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NCERT Solutions for class 12 Maths | Chapter 6 - Application of Derivatives

Questions
1 The function f(x) = tan x – x
A always increases
B always decreases
C sometimes increases and sometimes decreases
D never increases

Answer:always increases
2 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:one maxima and one minima
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3 f(x) = xx has a stationary point at
A x = e
B x = 1/e
C x = 1
D x = √e

Answer:x = 1/e
4 If the volume of a sphere is increasing at a constant rate, then the rate at which its radius is increasing is
A a constant
B proportional to the radius
C inversely proportional to the radius
D inversely proportional to the surface area

Answer:inversely proportional to the surface area
5 The function f(x) = cot-1 x + x increases in the interval
A (1, ∞)
B (-1, ∞)
C (0, ∞)
D (-∞, ∞)

Answer:(-∞, ∞)
6 If f (x) = x³ – 6x² + 9x + 3 be a decreasing function, then x lies in
A (-∞, -1) ∩ (3, ∞)
B (1, 3)
C (3, ∞)
D None of these

Answer:(1, 3)
7 2x³ – 6x + 5 is an increasing function, if
A 0 < x < 1
B -1 < x < 1
C x < -1 or x > 1
D -1 < x < –1/2

Answer:x < -1 or x > 1
8 The function f(x) = x + cos x is
A always increasing
B always decreasing
C increasing for certain range of x
D None of these

Answer:always increasing
9 The value of b for which the function f (x) = sin x – bx + c is decreasing for x ∈ R is given by
A b < 1
B b ≥ 1
C b > 1
D b ≤ 1

Answer:b > 1
10 The function f (x) = 1 – x³ – x5 is decreasing for
A 1 < x < 5
B x < 1
C x > 1
D all values of x

Answer:all values of x
11 The function /’defined by f(x) = 44 – 2x + 1 is increasing for
A x < 1
B x > 0
C x < 1/2
D x > 1/2

Answer:x > 1/2
12 If f (x) = Class 12 Maths Application of Derivatives
A both f (x) and g (x) are increasing functions
B both f (x) and g (x) are decreasing functions
C f(x) is an increasing function
D g (x) is an increasing function

Answer:f(x) is an increasing function
13 The length of the longest interval, in which the function 3 sin x – 4 sin³ x is increasing is
A π/3
B π/2
C 3π/2
D π

Answer:π
14 The function f(x) = x/logx increases on the interval
A (0, ∞)
B (0, e)
C (e, ∞)
D None of these

Answer:(e, ∞)
15 The function f(x) = log (1 + x) –Class 12 Maths Application of Derivatives is increasing on
A (-1, ∞)
B (-∞, 0)
C (-∞, ∞)
D None of these

Answer:(-1, ∞)
16 A particle is moving along the curve x = at² + bt + c. If ac = b², then particle would be moving with uniform
A rotation
B velocity
C acceleration
D retardation

Answer:acceleration
17 The smallest value of the polynomial x³ – 18x² + 96x in [0, 9] is
A 126
B 0
C 135
D 160

Answer:0
18 Maximum slope of the curve y = -x³ + 3x² + 9x – 27 is
A 0
B 12
C 16
D 32

Answer:0
19 Function, f (x) = Class 12 Maths Application of Derivatives is monotonic increasing, if
A λ > 1
B λ < 1
C λ < 4
D λ > 4

Answer:λ > 4
20 The position of a point in time Y is given by x = a + bt + ct², y = at + bt². Its acceleration at timet Y is
A b – c
B b + c
C 2b – 2c
D

Answer:

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