List of top Questions asked in Bihar Board X - 2025

Find the sum of \(3 + 11 + 19 + \dots + 67\).
If 5th and 9th terms of an A.P. are 43 and 79 respectively, find the A.P.
Draw the graphs of the pair of linear equations \(x+3y-6=0\) and \(2x-3y-12=0\) and solve them.
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.
A two digit number is four times of the sum of its digits and twice the product of its digits. Find the number.
Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure both parts.
Prove that \(5 - \sqrt{3}\) is an irrational number.
For what value of k points (1, 1), (3, k) and (-1, 4) are collinear?
Find such a point on y-axis which is equidistant from the points (6, 5) and (-4, 3).
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.
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 \(\triangle ABE \sim \triangle CFB\).
ABC is an isosceles right triangle with C as right angle. Prove that \(AB^2 = 2AC^2\).
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 area of the triangle whose vertices are (-5, -1), (3, -5) and (5, 2).
Divide \(x^3 + 1\) by \(x + 1\).
Using Euclid's division algorithm, find the H.C.F. of 504 and 1188.
Find the discriminant of the quadratic equation \(2x^2 + 5x - 3 = 0\) and find the nature of the roots also.
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.
In a triangle PQR, two points S and T are on the sides PQ and PR respectively such that \(\frac{PS}{SQ} = \frac{PT}{TR}\) and \(\angle PST = \angle PRQ\), then prove that \(\triangle PQR\) is an isosceles triangle.
If the radius of base of a cone is 7 cm and its height is 24 cm then find its curved surface area.
The length of the minute hand for a clock is 7 cm. Find the area swept by it in 40 minutes.
Prove that \(\tan 7^\circ \cdot \tan 60^\circ \cdot \tan 83^\circ = \sqrt{3}\).
Sides AB and BC and median AD of a \(\triangle ABC\) are respectively proportional to sides PQ and QR and median PM of another \(\triangle PQR\). Then prove that \(\triangle ABC \sim \triangle PQR\).
\(\triangle ABC\) and \(\triangle DEF\) are similar and their areas are 9 cm\(^2\) and 64 cm\(^2\) respectively. If DE = 5.1 cm then find AB.