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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
$\frac{π}{2}$
$- \frac{π}{2}$

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

$\frac{π}{2 ab}$

$\frac{πb}{4 a}$

$\frac{πa}{2 b}$

$\frac{πa}{4 b}$

$\frac{π}{2 ab}$

$I = \int_{0}^{\frac{π}{2}} \frac{1}{a^{2} . \sin^{2} (x) + b^{2} . \cos^{2} (x)} dx = \int_{0}^{\frac{π}{2}} \frac{\sec^{2} (x)}{a^{2} . \tan^{2} (x) + b^{2}} dx Put \tan (x) = t \Rightarrow \sec^{2} (x) dx = dt When x = 0, t = \tan (0) and x = \frac{π}{2}, t = \tan (\frac{π}{2}) = \infty ∴ I = \int_{0}^{\infty} \frac{dt}{a^{2} t^{2} + b^{2}} = \frac{1}{a^{2}} \int_{0}^{\infty} \frac{dt}{t^{2} + {(\frac{b}{a})}^{2}} = \frac{1}{a^{2}} . \frac{1}{(\frac{b}{a})} {[\tan^{- 1} (\frac{t}{(\frac{b}{a})})]}_{0}^{\infty} = \frac{1}{ab} [\tan^{- 1} (\infty) - \tan^{- 1} (0)] = \frac{1}{ab} \frac{π}{2} = \frac{π}{2 ab}$

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