List of top Mathematics Questions asked in CBSE Class X

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.

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.

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.

In \(\triangle ABC\), \(DE \parallel BC\). If \(AD = x\), \(DB = x - 2\), \(AE = x + 2\) and \(EC = x - 1\), then find the value of \(x\).

The coordinates of the centre of a circle are \((x - 7, 2x)\). Find the value(s) of ‘x’, if the circle passes through the point \((-9, 11)\) and has radius \(5\sqrt{2}\) units.

If \(\tan \theta = \frac{24}{7}\), then find the value of \(\sin \theta + \cos \theta\).

If \(\cot \theta = \frac{7}{8}\), then find the value of \(\frac{(1+\sin \theta)(1-\sin \theta)}{(1+\cos \theta)(1-\cos \theta)}\).

Two concentric circles are of radii 5 cm and 4 cm. Find the length of the chord of the larger circle which touches the smaller circle.

Prove that \(\sqrt{3}\) is an irrational number.

Find the ratio in which the x-axis divides the line segment joining the points \((-6, 5)\) and \((-4, -1)\). Also, find the point of intersection.

If \(x = h + a \cos \theta\), \(y = k + b \sin \theta\), then prove that : \(\left( \frac{x - h}{a} \right)^2 + \left( \frac{y - k}{b} \right)^2 = 1\)

Prove that : \(\frac{\tan A}{1 + \sec A} - \frac{\tan A}{1 - \sec A} = 2 \csc A\)

In the given figure, \(\triangle ABC\) is a right triangle in which \(\angle B = 90^\circ\), \(AB = 4\) cm and \(BC = 3\) cm. Find the radius of the circle inscribed in the triangle ABC.

Prove that : \(PM = \frac{1}{2} (PQ + QR + PR)\)

A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is 20 cm and the diameter of the cylinder is 7 cm. Find the total volume of the solid. (Use \(\pi = \frac{22}{7}\))