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IIT JEE previous years question papers
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IIT-JEE-Mathematics–1997
Time : Three Hours
Max.
Marks : 100
______________________________________________________________________
Instructions :
1. Answer all questions in the language of your choice as shown
in your admit card.
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.
_____________________________________________________________________
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 + p) equals :
(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 :
.JPG)
(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.
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