1. | 1. Consider the two curves C1 : y2 = 4 x C2 : x2 + y2 − 6x + 1 = 0 | Then, |
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Half-n-half Clue
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2. | 2. If 0 < x < 1, then √(1 + x2 ) [ {x cos (cot−1 x) + sin (cot−1 x)}2 −1 ]1/2 = |
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3. | 3. The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors a^, b^, c^such that a^ ⋅ b^ = b^ ⋅ c^ = c^ ⋅ a^ = | 1 2 | . | Then, the volume of the parallelopiped is |
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4. | 4. Let a and b be non-zero real numbers. Then, the equation (a x2 + b y2 + c) (x2 − 5 x y + 6 y2) = 0 represents |
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5. | 5. Let g (x) = | (x − 1)n log cosm (x − 1) | ; | 0 < x < 2, m and n are integers, m ≠ 0, n > 0, and let p be the left hand derivative of |x − 1| at x = 1. If then |
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6. | 6. The total number of local maxima and local minima of the function f (x) = | { | (2 + x)3 , | −3 < x ≤ −1 | x2/3 , | −1 < x < 2 | is |
| Half-n-half Clue
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7. | 7. A straight line through the vertex P of a triangle PQR intersects the side QR at the point S and the circumcircle of the triangle PQR at the point T . If S is not the centre of the circumcircle, then |
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