List of top Mathematics Questions

In the given figure, PQ and PR are tangents to a circle with centre O and radius 3 cm. If $\angle QPR = 60^\circ$, then the length of each tangent is :

The roots of the quadratic equation $(x - 1)^2 = 16$ are :

Two different dice are thrown together. Find the probability that the numbers obtained have : (i) even sum, (ii) even product.

Represent the following pair of linear equations graphically and hence comment on the condition of consistency of this pair : \(x - 5y = 6; 2x - 10y = 12\)

An SBI health insurance agent found the following data for distribution of ages of 100 policy holders. The health insurance policies are given to persons of age 15 years and onwards, but less than 60 years. Find the modal age and median age of the policy holders.

In the given figure \(\Delta ABC\) is shown, in which \(DE \parallel BC\). If \(AD = 5\text{ cm}\), \(DB = 2\cdot5\text{ cm}\) and \(DE = 8\text{ cm}\), then the length of \(BC\) is :

The three vertices of a rhombus PQRS are P(2, – 3), Q(6, 5) and R(– 2, 1). Find the coordinates of the fourth vertex S and coordinates of the point where both the diagonals PR and QS intersect.

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

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

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 distance between the points (4, p) and (1, 0) is 5, what is the value of p ?

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

The area of a semicircle of diameter 'd' 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 \(cm^3\)) 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 :

How many zeroes does \(p(x) = (x - 2)(x + 3)\) have ?

Given \(\cot \theta = 3\), the value of \(\cos \theta\) is :

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

Find the value of p, for which one zero of the quadratic polynomial \(px^2 - 14x + 8\) is 6 times the other.

If the median of the following distribution is 32.5, then find the values of x and y.
Class: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60, 60-70
Frequency: x, 5, 9, 12, y, 3, 2 [Total = 40]

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.

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

Find the area of the segment AYB shown in the figure, if the radius of the circle is 21 cm and \(\angle AOB = 120^\circ\). [Use \(\pi = \frac{22}{7}\)]

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 :