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JEE Mathematics Solved Question Paper 2017

Multiple Choice Questions

31.

The degree of the differential equation ${[1 + {(\frac{dy}{dx})}^{2}]}^{2} = \frac{d^{2} y}{{dx}^{2}}$ is

32.

$\int \frac{\cos (2 x) - \cos (2 θ)}{\cos (x) - \cos (θ)} dx$ is equal to

$2 (\sin (x) + xcos (θ))$
$2 (\sin (x) - xcos (θ))$
$2 (\sin (x) + 2 xcos (θ))$
$2 (\sin (x) - 2 xcos (θ))$

33.

If a $= 2 \hat{i} + λ \hat{j} + \hat{k}$ and b = $\hat{i} + 2 \hat{j} + 3 \hat{k}$ are orthogonal, then value of $λ$ is

3/2
1
0
- 5/2

34.

If a, b, c are unit vectors such that a + b + c = 0, then the value of a · b + b · c + c · a is equal to

3/2
1
3
- 3/2

35.

The plane 2x - 3y + 6z - 11 = 0 makes an angle sin^-1( $α$ ) with X-axis, the value of $α$ is equal to

$\frac{\sqrt{2}}{3}$
$\frac{2}{7}$
$\frac{\sqrt{3}}{2}$
$\frac{3}{7}$

36.

$\int_{0.2}^{3.5} [x] dx$ is equal to

37.

The perpendicular distance of the point P(6, 7, 8) from XY-plane is

38.

The integrating factor of the differential equation $x . \frac{dy}{dx} + 2 y = x^{2} is (x \neq 0)$

x
$\log |x|$
x²
$e^{\log (x)}$

39.
$\int_{0}^{\frac{π}{2}} \frac{\tan^{7} (x)}{\cot^{7} (x) + \tan^{7} (x)} dx$ is equal to

$\frac{π}{4}$

$\frac{π}{2}$

$\frac{π}{6}$

$\frac{π}{3}$

$\frac{π}{4}$

$Let I = \int_{0}^{\frac{π}{2}} \frac{\tan^{7} (x)}{\cot^{7} (x) + \tan^{7} (x)} dx . . . (i) \Rightarrow I = \int_{0}^{\frac{π}{2}} \frac{\tan^{7} (\frac{π}{2} - x)}{\cot^{7} (\frac{π}{2} - x) + \tan^{7} (\frac{π}{2} - x)} dx \Rightarrow I = \int_{0}^{\frac{π}{2}} \frac{\cot^{7} (x)}{\cot^{7} (x) + \tan^{7} (x)} d x . . . (ii) On adding Eqs . (i) and (ii), we get 2 I = \int_{0}^{\frac{π}{2}} \frac{\tan^{7} (x) + \cot^{7} (x)}{\cot^{7} (x) + \tan^{7} (x)} dx = \int_{0}^{\frac{π}{2}} 1 dx = {[x]}_{0}^{\frac{π}{2}} = \frac{π}{2} ∴ I = \frac{π}{4}$