List of top Questions asked in CBSE Class X

An arc of length \(2.2\) cm subtends an angle \(\theta\) at the centre of the circle with radius \(2.8\) cm. The value of \(\theta\) is

Assertion (A) : The system of linear equations \(3x - 5y + 7 = 0\) and \(-6x + 10y + 14 = 0\) is inconsistent.
Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

Evaluate : \(\frac{\sin^3 60^{\circ} - \tan 30^{\circ}}{\cos^2 45^{\circ}}\)

For acute angles A and B and \(A + 2B\) and \(2A + B\) are acute if \(\tan (A + 2B) = \sqrt{3}\) and \(\sin (2A + B) = \frac{1}{\sqrt{2}}\), then find the measures of angles A and B.}

Prove that \(14 - 2\sqrt{3}\) is an irrational number, given that \(\sqrt{3}\) is irrational.

A circle centered at (2, 1) passes through the points A(5, 6) and B(-3, K). Find the value(s) of K. Hence find length of chord AB.

Prove that the point P dividing the line segment joining the points A(-1, 7) and B(4, -3) in the ratio 3 : 2, lies on the line \(x - 3y = -1\). Also find length of PA and PB.

Use graphical method to solve the system of linear equations : \(x = -3\) and \(5x - 2y = -5\).

The sum of first n terms of an A.P. is \(2n^{2} + 13n\). Find its \(n^{th}\) term and hence \(10^{th}\) term.

In the same figure as 32(a), prove that \(EF \parallel BC\).

In the same figure as 32(a), prove that \(\triangle AEF \sim \triangle ABC\).

Using the conditions from 32(b), prove that \(AP = 2PQ\).

The mean of the following distribution is 53. Find the missing frequency p.

Hence, find mode of the distribution.}

Compute median of the following data :

Two water taps together can fill a tank in \(8\frac{8}{9}\) hours. The tap of larger diameter takes 4 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

If the pair of linear equations : \( a_1x + b_1y + c_1 = 0 \) and \( a_2x + b_2y + c_2 = 0 \) is consistent and dependent, then

If \( \cos A = \frac{4}{5} \), then the value of \( \tan A \) is :

Area of a segment of a circle of radius 'r' and central angle \( 60^\circ \) is :

The mean and median of a frequency distribution are 43 and 43.4 respectively. The mode of the distribution is :

The probability for a randomly selected number out of 1, 2, 3, 4, ..., 25 to be a composite number is :

Assertion (A) : The surface area of the cuboid formed by joining two cubes of sides 4 cm each, end-to-end, is \( 160 \text{ cm}^2 \).
Reason (R) : The surface area of a cuboid of dimensions \( l \times b \times h \) is \( (lb + bh + hl) \).

In the given figure, \( \triangle AHK \sim \triangle ABC \). If \( AK = 10 \text{ cm} \), \( BC = 3.5 \text{ cm} \) and \( HK = 7 \text{ cm} \), find the length of \( AC \).

If the points \( A(4, 5), B(m, 6), C(4, 3) \) and \( D(1, n) \) taken in this order are the vertices of a parallelogram ABCD, then find the values of \( m \) and \( n \).

If \( \tan \theta + \frac{1}{\tan \theta} = 2 \), find the value of \( \tan^2 \theta + \frac{1}{\tan^2 \theta} \).