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

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
If \( 2a + 3b = 8 \) and \( 3a - 4b = -5 \), then
Which of the following quadratic polynomials has zeroes 4 and -2?
If \( \alpha \) and \( \beta \) are the zeroes of the polynomial \( p(x) = x^2 + 3x - 4 \), then the value of \( \frac{\alpha \beta}{4} \) is
If the product of zeroes of the polynomial \( x^2 - 9x + a \) is 8, then the value of \( a \) is
Draw a circle of radius 6 cm. From a point 10 cm away from its center, construct the pair of tangents to the circle and measure their lengths.
Find the median of the following data:
\[ \begin{array}{|c|c|} \hline \text{Class Interval} & \text{Frequency} \\ \hline 40-45 & 2 \\ 45-50 & 3 \\ 50-55 & 8 \\ 55-60 & 6 \\ 60-65 & 6 \\ 65-70 & 3 \\ 70-75 & 2 \\ \hline \end{array} \]
The angles of elevation of the top of a tower from two points at distances of 4 m and 9 m from the base of the tower, which are in the same straight line, are complementary. Prove that the height of the tower is 6 m.
The zeroes of the polynomial \( x^2 - 11 \) are:
If -2 and -3 are the zeroes of the quadratic polynomial \( x^2 + (a+1)x + b \), then
The degree of the polynomial \( (x^5 + x^2 + 3x) (x^6 + x^5 + x^2 + 1) \) is:
Which of the following is not a polynomial?
Divide polynomial \( 2x^4 + 3x^3 - 2x^2 - 9x - 12 \) by polynomial \( x^2 - 3 \).
If one zero of the polynomial \( (a^2 + 9)x^2 + 13x + 6a \) is reciprocal of the other, find \( a \).
Find the sum of 10 terms of A.P. 9, 17, 25, ...
Find the sum of the first 15 multiples of 8.
On adding 1 to the numerator of a fraction it becomes \( \frac{1}{2} \) and on adding 1 to the denominator it becomes \( \frac{1}{3} \). Write the equation for this statement.
Solve the pair of equations \( 8x + 5y = 9 \) and \( 3x + 2y = 4 \) by substitution method.
Metallic spheres of radii 6 cm, 8 cm, and 10 cm respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.
In triangle \( \triangle PQR \), two points \( S \) and \( T \) are on sides \( PQ \) and \( PR \) such that \( \frac{PS}{SQ} = \frac{PT}{TR} \) and \( \angle PST = \angle PRQ \). Prove that \( \triangle PQR \) is an isosceles triangle.
Prove that
\[ \left( \frac{\sin A}{1+\cos A} + \frac{1+\cos A}{\sin A} \right) \left( \frac{\sin A}{1-\cos A} + \frac{1-\cos A}{\sin A} \right) = 4 \csc A \cot A. \]
Find the zeroes of the quadratic polynomial \( 3x^2 - x - 4 \) and verify the relationship between the zeroes and the coefficients.
Find the discriminant of the quadratic equation \( \sqrt{2}x^2 - x - \sqrt{2} = 0 \) and hence find the nature of the roots.
For what value of \( k \) will the equation \( kx(x-2) + 6 = 0 \) have equal roots?
Check whether 301 is a term of the sequence \( 5, 11, 17, 23, \dots \).