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    Let a, b, c be any real numbers. Suppose that there are real numbers x, y, z not all zero such that x = cy + bz, y = az + cx and z = bx + ay. Then a^2 + b^2 + c^2 + 2abc is equal to

  • Question 3
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    Let the line (x - 2)/3 = (y - 1)/ -5 = (z + 2)/2 lies in the plane x + 3y - αz + β= . Then (α, β) equals

  • Question 4
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    If the mean deviation of number 1, 1 + d, 1 + 2d, ….. , 1 + 100d from their mean is 255, then the d is equal to

  • Question 5
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    The solution of the differential equation dy/dx = (x + y)/ x satisfying the condition y (1) = 1 is

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    Three distinct points A, B and C are given in the 2 – dimensional coordinate plane such that the ratio of the distance of any one of them from the point (1, 0) to the distance from the point ( - 1, 0) is equal to 1/3 . Then the circumcentre of the triangle ABC is at the point

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  • Question 10
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    The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is

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