If $\frac{ax^2 + bx + c}{(x - 1)(x + 2)(2x + 3)} = \frac{3}{x - 1} + \frac{2}{x + 2} - \frac{5}{2x + 3}$,then:

$A$ body cools from $60\,^oC$ to $50\,^oC$ in $10\,minutes$. If the room temperature is $25\,^oC$ and assuming Newton's law of cooling to hold good,the temperature of the body at the end of the next $10\,minutes$ will be ......... $^oC$.

Starting from rest, the time taken by a body sliding down on a rough inclined plane at $45^{\circ}$ with the horizontal is twice the time taken to travel on a smooth plane of the same inclination and same distance. Then the coefficient of kinetic friction is:

If the harmonic mean of the roots of the equation $\sqrt{2}x^2 - bx + (8 - 2\sqrt{5}) = 0$ is $4$,then the value of $b$ is:

$A$ deflection magnetometer is adjusted and a magnet of magnetic moment $M$ is placed on it in the usual manner and the observed deflection is $\theta$. The period of oscillation of the needle before settling of the deflection is $T$. When the magnet is removed,the period of oscillation of the needle is $T_0$ before settling to $0^{\circ}-0^{\circ}$. If the earth's horizontal magnetic field is $B_H$,the relation between $T$ and $T_0$ is

$A$ pair of lines $S=0$ together with the lines given by the equation $8 x^2-14 x y+3 y^2+10 x+10 y-25=0$ form a parallelogram. If its diagonals intersect at the point $(3,2)$,then the equation $S=0$ is