Arts (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

Mathematics

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

[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

(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

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Arts (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

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