List of top Mathematics Questions asked in CBSE Class X

In the given figure, O is the centre of the circle. PQ and PR are tangents. Show that the quadrilateral PQOR is cyclic.

Find the area of the segment AYB shown in the figure, if the radius of the circle is 21 cm and \(\angle AOB = 120^\circ\). [Use \(\pi = 22/7\)]

Find the value of p, for which one zero of the quadratic polynomial \(px^2 - 14x + 8\) is 6 times the other.

Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

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

If a regular hexagon ABCDEF circumscribes a circle, then prove that AB + CD + EF = BC + DE + FA.

In a flight of 600 km, an aircraft slowed down its speed due to bad weather. Its average speed for the trip reduced by 200 km/h from its usual speed and time of flight increased by 30 minutes. Find the scheduled duration of the flight.

Two pipes are used to fill a swimming pool. If the pipe of the larger diameter is used for 4 hours and the pipe of the smaller diameter for 9 hours, only half of the pool can be filled. Find how long it would take for each pipe to fill the pool, separately, if the pipe of smaller diameter takes 10 hours more than the pipe of larger diameter to fill the pool.

If 2 sin A = 1, then the value of tan A + cot A is :

Which of the following sequence is not an A.P. ?

The area of a semicircle of diameter 'd' is :

In the given figure \(\triangle\)ABC is shown, in which DE \(\parallel\) BC. If AD = 5 cm, DB = 2.5 cm and DE = 8 cm, then the length of BC is :

In the given figure, XY || QR, \(\frac{PQ}{XQ} = \frac{7}{3}\) and PR = 6.3 cm. Find the length of YR.

If tan A = \(\frac{4}{3}\), find sin A and cos A.

Express cos A and tan A in terms of sin A.

The three vertices of a rhombus PQRS are P(2, \(-\)3), Q(6, 5) and R(\(-\)2, 1). Find the coordinates of the fourth vertex S and coordinates of the point where both the diagonals PR and QS intersect.

Two different dice are thrown together. Find the probability that the numbers obtained have : (i) even sum, (ii) even product.

The length of hypotenuse (in cm) of a right-angled triangle is 6 cm more than twice the length of its shortest side. If the length of its third side is 6 cm less than thrice the length of its shortest side, find the dimensions of the triangle.

\(\frac{1 + \tan^2 A}{1 + \cot^2 A}\) equals to:

\(PQ\) is tangent to a circle with centre \(O\). If \(\angle POR = 65^{\circ}\), then \(m\angle OPR\) is

A circle centred at \((-1, 2)\) passes through the point \((0, 3)\). Radius of the circle is

It is given that \(\triangle ABC \sim \triangle EDF\). Which of the following is not true?

If roots of the quadratic equation \(x^2 - k\sqrt{3}x + 2 = 0\) are real and equal, then value of \(k\) is

Observe the graph of polynomial \(p(x)\). Number of zeroes of \(p(x)\) is