List of top Mathematics Questions asked in CBSE Class X

In an A.P., \(15^{th}\) term exceeds the \(8^{th}\) term by 21. If sum of first 10 terms is 55, then form the A.P.

The internal and external radii of a hollow hemisphere are \(5\sqrt{2} \text{ cm}\) and \(10 \text{ cm}\) respectively. A cone of height \(5\sqrt{7} \text{ cm}\) and radius \(5\sqrt{2} \text{ cm}\) is surmounted on the hemisphere as shown in the figure. Find the total surface area of the object in terms of \(\pi\). (Use \(\sqrt{2} = 1.4\))

Represent the following pair of linear equations graphically and hence comment on the condition of consistency of this pair : \( x - 5y = 6; 2x - 10y = 12 \)

If \(\sin x = p\), then prove that : (i) \(\cot x = \frac{\sqrt{1 - p^2}}{p}\) (ii) \(\frac{1 + \tan^2 x}{1 + \cot^2 x} = \frac{p^2}{1 - p^2}\)

The sum of squares of two positive numbers is 100. If one number exceeds the other by 2, find the numbers.

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

In the given figure, a circle is centred at \((1, 2)\). The diameter of the circle is

Assertion (A) : The polynomial \(p(y) = y^{2 + 4y + 3}\) has two zeroes.
Reason (R) : A quadratic polynomial can have at most two zeroes.

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

Through the mid-point Q of side CD of a parallelogram ABCD, the line AR is drawn which intersects BD at P and produced BC at R. Prove that \(AQ = QR\).

In a class test, the sum of Anamika's marks obtained in Maths and Science is 30. Had she got 2 marks more in Maths and 3 marks less in Science, the product of the marks would have been 210. Find the marks she got in the two subjects.

The pair of linear equations \( \frac{3x}{2} + \frac{5y}{3} = 7 \) and \( 9x + 10y = 14 \), is :

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 ?

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 \(n\).

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.