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JEE Mathematics Solved Question Paper 2011

Multiple Choice Questions

21.

A unit vector perpendicular to both i + j + k and 2i + j + 3k is

$2 i - j - k$
$\frac{(3 i + j - 2 k)}{\sqrt{6}}$

22.

The value of $\int_{0}^{4} |x - 1| dx$ is

$\frac{5}{2}$
5
4
1

23.

If I_n = $\int_{0}^{\frac{π}{4}} \tan^{n} (x) dx$ , where where n is apositive integer, then $I_{10} + I_{8}$ is

$\frac{1}{9}$
$\frac{1}{8}$
$\frac{1}{7}$
9

24.

If I_n = $\int e^{x} [\frac{\sin (x) + \cos (x)}{1 - \sin^{2} (x)}] dx$ is

$(e^{x} . \csc (x)) + C$
$(e^{x} . \cot (x)) + C$
$(e^{x} . \sec (x)) + C$
$(e^{x} . \tan (x)) + C$

25.

When x > 0, then $\int \cos^{- 1} (\frac{1 - x^{2}}{1 + x^{2}}) dx$ is

$2 [{xtan}^{- 1} (x) - \log (1 + x^{2})] + C$
$2 [{xtan}^{- 1} (x) + \log (1 + x^{2})] + C$
$2 {xtan}^{- 1} (x) + \log (1 + x^{2}) + C$
$2 {xtan}^{- 1} (x) - \log (1 + x^{2}) + C$

26.

If the area between y = mx² and x = my² (m > 0) is 1/4 sq units, then the value of m is

$\pm 3 \sqrt{2}$
$\pm \frac{2}{\sqrt{3}}$
$\sqrt{2}$
$\sqrt{3}$

27.
If m and n are degree and order of ${(1 + y_{1}^{2})}^{\frac{2}{3}} = y_{2}$ , then the value of $\frac{m + n}{m - n}$ is

3

4

5

2

$Given differential equation is {(1 + y_{1}^{2})}^{\frac{2}{3}} = y_{2} {(1 + {(\frac{dy}{dx})}^{2})}^{\frac{2}{3}} = (\frac{d^{2} y}{{dx}^{2}}) \Rightarrow {(1 + {(\frac{dy}{dx})}^{2})}^{2} = {(\frac{d^{2} y}{{dx}^{2}})}^{3} Now, order = n = 2 and degree = m = 3 Then, \frac{m + n}{m - n} = \frac{3 + 2}{3 - 2} = 5$