An object is subjected to a force in the north-east direction. To balance this force,a second force should be applied in the direction:

Which of the following colours has the highest energy if the wavelengths of violet, blue, yellow, and red light are $410 \text{ nm}$, $470 \text{ nm}$, $580 \text{ nm}$, and $750 \text{ nm}$ respectively?

If the velocity of the electron in Bohr's first orbit is $2.19 \times 10^6 \text{ m s}^{-1}$, calculate the de Broglie wavelength associated with it. [$h = 6.626 \times 10^{-34} \text{ J s}$ and mass of electron = $9.10938 \times 10^{-31} \text{ kg}$] (in $\text{ pm}$)

$A$ vector has magnitude and direction. Does it have a location in space? Can it vary with time? Will two equal vectors $a$ and $b$ at different locations in space necessarily have identical physical effects? Give examples in support of your answer.

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

The resultant magnitude of two vectors of same magnitude is equal to the magnitude of either. The angle between the two vectors is (in $^{\circ}$)