Commerce (English Medium) कक्षा १२ - CBSE Question Bank Solutions

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

[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

(y'')² + (y')³ + sin y = 0

[9] Differential Equations

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

The top of a ladder 6 metres long is resting against a vertical wall on a level pavement, when the ladder begins to slide outwards. At the moment when the foot of the ladder is 4 metres from the wall, it is sliding away from the wall at the rate of 0.5 m/sec. How fast is the top-sliding downwards at this instance?
How far is the foot from the wall when it and the top are moving at the same rate?

[6] Applications of Derivatives

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

\[\frac{d^2 y}{d x^2} + 5x\left( \frac{dy}{dx} \right) - 6y = \log x\]

[9] Differential Equations

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

\[\frac{d^3 y}{d x^3} + \frac{d^2 y}{d x^2} + \frac{dy}{dx} + y \sin y = 0\]

[9] Differential Equations

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

\[\frac{dy}{dx} + e^y = 0\]

[9] Differential Equations

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

\[\left( \frac{dy}{dx} \right)^3 - 4 \left( \frac{dy}{dx} \right)^2 + 7y = \sin x\]

[9] Differential Equations

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

A balloon in the form of a right circular cone surmounted by a hemisphere, having a diameter equal to the height of the cone, is being inflated. How fast is its volume changing with respect to its total height h, when h = 9 cm.

[6] Applications of Derivatives

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

Water is running into an inverted cone at the rate of π cubic metres per minute. The height of the cone is 10 metres, and the radius of its base is 5 m. How fast the water level is rising when the water stands 7.5 m below the base.

[6] Applications of Derivatives

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

A man 2 metres high walks at a uniform speed of 6 km/h away from a lamp-post 6 metres high. Find the rate at which the length of his shadow increases ?

[6] Applications of Derivatives

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

The surface area of a spherical bubble is increasing at the rate of 2 cm²/s. When the radius of the bubble is 6 cm, at what rate is the volume of the bubble increasing?

[6] Applications of Derivatives

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

The radius of a cylinder is increasing at the rate 2 cm/sec. and its altitude is decreasing at the rate of 3 cm/sec. Find the rate of change of volume when radius is 3 cm and altitude 5 cm.

[6] Applications of Derivatives

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

The volume of metal in a hollow sphere is constant. If the inner radius is increasing at the rate of 1 cm/sec, find the rate of increase of the outer radius when the radii are 4 cm and 8 cm respectively.

[6] Applications of Derivatives

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

Sand is being poured onto a conical pile at the constant rate of 50 cm³/ minute such that the height of the cone is always one half of the radius of its base. How fast is the height of the pile increasing when the sand is 5 cm deep ?

[6] Applications of Derivatives

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

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Commerce (English Medium) कक्षा १२ - CBSE Question Bank Solutions

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