$4 \ g$ of a hydrocarbon on complete combustion gave $12.571 \ g$ of $CO_2$ and $5.143 \ g$ of water. What is the empirical formula of the hydrocarbon?

If $a, b$ and $c$ are three non-coplanar vectors and $p, q$ and $r$ are vectors defined by $p=\frac{b \times c}{[a b c]}, q=\frac{c \times a}{[a b c]}$ and $r=\frac{a \times b}{[a b c]}$,then the value of $(a+b) \cdot p+(b+c) \cdot q+(c+a) \cdot r$ is equal to

If the circle $x^2+y^2+6x-2y+k=0$ bisects the circumference of the circle $x^2+y^2+2x-6y-15=0$,then $k=$

If the slope of one of the lines given by $ax^2+2hxy+by^2=0$ is two times the other,then:

The principal nitrogenous excretory compound in humans is synthesized:

$A$ body executes simple harmonic motion under the action of a force $F_1$ with a time period $T_1 = \frac{4}{5} \ s$. If the force is changed to $F_2$,it executes $SHM$ with a time period $T_2 = \frac{3}{5} \ s$. If both the forces $F_1$ and $F_2$ act simultaneously in the same direction on the body,what is its new time period in seconds?