List of top Mathematics Questions

The diagonal of a cube is \(9\sqrt{3}\) cm. Find the total surface area of cube.
Find the sum of \(3 + 11 + 19 + \dots + 67\).
If one angle of a triangle is equal to one angle of the other triangle and the sides included between these angles are proportional then prove that the triangles are similar.
Draw the graphs of the pair of linear equations \(x+3y-6=0\) and \(2x-3y-12=0\) and solve them.
Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure both parts.
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.
Find such a point on y-axis which is equidistant from the points (6, 5) and (-4, 3).
For what value of k points (1, 1), (3, k) and (-1, 4) are collinear?
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 the co-ordinates of the point which divides line segment joining the points (-1, 7) and (4, -3) in the ratio 2:3 internally.
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 \(\triangle ABE \sim \triangle CFB\).
ABC is an isosceles right triangle with C as right angle. Prove that \(AB^2 = 2AC^2\).
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.
Find the discriminant of the quadratic equation \(2x^2 + 5x - 3 = 0\) and find the nature of the roots also.
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.
Using Euclid's division algorithm, find the H.C.F. of 504 and 1188.
Divide \(x^3 + 1\) by \(x + 1\).
The length of the minute hand for a clock is 7 cm. Find the area swept by it in 40 minutes.
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.
Prove that \(\tan 7^\circ \cdot \tan 60^\circ \cdot \tan 83^\circ = \sqrt{3}\).
Prove that \(\tan 9^\circ \cdot \tan 27^\circ = \cot 63^\circ \cdot \cot 81^\circ\).
If \(\cos A = \frac{4}{5}\), then find the values of \(\cot A\) and \(\csc A\).
If \(\tan\theta = \frac{5}{12}\), then find the value of \(\sin\theta + \cos\theta\).