Q87.If p and q are positive real numbers such that p2 + q2 = 1 , then the maximum value of (p + q) is (1) 2 (2) 1/2 (3) 1 (4) √2 √2

Q93.Suppose the cube x3 −px + q has three distinct real roots where p > 0 and q > 0. Then which one of the following holds? (1) The cubic has minima at √p3 and maxima at (2) The cubic has minima at −√p3 and maxima at −√p3 √p3 and The cubic has maxima at both and (3) The cubic has minima at both √p3 −√p3 (4) √p3 −√p3

Q94.How many real solutions does the equation x7 + 14x5 + 16x3 + 30x −560 = 0 have? (1) 7 (2) 1 (3) 3 (4) 5

Q81.Given P(x) = x4 + ax3 + bx2 + cx + d such that x = 0 is the only real root of P ′(x) = 0 . If P(−1) < P(1), then in the interval [−1, 1] (1) P(−1) is the minimum and P(1) is the (2) P(−1) is not minimum but P(1) is the maximum maximum of P of P (3) P(−1) is the minimum and P(1) is not the (4) neither P(−1) is the minimum nor P(1) is the maximum of P maximum of P