Two trains of equal length are running on parallel lines in the same direction at 46 km/hour and 36 km/hour. The faster train passes the slower train in 36 seconds. The length of each train is

What is the equation of a line perpendicular to the line x – 7y + 5 = 0 and having x-intercept 3?

If $\tan \alpha=\frac{m}{m+1}, \tan \beta=\frac{1}{2 m+1}$, then $\alpha+\beta$ equal to

If A, B and C can complete a work in 6 days. If A can work twice faster than B and thrice faster than C, then the number of days C alone can complete the work is :

A man walking at 3 km/hour crosses a square field diagonally in 2 minutes. The area of the field (in square metre) is

The internal bisectors of the $\angle B$ and $\angle C$ of the $\triangle A B C$, intersect at $O$. If $\angle A=100^{\circ}$, then the measure of $\angle \mathrm{BOC}$ is :

The area of the triangle formed by the graphs of the equations x = 4, y = 3 and 3x + 4y = 12 is

A conical iron piece having diameter 28 cm and height 30cm is totally immersed into the water of a cylindrical vessel, resulting in the rise of water level by 6.4 cm. The diameter, in cm, of the vessel is : (1) $3.5$

A and B together can do a piece of work in 30 days. B and C together can do it in 20 days. A starts the work and works on it for 5 days, then B takes up and works for 15 days. Finally C finishes the work in 18 days. The number of days in which C alone can do the work when doing it separately is

The percentage of metals in a mine of lead ore is $60 \%$. Now the percentage of silver is $\frac{3}{4} \%$ of metals and the rest is lead. If the mass of ore extracted from this mine is $8000 \mathrm{~kg}$, the mass (in kg.) of lead is :