Maths
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Easy
Question
If the chord joining two points whose eccentric angles are and cuts the major axis of an ellipse + = 1 at a distance c from the centre, then tan . tan is equal to
 1
 c


The correct answer 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
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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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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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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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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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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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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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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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