$A$ lead bullet of mass $10 \ g$ travelling at $300 \ m/s$ strikes against a block of wood and comes to rest. Assuming $50\%$ of heat is absorbed by the bullet,the increase in its temperature is (Specific heat of lead $= 150 \ J/kg \cdot ^{\circ}C$) (in $^{\circ}C$)

For $k=1, 2, 3$, the box $B_k$ contains $k$ red balls and $(k+1)$ white balls. Let $P(B_1)=\frac{1}{2}$, $P(B_2)=\frac{1}{3}$, and $P(B_3)=\frac{1}{6}$. $A$ box is selected at random and a ball is drawn from it. If a red ball is drawn, then the probability that it has come from box $B_2$ is:

Let $\alpha, \beta$ be the roots of the equation $x^2-px+r=0$ and $\frac{\alpha}{2}, 2\beta$ be the roots of the equation $x^2-qx+r=0$. Then the value of $r$ is

$A$ body of mass $m_1 = 4 \ kg$ moves at $5 \hat{i} \ m/s$ and another body of mass $m_2 = 2 \ kg$ moves at $10 \hat{i} \ m/s$. The kinetic energy of the centre of mass is

Which one of the following is commonly used in the transfer of foreign $DNA$ into crop plants?

$A$ man weighing $60\, kg$ stands on the horizontal platform of a spring balance. The platform starts executing simple harmonic motion of amplitude $0.1\, m$ and frequency $\frac{2}{\pi }\, Hz$. Which of the following statements is correct?