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

If in division algorithm \( a = bq + r \), \( b = 61 \), \( q = 27 \), and \( r = 32 \), what is the value of \( a \)?
If \( q \) is a positive integer, which of the following is an odd positive integer?
If one side of an equilateral triangle is 12 cm, then its height is
\( \sqrt{\frac{64}{81}} + \sqrt{\frac{16}{9}} \) is
The product of two irrational numbers \( 3 + \sqrt{6} \) and \( 3 - \sqrt{5} \) will be a/an
If the ratio of corresponding sides of two similar triangles is 5:6, then the ratio of their perimeters is
If one side of an equilateral triangle \( ABC \) is 12 cm and one side of equilateral triangle \( DEF \) is 6 cm, then the ratio of areas of \( \frac{\triangle ABC}{\triangle DEF} \) is:
In \( \triangle ABC \), \( AB = 6\sqrt{3} \, \text{cm}, AC = 12 \, \text{cm}, \) and \( BC = 6 \, \text{cm} \), then \( \angle B \) is
If \( \triangle ABC \) and \( \triangle PQR \) are similar triangles in which \( AD \) is perpendicular from vertex \( A \) to \( BC \) and \( PT \) is perpendicular from vertex \( P \) to \( QR \), \( AD = 9 \, \text{cm} \) and \( PT = 7 \, \text{cm} \), then the ratio of areas of triangle \( \triangle AB \) and triangle \( \triangle PQR \) is
If \( A(-1, 0), B(5, -2) \), and \( C(8, 2) \) are the vertices of a triangle, the coordinates of its centroid are
If \( P \left( \frac{a}{2}, 4 \right) \) is the midpoint of the line segment joining the points \( A (-6, 5) \) and \( B (-2, 3) \), then the value of \( a \) is
If three points are collinear, then what is the area of the triangle made by them?
If in \( \triangle ABC \), \( AD \) is the bisector of \( \angle BAC \) and \( AB = \frac{1}{10} \, \text{cm}, AC = 14 \, \text{cm}, BC = 6 \, \text{cm} \), then the value of \( DC \) is
If the sum of the first \( n \) terms of an A.P. is \( (5n - n^2) \), then the common difference of the A.P. is
In \( \triangle ABC \), \( DE \parallel BC \) such that \( \frac{AD}{DB} = \frac{3}{5} \). If \( AC = 5.6 \, \text{cm} \), then \( AE \)= ?
The 2nd term of an A.P. is 13 and its 5th term is 25. The common difference of the A.P. is
The pair of linear equations \( 2x - 3y = 8 \) and \( 4x - 6y = 9 \) are
The graphs of the equations \( 2x + 3y = 4 \) and \( 4x + 6y = 12 \) are which type of straight lines?
Which of the following is an A.P.?
How many solutions does the system of linear equations \( 2x - 3y + 1 = 0 \) and \( 3x + y + 2 = 0 \) have?
For what value of \( k \) has the system of linear equations \( x + 2y = 3 \) and \( 5x + ky = 15 \) infinite solutions?
For what value of \( p \), the terms \( (2p + 1), 13, (5p - 3) \) are in A.P.?
If \( a_n \) is the \( n \)-th term of A.P. \( 3, 8, 13, 18, \dots \), then what is the value of \( a_{25} - a_{10} \)?
If \( f(x) = x^4 - 2x^3 - x + 2 \) is divided by \( g(x) = x^2 - 3x + 2 \), the degree of the quotient is
If \( \alpha \) and \( \beta \) are the zeroes of the polynomial \( x^2 - 3(x+1) - 5 \), then the value of \( (\alpha + 1)(\beta + 1) \) is