List of top Mathematics Questions

The value of x for which 2x, (x + 10) and (3x + 2) are the three consecutive terms of an A.P. is :

The pair of linear equations \(\frac{3x}{2} + \frac{5y}{3} = 7\) and \(9x + 10y = 14\), is :

In the given figure, PA and PB are tangents to a circle centred at O. If \(\angle AOB = 130^\circ\), then \(\angle APB\) is equal to :

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

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 ?

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

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 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 \(\pi = \frac{22}{7}\)]

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

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

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.

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

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

The probability for a randomly selected number out of 1, 2, 3, 4, ..., 25 to be a composite number is :

A hemispherical bowl is made of steel of thickness 1 cm. The outer radius of the bowl is 6 cm. The volume of steel used (in \(\text{cm}^3\)) is :

The mean and median of a frequency distribution are 43 and 43.4 respectively. The mode of the distribution is :

Assertion (A) : The surface area of the cuboid formed by joining two cubes of sides 4 cm each, end-to-end, is 160 \(\text{cm}^2\).
Reason (R) : The surface area of a cuboid of dimensions \(l \times b \times h\) is \((lb + bh + hl)\).

Assertion (A) : The mean of first 'n' natural numbers is \(\frac{n - 1}{2}\).
Reason (R) : The sum of first 'n' natural numbers is \(\frac{n(n + 1)}{2}\).

In the given figure, PA and PB are tangents to a circle centred at O. If \(\angle AOB = 130^\circ\), then \(\angle APB\) is equal to :

If \(\cos A = \frac{4}{5}\), then the value of \(\tan A\) is :

Area of a segment of a circle of radius 'r' and central angle \(60^\circ\) is :

If \(2 \sin A = 1\), then the value of \(\tan A + \cot A\) is :

In the given figure, PA and PB are tangents to a circle centred at O. If \(\angle OAB = 15^\circ\), then \(\angle APB\) equals :

From a point on the ground, which is 60 m away from the foot of a vertical tower, the angle of elevation of the top of the tower is found to be \(45^\circ\). The height (in metres) of the tower is :