List of top Questions asked in CBSE Class X- 2026

The value of k for which the equation $kx^2 - 6x - 4 = 0$ has real and equal roots, is
Find the greatest number which divides 764 and 1198, leaving remainders 8 and 10 respectively.
Chord AB subtends an angle of 120º at the centre O of the circle with radius \(\frac{21}{2}\) cm. Find the perimeter of shaded segment ACB. (Use \(\sqrt{3} = 1.7\))
If sec \(\theta\) + tan \(\theta\) = m, show that \(\frac{m^2 - 1}{m^2 + 1} = \sin \theta\).

A kite is flying at a height of 60 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 30º. From the bottom of the same building, the angle of elevation of kite is 45º. Find the length of the string and height of roof from the ground. (Use \(\sqrt{3} = 1.73\))
Verify that roots of the quadratic equation (p – q)x\(^2\) + (q – r)x + (r – p) = 0 are equal when q + r = 2p.
In the given figure, DEFG is a square. \(\Delta ABC\) is right angle triangle with \(\angle A = 90^\circ\). Prove that AG \(\times\) DG = AF \(\times\) DB.
Assertion (A) : (\(\sqrt{3}\) + \(\sqrt{5}\)) is an irrational number.
Reason (R) : Sum of the any two irrational numbers is always irrational.
\(\alpha\) and \(\beta\) are the zeroes of the polynomial \(5x^2 - 16x - 10\). Find the value of \(\frac{\alpha}{\beta} + \frac{\beta}{\alpha}\).
Arc PQ subtends an angle \(\theta\) at the centre of the circle with radius 6.3 cm. If PQ = 11 cm, then the value of \(\theta\) is
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.
If the quadratic equation \(9x^2 + 8kx + 16 = 0\) has real and equal roots, then the value of k is
It is given that \(\Delta ABC \sim \Delta EDF\). Which of the following is not true ?
If sum of first ten terms of an A.P. is zero with a as the first term and d, the common difference, which of the following relation is true ?
\(\frac{1 + \tan^2 A}{1 + \cot^2 A}\) equals to :
Two dice are rolled together. The probability that sum of the numbers obtained is atmost 12, is
In the given figure, DE \(\parallel\) BC. If \(\frac{AD}{DB} = \frac{1}{3}\) and AC = 6 cm, then length AE is
PQ is tangent to a circle with centre O. If \(\angle POR = 65^\circ\), then m\(\angle PTR\) is
In the given figure, a circle is centred at (1, 2). The diameter of the circle is
\(\frac{\sec^2 A - 1}{\sin^2 A}\) is same as
Mean and Median of a frequency distribution are 43 and 40 respectively. The value of mode is
From an external point P, a tangent PT has been drawn to a circle with centre at O and radius 3 cm, intersecting its concentric circle at A and B. If AB = 8 cm and OA = AP, the length PQ equals.
Observe the graph of polynomial p(x). The zeroes of the polynomial are
Three tennis balls are just packed in a cylindrical jar. If radius of each ball is r, volume of air inside the jar 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