List of top Questions asked in CBSE Class X

There are two sections A and B of Grade X. There are 28 students in Section A and 30 students in Section B. What is the minimum number of books you will acquire for the class library so that they can be distributed equally among students of Section A or Section B ?

PQ is tangent to a circle with centre O. If \(OQ = a\), \(OP = a + 2\) and \(PQ = 2b\), then relation between \(a\) and \(b\) is

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

The value of x for which \( 2x, (x + 10) \) and \( (3x + 2) \) are the three consecutive terms of an A.P. is :

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

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

Evaluate: \(\frac{5 \cos^2 60^\circ + 4 \sec^2 30^\circ - \tan^2 45^\circ}{\sin^2 30^\circ + \cos^2 30^\circ}\)

Prove that: \(1 + \frac{\cot^2 \alpha}{1 + \csc \alpha} = \csc \alpha\)

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 \(n\).

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

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.

If the median of the following distribution is 32.5, then find the values of x and y.

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.

Given cot \(\theta\) = 3, the value of cos \(\theta\) is :

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

How many zeroes does p(x) = (x $-$ 2)(x + 3) have ?

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 :