CBSE Class 12 Mathematics Application Of Derivative Worksheet Set A

Question. The function 𝑓(𝑥) = 𝑥³ − 6𝑥² + 15 𝑥 − 12 is:
a) strictly decreasing on R
b) strictly increasing on R
c) increasing on (−∞, 2] and decreasing on (2, ∞)
d) none of these
Answer : B

Question. The function 𝑓(𝑥) = 𝑥/2𝑥 +1 is increasing in :
a) (−1, 1)
b) (−1, ∞)
c) (− ∞, −1) ∪ (1, ∞)
d) none of these π
Answer : A

Question. The two curves 𝑥³ – 3x𝑦² + 2 = 0 and 3𝑥²𝑦²– 𝑦³ = 2
a) Touch each other
c) Cut at an angle π/3
b) Cut at right angle
d) Cut at an angle π/4
Answer : B

Question. Is the function 𝑓(𝑥) = cos(2𝑥 + 𝜋/4); is increasing or decreasing in the interval (3 𝜋/8 , 7𝜋/8)
a) increasing
b) decreasing
c) neither increasing nor decreasing
d) none of these
Answer : A

Question. The equation of the normal to the curve y = sin x at (0, 0) is
a) x = 0
b) y = 0
c) x + y = 0
d) x – y = 0
Answer : A

Question. The function 𝑓(𝑥) = [𝑥(𝑥 − 3)]² is increasing in :
a) (0, ∞)
b) (− ∞, 0)
c) (1, 3)
d) [0, 1.5] ∪ (3, ∞)
Answer : D

Question. The slope of normal to the curve y = 2x² + 3 sin x at x = 0 is
a) -1/3
b) ½
c) 1/3
d) 3
Answer : A

Question. The function 𝑓(𝑥) = tan 𝑥 − 𝑥 is:
a) always increasing
b) always decreasing
c) not always decreasing
d) sometimes increasing and sometimes decreasing
Answer : A

Question. The least value of a such that f(x) =𝑥² + ax +1 is strictly increasing on ( 1 , 2) is
a) - 2
b) -4
c) 2
d) 4
Answer : A

Question. The slope of tangent to the curve x = t² + 3t − 8 and y = 2t² − 2t − 5 at t = 2 is
a) 7/6
b) 6/7
c) -7/6
d) -6/7
Answer : B

Question. The tangent to the curve given by x = et.cos t, y =et.sin t at t = π/4 makes with x-axis an angle
a) 0
b) π/4
c) π/3
d) π/2
Answer : D

Question. The equation of normal x = acos³θ , y=a sin3θ at the point θ= 𝜋/4 is
a) x = 0
b) y = 0
c) x = y
d) x + y = a
Answer : C

Question. If the curve ay + x² = 7 and x³ = y cut each other at 90⁰ at ( 1 , 1) , then value of a is :
a) 1
b) -6
c) 6
d) 0
Answer : C

Question. The point on the curve y² = x, where the tangent makes an angle of π/4 with x-axis is
a) (½, ¼)
b) ( ¼ , ½ )
c) (4, 2)
d) (1, 1)
Answer : A

Question. The angle between the curves y² = x and x² = y at (1,1)is:
a) tan^-1 4/3
b) tan^-1 3/4
c) 900
d) 450
Answer : B

Question. The line y = x + 1 is a tangent to the curve y² = 4x at the point
a) (1, 2)
b) ( 2 , 1)
c) ( -1, 2 )
d) ( -1 , -2)
Answer : A

Question. Which of the following functions are strictly decreasing on (0 ,2 )
a) Cos x
b) tan 2x
c) Cos 3x
d) tan x
Answer : A

Question. The tangent to the curve y = e2x at the point (0, 1) meets x-axis at
a) (−1/2, 0)
b) (1/2, 0)
c) (2/3, 0)
d) None these
Answer : A

Question. The Curve y = 4x²+ 2x -8 and y = x³ – x + 13 touch each other at the point
a) ( 3 , 23)
b) (23 , -3 )
c) ( 34 , 3)
d) ( 3 , 34)
Answer : D

Question. The abscissaof the point on the curve 3y = 6x − 5x³, the normal at which passes through the origin is
a) 1
b) 2
c) -1
d) -2
Answer : A