IITJEE-2011-Maths-Paper-2-PSS-1

1) If , then the value of  is (a) (b) (c) (d)  (2) Let be a continuous function such that f(x) = f(1 – x) for all Let and be the area of the region bounded by y = f(x) ,x = –1, x = 2 and the x-axis. Then (a) (b) (c) (d)  (3) Let and g(x) = sin x for all . Then the set of all x satisfying (f o g o g o f) (x) = (g o g o f) (x). where (f o g) (x) = f(g(x)), is (a) (b) (c) (d)  (4) Let (x, y) be any point on the parabola . Let b the point that divides the line segment from (0, 0) to (x, y) in the ratio 1 : 3. Then the locus of P is (a) (b) (c) (d)  (5) Let (6, 3) be a point on the hyperbola . If the normal at the point P intersects the x-axis at (9, 0), then the eccentricity of the hyperbola is (a) (b) (c) (d)  (6) A value of b for which the equations have one root in common is (a) (b) (c) (d)  (7) Let be a cube root of unity and S be the set of all non-singular matrices of the form , where each of a, b and c is either . Then the number of the distinct matrices in the set S is (a) 2 (b) 6 (c) 4 (d) 8  (8) The circle passing through the point (–1, 0) and touching the y-axis at (0, 2) also passes through the point (a) (b) (c) (d) (–4, 0)  (9) If then (a) f(x) is continuous at x = –/2 (b) f(x) is differentiable at x = 0 (c) f(x) is differentiable at x = 1 (d) f(x) is differentiable at x = –3/2  (10) Let be defined , where be is a constant such that 0 < b < 1. Then (a) f is not invertible on (0, 1) (b) (c) (d) is differentiable on (0, 1)  (11) Let L be a normal to the parabola . If L passes through the point (9, 6), then L is given by (a) y – x + 3 = 0 (b) y + 3x – 33 = 0 (c) y + x – 15 = 0 (d) y – 2x + 12 = 0  (12) Let E and F be two independent events. The probability that exactly one of them occurs is and the probability of none of them occurring is . If P(T) denotes the probability of occurrence of the event T, then (a) (b) (c) (d)  IITJEE – 2011 - Maths Paper–2-PSS-1 www.learnersplanet.com www.learnersplanet.com IITJEE – 2011 - Maths Paper-2-PSS–1 www.learnersplanet.com