Practice Questions

Q78.The number of values of k for which the system of linear equations (k + 2)x + 10y = k & kx + (k + 3)y = k −1 has no solution is (1) 1 (2) 2 (3) 3 (4) 4

Q78.Let f : A → B be a function defined as f(x) = x−1x−2 , where A = R −{2} and B = R −{1}. Then f is (1) invertible and f −1(y) = 2y+1y−1 (2) invertible and f −1(y) = 3y−1y−1 (3) no invertible (4) invertible and f −1(y) = 2y−1y−1 1 −1) 2−x , x > 1, x ≠2

Q78. cos x x 1 f ′(x) If f(x) = 2 sin x x2 2x , then lim x x→0 tan x x 1 (1) does not exist (2) exists and is equal to −2 (3) exists and is equal to 0 (4) exists and is equal to 2

Q78. cos x x 1 f ′(x) If f(x) = 2 sin x x2 2x , then limx→0 x tan x x 1 (1) Exists and is equal to −2 (2) Does not exist (3) Exist and is equal to 0 (4) Exists and is equal to 2

Q78.If the system of linear equations x + ky + 3z = 0 3x + ky −2z = 0 2x + 4y −3z = 0 has a non-zero solution (x, y, z), then xz is equal to: y2 (1) 30 (2) −10 (3) 10 (4) −30

Q79.Let S be the set of all real values of k for which the system of linear equations x + y + z = 2 2x + y −z = 3 3x + 2y + kz = 4 has a unique solution. Then S is (1) an empty set (2) equal to R −{0} (3) equal to {0} (4) equal to R

Q79.Let S be the set of all real values of k for which the system of linear equations x + y + z = 2 2x + y −z = 3 3x + 2y + kz = 4 has a unique solution. Then, S is : (1) equal to R –{0} (2) an empty set (3) equal to R (4) equal to {0}

Q79.Let f(x) = {(x k, x = 2 The value of k for which f is continuous at x = 2 is (1) e−2 (2) e (3) e−1 (4) 1

Q79.If the function f defined as f(x) = x1 − e2x−1k−1 , x ≠0 is continuous at x = 0, then ordered pair (k, f(0)) is equal to (1) (2, 1) (2) (3, 1) (3) (3, 2) (4) ( 13 , 2)

Q79. x −4 2x 2x If 2x x −4 2x = (A + Bx) (x −A)2, then the ordered pair (A, B) is equal to 2x 2x x −4 (1) (4, 5) (2) (−4, −5) (3) (−4, 3) (4) (−4, 5)

Q80.Let S = {(λ, μ) ∈R × R : f(t) = (|λ|et −μ) ⋅sin(2|t|), t ∈R, is a differentiable function } . Then S is a subest of? (1) R × [0, ∞) (2) (−∞, 0) × R (3) [0, ∞) × R (4) R × (−∞, 0)

Q80.If f(x) = sin−1 ( 2×3x1+9x ), then f ′ (−12 ) equals. (1) √3 loge √3 (2) −√3 loge √3 (3) −√3 loge 3 (4) √3 loge 3 JEE Main 2018 (15 Apr Shift 2 Online) JEE Main Previous Year Paper

Q80.If x = √2cosec−1 t and y = √2sec−1 t, (|t| ≥1), then dxdy is equal to (1) x y (2) −yx (3) −xy (4) xy

Q80.Let S = {(λ, μ) ∈R × R : f(t) = (|λ |e|t| −μ) sin(2|t|), t ∈R is a differential function}. Then, S is a subset of : (1) (−∞, 0) × R (2) R × [0 , ∞) (3) [0 , ∞) × R (4) R × (−∞, 0)

Q80.Let S = {t ∈R : f(x) = |x −π| ⋅(e|x| −1) sin|x| is not differentiable at t}. Then, the set S is equal to: (1) {0, π} (2) ϕ (an empty set) (3) {0} (4) {π}

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.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 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

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.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

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.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 ∫ 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

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