If $\vec{a} = \hat{i} - \hat{j} - \hat{k}$ and $\vec{b} = \lambda \hat{i} - 3\hat{j} + \hat{k}$ and the orthogonal projection of $\vec{b}$ on $\vec{a}$ is $\frac{4}{3}(\hat{i} - \hat{j} - \hat{k})$,then $\lambda$ is equal to

$A$ mercury drop of radius $1 ~cm$ is sprayed into $10^6$ drops of equal size. The energy expended in joules is (Surface tension of mercury is $460 \times 10^{-3} ~N/m$)

In Young's double slit experiment,the wavelength of red light is $7800 \, \mathring{A}$ and that of blue light is $5200 \, \mathring{A}$. The value of $n$ for which the $n^{th}$ bright band due to red light coincides with the $(n + 1)^{th}$ bright band due to blue light is:

The mitral valve is supported by which of the following?

If the line $y=mx$ is one of the bisectors of $x^2+4xy-y^2=0$,then the value of $2m$ is:

If $f: R \rightarrow R$ is defined by $f(x) = \begin{cases} \frac{2 \sin x - \sin 2x}{2x \cos x}, & \text{if } x \neq 0 \\ a, & \text{if } x = 0 \end{cases}$,then the value of $a$ so that $f$ is continuous at $x = 0$ is