List of top Mathematics Questions asked in Bihar Board X

Find the area of the triangle whose vertices are \( A(2,1) \), \( B(4,5) \) and \( C(0,3) \).
Prove that \( (2+\sqrt{3})^2 \) is not a rational number.
Prove that \( \frac{\sec\theta + \tan\theta}{\sec\theta - \tan\theta} = \left(\frac{1 + \sin\theta}{\cos\theta}\right)^2 \).
For what value of \( k \) equations \( kx + y = 1 \) and \( (k-1)x + 2y = 3 \) have no solution?
Write the solution of the equation \( 3x + y = 11 \) in natural numbers.
Find the roots of the equation \( \frac{1}{x} - \frac{1}{x-2} = 3 \), \( x \neq 0,2 \).
In \( \triangle ABC \), \( \angle C = 90^\circ \) and \( P, Q \) are midpoints of \( CA \) and \( CB \) respectively. Prove that \( 4AQ^2 = 4AC^2 + BC^2 \).
Find the mean of the following data: \ \[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Variable} & 2 & 4 & 6 & 10 & 12 \\ \hline \text{Frequency} & 3 & 2 & 3 & 1 & 2 \\ \hline \end{array} \]
If the angle between two tangents drawn from an external point \( P \) to a circle of radius 3 cm and centre \( O \) is \( 60^\circ \), find the length of \( OP \).
Using Euclid division algorithm find the HCF of 148 and 185.
In what ratio does the point \( (-4,6) \) divide the line segment joining \( A(-6,10) \) and \( B(3,-8) \)?
If point \( A(x,2) \) is equidistant from the points \( B(8,-2) \) and \( C(2,-2) \), find the value of \( x \).
For what value of \( m \), \( -4 \) is one of the zeros of the polynomial \( x^2 - x - (2m+2) \)?
If 1 is one zero of the polynomial \( p(x) = ax^2 - 3(a-1)x - 1 \), then the value of \( a \) is:
Which of the following quadratic polynomials has zeros \( \frac{3}{5} \) and \( -\frac{1}{2} \)?
If \( \alpha \) and \( \beta \) are the zeros of the polynomial \( p(x) = x^2 - 3x - 4 \), then the value of \( \frac{4}{3} (\alpha + \beta) \) is:
If one zero of the polynomial \( p(x) \) is 5, then one factor of \( p(x) \) is:
If \( p(x) = x^4 + 2x^3 - 17x^2 - 4x + 30 \) is divided by \( q(x) = x^2 + 2x - 15 \), then the degree of the quotient is:
If \( \alpha \) and \( \beta \) are the zeros of the polynomial \( x^2 + 5x + 8 \), then the value of \( \alpha^2 + \beta^2 + 2\alpha\beta \) is:
Which of the following is not a polynomial
What is the degree of the polynomial \( (3x^2 - 7x + 2)(2x^4 + 3x^3 - 5x + 2) \)?
The zeros of the polynomial \( x^2 - 13 \) are:
If \( \tan 2A = \cot (A - 18^\circ) \) where \( 2A \) is an acute angle, then the value of \( A \) is:
If \( \sin \theta = \frac{a}{b} \), then the value of \( \cos \theta \) is:
If \( TP \) and \( TQ \) are two tangents drawn from an external point \( T \) to a circle whose centre is \( O \) such that \( \angle POQ = 120^\circ \), then the value of \( \angle OTP \) is: