List of top Mathematics Questions asked in Bihar Board Class X Exam

The area of a rectangular field is 260 square meters. If its length becomes 5 meters less and breadth 2 meters more, it becomes a square field. Find the length and breadth of the rectangular field.
Two dice are thrown at the same time. Find the probability that the sum of the two numbers appearing on the top of the dice is more than 9.
A ladder 15 m long makes an angle of \( 60^\circ \) with the wall. Find the height of the point on the wall where the ladder touches the wall.
Find the value of \( x \) for which the distance between the points \( P(x, 4) \) and \( Q(9,10) \) is 10 units.
In what ratio does the point \( (-1,6) \) divide the line segment joining the points \( (-3,10) \) and \( (6,-8) \)?
Find the roots of the equation \( x + \frac{1}{x} = 3, \quad x \neq 0 \).
Find the value of \( 4\tan^2 45^\circ + \cos^2 30^\circ - \sin^2 60^\circ \).
Each side of an equilateral triangle \( ABC \) is \( a \). Prove that the altitude of the triangle is \( \frac{\sqrt{3}}{2} a \).
If the sum of the first 14 terms of an A.P. is 1050 and its first term is 10, find the 20th term.
Find the sum of the first 22 terms of an A.P. in which the common difference is 7 and the 22nd term is 149.
If the 3rd and 9th terms of an A.P. are 4 and -8 respectively, which term of this A.P. is zero?
Find the discriminant of the quadratic equation \( 9x^2 - 6x + 1 = 0 \) and hence find the nature of the roots.
For what values of \( k \) does the quadratic equation \( (k+1)x^2 - 2(k-1)x + 1 = 0 \) have equal roots?
For what value of \( k \), do the equations \( kx + y = 1 \) and \( (k+1)x + 2y = 3 \) have no solution?
The sum of the digits of a two-digit number is 9. If 9 is added to the number, the digits of the number are reversed. Write the equation for these statements.
Solve the pair of equations \( \sqrt{2} x + \sqrt{3}y = 0 \) and \( \sqrt{3}x - \sqrt{8}y = 0 \) by the method of substitution or elimination.
The length, breadth, and height of a cuboid are 26 m, 14 m, and 6.5 m, respectively. Find the lateral surface area of the cuboid.
The curved surface area and volume of a cylinder are 264 m\(^2\) and 396 m\(^3\) respectively. Find the radius and height of the cylinder.
The base radius of a cone is \( 7\sqrt{7} \) cm and its height is 21 cm. Find the volume of the cone.
Find the mean of the following data:
\[ \begin{array}{c|c|c|c|c|c} \text{Variable} & 4 & 6 & 8 & 10 & 12 \\ \hline \text{Frequency} & 4 & 8 & 14 & 11 & 3 \end{array} \]
A circle has a radius of 6 cm. Find the length of that chord which is at a distance of 4 cm from the center.
If one zero of the polynomial \( (a+2)x^2 - 3ax -2 \) is negative of the other, then find the polynomial.
Prove that \( \sec^4 \theta - \tan^4 \theta = 1 + 2\tan^2 \theta \).
If \( q \) is a positive integer, which of the following is an odd positive integer?
The H.C.F. of two consecutive odd numbers is: