If the amplitude of $z - 2 - 3i$ is $\pi / 4$,then the locus of $z = x + iy$ is

All wires have the same resistance $r$. The equivalent resistance between $A$ and $B$ is $R$ when the keys $K_1$ and $K_2$ are open. Now,if the keys are closed,what will be the new equivalent resistance?

The system shown in the figure is released from rest. The pulley and spring are massless,and friction is absent everywhere. The speed of the $5\, kg$ block when the $2\, kg$ block leaves contact with the ground is: (Take the force constant of the spring $K = 40\, N/m$ and $g = 10\, m/s^2$)

The displacement of a particle varies according to the relation $x = 3 \sin(100t) + 8 \cos^2(50t)$. Which of the following is $INCORRECT$ about this motion?

When compound $X$ is oxidised by acidified potassium dichromate,compound $Y$ is formed. Compound $Y$ on reduction with $LiAlH_4$ gives $X$. $X$ and $Y$ respectively are :

Suppose $\overrightarrow{a}=\lambda \hat{i}-7 \hat{j}+3 \hat{k}$ and $\overrightarrow{b}=\lambda \hat{i}+\hat{j}+2 \lambda \hat{k}$. If the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is greater than $90^{\circ}$,then $\lambda$ satisfies the inequality