PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Mathematics

Mathematics

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A stone is dropped into a quiet lake and waves move in circles at a speed of 4 cm/sec. At the instant when the radius of the circular wave is 10 cm, how fast is the enclosed area increasing?

[6] Applications of Derivatives

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Chapter: [6] Applications of Derivatives
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A man 160 cm tall, walks away from a source of light situated at the top of a pole 6 m high, at the rate of 1.1 m/sec. How fast is the length of his shadow increasing when he is 1 m away from the pole?

[6] Applications of Derivatives

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Chapter: [6] Applications of Derivatives
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A man 180 cm tall walks at a rate of 2 m/sec. away, from a source of light that is 9 m above the ground. How fast is the length of his shadow increasing when he is 3 m away from the base of light?

[6] Applications of Derivatives

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Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined

A ladder 13 m long leans against a wall. The foot of the ladder is pulled along the ground away from the wall, at the rate of 1.5 m/sec. How fast is the angle θ between the ladder and the ground is changing when the foot of the ladder is 12 m away from the wall.

[6] Applications of Derivatives

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Chapter: [6] Applications of Derivatives
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\[s^2 \frac{d^2 t}{d s^2} + st\frac{dt}{ds} = s\]

[9] Differential Equations

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Chapter: [9] Differential Equations
Concept: undefined >> undefined

A particle moves along the curve y = x² + 2x. At what point(s) on the curve are the x and y coordinates of the particle changing at the same rate?

[6] Applications of Derivatives

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Chapter: [6] Applications of Derivatives
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If y = 7x − x³ and x increases at the rate of 4 units per second, how fast is the slope of the curve changing when x = 2?

[6] Applications of Derivatives

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Chapter: [6] Applications of Derivatives
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A particle moves along the curve y = x³. Find the points on the curve at which the y-coordinate changes three times more rapidly than the x-coordinate.

[6] Applications of Derivatives

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Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined

\[\frac{d^3 y}{d x^3} + \left( \frac{d^2 y}{d x^2} \right)^3 + \frac{dy}{dx} + 4y = \sin x\]

[9] Differential Equations

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Chapter: [9] Differential Equations
Concept: undefined >> undefined

Find an angle θ which increases twice as fast as its cosine ?

[6] Applications of Derivatives

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Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined

(xy² + x) dx + (y − x²y) dy = 0

[9] Differential Equations

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Chapter: [9] Differential Equations
Concept: undefined >> undefined

\[\sqrt{1 - y^2} dx + \sqrt{1 - x^2} dx = 0\]

[9] Differential Equations

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Chapter: [9] Differential Equations
Concept: undefined >> undefined

Find an angle θ whose rate of increase twice is twice the rate of decrease of its cosine ?

[6] Applications of Derivatives

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Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined

\[\frac{d^2 y}{d x^2} = \left( \frac{dy}{dx} \right)^{2/3}\]

[9] Differential Equations

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Chapter: [9] Differential Equations
Concept: undefined >> undefined

\[2\frac{d^2 y}{d x^2} + 3\sqrt{1 - \left( \frac{dy}{dx} \right)^2 - y} = 0\]

[9] Differential Equations

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Chapter: [9] Differential Equations
Concept: undefined >> undefined

\[5\frac{d^2 y}{d x^2} = \left\{ 1 + \left( \frac{dy}{dx} \right)^2 \right\}^{3/2}\]

[9] Differential Equations

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Chapter: [9] Differential Equations
Concept: undefined >> undefined

\[y = x\frac{dy}{dx} + a\sqrt{1 + \left( \frac{dy}{dx} \right)^2}\]

[9] Differential Equations

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Chapter: [9] Differential Equations
Concept: undefined >> undefined

\[y = px + \sqrt{a^2 p^2 + b^2},\text{ where p} = \frac{dy}{dx}\]

[9] Differential Equations

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Chapter: [9] Differential Equations
Concept: undefined >> undefined

\[\frac{d^2 y}{d x^2} + 3 \left( \frac{dy}{dx} \right)^2 = x^2 \log\left( \frac{d^2 y}{d x^2} \right)\]

[9] Differential Equations

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Chapter: [9] Differential Equations
Concept: undefined >> undefined

\[\left( \frac{d^2 y}{d x^2} \right)^2 + \left( \frac{dy}{dx} \right)^2 = x \sin \left( \frac{d^2 y}{d x^2} \right)\]

[9] Differential Equations

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Chapter: [9] Differential Equations
Concept: undefined >> undefined

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PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Mathematics

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