List of top Mathematics Questions

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 \(\triangle ABE \sim \triangle CFB\).
For what value of k points (1, 1), (3, k) and (-1, 4) are collinear?
Find the area of the triangle whose vertices are (-5, -1), (3, -5) and (5, 2).
Prove that \(5 - \sqrt{3}\) is an irrational number.
ABC is an isosceles right triangle with C as right angle. Prove that \(AB^2 = 2AC^2\).
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.
Find such a point on y-axis which is equidistant from the points (6, 5) and (-4, 3).
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.
Prove that \(\tan 7^\circ \cdot \tan 60^\circ \cdot \tan 83^\circ = \sqrt{3}\).
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.
The length of the minute hand for a clock is 7 cm. Find the area swept by it in 40 minutes.
Divide \(x^3 + 1\) by \(x + 1\).
Find two consecutive positive integers, sum of whose squares is 365.
If the radius of base of a cone is 7 cm and its height is 24 cm then find its curved surface area.
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.
If \(\tan\theta = \frac{5}{12}\), then find the value of \(\sin\theta + \cos\theta\).
\(\triangle ABC\) 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.
If \(\sin 3A = \cos(A - 26^\circ)\), where 3A is an acute angle, then find the value of A.
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 \(\triangle ABC \sim \triangle PQR\).
Prove that \(\sqrt{\frac{1+\cos\theta}{1-\cos\theta}} = \frac{1+\cos\theta}{\sin\theta}\)
The sum of two numbers is 50 and one number is \(\frac{7}{3}\) times of the other; then find the numbers.
If \(\cos A = \frac{4}{5}\), then find the values of \(\cot A\) and \(\csc A\).
Prove that \(\tan 9^\circ \cdot \tan 27^\circ = \cot 63^\circ \cdot \cot 81^\circ\).