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    For three events A, B and C, P(Exactly one of A or B occurs) = P(Exactly one of B or C occurs) = P(Exactly one of C or A occurs) = 1/4 and P(All the three events occur simultaneously) = 1/16. Then the probability that at least one of the events occurs, is:

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    PQR is a triangular park with PQ = PR = 200m. A T.V. tower stands at the mid-point of QR. If the angles of elevation of the top of the tower at P, Q and R are respectively 45°, 30° and 30°, then the height of the tower (in m) is :

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    If S is the set of distinct values of 'b' for which the following system of linear equationsx + y + z = 1x + ay + z = 1ax + by + z = 0has no solution, then S is:

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    The eccentricity of an ellipse whose centre is at the origin is 1/2. If one of its directrices is x = – 4, then the equation of the normal to it at (1, 3/2) is:

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    Let a vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point on the ground such that AP = 2AB. If angle BPC = β , then tan β is equal to:

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