If the pair of lines $2x^2 + 3xy + y^2 = 0$ makes angles $\theta_1$ and $\theta_2$ with the positive direction of the $X$-axis,then $|\tan(\theta_1 - \theta_2)| = $

$A$ stationary wave is represented by $y = 10 \sin \frac{\pi x}{4} \cos 20 \pi t$,where $x$ and $y$ are expressed in $cm$ and $t$ in seconds. The distance between two consecutive nodes is: (in $cm$)

Consider the following reaction equilibrium:
$N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$
Initially,$1 \text{ mole}$ of $N_2$ and $3 \text{ moles}$ of $H_2$ are taken in a $2 \text{ L}$ flask. At equilibrium state,if the number of moles of $N_2$ is $0.6$,what is the total number of moles of all gases present in the flask?

Which of the following is not a colligative property?

$A$ transformer is employed to reduce $220\, V$ to $11\, V$. The primary draws a current of $5\, A$ and the secondary $90\, A$. The efficiency of the transformer is......$\%$

$A$ simple pendulum is executing simple harmonic motion with a time period $T$. If the length of the pendulum is increased by $21\%$,the percentage increase in the time period of the pendulum of increased length is ..... $\%$