CBSE Class 12 Mathematics Applications Of Derivatives Assignment Set 02

Question. The function 𝑓(𝑥) = 4 − 3𝑥 + 3 𝑥² − 𝑥³ is:
a) decreasing on R
b) increasing on R
c) strictly decreasing on R
d) strictly increasing on R
Answer : A

Question. The Equation normal to the curve y=x + Sinx + Cosx at x = π/2 is
a) x = 2
b) x = 𝜋
c) x + 𝜋 = 0
d) 2x = π
Answer : D

Question. The point on the curve y² = x where tangent makes 450 angle with x-axis is
a) (0,0)
b) (2,16)
c) (3, 9)
d) none of these
Answer : B

Question. The equation of the normal to the curve 3x² − y² = 8 which is parallel to the line x + 3y = 8 is
a) x + 3y = 8
b) x + 3y + 8 = 0
c) x + 3y ± 8 = 0
d) None of These
Answer : C

Question. The Maximum value of f(x) = logx/x is
a) 1/e
b) 2/e
c) e
d) 1
Answer : A

Question. At what point the slope of the tangent to the curve x²+y²− 2x −3 is zero?
a) (3, 0), (−1, 0)
b) (3,0),(1,2)
c) (−1, 0),(1,2)
d) (1, 2),(1, − 2)
Answer : D

Question. The function 𝑓(𝑥) = 𝑥𝑥 is decreasing in the interval:
a) (0, 𝑒)
b) [0, 1/e)
c) ) (0, 1)
d) none of these
Answer : B

Question. The smallest value of polynomial 3x⁴− 8x³ + 12x²− 48x +1 in [1, 4] is:
a)-49
b) 59
c) -59
d) 257
Answer : C

Question. The angle of intersection of the parabolas y² =4ax and x² = 4ay at the origin is
a) 𝜋/6
b) 𝜋/3
c) 𝜋/2
d) 𝜋/4
Answer : C

Question. The Point on the curve y = x²- 3x + 2 where tangent is perpendicular to y=x is
a) ( ½ , ¼)
b) (¼ , ½)
c) ( 4 , 2 )
d) ( 1 ,1 )
Answer : B

Question. The tangent to the curve y = e^2x at the point ( 0 , 1) meets x-axix at
a) ( 0 , 1)
b) [-1/2 , 0]
c) (2 , 0 )
d) (0 ,2)
Answer : B

Question. The maximum value of x²+ 250/x is
a) 0
b) 25
c) 50
d) 75
Answer : D

Question. The equation of tangent at those points where the curve y = x² – 3x + 2 meets x- axis are
a) x − y  +2 = 0, x − y −1 = 0
b) x − y −1 = 0 , x − y = 0
c) x + y −1 = 0 , x − y − 2 = 0
d) x − y = 0 , x +y = 0
Answer : B

Question. The sum of two non-zero numbers is 8, the minimum value of the sum of their reciprocals is:
a) ¼
b) ½
c) 1/8
d) None of these
Answer : B

Question. The point on the curve x² = 2y which is nearest to the point ( 0 , 5 ) is
a) (2√2 , 4)
b) (2√2 , 0 )
c) ( 0 , 0 )
d) ( 2 , 2 )
Answer : A

Question. The value of f(x) = ( x-2 )(x – 3)² is
a) 7/3
b) 3
c) 4/27
d) 0
Answer : C

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

Question. The maximum value of y = sinx. cosx is
a) 1/4
b) 1/2
c) √2
d) 2√2
Answer : B

Question. If the function f(x) = x³ + ax² + bx + 1 is maximum at x = 0 and x = 1 then :
a) a = 2/3, b = 0
b) a = - 3/2, b = 0
c) a = 0 , b = 2
d) None of These
Answer : B

Question. The function f (x)=2x³−3x²−12x + 4, has:
a) Two points of local maximum
b) Two points of local minimum
c) one maxima and one minima
d) no maxima or minima
Answer : C

Question. The Least value f(x) = e^x + e^-x
a) -2
b) 0
c) 2
d) can’t be determine
Answer : C