If $\overline{a}, \overline{b}, \overline{c}$ are non-coplanar unit vectors such that $\overline{a} \times (\overline{b} \times \overline{c}) = \frac{\overline{b} + \overline{c}}{\sqrt{2}}$,then the angle between $\overline{a}$ and $\overline{b}$ is

$A$ particle of mass $1 \times 10^{-26} \ kg$ and charge $1.6 \times 10^{-19} \ C$ travelling with a velocity $1.28 \times 10^6 \ ms^{-1}$ along the positive $X$-axis enters a region in which a uniform electric field $E$ and a uniform magnetic field of induction $B$ are present. If $E = -102.4 \times 10^3 \ \hat{k} \ NC^{-1}$ and $B = 8 \times 10^{-2} \ \hat{j} \ Wbm^{-2}$,the direction of motion of the particle is:

Assertion : Yeasts such as $Saccharomyces \text{ } cerevisiae$ are used in baking industry.
Reason : Carbon dioxide produced during fermentation causes bread dough to rise by thermal expansion.

Which one of the following is a correct statement?

One line of the pair of lines $x^2+xy-2y^2=0$ is perpendicular to one line of the pair of lines $3y^2-5xy-2x^2=0$. If the combined equation of the two lines other than those two perpendicular lines is $ax^2+2hxy+by^2=0$,then $a+2h+b=$

The numbers $a_n = 6^n - 5n$ for $n = 1, 2, 3, \ldots$ when divided by $25$ leave the remainder: