List of top Mathematics Questions

The arithmetic mean of the even positive numbers from 1 to 10 will be:
In the given figure, if $AD=(x+3)$ cm, $DB=(3x+19)$ cm, $AE=x$ cm, $EC=(3x+4)$ cm and $DE \parallel BC$, then the value of $x$ is:
If the mean of the numbers $7, 8, x, 11, 14$ is $x$, then the value of $x$ is:
The value of $\sin^2 18^\circ - \cos^2 72^\circ$ is:
If the roots of the quadratic equation \( ax^2 + bx + c = 0 \) are equal, then the value of \( c \) is:
From a boat which is coming towards a bridge, at any instant the angle of elevation of the bridge is 30°. After travelling 4 minutes with the same velocity, the angle of elevation of the bridge becomes 60°. How much more time will be taken by the boat to reach the bridge?
The father is 7 times older than his son. Two years ago, the father was 13 times as old as his son. What are their present ages?
The distance of the point $(5, 9)$ from the $y$-axis is:
The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60°. From point Y, 40 m vertically above X, the angle of elevation of the top Q of the tower is 45°. Find the height of the tower PQ and the distance PX.
If one side of an isosceles right triangle is \( 5\sqrt{2} \) cm, then the length of its hypotenuse is:
Solve the following pair of equations by reducing them to a pair of linear equations: \[ \frac{10}{x + y} + \frac{2}{x - y} = 4 \] \[ \frac{15}{x + y} - \frac{5}{x - y} = 2 \]
In the following numbers, the rational number is:
The solution of the pair of linear equations \( x + y = 10 \), \( x - y = 4 \) is:
Solve \( 2x + 3y = 11 \) and \( 2x - 4y = -24 \) and hence find the value of \( m \) for which \( y = mx + 3 \).
A fraction becomes \( \frac{1}{3} \) when 1 is subtracted from the numerator and it becomes \( \frac{1}{4} \) when 8 is added to its denominator. Find the fraction.
Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts.
If the median of the frequency distribution given is 28.5, find the values of \( x \) and \( y \) while the total of frequencies is 60.
Two cubes of volume 64 cm\(^3\) each are joined end to end to make a solid. Find the surface area of the resulting cuboid.
A sphere of diameter 12 cm is dropped into a right circular cylindrical vessel partly filled with water. If the sphere is emersed completely in the water, the water level in the cylindrical vessel rises by \( \frac{35}{9} \) cm. Find the diameter of the cylindrical vessel.
If a line intersects sides \( AB \) and \( AC \) of a triangle \( ABC \) at \( D \) and \( E \) respectively and is parallel to \( BC \), prove that \( \frac{AD}{AB} = \frac{AE}{AC} \).
Find the roots of the equation \( x + \frac{1}{x} = 3, \, x \neq 0 \).
Find the distance between the points \( (a, b) \) and \( (-a, -b) \).
If \( 2 \cos^2 45^\circ - 1 = \cos \theta \), then find the value of \( \theta \).
Relation between mean, median, and mode will be:
Find the relation between \( x \) and \( y \) such that the point \( (x, y) \) is equidistant from the points \( (3, 6) \) and \( (-3, 4) \).