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# ISC Class XII Prelims 2020 : Mathematics (Deepti Convent Higher Secondary School, Shujalpur, Shajapur)

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PRE-BOARD EXAMINATION 2019 20 (Maximum Marks: 100) Class XII Time: 3 Hours MATHEMATICS Candidates are allowed additional 15 minutes for only reading the paper. They must NOT start writing during this time. The question paper consists of three sections A, B and C. Candidates are required to attempt all questions from Section A and all questions EITHER from Section B OR Section C. Section A: Internal choice has been provided in three questions of four marks each and two questions of six marks each. Section B: Internal choice has been provided in two questions of four marks each. Section C: Internal choice has been provided in two questions of four marks each. All working, including rough work, should be done on the same sheet as, and adjacent to the rest of the answer. SECTION A (80 Marks) Question 1. Each question carry 2 marks [10x2 =20 marks] 1. Determine whether the binary operation * defined on Q defined as a * b ab 1 , is commutative and associative. 2. Find the intervals in which the function f ( x) sin x cos x , 0 x 2 , is strictly increasing. 3. Two integers are selected at random from the integers 1 to 11. If the sum is even, find the probability that both the numbers are odd. 4. Using LHospital s Rule, evaluate: Lt x x . x 0 5. Evaluate: 1 sin x cos 2 x dx 2 6. Using properties of definite integrals, evaluate: sin 2 x a b cos xdx 0 dy sin x y sin x y . 7. Solve the differential equation: dx 3 1 8. Evaluate: sin 1 2 tan 1 . 3 2 9. Find a point on the curve x 2 y 2 2 x 4 y 1 0 at which the tangent is parallel to the chord joining (2, 0) and (4, 4). 10. Using matrix method, check whether the following system of equations is consistent or not: 2 x 5 y 7; 6 x 15 y 13.

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