Class 12 Mathematics - Chapter 6: Application of Derivatives MCQ Questions

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D (-âˆž, âˆž)

A (frac { 1 }{2})

C (frac { 1 }{3})

A (frac { -6 }{7})

B (frac { 7 }{6})

C (frac { 6 }{7})

D (frac { 22 }{7})

A cut at an angle (frac { Ï€ }{4})

B cut at an angle (frac { Ï€ }{3})

C cut at right angle

D touch each other

A x – y + 1 = 0.

B x + y + 1 = 0

C ((frac { 1 }{4}), (frac { 1 }{2}))

D ((frac { 1 }{2}), (frac { 1 }{4}))

A x – y = 1.

B (frac { 3 }{2})

C (frac { 2 }{3})

A x – y = 0.

A (frac { 1 }{3})

A (frac { Ï€ }{2})

B (frac { Ï€ }{3})

C (frac { Ï€ }{4})

A –(frac { 1 }{3})

C (frac { 1 }{3})

A (Â±4, (frac { 3 }{8}))

B (4, Â±(frac { 3 }{8}))

C (4, –(frac { 8 }{3}))

D (4, Â±(frac { 8 }{3}))

C (2 âˆš2, 0)

D (2 âˆš2, 4)

A (frac { 1 }{2})

A 0 Ã— 5 m/minute.

B 1 Ã— 1 m/minute

C 0 Ã— 1 m/minute

D 1 m/minute

C (frac { 1 }{2})

D ((frac { 1 }{3}))^{(frac { 1 }{3})}

A 0.9 xÂ³ mÂ³

B 0.09 xÂ³mÂ³

C 0.6 xÂ³ mÂ³

D 0.06 xÂ³ mÂ³

A lies between 1 and 2.

B does not exist

C lies between -1 and 0

D lies between 2 and 3

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Class 12 Mathematics - Chapter 6: Application of Derivatives MCQ Questions

Your Class 12 Mathematics Study Path

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Class 12 Mathematics - Chapter 6: Application of Derivatives MCQ Questions

Your Class 12 Mathematics Study Path

The interval in which y = xÂ² e-x is increasing with respect to x is:

The abscissa of the point on the curve 3y = 6x – 5xÂ³, the normal at which passes through origin is:

The rate of change of the area of a circle with respect to its radius r at r = 6 cm is:

The slope of the tangent to the curve x = tÂ² + 3t – 8, y = 2 tÂ² – 2t – 5 at the point (2, -1) is:

The two curves xÂ³ – 3xyÂ² + 2 = 0 and 3xÂ²y – yÂ³ = 2

The normal at the point (1, 1) on the curve 2y + xÂ² = 3 is

The point on the curve yÂ² = x, where the tangent makes an angle of (frac { Ï€ }{4}) with x-axis is:

The normal to the curve xÂ² = 4y passing through (2, 1) is:

( lim _{x rightarrow infty}) (frac { f(3x) }{f(x)}) = 1. Then ( lim _{x rightarrow infty}) (frac { f(2x) }{f(x)}) =

The equation of the normal to the curve y = sin x at (0, 0) is

For all real values of x, the minimum value of (frac { 1-x+x^2 }{1+x+x^2}) is

x = et cos t, y = et sm t at t = (frac { Ï€ }{4}) makes with x-axis an angle:

The slope of the normal to the curve y = 2xÂ² + 3 sin x at x = 0 is

The points on the curve 9yÂ² = xÂ³, where the normal to the curve makes equal intercepts with the axes are

The point on the curve xÂ² = 2y, which is nearest to the point (0, 5), is:

The line y = mx + 1 is a tangent to the curve yÂ² = 4x if the value of m is:

A cylindrical tank of radius 10 mis being filled with wheat at the rate of 314 cubic m per minute. Then the depth of the wheat is increasing at the rate of:

The total revenue received from the sale of x units of a product is given by R (x) = 3xÂ² + 36x + 5. The marginal revenue, when x = 15 is:

The maximum value of [x (x – 1) + 1]1/3, 0 â‰¤ x â‰¤ 1 is

The line y = x + 1 is a tangent to the curve yÂ² = 4x at the point:

Let f (x) = xÂ² – (frac { 1 }{x^2}) and g(x) = x – (frac { 1 }{x}), x âˆˆ R – {-1, 0, 1}. If h(x) = (frac { f(x) }{g(x)}), then the local minimum value of h(x) is:

If f(x) = 3xÂ² + 15x + 5, then the approximate value of f(3.02) is:

Twenty metres of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower bed is:

The approximate change in the volume of a cube of side x metres caused by increasing the side by 3% is:

The real number k for which the equation 2xÂ³ + 3x + k = 0 has two distinct real roots in [0,1]:

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The interval in which y = xÂ² e^-x is increasing with respect to x is:

x = e^t cos t, y = e^t sm t at t = (frac { Ï€ }{4}) makes with x-axis an angle:

The maximum value of [x (x – 1) + 1]^1/3, 0 â‰¤ x â‰¤ 1 is