If $(p \wedge \sim q) \wedge (p \wedge r) \to \sim p \vee q$ is false,then the truth values of $p, q$ and $r$ are respectively

$A$ block rests on a rough inclined plane making an angle of $30^{\circ}$ with the horizontal. The coefficient of static friction between the block and the plane is $0.8$. If the frictional force on the block is $10 \, N$,the mass of the block (in $kg$) is (take $g = 10 \, m/s^2$)

Consider the two following statements $A$ and $B$,and identify the correct choice given in the answers: $(A)$ Duddell's thermo galvanometer is suitable to measure direct current only. $(B)$ Thermopile can measure temperature differences of the order of $10^{-3} {}^{\circ}C$.

Observe the following lists. Then the correct match for List-$I$ from List-$II$ is:

List-$I$	List-$II$
$(A)$ $[\mathbf{a} \mathbf{b} \mathbf{c}]$	$1. |\mathbf{a}||\mathbf{b}|\cos(\mathbf{a}, \mathbf{b})$
$(B)$ $(\mathbf{c} \times \mathbf{a}) \times \mathbf{b}$	$2. (\mathbf{a} \cdot \mathbf{c})\mathbf{b} - (\mathbf{a} \cdot \mathbf{b})\mathbf{c}$
$(C)$ $\mathbf{a} \times (\mathbf{b} \times \mathbf{c})$	$3. \mathbf{a} \cdot \mathbf{b} \times \mathbf{c}$
$(D)$ $\mathbf{a} \cdot \mathbf{b}$	$4. |\mathbf{a}||\mathbf{b}|$
	$5. (\mathbf{b} \cdot \mathbf{c})\mathbf{a} - (\mathbf{a} \cdot \mathbf{b})\mathbf{c}$

The magnetic field due to a straight conductor of uniform cross section of radius $a$ and carrying a steady current is represented by

Two bodies of masses $0.1 \,kg$ and $0.4 \,kg$ move towards each other with the velocities $1 \,m/s$ and $0.1 \,m/s$ respectively. After collision,they stick together. In $10 \,s$,the combined mass travels .......... $m$.