List of top Mathematics Questions asked in CBSE Class X

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.

Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that \( \angle PTQ = 2 \angle OPQ \).

Find the area of the sector of a circle of radius 42 cm and of central angle \( 30^\circ \). Also, find the area of the corresponding major sector. [Use \( \pi = \frac{22}{7} \)]

Two dice are thrown at the same time. Determine the probability that the sum of the numbers on the two dice is 5.

Two dice are thrown at the same time. Determine the probability that the difference of the numbers on the two dice is 3.

Aarush bought 2 pencils and 3 chocolates for Rs 11 and Tanish bought 1 pencil and 2 chocolates for Rs 7 from the same shop. Represent this situation in the form of a pair of linear equations. Find the price of 1 pencil and 1 chocolate, graphically.

A person on a tour has Rs 4,200 for expenses. If he extends his tour for 3 days, he has to cut down his daily expenses by Rs 70. Find the original duration of the tour.

The area of a right-angled triangle is \( 600 \text{ cm}^2 \). If the base of the triangle exceeds the altitude by 10 cm, find all the three dimensions of the triangle.

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

As shown in the given figure, a girl of height 90 cm is walking away from the base of a lamp post at a speed of 1.2 m/s. If the lamp is 3.6 m above the ground, find the length of her shadow after 4 seconds.

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

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

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 \(BC = 8\) cm, then \(EF\) is equal to :

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

Given that \(\sin \theta = a/b\), then \(\cos \theta\) is equal to :

If \(\cos A = 1/2\), then the value of \(\sin^2 A + \cos^2 A\) is :

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

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 cm and of central angle 60°, is :