English Medium Class 9 - CBSE Question Bank Solutions

A field is 200 m long and 150 m broad. There is a plot, 50 m long and 40 m broad, near thefield. The plot is dug 7 m deep and the earth taken out is spread evenly on the field. Byhow many meters is the level of the field raised? Give the answer to the second place of decimal.

A field is in the form of a rectangle of length 18 m and width 15 m. A pit, 7.5 m long, 6 m broad and 0.8 m deep, is dug in a corner of the field and the earth taken out is spread over the remaining area of the field. Find out the extent to which the level of the field has been raised.

A rectangular tank is 80 m long and 25 m broad. Water flows into it through a pipe whose cross-section is 25 cm2, at the rate of 16 km per hour. How much the level of the water rises in the tank in 45 minutes.

Water in a rectangular reservoir having base 80 m by 60 m i s 6.5 m deep. In what time can the water be emptied by a pipe ôf which the cross-section is a square of side 20 cm, if the water runs through the pipe at the rate of 15 km/hr.

A village having a population of 4000 requires 150 litres of water per head per day. It has a tank measuring 20 m × 15 m × 6 m. For how many days will the water of this tank last?

A child playing with building blocks, which are of the shape of the cubes, has built a structure as shown in Fig. 18.12 If the edge of each cube is 3 cm, find the volume of the structure built by the child.

A godown measures 40m × 25 m × 10 m. Find the maximum number of wooden crates each measuring 1.5 m
× 1.25 m × 0.5 m that can be stored in the godown.

A wall of length 10 m was to be built across an open ground. The height of the wall is 4 m and thickness of the wall is 24 cm. If this wall is to be built up with bricks whose dimensions are 24 cm × 12 cm × 8 cm, How many bricks would be required?

Simplify: \[\frac{7 + 3\sqrt{5}}{3 + \sqrt{5}} - \frac{7 - 3\sqrt{5}}{3 - \sqrt{5}}\]

Simplify: \[\frac{3\sqrt{2} - 2\sqrt{3}}{3\sqrt{2} + 2\sqrt{3}} + \frac{\sqrt{12}}{\sqrt{3} - \sqrt{2}}\]

Write the value of \[\left( 2 + \sqrt{3} \right) \left( 2 - \sqrt{3} \right) .\]

Write the reciprocal of \[5 + \sqrt{2}\].

Write the rationalisation factor of \[7 - 3\sqrt{5}\].

If\[\frac{\sqrt{3} - 1}{\sqrt{3} + 1} = x + y\sqrt{3},\]  find the values of x and y.

If x= \[\sqrt{2} - 1\], then write the value of \[\frac{1}{x} . \]

If \[a = \sqrt{2} + 1\],then find the value of  \[a - \frac{1}{a}\].

If \[x = 2 + \sqrt{3}\] ,  find the value of \[x + \frac{1}{x}\].

Write the rationalisation factor of \[\sqrt{5} - 2\].

Simplify \[\sqrt{3 + 2\sqrt{2}}\].

Simplify \[\sqrt{3 - 2\sqrt{2}}\].