M L Aggarwal Solutions for Chapter: Sample Question Paper, Exercise 4: SECTION D

Construct a pair of tangents to a circle of radius $3 \mathrm{cm}$ which are inclined to each other at an angle of $60°$.

Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.

A train covers a distance of $360 \mathrm{km}$ at a uniform speed. Had the speed been $5 \mathrm{km}/\mathrm{h}$ more, it would have taken $48$ minutes less for the journey. Find the original speed of the train.

Solve: $\frac{1}{x}-\frac{1}{x-2}=3, x\ne 0, 2$

A petrol tank is in the form of a frustum of a cone of height $20 \mathrm{m}$ with diameters of its lower and upper ends as $20 \mathrm{m}$ and $50 \mathrm{m}$ respectively. Find the cost of petrol which can fill in the tank completely at the rate of $₹70$ per litre. Also find the curved surface area of the tank.

Water is flowing at the rate of $15 \mathrm{km}/\mathrm{h}$ through a pipe of diameter $14 \mathrm{cm}$ into a cuboidal pond which is $50 \mathrm{m}$ long and $44 \mathrm{m}$ wide. At what time will the level of water in the pond rise by $21 \mathrm{cm}$.

The angle of elevation of an aeroplane from a point on the ground is $60°$. After a flight of $30$ seconds, the angle of elevation becomes $30°$. If the aeroplane is flying at a constant height of $3000\sqrt{3} \mathrm{m}$, find the speed of the aeroplane.

Daily wages of $110$ workers, obtained in a survey are tabulated below. Compute the mean daily wages and the modal daily wages of these workers.