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# IIT-JEE-Mathematics–1997

Time : Three Hours                                                           Max. Marks : 100
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Instructions :

2. The paper consists of seven printed pages (17 questions).
3. Answer to next question should start after drawing a separating horizontal line with a space of 3cm.
4. All sub-questions of a question should be answered at one place in the same order as in the question paper.
5. There is no negative marking.
6. Use of all type of calculating devices, Graph paper, Logarithmic/Trigonometric/ Statistical Tables is prohibited.
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1. There are five sub-questions in this question. For answering each sub-question, four alternatives are given, and only one of them is correct. Indicate your answer for each sub-question by writing one of the letters A, B, C or D ONLY in the answer-book.

(i) If g (x)= ∫0xcos4  t dt, then g (x + pequals :

(A) g (x)+ g (π)                         (B) g (x)- g (π)
(C) g (x)g (π)                            (D) (g (x))/(g (x))

(ii) If f (x)= x / sinx and g (x)= x  / tanx , where 0 < x £ 1, then in this interval :
(A) Both f (x) and g (x) are increasing functions.
(B) Both f (x) and g (x) are decreasing functions.
(C) f (x) is an increasing function.
(D) g (x) is an increasing function.

(iii) The parameter, on which the value of the determinant does not depend upon is :

(A) a                                         (B) p
(C) d                                         (D) x

(iv) The graph of the function cos x (x + 2) – cos2 (x + 1) is:

(A) a straight line passing through (0, – sin2 1) with slope 2
(B) a straight line passing through (0, 0)
(C) a parabola with vertex (1, – sin2, 1)
(D) a straight line passing through the point (π/2,-sin2 1) and parallel to the x-axis.