The colour of light absorbed by an aqueous solution of $CuSO_4$ is

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

$A$ uniform conductor of resistance $R$ is cut into $20$ equal pieces. Half of them are joined in series and the remaining half of them are connected in parallel. If the two combinations are joined in series,the effective resistance of all the pieces is

When a current of $2\,A$ flows in a battery from negative to positive terminal,the potential difference across it is $12\,V$. If a current of $3\,A$ flows in the opposite direction,the potential difference across the terminals of the battery is $15\,V$. The emf of the battery is ............... $V$.

Observe the following statements:
$A$. Three vectors are coplanar if one of them is expressible as a linear combination of the other two.
$R$. Any three coplanar vectors are linearly dependent.
Then,which of the following is true?

$A$ coin is dropped in a lift. It takes time $t_1$ to reach the floor when the lift is stationary. It takes time $t_2$ when the lift is moving down with constant acceleration $a$. Then: