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12th Maths Sectionwise paper - 01 (R&F, Inv Trig, Matrices & Determinants)

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MATHEMATICS Class II PU Plus 2016-17 Topics Sectionwise Test - 01 Relation, Functions, Inverse Trigonometric Function, Matrices and Determinants Max. marks 100 Duration Date 3 hrs 15 min 22-12-2016 Instructions 1. The questions paper has four parts: A, B, C and D. All parts are compulsory. 2. Write balanced chemical equations and draw labeled diagrams wherever required. 3. Use log tables and the simple calculator if necessary. (Use of scientific calculators is not allowed). PART A I. Answer the following questions [10 1 = 10] 1. Show that the relation R in the set {1, 2, 3} given by R = {(1, 2) (2, 2) (3, 3) (1, 2) (2, 3)} is not transitive. 2. Let be a binary operation defined on the set of rational numbers Q defined by a b = ab + 1 prove that is commutative. 3. Define one-one function. 1 4. Find the principal value of cot 1 . 3 1 5. Find the value of tan 1 2cos 2sin 1 2 6. Write the domain of f(x) = cos 1 x. 7. Define a scalar matrix. 8. Construct a 3 2 matrix whose elements are given by a ij 1 i 3j . 2 4 7 9. If A find | 3 A |. 3 5 10. If 3 x 3 2 find the value of x. x 1 4 1 PART B II. Answer any TEN of the following questions [10 2 = 20] 11. Find g f and f g if f : R R and g : R R are given by f(x) = cos x and g(x) = 3x 12. Check whether the function f: R R given by f(x) = x2 is injectivity and surjectivity. 13. Verify whether the operation defined on Q by a b ab is associative or not. 2 2P1617MSWT1 1 2

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