.If f(x) = ∫x0 t(sin (1) f ′′′(x) −f ′′(x) = cos x −2x sin x (2) f ′′′(x) + f ′′(x) −f ′(x) = cos x (3) f ′′′(x) + f ′′(x) = sin x (4) f ′′′(x) + f ′(x) = cos x −2x sin x

Q83.If f ( x−4x+2 ) = 2x + 1, (x ∈R = {1, −2}), then ∫f ( x ) dx is equal to (where C is a constant of integration) (1) 12 loge |1 −x| −3x + c (2) −12 loge |1 −x| −3x + c (3) −12 loge |1 −x| + 3x + c (4) 12 loge |1 −x| + 3x + c JEE Main 2018 (15 Apr Shift 1 Online) JEE Main Previous Year Paper

Q84.The value of the integral ∫ sin4 x(1 + ln( 2−sin x ))dx −π2 (1) 3 (2) 3 π 4 8 (3) 0 (4) 163 π

Q84.The value of integral ∫ π 4 x 4 1+sin x (1) π 2 (√2 + 1) (2) π(√2 −1) (3) 2π(√2 −1) (4) π√2

Q84.If the area of the region bounded by the curves, y = x2, y = x1 and the lines y = 0 and x = t(t > 1) is 1 sq. unit, then t is equal to (1) e 23 (2) e 32 (3) 3 (4) 4 2 3

Q84.The value of the integral π 2 2 + sin x sin4 x + log is 2 −sin x ))dx ∫ −π2 (1 ( (1) 3 π (2) 0 16 (3) 3 π (4) 3 8 4

Q84.The values of ∫ 1+2x −π2 (1) π (2) π 4 8 (3) π (4) 4π 2 JEE Main 2018 (08 Apr) JEE Main Previous Year Paper

Q85.If I1 = ∫10 e−x cos2 xdx; I2 = ∫10 e−x2 cos2 xdx and I3 = ∫10 e−x3dx; then (1) I2 > I3 > I1 (2) I3 > I1 > I2 (3) I2 > I1 > I3 (4) I3 > I2 > I1

Q85.Let g(x) = cos x2, f(x) = √x, and α, β(α < β) be the roots of the quadratic equation 18x2 −9πx + π2 = 0. Then the area (in sq. units) bounded by the curve y = (gof)(x) and the lines x = α, x = β and y = 0, is (1) 1 (2) 1 2 (√2 −1) 2 (√3 −1) (3) + 2 1 (√3 1) (4) 21 (√3 −√2)

Q85.The area (in sq. units) of the region {x ∈R : x ≥0 , y ≥0 , y ≥x −2 and y ≤√x} is (1) 13 (2) 8 3 3 (3) 10 (4) 5 3 3 . If dy + 2y = f(x), where f(x) =

Q85.The area (in sq. units) of the region {x ∈R : x ≥0, y ≥0, y ≥x −2 and y ≤√x}, is (1) 13 (2) 10 3 3 (3) 5 (4) 8 3 3

Q85.The differential equation representing the family of ellipses having foci either on the x-axis or on the y-axis, center at the origin and passing through the point (0, 3) is (1) xyy′ −y2 + 9 = 0 (2) xyy′′ + x(y′)2 −yy′ = 0 (3) xyy′ + y2 −9 = 0 (4) x + yy′′ = 0 → → → →