List of top Questions asked in CBSE Class X

If the mean and mode of a data are 12 and 21 respectively, then its median is :

If $\alpha, \beta$ are the zeroes of the polynomial $p(x) = x^2 - 3x - 1$, then find the value of $\frac{1}{\alpha} + \frac{1}{\beta}$.

Assertion (A) : The polynomial $p(y) = y^2 + 4y + 3$ has two zeroes.
Reason (R) : A quadratic polynomial can have at most two zeroes.

A die is thrown once. Probability of getting a number other than 3 is :

Assertion (A) : The probability that a leap year has 53 Mondays is $\frac{2}{7}$.
Reason (R) : The probability that a non-leap year has 53 Mondays is $\frac{5}{7}$.

A car is moving away from the base of a $30\text{ m}$ high tower. The angle of elevation of the top of the tower from the car at an instant, when the car is $10\sqrt{3}\text{ m}$ away from the base of the tower, is :

If $\cos A = \frac{1}{2}$, then the value of $\sin^2 A + 2\cos^2 A$ is :

In the given figure, PA is a tangent from an external point P to a circle with centre O. If $\angle POB = 125^\circ$, then $\angle APO$ is equal to :

The length of the arc of the sector of a circle with radius $21\text{ cm}$ and of central angle $60^\circ$, is :

If TP and TQ are two tangents to a circle with centre O from an external point T so that $\angle POQ = 120^\circ$, then $\angle PTQ$ is equal to :

The hour hand of a clock is $7\text{ cm}$ long. The angle swept by it between 7:00 a.m. and 8:10 a.m. is :

The mid-point of the line segment joining the points $(5, -4)$ and $(6, 4)$ lies on :

Given that $\sin \theta = \frac{a}{b}$, then $\cos \theta$ is equal to :

The common difference of the AP : $\sqrt{2}, 2\sqrt{2}, 3\sqrt{2}, 4\sqrt{2}, \dots$ is :

If $\Delta ABC$ and $\Delta DEF$ are similar such that $2 AB = DE$ and $BC = 8\text{ cm}$, then $EF$ is equal to :

If a pair of linear equations in two variables is represented by two coincident lines, then the pair of equations has :

The HCF of 960 and 432 is :

The natural number 2 is :

The graph of $y = f(x)$ is given. The number of zeroes of $f(x)$ is :

For any natural number $n$, $6^n$ ends with the digit :

Find the mean and the mode for the following frequency distribution :

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

A chord PQ of a circle of diameter 28 cm subtends an angle of \(90^\circ\) at the centre O. Find the area of the sector OPCQ, where C is a point on minor arc PQ. Also, find the area of segment PCQ.

Prove that, if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

Find the smallest 5-digit number exactly divisible by 24 and 36.