List of top Mathematics Questions asked in CBSE Class X

There are two sections A and B of Grade X. There are 28 students in Section A and 30 students in Section B. What is the minimum number of books you will acquire for the class library so that they can be distributed equally among students of Section A or Section B ?

The graph of y = f(x) is given. The number of distinct zeroes of y = f(x) is :

An SBI health insurance agent found the following data for distribution of ages of 100 policy holders. Find the modal age and median age of the policy holders.
Age (in yrs): 15-20, 20-25, 25-30, 30-35, 35-40, 40-45, 45-50, 50-55, 55-60
Number of policy holders: 2, 4, 18, 21, 33, 11, 3, 6, 2

Find the area of the sector of a circle of radius 42 cm and of central angle \(30^\circ\). Also, find the area of the corresponding major sector. [Use \(\pi = \frac{22}{7}\)]

Aarush bought 2 pencils and 3 chocolates for Rs 11 and Tanish bought 1 pencil and 2 chocolates for Rs 7 from the same shop. Represent this situation in the form of a pair of linear equations. Find the price of 1 pencil and 1 chocolate, graphically.

Two dice are thrown at the same time. Determine the probability that (i) sum of the numbers on the two dice is 5, and (ii) difference of the numbers on the two dice is 3.

Find the coordinates of the points of trisection of the line segment joining the points A\(-1, 4\) and B\(-3, -2\).

In the given figure, O is the centre of the circle. PQ and PR are tangents. Show that the quadrilateral PQOR is cyclic.

If the points A(4, 5), B(m, 6), C(4, 3) and D(1, n) taken in this order are the vertices of a parallelogram ABCD, then find the values of m and n.

Prove that \(\sqrt{5}\) is an irrational number.

If \(\alpha\), \(\beta\) are the zeroes of the quadratic polynomial \(px^2 + qx + r\), then find the value of \(\alpha^3\beta + \beta^3\alpha\).

In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato. The other potatoes are arranged 3 m apart in a straight line, with a total of 10 potatoes.

(i) What is the distance covered to pick up the first potato and drop it in the bucket?

A brooch is crafted from silver wire in the shape of a circle with a diameter of 35 cm. The wire is also used to create 5 diameters, dividing the circle into 10 equal sectors.

37(i) What is the radius of the circle?

Radio towers are used for transmitting a range of communication services including radio and television. The tower will either act as an antenna itself or support one or more antennas on its structure. On a similar concept, a radio station tower was built in two sections 'A' and 'B'. Tower is supported by wires from a point 'O' (as shown in figure). Distance between the base of the tower and point 'O' is 6 m. From point 'O', the angle of elevation of the top of the section 'B' is $30^\circ$ and the angle of elevation of the top of section 'A' is $60^\circ$.

(i) Find the length of the wire from the point 'O' to the top of section 'B'.

Parthi and Alisha found a treasure that is exactly on the straight line joining their locations. Parthi's location is at point $(-6, -5)$ and Alisha's location is at point $(10, 11)$. The distance from the treasure to Parthi's location is three times that of the distance to Alisha's location. Find the coordinates of the location of the treasure.

The monthly expenditure on fruits in 200 families of a Housing Society is given below. Find the value of $x$ and also find the mode and mean expenditure on fruits.

Two sections, A and B, of class X contributed a total of Rs. 1500 for the Uttarakhand flood victims. The contribution from X-A was Rs. 100 less than that of X-B. Graphically, find the amounts contributed by both sections.

Two dice of different colours are thrown at the same time. Write down all the possible outcomes. What is the probability that:
(i) same number appears on both the dice?
(ii) different number appears on both the dice?

Find the zeroes of the quadratic polynomial $x^2 + 7x + 10$, and verify the relationship between the zeroes and its coefficients.

The coordinates of the centre of a circle are $(x - 7, 2x)$. Find the value(s) of '$x$', if the circle passes through the point $(-9, 11)$ and has radius $5\sqrt{2}$ units.

In the given figure, a circle with centre O is inscribed inside $\Delta LMN$. A and B are the points of tangency. Find $\angle ANB$.

A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is 20 cm and the diameter of the cylinder is 7 cm. Find the total volume of the solid. (Use $\pi = \frac{22}{7}$)

A car is moving away from the base of a 30 m high tower. The angle of elevation of the top of the tower from the car at an instant, when the car is $10\sqrt{3}$ m away from the base of the tower, is :

The length of the arc of the sector of a circle with radius 21 cm and of central angle $60^\circ$, is :

The hour hand of a clock is 7 cm long. The angle swept by it between 7:00 a.m. and 8:10 a.m. is :