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

Find the mean of the following distribution: 
\[\begin{array}{|c|c|c|c|c|c|c|c|} \hline \textbf{Class-interval} & 11-13 & 13-15 & 15-17 & 17-19 & 19-21 & 21-23 & 23-25 \\ \hline \text{Frequency} & \text{7} & \text{6} & \text{9} & \text{13} & \text{20} & \text{5} & \text{4} \\ \hline \end{array}\] 
 

Prove that \( \frac{\sec\theta - \tan\theta}{\sec\theta + \tan\theta} = 1 + 2\tan^2\theta - 2\sec\theta\tan\theta \)
The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.
The slant height of a frustum of a cone is 4 cm and the perimeters (circumferences) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum.
Draw the graphs of the pair of linear equations \(x+3y-6=0\) and \(2x-3y-12=0\) and solve them.
Using quadratic formula find the roots of the equation \(2x^2 - 2\sqrt{2}x + 1 = 0\).
If one angle of a triangle is equal to one angle of the other triangle and the sides included between these angles are proportional then prove that the triangles are similar.
Find the sum of \(3 + 11 + 19 + \dots + 67\).
A two digit number is four times of the sum of its digits and twice the product of its digits. Find the number.
The diagonal of a cube is \(9\sqrt{3}\) cm. Find the total surface area of cube.
Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure both parts.
If 5th and 9th terms of an A.P. are 43 and 79 respectively, find the A.P.
ABC is an isosceles right triangle with C as right angle. Prove that \(AB^2 = 2AC^2\).
Find the area of the triangle whose vertices are (-5, -1), (3, -5) and (5, 2).
Prove that \(5 - \sqrt{3}\) is an irrational number.
A ladder 7 m long makes an angle of 30\(^\circ\) with the wall. Find the height of the point on the wall where the ladder touches the wall.
Find such a point on y-axis which is equidistant from the points (6, 5) and (-4, 3).
For what value of k points (1, 1), (3, k) and (-1, 4) are collinear?
E is a point on the extended part of the side AD of a parallelogram ABCD and BE intersects CD at F; then prove that \(\triangle ABE \sim \triangle CFB\).
Find the co-ordinates of the point which divides line segment joining the points (-1, 7) and (4, -3) in the ratio 2:3 internally.
Find the discriminant of the quadratic equation \(2x^2 + 5x - 3 = 0\) and find the nature of the roots also.
If the radius of base of a cone is 7 cm and its height is 24 cm then find its curved surface area.
Find two consecutive positive integers, sum of whose squares is 365.
The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Write the equation for this statement.
Divide \(x^3 + 1\) by \(x + 1\).