English Medium कक्षा १० - CBSE Question Bank Solutions for Mathematics

Tick the correct answer in the following and justify your choice: If the perimeter and the area of a circle are numerically equal, then the radius of the circle is:

If the circumference of a circle and the perimeter of a square are equal, then ______.

If the perimeter of a circle is equal to that of a square, then the ratio of their areas is ______.

Is it true to say that area of a square inscribed in a circle of diameter p cm is p² cm²? Why?

Will it be true to say that the perimeter of a square circumscribing a circle of radius a cm is 8a cm? Give reasons for your answer.

Find the area of the shaded region in figure, where arcs drawn with centres A, B, C and D intersect in pairs at mid-points P, Q, R and S of the sides AB, BC, CD and DA, respectively of a square ABCD (Use π = 3.14).

The radius of a circle is same as the side of a square. Their perimeters are in the ratio

In the below given figure, a tower AB is 20 m high and BC, its shadow on the ground, is 20√3 m long. Find the sun’s altitude. 

Two different dice are tossed together. Find the probability that the product of the two numbers on the top of the dice is 6.

Due to sudden floods, some welfare associations jointly requested the government to get 100 tents fixed immediately and offered to contribute 50% of the cost. If the lower part of each tent is of the form of a cylinder of diameter 4.2 m and height 4 m with the conical upper part of same diameter but of height 2.8 m, and the canvas to be used costs Rs. 100 per sq. m, find the amount, the associations will have to pay. What values are shown by these associations? [Use π=22/7]

A hemispherical bowl of internal diameter 36 cm contains liquid. This liquid is filled into 72 cylindrical bottles of diameter 6 cm. Find the height of each bottle, if 10% liquid is wasted in this transfer.

A cubical block of side 10 cm is surmounted by a hemisphere. What is the largest diameter that the hemisphere can have? Find the cost of painting the total surface area of the solid so formed, at the rate of Rs. 5 per 100 sq. cm. [Use π = 3.14]

504 cones, each of diameter 3.5 cm and height 3 cm, are melted and recast into a metallic sphere. Find the diameter of the sphere and hence find its surface area.
[Use π=22/7]

The angle of elevation of an aeroplane from point A on the ground is 60˚. After flight of 15 seconds, the angle of elevation changes to 30˚. If the aeroplane is flying at a constant height of 1500√3 m, find the speed of the plane in km/hr.

Find the area of the minor segment of a circle of radius 14 cm, when its central angle is 60˚. Also find the area of the corresponding major segment.[use π=22/7]

The 13^th term of an A.P. is four times its 3^rd term. If its 5^th term is 16, then find the sum of its first ten terms.

A bag contains, white, black and red balls only. A ball is drawn at random from the bag.If the probability of getting a white ball is 3/10 and that of a black ball is 2/5 then find the
probability of getting a red ball. If the bag contains 20 black balls, then find the total number of balls in the bag.

At a point A, 20 metres above the level of water in a lake, the angle of elevation of a cloud is 30˚. The angle of depression of the reflection of the cloud in the lake, at A is 60˚.
Find the distance of the cloud from A.

A card is drawn at random from a well-shuffled deck of playing cards. Find the probability that the card drawn is a card of spade or an ace.

A truck covers a distance of 150 km at a certain average speed and then covers another 200 km at an average speed which is 20 km per hour more than the first speed. If the truck covers the total distance in 5 hours, find the first speed of the truck.