$A$ tangent galvanometer has a coil of $25$ turns and a radius of $15 \, cm$. The horizontal component of the earth's magnetic field is $3 \times 10^{-5} \, T$. The current required to produce a deflection of $45^o$ in it is.....$A$

If $\overrightarrow{a}=\hat{i}-\hat{j}-\hat{k}$ and $\overrightarrow{b}=\lambda \hat{i}-3 \hat{j}+\hat{k}$ and the orthogonal projection of $\overrightarrow{b}$ on $\overrightarrow{a}$ is $\frac{4}{3}(\hat{i}-\hat{j}-\hat{k})$,then $\lambda$ is equal to

Which of the following reagents reacts with benzaldehyde to produce $1$-phenylethanol?

$A$ wire in the form of a square of side $a$ carries a current $i$. Then,the magnetic induction at the centre of the square is (Magnetic permeability of free space $= \mu_0$)

$A$ spring balance is attached to the ceiling of a lift. $A$ man hangs his bag on the spring and the spring reads $49 \, N$,when the lift is stationary. If the lift moves downward with an acceleration of $5 \, m/s^2$,the reading of the spring balance will be .......... $N$.

The eccentricity of the ellipse $9x^2 + 5y^2 - 18x - 20y - 16 = 0$ is: