Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

JEE Mathematics Solved Question Paper 2007

Multiple Choice Questions

31.
If $\vec{a} and \vec{b}$ are unit vectors such that $[\vec{a} \vec{b} \vec{a} \times \vec{b}] = \frac{1}{4}$ , then angle between $\vec{a} and \vec{b}$ is :

$\frac{π}{3}$

$\frac{π}{4}$

$\frac{π}{6}$

$\frac{π}{2}$

$\frac{π}{6}$

$|\vec{a}| = 1, |\vec{b}| = 1, [\vec{a} \vec{b} \vec{a} \times \vec{b}] = \frac{1}{4} \Rightarrow (\vec{a} \times \vec{b}) . (\vec{a} \times \vec{b}) = \frac{1}{4} \Rightarrow {(|\vec{a}| |\vec{b}| \sin (θ))}^{2} = \frac{1}{4} \Rightarrow \sin^{2} (θ) = \frac{1}{4} \Rightarrow \sin (θ) = \frac{1}{2} \Rightarrow θ = \frac{π}{6}$

32.

The order and degree of the differential equation $\sqrt{\sin (x)} (dx + dy) = \sqrt{\cos (x)} (dx - dy)$ is :

(1, 2)
(2, 2)
(1, 1)
(2, 1)

33.

$\int_{0}^{π} |\cos (x)| dx$ is equal to :

$\frac{1}{2}$
- 2
1
- 1

34.

$\int (\frac{\sin (2 x)}{\sin (3 x) \sin (5 x)}) dx$ is equal to :

$\frac{1}{5} \log_{e} |\sin (5 x)| - \frac{1}{3} \log_{e} |\sin (3 x)| + c$
$\frac{1}{3} \log_{e} |\sin (3 x)| - \frac{1}{5} \log_{e} |\sin (5 x)|$
$\frac{1}{3} \log_{e} |\sin (3 x)| + \frac{1}{5} \log_{e} |\sin (5 x)|$
$- \frac{1}{2} \cos (2 x) + \frac{1}{3} \log_{e} |\sin (3 x)|$

35.

$\int e^{x} \{\log (\sin (x)) + \cot (x)\} dx$ is equal to

e^xcot(x) + c
e^xlog(sin(x)) + c
e^xlog(sin(x)) + tan(x) + c
e^x + sin(x) + c

36.

$\int_{- 10}^{10} \log (\frac{a + x}{a - x}) dx$ is equal to :

0
- 2log(a + 10)
$2 \log (\frac{a + 10}{a - 10})$
2log(a + 10)

37.

The point of intersection of the line $\vec{r} = 7 \hat{i} + 10 \hat{j} + 13 \hat{k} + s (2 \hat{i} + 3 \hat{j} + 4 \hat{k})$ and $\vec{r} = 3 \hat{i} + 5 \hat{j} + 7 \hat{k} + s (\hat{i} + 2 \hat{j} + 3 \hat{k})$ is :