List of top Mathematics Questions

If \(\Delta DEF \sim \Delta PQR\) such that \(3 DE = PQ\) and \(EF = 6\) cm, then the length of QR is :

If the mean of first n natural numbers is \(\frac{6n}{11}\), then n is

From a point P, tangents PQ and PR are drawn to a circle with centre O and radius 6 cm. If OP = 10 cm, then area of quadrilateral PQOR is :

The perimeter of sector of a circle of radius 21 cm and central angle 60\(^\circ\), is

ABCD is a trapezium in which AB || DC and E, F are points on AD and BC respectively such that EF || DC. If ED = 36 cm, BF = 70 cm and FC = 30 cm, then the length of AD is :

If pair of linear equations given by \(a_1x + b_1y + c_1 = 0\) and \(a_2x + b_2y + c_2 = 0\) has infinitely many solutions, then which of the following is definitely true ?

The 31st term of the A.P. : \(-\frac{5}{6}, -\frac{3}{4}, -\frac{2}{3}, -\frac{7}{12}, \dots\) is

Four tangents drawn to a circle are extended from both the sides to form a quadrilateral. Which of these quadrilateral is not possible ?

If \(x \cdot \tan 45^\circ \cdot \sin 30^\circ = \cos 30^\circ \cdot \cot 60^\circ\), then x is equal to

The graph of a quadratic polynomial f(x) passes through (5,0), (0, -1) and (-2, 0). The two factors of the polynomial are

At which of the following points, the quadratic polynomial \(p(x) = - 3x + 18x^2 - 1\) intersects the positive x-axis ?

Draw the graph of the pair of linear equations $x - y + 2 = 0$ and $4x - y - 4 = 0$. Calculate the area of the triangle formed by the lines so drawn and the x-axis.

The marks obtained by 80 students of class X in a mock test of Mathematics are given below in the table. Find median and the mode of the data :

Find the ratio in which the x-axis divides the line segment joining the points ($-$6, 5) and ($-$4, $-$1). Also, find the point of intersection.

Prove that $\sqrt{3}$ is an irrational number.

Find a quadratic polynomial whose zeroes are $(5 - 2\sqrt{3})$ and $(5 + 2\sqrt{3})$.

Two concentric circles are of radii 5 cm and 4 cm. Find the length of the chord of the larger circle which touches the smaller circle.

A right circular cylinder and a right circular cone have equal bases and equal heights. If their curved surface areas are in the ratio 8 : 5, then find the ratio between the radius of their bases to their height.

Assertion (A) : The polynomial $p(y) = y^2 + 4y + 3$ has two zeroes.
Reason (R) : A quadratic polynomial can have at most two zeroes.

Assertion (A) : The probability that a leap year has 53 Mondays is $\frac{2}{7}$.
Reason (R) : The probability that a non-leap year has 53 Mondays is $\frac{5}{7}$.

The natural number 2 is :

Do the points P(1, 0), Q($-$5, 0) and R($-$2, 5) form a triangle ? If so, name the type of triangle formed.

The HCF of 960 and 432 is :

A die is thrown once. Probability of getting a number other than 3 is :

Shown in the given figure is a circle with centre O. The area of the minor sector is $7 \text{ cm}^2$. Area of circle is :