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12th Maths Practice paper-04

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MATHEMATICS Class II PreUni Plus 2016-2017 Practice Paper - 04 Take Home Max. Marks Duration 100 3 hours 15 minutes Instructions 1. Do not overwrite. 2. Draw a line using pen at the end of each answer. 3. Steps adopted in solving problems should be clearly shown. 4. In case of violation of the above conditions, the answer scripts will not be considered for valuation. PART - A I. Answer ALL the following (ONE mark each) [10 1 = 10] 1. Give an example of a relation which is transitive but neither reflexive nor symmetric. 3 2. Find the value of sin 1 sin . 5 3. Construct a 2 2 matrix A = [aij] whose elements are given by a ij i j 2 2 . 3 2 1 0 4. Find X if Y = and 2X Y 1 4 3 2 5. If y = sec tan x find dy . dx 6. Find the integral of tan2(2x 3) w.r.t. x. 7. Find the direction cosines of the vector i 2 j 3k . 8. Find the distance of the plane 2x 3y + 4z 6 = 0 from the origin. 9. Define feasible region of a linear programming problem. 3 1 1 10. If P A , P B find P(A B). If A and B are independent events such that P(A) , then find 5 5 5 P(A B). PART - B II. Answer any TEN of the following (TWO marks each) 11. Show that f : R0 R0 defined by f(x) = 1 is one-one and onto where R0 is the set of all non-zero real x numbers. 3 cos x 12. Express tan 1 x in the simplest form. , 2 1 sin x 2 3 3 13. Evaluate tan sin 1 cot 1 . 5 2 2P1617MPP4 [10 2 = 20] 1

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