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1

### 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.

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

### IIT-JEE 1985

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

$${{{\pi ^2}} \over {16}}$$
3

### IIT-JEE 1984

Subjective
Find the area of the region bounded by the $$x$$-axis and the curves defined by $$y = \tan x, - {\pi \over 3} \le x \le {\pi \over 3};\,\,y = \cot x,{\pi \over 6} \le x \le {{3\pi } \over 2}$$\$

$$\log {3 \over 2}$$ sq. units
4

### IIT-JEE 1984

Subjective
Given a function $$f(x)$$ such that
(i) it is integrable over every interval on the real line and
(ii) $$f(t+x)=f(x),$$ for every $$x$$ and a real $$t$$, then show that
the integral $$\int\limits_a^{a + 1} {f\,\,\left( x \right)} \,dx$$ is independent of a.

Solve it.

### Joint Entrance Examination

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NEET

Class 12