Two particles having position vectors $r_1 = (3 \hat{i} + 5 \hat{j}) \ m$ and $r_2 = (-5 \hat{i} - 3 \hat{j}) \ m$ are moving with velocities $v_1 = (4 \hat{i} + 3 \hat{j}) \ m/s$ and $v_2 = (a \hat{i} + 7 \hat{j}) \ m/s$. If they collide after $2 \ s$,then the value of $a$ is:

Match the items given in Column $I$ with those in Column $II$ and select the correct option given below:
Column $I$ | Column $II$
$a$. $p \land q$ | $i$. $p \to q$
$b$. $p \lor q$ | $ii$. $\sim p \lor \sim q$
$c$. $\sim(p \land q)$ | $iii$. $\sim p \lor q$
$d$. $p \to q$ | $iv$. $\sim p \land \sim q$

If $200 \text{ MeV}$ of energy is released in the fission of one nucleus of ${ }_{92}^{235} \text{U}$,then the number of nuclei that must undergo fission to release an energy of $1000 \text{ J}$ is

If the lines,joining the origin to the points of intersection of the curve $2x^2 - 2xy + 3y^2 + 2x - y - 1 = 0$ and the line $x + 2y = k$,are at right angles,then $k^2$ equals

For $a, b, h > 0$,if the slope of one of the lines represented by $a^2 x^2 + 2hxy + b^2 y^2 = 0$ is twice that of the other,then the value of $\frac{h}{ab}$ is

Which of the following molecules has a zero dipole moment?