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Maths-

General

Easy

Question

P(a cos $theta$ , b sin $theta$ ) is any point on the ellipse $fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction$ + $fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction$ = 1 $left parenthesis a greater than b right parenthesis$ Now if this ellipse is rotated anticlockwise by 90º and P reaches $straight P to the power of straight prime$ then co-ordinate of $straight P to the power of straight prime$ are -

(a sin $θ$ , b cos $θ$ )
(b sin $θ$ , a cos $θ$ )
(–b sin $θ$ , a cos $θ$ )
None of these

The correct answer is: (–b sin $theta$ , a cos $theta$ )

Related Questions to study

Normal to the ellipse $fraction numerator x to the power of 2 end exponent over denominator 84 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 49 end fraction equals 1$ intersects the major and minor axis at P and Q respectively then locus of the point dividing segment PQ in 2 : 1 is -

Normal to the ellipse $fraction numerator x to the power of 2 end exponent over denominator 84 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 49 end fraction equals 1$ intersects the major and minor axis at P and Q respectively then locus of the point dividing segment PQ in 2 : 1 is -

Given graph gives variation of $fraction numerator P V over denominator T end fraction$ with P for 1gm of oxygen at two different temperatures T₁ and T₂. If density of oxygen $1.427 k g divided by m to the power of 3 end exponent.$ The value of $fraction numerator P V over denominator T end fraction$ at point A and relation $b divided by w T subscript 1 end subscript & T subscript 2 end subscript text is end text$

Given graph gives variation of $fraction numerator P V over denominator T end fraction$ with P for 1gm of oxygen at two different temperatures T₁ and T₂. If density of oxygen $1.427 k g divided by m to the power of 3 end exponent.$ The value of $fraction numerator P V over denominator T end fraction$ at point A and relation $b divided by w T subscript 1 end subscript & T subscript 2 end subscript text is end text$

physics-General

Legume plants are important for crop production because they :

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parallel

The limiting value of (cos x)^{1/sin x} as x → 0 is :

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Let f : R → R be a differentiable function satisfying f (x) = f (x – y) f (y) " x, y Î R and f ¢ (0) = a, f ¢ (2) = b then f ¢ (-2) is

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A thin equiconvex lens of refractive index 3/2 is placed on a horizontal plane mirror as shown in figure. The space between the lens and the mirror is filled with a liquid of refractive index 4/3. It is found that when a point object is placed 15 cm above the lens on its principal axis, the object coincides with its own image. If another liquid is filled instead of water, the object and the image coincide at a distance 25 cm from the lens. Calculate the refractive index of the liquid

A thin equiconvex lens of refractive index 3/2 is placed on a horizontal plane mirror as shown in figure. The space between the lens and the mirror is filled with a liquid of refractive index 4/3. It is found that when a point object is placed 15 cm above the lens on its principal axis, the object coincides with its own image. If another liquid is filled instead of water, the object and the image coincide at a distance 25 cm from the lens. Calculate the refractive index of the liquid

physics-General

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A thin equiconvex lens of refractive index 3/2 is placed on a horizontal plane mirror as shown in figure. The space between the lens and the mirror is filled with a liquid of refractive index 4/3. It is found that when a point object is placed 15 cm above the lens on its principal axis, the object coincides with its own image. The radius of curvature of the convex surface is

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physics-General

A glass shere of radius 2R and refractive index ‘n’ has a spherical. When viewer is on right side of the hollow sphere, what will be the apparent change in position of the object?

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physics-General

A glass shere of radius 2R and refractive index ‘n’ has a spherical. When viewer is on left side of the hollow sphere, what will be the shift in position of the object?

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physics-General

parallel

Consider the situation in the figure. The bottom of the pot is a reflecting plane mirror, S is a small fish, and T is a human eye. Refractive index of water is m. At what distance from itself will the eye see the image of the fish by observing from the mirror?

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Consider the situation in the figure. The bottom of the pot is a reflecting plane mirror, S is a small fish, and T is a human eye. Refractive index of water is m. At what distance from it self will the eye see the image of the fish upon direct observation?

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physics-General

Consider the situation in the figure. The bottom of the pot is a reflecting plane mirror, S is a small fish, and T is a human eye. Refractive index of water is m. At what distance from itself will the fish see or observe the image of eye by observing through mirror is

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physics-General

parallel

Consider the situation in the figure. The bottom of the pot is a reflecting plane mirror, S is a small fish, and T is a human eye. Refractive index of water is m. At what distance from itself will the fish see the image of the eye by direct observation?

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physics-General

A point object O is placed in front of a concave mirror of focal length 10 cm. A glass slab of refractive index m = 3/ 2 and thicikness 6 cm is inserted between the object and mirror. Find the position of the final image when the distance x shown in figure is 20cm

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A point object O is placed in front of a concave mirror of focal length 10 cm. A glass slab of refractive index m = 3/ 2 and thicikness 6 cm is inserted between the object and mirror. Find the position and nature of the final image when the distance x shown in figure, is 5 cm

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