List of top Questions asked in CBSE Class X

Verify that roots of the quadratic equation \((p - q)x^2 + (q - r)x + (r - p) = 0\) are equal when \(q + r = 2p\).
\(\alpha\) and \(\beta\) are the zeroes of the polynomial \(5x^2 - 16x - 10\). Find the value of \(\frac{\alpha}{\beta} + \frac{\beta}{\alpha}\).
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.
The distance between the points (a cos \(\theta\) + b sin \(\theta\), 0) and (0, a sin \(\theta\) – b cos \(\theta\)) 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
PQ is tangent to a circle with centre O. If \(\angle POR = 65^\circ\), then m\(\angle PTR\) is
Mean and Median of a frequency distribution are 43 and 40 respectively. The value of mode 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
\(\frac{1 + \tan^2 A}{1 + \cot^2 A}\) 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
Observe the graph of polynomial p(x). Number of zeroes of p(x) is
A circle is divided into 16 identical sectors. If radius of the circle is 7 cm, area of each sector is
In the given figure, a circle is centred at (1, 2). The diameter of the circle 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
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
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]
If \(\cos A + \sin A = \sqrt{2} \cos A\), prove that \(\cos A - \sin A = \sqrt{2} \sin A\).
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.
Find the mean of the following distribution :