In the given transistor circuit,the base current is $35\,\mu A$. The value of $R_b$ is.......$k\Omega $

$A$ coin is tossed $n$ times. The probability of getting a head at least once is greater than $0.8$. Then,the least value of such $n$ is:

$X + H_2SO_4 \to Y$ (a colorless gas with a pungent smell).
$Y + K_2Cr_2O_7 + H_2SO_4 \to$ green colored solution.
What are $X$ and $Y$?

The structure of $PCC$ is

If the angle between the asymptotes of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{3} = 4$ is $\frac{\pi}{3}$,then its conjugate hyperbola is:

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