List of top Questions asked in CBSE Class X- 2026

Chord AB of a circle with centre O and radius 21 mm subtends an angle of \(120^\circ\) at the centre. Find the perimeters of the shaded region. (Use \(\sqrt{3} = 1.73\))

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

Assertion (A) : (\(\sqrt{3}\) + \(\sqrt{5}\)) is an irrational number.
Reason (R) : Sum of the any two irrational numbers is always irrational.

D is a point on the side BC of \(\Delta ABC\) such that \(\angle CAB = \angle CDA\). Show that \(CA^2 = CB \times CD\).

\(\alpha\) and \(\beta\) are the zeroes of the polynomial \(5x^2 - 16x - 10\). Find the value of \(\frac{\alpha}{\beta} + \frac{\beta}{\alpha}\).

Verify that roots of the quadratic equation \((p - q)x^2 + (q - r)x + (r - p) = 0\) are equal when \(q + r = 2p\).

Assertion (A) : If probability of happening of an event is 0.2p, p $\gt $ 0, then p can't be more than 5.
Reason (R) : P(\(\overline{E}\)) = 1 – P(E) for an event E.

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

An ice-cream cone of radius r and height h is completely filled by two spherical scoops of ice-cream. If radius of each spherical scoop is \(\frac{r}{2}\), then h : 2r equals

The distance between the points (a cos \(\theta\) + b sin \(\theta\), 0) and (0, a sin \(\theta\) – b cos \(\theta\)) is

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

Arc PQ subtends an angle \(\theta\) at the centre of the circle with radius 6.3 cm. If \(\text{Length of arc } PQ = 11\) cm, then the value of \(\theta\) is

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

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

Two different dice are rolled together. The probability that both the obtained numbers are less than 4, 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 the given figure, \(DE \parallel BC\). If \(\frac{AD}{DB} = \frac{1}{3}\) and \(AC = 6\) cm, then length AE 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, a circle is centred at (1, 2). The diameter of the circle 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 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

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