If $\overrightarrow{a}=-\hat{i}+\hat{j}+2 \hat{k}$,$\overrightarrow{b}=2 \hat{i}-\hat{j}-\hat{k}$ and $\overrightarrow{c}=-2 \hat{i}+\hat{j}+3 \hat{k}$,then the angle between $2 \overrightarrow{a}-\overrightarrow{c}$ and $\overrightarrow{a}+\overrightarrow{b}$ is

If a root of the equations $x^2+px+q=0$ and $x^2+\alpha x+\beta=0$ is common,then its value will be (where $p \neq \alpha$ and $q \neq \beta$)

Which of the following forms a stable $+4$ oxidation state?

Consider the following statements $A$ and $B$ and identify the correct answer:
$A$. Fresnel's diffraction pattern occurs when the source of light or the screen on which the diffraction pattern is seen,or when both,are at a finite distance from the aperture.
$B$. Diffracted light can be used to estimate the helical structure of nucleic acids.

$\int \frac{1+x+\sqrt{x+x^2}}{\sqrt{x}+\sqrt{1+x}} d x$ is equal to

With which of the following does hydrogen combine directly?