The remainder obtained when the polynomial $x^{64} + x^{27} + 1$ is divided by $(x + 1)$ is:

Total emf produced in a thermocouple does not depend on

Three processes form a thermodynamic cycle as shown on the $P-V$ diagram for an ideal gas. Process $1 \to 2$ takes place at a constant temperature $(300\,K)$. Process $2 \to 3$ takes place at a constant volume. During this process,$40\,J$ of heat leaves the system. Process $3 \to 1$ is adiabatic and the temperature $T_3$ is $275\,K$. The work done by the gas during the process $3 \to 1$ is...... $J$.

$A$ sonometer wire has a length of $114 ~cm$ between two fixed ends. Where should two bridges be placed so as to divide the wire into three segments (in $cm$) whose fundamental frequencies are in the ratio $1:3:4$?

The plant body is differentiated into which of the following parts?

If $\cos x = \tan y$,$\cot y = \tan z$ and $\cot z = \tan x$,then $\sin x$ equals to