List of top Mathematics Questions asked in CBSE Class X

Three tennis balls are just packed in a cylindrical jar. If radius of each ball is r, volume of air inside the jar is

When \(\sin A = \frac{1}{3}\), the value of \(\cot A\) is

In the given figure, a circle is centred at (1, 2). The diameter of the circle is

A circle is divided into 16 identical sectors. If radius of the circle is 7 cm, area of each sector is

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

In the given figure, \(DE \parallel BC\). If \(\frac{AD}{DB} = \frac{1}{3}\) and \(AC = 6\) cm, then length AE 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

If PQ and PR are tangents to the circle with centre O and radius 4 cm such that \(\angle QPR = 90^\circ\), then the length OP is

The \(n^{\text{th}}\) term of an A.P. is \(\sqrt{2}n + 1\). Its common difference is

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

If the quadratic equation \(9x^2 + 8kx + 16 = 0\) has real and equal roots, then the value of k is

From a solid cylinder whose height is 2.8 cm and radius 2.1 cm, a conical cavity of the same height and same radius is hollowed out. Find the volume and the total surface area of the remaining solid.

If \(\cos A + \sin A = \sqrt{2} \cos A\), prove that \(\cos A - \sin A = \sqrt{2} \sin A\).

Find the mean of the following distribution :

Two poles of equal heights are standing opposite to each other on either side of the road which is 90 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 30\(^\circ\) and 60\(^\circ\) respectively. Find the height of the poles and the distances of the point from the poles. [Use \(\sqrt{3}\) = 1.732]

Find the quadratic polynomial the sum of whose zeroes is 1 and their product is –12. Hence find the zeroes of the polynomial.

Two numbers are in the ratio 3 : 5 and their LCM is 180. Find the HCF of these two numbers.

Find a relation between x and y such that the point P(x, y) is equidistant from the points A(5, 3) and B(1, 7).

Prove that \(\frac{2 + 3\sqrt{5}}{7}\) is an irrational number, given that \(\sqrt{5}\) is an irrational number.

A circle is inscribed in a right triangle ABC, right angled at B. If the lengths of the two sides containing the right angle are 8 cm and 15 cm, find the radius of the incircle.

Assertion (A) : If the Mode and Mean of a data are 12 k and 15 k, then Median of the data is 14 k.
Reason (R) : The relation between the Mean, Mode and Median of a data is : Mean = 3 Median – 2 Mode.

Two dice are thrown simultaneously. The probability of getting a sum of 7 is :

One ticket is drawn at random from a bag containing 50 tickets numbered 1 to 50. The probability that the drawn ticket has a number which is a multiple of 7 is :

\(\sin 2 \theta = 2 \sin \theta\) is true, when \(\theta\) is equal to

Assertion (A) : In a circle of radius 21 cm, an arc of length 22 cm subtends an angle of 60\(^\circ\) at the centre.
Reason (R) : The length of arc of a sector of a circle of radius r and central angle \(\theta\) is \(\frac{2\pi r\theta}{360}\).