List of top Mathematics Questions

Find the median of the following data:
\[ \begin{array}{|c|c|} \hline \text{Class Interval} & \text{Frequency} \\ \hline 40-45 & 2 \\ 45-50 & 3 \\ 50-55 & 8 \\ 55-60 & 6 \\ 60-65 & 6 \\ 65-70 & 3 \\ 70-75 & 2 \\ \hline \end{array} \]
If -2 and -3 are the zeroes of the quadratic polynomial \( x^2 + (a+1)x + b \), then
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.
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.
Find the sum of 10 terms of A.P. 9, 17, 25, ...
If one zero of the polynomial \( (a^2 + 9)x^2 + 13x + 6a \) is reciprocal of the other, find \( a \).
Find the sum of the first 15 multiples of 8.
Divide polynomial \( 2x^4 + 3x^3 - 2x^2 - 9x - 12 \) by polynomial \( x^2 - 3 \).
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.
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.
Prove that
\[ \left( \frac{\sin A}{1+\cos A} + \frac{1+\cos A}{\sin A} \right) \left( \frac{\sin A}{1-\cos A} + \frac{1-\cos A}{\sin A} \right) = 4 \csc A \cot A. \]
Prove that \( \frac{\sec\theta + \tan\theta}{\sec\theta - \tan\theta} = \left(\frac{1 + \sin\theta}{\cos\theta}\right)^2 \).
Find the area of the triangle whose vertices are \( A(2,1) \), \( B(4,5) \) and \( C(0,3) \).
Check whether 301 is a term of the sequence \( 5, 11, 17, 23, \dots \).
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?
Find the zeroes of the quadratic polynomial \( 3x^2 - x - 4 \) and verify the relationship between the zeroes and the coefficients.
Prove that \( (2+\sqrt{3})^2 \) is not a rational number.
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 \( x \).
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 \( OP \).
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 \( \frac{1}{x} - \frac{1}{x-2} = 3 \), \( x \neq 0,2 \).