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1

IIT-JEE 1987

Subjective
Find the area bounded by the curves, $${x^2} + {y^2} = 25,\,4y = \left| {4 - {x^2}} \right|$$ and $$x=0$$ above the $$x$$-axis.

Answer

$$4 + 25{\sin ^{ - 1}}{4 \over 5}$$
2

IIT-JEE 1986

Subjective
Evaluate : $$\int\limits_0^\pi {{{x\,dx} \over {1 + \cos \,\alpha \,\sin x}},0 < \alpha < \pi } $$

Answer

$${{\pi \alpha } \over {\sin x}}$$
3

IIT-JEE 1985

Subjective
Sketch the region bounded by the curves $$y = \sqrt {5 - {x^2}} $$ and $$y = \left| {x - 1} \right|$$ and find its area.

Answer

$${{5\pi - 2} \over 4}$$ sq. units
4

IIT-JEE 1985

Subjective
Evaluate the following : $$\,\,\int\limits_0^{\pi /2} {{{x\sin x\cos x} \over {{{\cos }^4}x + {{\sin }^4}x}}} dx$$

Answer

$${{{\pi ^2}} \over {16}}$$

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Class 12