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Maths Application of Derivatives Class 12 MCQ Questions

Question 1 of 14
Question 1 of 14
Assertion (A): The absolute maximum of \(f(x)=x^2\) on the interval \([-2,2]\) is 4 .
Reason (R): The absolute maximum of a function on a closed interval must occur at a critical point or an endpoint.
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Question 2 of 14
Assertion (A): A cylindrical can of a given volume has minimum surface area when its height is equal to its diameter.
Reason (R): The second derivative of the surface area function with respect to the radius is positive at the critical point.
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Question 3 of 14
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The radius of a spherical balloon is increasing. The rate of change of its volume is fastest when:
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Question 4 of 14
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Water is draining from a conical tank. The rate at which the water level \(h\) is dropping is related to the radius \(r\) of the water's surface. This is a classic example of
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Question 5 of 14
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The interval on which the function \(f(x)=2 x^3+9 x^2+12 x-1\) is decreasing is:
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Question 6 of 14
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The tangent to the curve \(y=e^{2 x}\) at the point \((0,1)\) meets \(x\)-axis at:
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Question 7 of 14
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The points at which the tangents to the curve \(y=x^3-12 x+18\) are parallel to \(x\)-axis are:
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Question 8 of 14
The Relation between
The Relation between
The Relation between the height of the plant (y in cm) with respect to exposure to sunlight is governed by the following equation \(y=4 x-\frac{1}{2} x^2\) where \(x\) is the number of days exposed to sunlight.
The rate of growth of the plant with respect to sunlight is \(\_\_\_\_\) .
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Question 9 of 14
The Relation between
The Relation between
The Relation between the height of the plant (y in cm) with respect to exposure to sunlight is governed by the following equation \(y=4 x-\frac{1}{2} x^2\) where \(x\) is the number of days exposed to sunlight.
What is the number of days it will take for the plant to grow to the maximum height?
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Question 10 of 14
The Relation between
The Relation between
The Relation between the height of the plant (y in cm) with respect to exposure to sunlight is governed by the following equation \(y=4 x-\frac{1}{2} x^2\) where \(x\) is the number of days exposed to sunlight.
What is the maximum height of the plant?
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Question 11 of 14
The Relation between
The Relation between
The Relation between the height of the plant (y in cm) with respect to exposure to sunlight is governed by the following equation \(y=4 x-\frac{1}{2} x^2\) where \(x\) is the number of days exposed to sunlight.
What will be the height of the plant after 2 days?
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Question 12 of 14
The Relation between
The Relation between
The Relation between the height of the plant (y in cm) with respect to exposure to sunlight is governed by the following equation \(y=4 x-\frac{1}{2} x^2\) where \(x\) is the number of days exposed to sunlight.
If the height of the plant is \(7 / 2 \mathrm{~cm}\), the number of days it has been exposed to the sunlight is \(\_\_\_\_\).
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Question 13 of 14
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The profit function for a product is \(P(x)\). To maximize profit, the company should produce a quantity \(x\) where:
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Question 14 of 14
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The equation of the normal to the curve \(y=\sin x\) at \((0,0)\) is:
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10 Question MCQ (including Assertion) · Class 12 · Maths · CBSE

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Chapter 6 Class 12 Application of Derivatives | 14 questions | about 11 minutes

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