List of practice Questions

If the roots of the quadratic equation \( ax^2 + bx + c = 0 \) are equal, then the value of \( c \) is:
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:
The arithmetic mean of the even positive numbers from 1 to 10 will be:
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.
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?
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:
The distance of the point $(5, 9)$ from the $y$-axis is:
If one side of an isosceles right triangle is \( 5\sqrt{2} \) cm, then the length of its hypotenuse is:
Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts.
Solve \( 2x + 3y = 11 \) and \( 2x - 4y = -24 \) and hence find the value of \( m \) for which \( y = mx + 3 \).
If a line intersects sides \( AB \) and \( AC \) of a triangle \( ABC \) at \( D \) and \( E \) respectively and is parallel to \( BC \), prove that \( \frac{AD}{AB} = \frac{AE}{AC} \).
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.
Find the roots of the equation \( x + \frac{1}{x} = 3, \, x \neq 0 \).
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.
Relation between mean, median, and mode will be:
If \( 2 \cos^2 45^\circ - 1 = \cos \theta \), then find the value of \( \theta \).
Find two consecutive positive integers, the sum of whose squares is 365.
Find the relation between \( x \) and \( y \) such that the point \( (x, y) \) is equidistant from the points \( (3, 6) \) and \( (-3, 4) \).
The base radius of a right circular cone is 3.5 cm and height is 12 cm. Find the slant height of the cone.
Find the distance between the points \( (a, b) \) and \( (-a, -b) \).