List of top Questions asked in CBSE Class X

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.

The natural number 1 is :

For any natural number n, \( 5^n \) ends with the digit :

If \( \alpha \) and \( \beta \) are two zeroes of a polynomial \( f(x) = px^2 - 2x + 3p \) and \( \alpha + \beta = \alpha\beta \), then value of p is :

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

In triangles ABC and PQR, \( \angle A = \angle Q \) and \( \angle B = \angle R \), then \( AB : AC \) is equal to :

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

From a point on the ground, which is 60 m away from the foot of a vertical tower, the angle of elevation of the top of the tower is found to be \( 45^\circ \). The height (in metres) of the tower is :

In the given figure, PA and PB are tangents to a circle centred at O. If \( \angle OAB = 15^\circ \), then \( \angle APB \) equals :

In the given figure, PA and PB are tangents to a circle centred at O. If \( \angle AOB = 130^\circ \), then \( \angle APB \) is equal to :

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 \( (lb + bh + hl) \).

If \( \alpha, \beta \) are the zeroes of the quadratic polynomial \( px^2 + qx + r \), then find the value of \( \alpha^3\beta + \beta^3\alpha \).

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 \( \tan^2 \theta + \frac{1}{\tan^2 \theta} \).

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

Prove that \( \sqrt{5} \) is an irrational number.

Find the coordinates of the points of trisection of the line segment joining the points \( A(-1, 4) \) and \( B(-3, -2) \).

Prove that : \( \frac{\sec^3 \theta}{\sec^2 \theta - 1} + \frac{\text{cosec}^3 \theta}{\text{cosec}^2 \theta - 1} = \sec \theta \cdot \text{cosec} \theta (\sec \theta + \text{cosec} \theta) \)

If \( \frac{\sec \alpha}{\text{cosec} \beta} = p \) and \( \frac{\tan \alpha}{\text{cosec} \beta} = q \), then prove that \( (p^2 - q^2) \sec^2 \alpha = p^2 \).

Prove that the lengths of tangents drawn from an external point to a circle are equal.