The component of a vector $P=3 \hat{i}+4 \hat{j}$ along the direction $(\hat{i}+2 \hat{j})$ is

$A$ vector has a magnitude $x$. If it is rotated by an angle $\theta$, then the magnitude of the change in the vector is $nx$. Match the following two columns:

Column $I$	Column $II$
$(A)$ $\theta=60^{\circ}$	$(p)$ $n=\sqrt{3}$
$(B)$ $\theta=90^{\circ}$	$(q)$ $n=1$
$(C)$ $\theta=120^{\circ}$	$(r)$ $n=\sqrt{2}$
$(D)$ $\theta=180^{\circ}$	$(s)$ $n=2$

$A$ particle has a displacement of $12 \, m$ towards east,$5 \, m$ towards north,and $6 \, m$ vertically upward. The magnitude of the resultant displacement is ......... $m$.

If $|\vec{A} + \vec{B}| = |\vec{A}| + |\vec{B}|$,the angle between $\vec{A}$ and $\vec{B}$ is ....... $^o$.

If $\alpha, \beta$ and $\gamma$ are the angles made by a vector with $x, y$ and $z$ axes respectively,then $\sin ^2 \alpha + \sin ^2 \beta =$

Which of the following dopant is $NOT$ used in $Ge$ to obtain $n$-type semiconductor?