T2.doc - IIT-JEE AIPMT Engineer Your Education to Success...

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IIT-JEE/ AIPMT Engineer Your Education to Success with a Group Exclusive of NITIANS D-8 KOELNAGAR, D-71 KOELNAGAR, L-46 BASANTI COLONY CBSE X | Mathematics Time: 3 hours Total Marks: 90 General Instructions: 1. All questions are compulsory. 2. The question paper consists of 31 questions divided into four sections – A, B, C and D. 3. Section A contains 4 questions of 1 mark each. Section B contains 6 questions of 2 marks each, Section C contains 10 questions of 3 marks each and Section D contains 11 questions of 4 marks each. 4. Use of calculator is not permitted. SECTION A 1. In the below given figure, a tower AB is 20 m high and BC, its shadow on the ground, is 20 3 m long. Find the sun’s altitude. 2. Two different dice are tossed together. Find the probability that the product of the two numbers on the top of the dice is 6. 3. If the quadratic equation px 2 − 2 5px + 15 = 0 has two equal roots then find the value of p. 4. In the figure given below, PQ is a chord of a circle with centre O and PT is a tangent. If QPT = 60°, find PRQ.
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SECTION B 5. In an A.P., if S5 + S7 = 167 and S10 = 235, then find the A.P., where Sn de notes the sum of its first n terms. 6. The points A(4, 7), B(p, 3) and C(7, 3) are the vertices of a right triangle, right-angled at B. Find the values of p. 7. In the below given figure, fig 2.two tangents RQ and RP are drawn from an external point R to the circle with centre O. If PRQ = 120°, then prove that OR = PR + RQ.
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