If $y = \frac{3}{4} + \frac{3 \cdot 5}{4 \cdot 8} + \frac{3 \cdot 5 \cdot 7}{4 \cdot 8 \cdot 12} + \ldots \infty$,then:

If the chord $y=mx+1$ of the circle $x^2+y^2=1$ subtends an angle of $45^{\circ}$ at the major segment of the circle,then the value of $m$ is:

When the engine is switched off,a vehicle of mass $M$ is moving on a rough horizontal road with momentum $p$. If the coefficient of friction between the road and the tyres of the vehicle is $\mu_k$,what is the distance travelled by the vehicle before it comes to rest?

If the series limit of the Lyman series for a Hydrogen atom is equal to the series limit of the Balmer series for a hydrogen-like atom,then the atomic number of this hydrogen-like atom will be:

If $0 < y < 2^{1/3}$ and $x(y^3 - 1) = 1$,then $\frac{2}{x} + \frac{2}{3x^3} + \frac{2}{5x^5} + \dots = $

The angle between the lines whose direction cosines satisfy the equations $l+m+n=0$ and $l^2+m^2-n^2=0$ is