List of top Mathematics Questions asked in CBSE Class X

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 \(\theta\).

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?

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

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

Devansh proved that \(\triangle ABC \sim \triangle PQR\) using SAS similarity criteria. If he found \(\angle C = \angle R\), then which of the following was proved true?

Which of the following can not be the probability of an event?

The value of \(m\) for which the quadratic equation \(3x^2 - 7x + m = 0\) has real and equal roots, is

If the zeroes of a polynomial \(p(x)\) are \(-3\) and \(8\), then \(p(x)\) equals

An arc of length \(2.2\) cm subtends an angle \(\theta\) at the centre of the circle with radius \(2.8\) cm. The value of \(\theta\) is

Evaluate : \(\frac{\sin^3 60^{\circ} - \tan 30^{\circ}}{\cos^2 45^{\circ}}\)

Prove that \(14 - 2\sqrt{3}\) is an irrational number, given that \(\sqrt{3}\) is irrational.

Prove that the point P dividing the line segment joining the points A(-1, 7) and B(4, -3) in the ratio 3 : 2, lies on the line \(x - 3y = -1\). Also find length of PA and PB.

Use graphical method to solve the system of linear equations : \(x = -3\) and \(5x - 2y = -5\).

The sum of first n terms of an A.P. is \(2n^{2} + 13n\). Find its \(n^{th}\) term and hence \(10^{th}\) term.

In the same figure as 32(a), prove that \(\triangle AEF \sim \triangle ABC\).

Using the conditions from 32(b), prove that \(AP = 2PQ\).

The mean of the following distribution is 53. Find the missing frequency p.

Hence, find mode of the distribution.}

Compute median of the following data :