IIT-JEE-Mathematics-Mains-2002

Mains

Time : Two hours    Max. Marks : 60
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Instructions

1.     The Question Paper has 4 printed pages and has 12 questions. Please ensure that the copy of the Question Paper you have received contains all the questions.

2.     Attempts ALL questions. Each question carries 5 marks.

3.     Answer each question starting on a new page. The corresponding Question number must be written in the left margin.

4.     Do not write more than one answers for the same question. In case you attempt a question more than once, please cancel the answer(s) you consider to be wrong. Otherwise, only the answer appearing last will be evaluated.

5.     Use only Arabic numerals (0, 1, 2 .............9) in answering the questions irrespective of the language in which your answer.

6.     Use of logarithmic tables is NOT PERMITTED.

7.     Use of calculators is NOT PERMITTED.

8.     Both magnitude and direction of vector quantities, if any, in your answer should be indicated clearly.

9.     Irrational numbers, if any, in your answer need not be expressed in decimal form.

10. If the final answer appears in the form of a ratio or a product of two numbers, that need not to be further simplified.
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1.         Let a, b be positive real numbers. If a, A₁, A₂, be are in arithmetic progression, a, G₁, G₂, b are in geometric progression and a, H₁, H₂, b are in harmonic progression, show that

       (G1 G2)/(H1 H2 ) = (A1+A2)/(H1+H2 ) = ((2a+b)(a+2b))/9ab

2.         Use mathematical induction to show that (25)ⁿ⁺¹ - 24n + 5735 is divisible by (24)² for all n = 1, 2

3.         Prove that cos tan^-1 sin cot^-1 x = √((x2+1)/(x2 +2))..

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