**CBSE Class 12 Maths – MCQ and Online Tests – Unit 6 – Application of Derivatives**

Every year CBSE conducts board exams for 12th standard. These exams are very competitive to all the students. So our website provides online tests for all the 12th subjects. These tests are also very effective and useful for those who preparing for competitive exams like NEET, JEE, CA etc. It can boost their preparation level and confidence level by attempting these chapter wise online tests.

These online tests are based on latest CBSE Class 12 syllabus. While attempting these our students can identify the weak lessons and continuously practice those lessons for attaining high marks. It also helps to revise the NCERT textbooks thoroughly.

**CBSE Class 12 Maths – MCQ and Online Tests – Unit 6 – Application of Derivatives**

Question 1.

The points at which the tangents to the curve y = x² – 12x +18 are parallel to x-axis are

(a) (2, – 2), (- 2, -34)

(b) (2, 34), (- 2, 0)

(c) (0, 34), (-2, 0)

(d) (2, 2),(-2, 34).

## Answer

Answer: (d) (2, 2),(-2, 34).

Question 2.

The tangent to the curve y = e^{2x} at the point (0, 1) meets x-axis at

(a) (0, 1)

(b) (-\(\frac{1}{2}\), 0)

(c) (2, 0)

(d) (0, 2)

## Answer

Answer: (b) (-\(\frac{1}{2}\), 0)

Question 3.

The slope of tangent to the curve x = t² + 3t – 8, y = 2t² – 2t – 5 at the point (2, -1) is

(a) \(\frac{22}{7}\)

(b) \(\frac{6}{7}\)

(c) \(\frac{-6}{7}\)

(d) -6

## Answer

Answer: (c) \(\frac{-6}{7}\)

Question 4.

The two curves; x³ – 3xy² + 2 = 0 and 3x²y – y³ – 2 = 0 intersect at an angle of

(a) \(\frac{π}{4}\)

(b) \(\frac{π}{3}\)

(c) \(\frac{π}{2}\)

(d) \(\frac{π}{6}\)

## Answer

Answer: (a) \(\frac{π}{4}\)

Question 5.

The interval on which the function f (x) = 2x³ + 9x² + 12x – 1 is decreasing is

(a) [-1, ∞]

(b) [-2, -1]

(c) [-∞, -2]

(d) [-1, 1]

## Answer

Answer: (b) [-2, -1]

Question 6.

Let the f: R → R be defined by f (x) = 2x + cos x, then f

(a) has a minimum at x = 3t

(b) has a maximum, at x = 0

(c) is a decreasing function

(d) is an increasing function

## Answer

Answer: (d) is an increasing function

Question 7.

The sides of an equilateral triangle are increasing at the rate of 2cm/sec. The rate at which the are increases, when side is 10 cm is

(a) 10 cm²/s

(b) √3 cm²/s

(c) 10√3 cm²/s

(d) \(\frac{10}{3}\) cm²/s

## Answer

Answer: (c) 10√3 cm²/s

Question 8.

y = x (x – 3)² decreases for the values of x given by

(a) 1 < x < 3

(b) x < 0

(c) x > 0

(d) 0 < x <\(\frac{3}{2}\)

## Answer

Answer: (a) 1 < x < 3

Question 9.

The function f(x) = 4 sin³ x – 6 sin²x + 12 sin x + 100 is strictly

(a) increasing in (π, \(\frac{3π}{2}\))

(b) decreasing in (\(\frac{π}{2}\), π)

(c) decreasing in [\(\frac{-π}{2}\),\(\frac{π}{2}\)]

(d) decreasing in [0, \(\frac{π}{2}\)]

## Answer

Answer: (c) decreasing in [\(\frac{-π}{2}\),\(\frac{π}{2}\)]

Question 10.

Which of the following functions is decreasing on(0, \(\frac{π}{2}\))?

(a) sin 2x

(b) tan x

(c) cos x

(d) cos 3x

## Answer

Answer: (c) cos x

Question 11.

The curve y – x^{1/5} at (0, 0) has

(a) a vertical tangent (parallel to y-axis)

(b) a horizontal tangent (parallel to x-axis)

(c) an oblique tangent

(d) no tangent

## Answer

Answer: (b) a horizontal tangent (parallel to x-axis)

Question 12.

The function f(x) = tan x – x

(a) always increases

(b) always decreases

(c) sometimes increases and sometimes decreases

(d) never increases

## Answer

Answer: (a) always increases

Question 13.

If x is real, the minimum value of x² – 8x + 17 is

(a) -1

(b) 0

(c) 1

(d) 2

## Answer

Answer: (d) 2

Question 14.

The equation of normal to the curve 3x² – y² = 8 which is parallel to the line ,x + 3y = 8 is

(a) 3x – y = 8

(b) 3x + y + 8 = 0

(c) x + 3y ± 8 = 0

(d) x + 3y = 0

## Answer

Answer: (c) x + 3y ± 8 = 0

Question 15.

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

Answer: (d) inversely proportional to the surface area

Question 16.

The smallest value of the polynomial x³ – 18x² + 96x in [0, 9] is

(a) 126

(b) 0

(c) 135

(d) 160

## Answer

Answer: (b) 0

Question 17.

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

Answer: (c) one maxima and one minima

Question 18.

If the curve ay + x² = 7 and x³ = y, cut orthogonally at (1, 1) then the value of a is

(a) 1

(b) 0

(c) -6

(d) 6

## Answer

Answer: (d) 6

Question 19.

The maximum value of sin x . cos x is

(a) \(\frac{1}{4}\)

(b) \(\frac{1}{2}\)

(c) √2

(d) 2√2

## Answer

Answer: (b) \(\frac{1}{2}\)

Question 20.

At x = \(\frac{5π}{6}\), f (x) = 2 sin 3x + 3 cos 3x is

(a) maximum

(b) minimum

(c) zero

(d) neither maximum nor minimum

## Answer

Answer: (d) neither maximum nor minimum

Question 21.

If y = x^{4} – 10 and if x changes from 2 to 1.99 what is the change in y

(a) 0.32

(b) 0.032

(c) 5.68

(d) 5.968

## Answer

Answer: (a) 0.32

Question 22.

The equation of tangent to the curve y (1 + x²) = 2 – x, w here it crosses x-axis is:

(a) x + 5y = 2

(b) x – 5y = 2

(c) 5x – y = 2

(d) 5x + y = 2

## Answer

Answer: (a) x + 5y = 2

Question 23.

Maximum slope of the curve y = -x³ + 3x² + 9x – 27 is

(a) 0

(b) 12

(c) 16

(d) 32

## Answer

Answer: (a) 0

Question 24.

f(x) = x^{x} has a stationary point at

(a) x = e

(b) x = \(\frac{1}{e}\)

(c) x = 1

(d) x = √e

## Answer

Answer: (b) x = \(\frac{1}{e}\)

Question 25.

The maximum value of (\(\frac{1}{x}\))^{x} is

(a) e

(b) e²

(c) e^{1/x}

(d) (\(\frac{1}{e}\))^{1/e}

## Answer

Answer: (d) (\(\frac{1}{e}\))^{1/e}

Question 26.

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

Answer: (c) acceleration

Question 27.

The distance Y metres covered by a body in t seconds, is given by s = 3t² – 8t + 5. The body will stop after

(a) 1 s

(b) \(\frac{3}{4}\) s

(c) \(\frac{4}{3}\) s

(d) 4 s

## Answer

Answer: (c) \(\frac{4}{3}\) s

Question 28.

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) 2\(\sqrt{b^2+c^2}\)

## Answer

Answer: (d) 2\(\sqrt{b^2+c^2}\)

Question 29.

The function f(x) = log (1 + x) – \(\frac{2x}{2+x}\) is increasing on

(a) (-1, ∞)

(b) (-∞, 0)

(b) (-∞, ∞)

(d) None of these

## Answer

Answer: (a) (-1, ∞)

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