List of top Mathematics Questions asked in CBSE Class X

Assertion (A): Zeroes of a polynomial \(p(x) = x^2 − 2x − 3\) are -1 and 3.
Reason (R): The graph of polynomial \(p(x) = x^2 − 2x − 3\) intersects the x-axis at (-1, 0) and (3, 0).
\(D\) is a point on the side \(BC\) of \(\triangle ABC\) such that \(\angle ADC = \angle BAC\). Show that:
\(AC^2 = BC \times DC\)
Problem Figure
The diameter of a circle is of length 6 cm. If one end of the diameter is \((-4, 0)\), the other end on \(x\)-axis is at:
Problem Figure
Assertion (A): If the PA and PB are tangents drawn to a circle with center O from an external point P, then the quadrilateral OAPB is a cyclic quadrilateral.
Reason (R): In a cyclic quadrilateral, opposite angles are equal.
Two dice are rolled together. The probability of getting a doublet is:
The value of \(k\) for which the pair of linear equations \(5x + 2y - 7 = 0\) and \(2x + ky + 1 = 0\) don't have a solution, is:
If a certain variable \(x\) divides a statistical data arranged in order into two equal parts; then the value of \(x\) is called the:
The mean and median of a statistical data are 21 and 23 respectively. The mode of the data is:
The height and radius of a right circular cone are 24 cm and 7 cm respectively. The slant height of the cone is:
For what value of \(\theta\), \(\sin^2\theta + \sin\theta + \cos^2\theta\) is equal to 2?
The radius of a sphere is \(\frac{7}{2}\) cm. The volume of the sphere is:
The distance between the points \((2, -3)\) and \((-2, 3)\) is:
A card is drawn from a well-shuffled deck of 52 playing cards. The probability that drawn card is a red queen, is:
If the roots of quadratic equation \(4x^2 - 5x + k = 0\) are real and equal, then value of \(k\) is:
The mid-point of the line segment joining the points \((-1, 3)\) and \(\left(8, \frac{3}{2}\right)\) is:
If \(\sin \theta = \frac{1}{3}\), then \(\sec \theta\) is equal to:
HCF \((132, 77)\) is:
If probability of winning a game is \(p\), then probability of losing the game is:
For what value of \(k\), the product of zeroes of the polynomial \(kx^2 - 4x - 7\) is 2?
In an A.P., if \(a = 8\) and \(a_{10} = -19\), then value of \(d\) is:

A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mode of the data :

Number of cars0 - 1010 - 2020 - 3030 - 4040 - 50 50 - 60 60 -7070 - 80
Frequency71413122011158
Solve 2x + 3y = 11 and 2x – 4y = – 24 and hence find the value of ‘m’ for which y = mx + 3.
Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
Fill in the blanks in the following table, given that a is the first term, d the common difference and an the nth term of the AP:
 adn\(a_n\)
(i)738….
(iI)-18…100
(iii)…-318-5
(iv)-18.92.5…3.6
(v)3.50105…

A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.