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JEE Mathematics Solved Question Paper 2017

Multiple Choice Questions

21.
$\int_{\frac{- π}{2}}^{\frac{π}{2}} \frac{dx}{e^{\sin (x)} + 1}$

1

0

$\frac{π}{2}$

$- \frac{π}{2}$

$\frac{π}{2}$

$Let I = \int_{\frac{- π}{2}}^{\frac{π}{2}} \frac{dx}{e^{\sin (x)} + 1} . . . (i) \Rightarrow I = \int_{\frac{- π}{2}}^{\frac{π}{2}} \frac{dx}{e^{- \sin (x)} + 1} [∵ \int_{a}^{b} f (a + b - x) dx = \int_{a}^{b} f (x) dx] = \int_{\frac{- π}{2}}^{\frac{π}{2}} \frac{e^{\sin (x)}}{e^{\sin (x)} + 1} dx . . . (ii) On adding Eqs . (i) and (ii), we get 2 I = \int_{\frac{- π}{2}}^{\frac{π}{2}} \frac{e^{\sin (x)} + 1}{e^{\sin (x)} + 1} dx = \int_{\frac{- π}{2}}^{\frac{π}{2}} 1 dx = {[x]}_{\frac{- π}{2}}^{\frac{π}{2}} = π ∴ I = \frac{π}{2}$

22.

If a and b are unit vectors, then angle between a and b for $\sqrt{3} a - b$ to be unit vectori

45°
60°
90°
30°

23.

$\int_{- 5}^{5} |x + 2| dx$ is equal to

24.

$\int_{0}^{\frac{π}{2}} \frac{1}{a^{2} . \sin^{2} (x) + b^{2} . \cos^{2} (x)} dx$

$\frac{π}{2 ab}$
$\frac{πb}{4 a}$
$\frac{πa}{2 b}$
$\frac{πa}{4 b}$

25.

$\int \sqrt{x^{2} + 2 x + 5} dx$ is equal to

$\frac{1}{2} (x + 1) \sqrt{x^{2} + 2 x + 5} + 2 \log |x + 1 + \sqrt{x^{2} + 2 x + 5}| + C$
$(x + 1) \sqrt{x^{2} + 2 x + 5} + \frac{1}{2} \log |x + 1 + \sqrt{x^{2} + 2 x + 5}| + C$
$(x + 1) \sqrt{x^{2} + 2 x + 5} + 2 \log |x + 1 + \sqrt{x^{2} + 2 x + 5}| + C$
$(x + 1) \sqrt{x^{2} + 2 x + 5} - 2 \log |x + 1 + \sqrt{x^{2} + 2 x + 5}| + C$

26.

A box has 100 pens of which 10 are defective. The probability that out of a sample of 5 pens drawn one by one with replacement and atmost one is defective, is