An object with a mass $10 \ kg$ moves at a constant velocity of $10 \ m/s$. $A$ constant force then acts for $4 \ s$ on the object and gives it a speed of $2 \ m/s$ in the opposite direction. The impulse acting on the object is ........ $N \cdot s$.

If the lines $\frac{x - 1}{2} = \frac{y + 1}{3} = \frac{z - 1}{4}$ and $\frac{x - 3}{1} = \frac{y - k}{2} = \frac{z}{1}$ intersect,then $k =$

The percentage composition of an organic compound $A$ is: carbon $85.71 \%$ and hydrogen $14.29 \%$. Its vapour density is $14$. Consider the following reaction sequence:
$A$ $\xrightarrow{Cl_2 / H_2O} B$ $\xrightarrow[(ii) H_3O^+]{(i) KCN / EtOH} C$
Identify $\underline{C}$.

If the pair of straight lines given by $Ax^2+2Hxy+By^2=0$ $(H^2 > AB)$ forms an equilateral triangle with the line $ax+by+c=0$,then $(A+3B)(3A+B)$ is equal to:

Which of the following statements is incorrect regarding saline hydrides?

The cosine of the angle $A$ of the triangle with vertices $A(1, -1, 2)$, $B(6, 11, 2)$, and $C(1, 2, 6)$ is: