$A$ transverse wave is passing through a stretched string with a speed of $20 \ m/s$. The tension in the string is $20 \ N$. At a certain point $P$ on the string,it is observed that energy is being transferred at a rate of $40 \ mW$ at a given instant. Find the speed of point $P$.

Which of the following statements is true?

$A$ bimetallic strip is formed out of two identical strips,one of copper and the other of brass. The coefficients of linear expansion of the two metals are $\alpha_C$ and $\alpha_B$. On heating,the temperature of the strip increases by $\Delta T$ and the strip bends to form an arc of radius $R$. Then $R$ is proportional to

Considering only the principal values of inverse functions,the set $A = \{x \geq 0, \tan^{-1}(2x) + \tan^{-1}(3x) = \frac{\pi}{4}\}$

An organic compound with the molecular formula $C_3H_6O$ does not give a precipitate with $2,4-$dinitrophenylhydrazine and does not react with sodium metal. What is this compound?

$A$ 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: