If $^nC_r$ denotes the number of combinations of $n$ things taken $r$ at a time,then the expression $^nC_{r+1} + ^nC_{r-1} + 2 \times ^nC_r$ equals

$A$ common-emitter amplifier is designed with a $n-p-n$ transistor $(\alpha = 0.99)$. The input impedance is $1 \, k\Omega$ and the load resistance is $10 \, k\Omega$. The voltage gain will be

During the mean life of a radioactive element,the fraction that disintegrates is

If $x^2+y^2+z^2 \neq 0, \quad x=c y+b z, \quad y=a z+c x$ and $z=b x+a y$,then $a^2+b^2+c^2+2 a b c$ is equal to

Which of the following is the correct sequence of the various steps of Herbarium formation?
$1$ Drying $2$ Poisoning $3$ Collection $4$ Labelling $5$ Mounting $6$ Deposition $7$ Stitching

The structure of a mixed oxide is cubic close packed $(ccp)$. The cubic unit cell of the mixed oxide is composed of oxide ions. One-fourth of the tetrahedral voids are occupied by divalent metal $A$ and the octahedral voids are occupied by a monovalent metal $B$. The formula of the oxide is