List of top Mathematics Questions asked in CBSE Class X

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.

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

The length of hypotenuse (in cm) of a right-angled triangle is 6 cm more than twice the length of its shortest side. If the length of its third side is 6 cm less than thrice the length of its shortest side, find the dimensions of the triangle.

\(\frac{1 + \tan^2 A}{1 + \cot^2 A}\) equals to:

\(PQ\) is tangent to a circle with centre \(O\). If \(\angle POR = 65^{\circ}\), then \(m\angle OPR\) is

A circle centred at \((-1, 2)\) passes through the point \((0, 3)\). Radius of the circle is

It is given that \(\triangle ABC \sim \triangle EDF\). Which of the following is not true?

If roots of the quadratic equation \(x^2 - k\sqrt{3}x + 2 = 0\) are real and equal, then value of \(k\) is

Observe the graph of polynomial \(p(x)\). Number of zeroes of \(p(x)\) is

Mean and Median of a frequency distribution are 43 and 40 respectively. The value of mode is

Area of sector of a circle with radius \(18 \text{ cm}\) is \(198 \text{ cm}^2\). The measure of central angle is

The value of \(k\) for which the system of linear equations \(\frac{x}{2} + \frac{y}{3} = 5\) and \(2x + ky = 7\) is inconsistent, is

In an A.P., \(a = -3\) and \(S_{17} = 357\). The value of \(a_{17}\) is

In the given figure, \(DE \parallel AC\) and \(DF \parallel AE\). Prove that : \(\frac{BF}{FE} = \frac{BE}{EC}\).

\(\alpha, \beta\) are zeroes of the polynomial \(p(x) = 3x^2 - 6x - 5\). Find the value of \(\frac{1}{\alpha^2} + \frac{1}{\beta^2}\).

Prove that : \(\sqrt{\frac{1 + \sin A}{1 - \sin A}} = \sec A + \tan A\).

Prove that : \(\frac{1}{\sec x - \tan x} - \frac{1}{\cos x} = \frac{1}{\cos x} - \frac{1}{\sec x + \tan x}\)

The perimeter of sector OAB of a circle with centre O and radius \(5.6 \text{ cm}\), is \(15.6 \text{ cm}\). Find length of the arc AB. Also find the value of \(\theta\).

A kite is flying at a height of \(60 \text{ m}\) above the ground level. Ravi, standing at the roof of the house is holding the string straight and observes the angle of elevation of kite as \(30^{\circ}\). From the bottom of the same building, the angle of elevation of kite is \(45^{\circ}\). Find the length of the string and height of roof from the ground. (Use \(\sqrt{3} = 1.73\))

The median of the following data is 32.5, find the missing frequencies \(x\) and \(y\) :

The total cost of certain piece of cloth was ₹ 2,100. During special sale time, the shopkeeper offered \(2 \text{ m}\) extra cloth for free thus reducing the price of cloth per metre by ₹ 120. What was the original per metre price of cloth and its length?

For any natural number \(n\), \(6^{n}\) ends with the digit :

In the given figure, point D divides the side BC of \(\triangle ABC\) in the ratio \(1 : 2\). Find length AD. (Given coordinates: \(A(1, 5), B(-2, 1), C(4, 2)\))

If for a data, median is 5 and mode is 4, then mean is equal to :

Simplest form of \(\frac{\sec A}{\sqrt{\sec^2 A - 1}}\) is