List of practice Questions

The mode and median of a frequency distribution are 42 and 38.1 respectively. Find its mean.
Find the zeroes of the quadratic polynomial $x^2 + 7x + 10$ and verify the relationship between the zeroes and the coefficients.
A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball, then determine the number of blue balls in the bag.
Sum of the areas of two squares is $157 \, m^2$. If the sum of their perimeters is 68 meters, then find the sides of both squares.
The velocity of a boat is 18 km/h in still water. It takes one hour more to travel 24 km in downstream and 24 km in upstream. Find the speed of the current.
A statue 1.6 m tall, stands on top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is $60^\circ$ and from the same point, the angle of elevation of the top of the pedestal is $45^\circ$. Find the length of the pedestal.
Two poles of equal heights are standing opposite to each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are $60^\circ$ and $30^\circ$ respectively. Find the height of the poles and the distance of the point from the pole.
If one root of the quadratic equation $x^2 + 3x - p = 0$ is 2, then find the value of $p$.
If $\cos \theta = \dfrac{15}{17}$, then find the value of $\sin \theta$.
Find the coordinates of the midpoint of the line segment joining the points $(-3, 10)$ and $(5, 4)$.
If the distance between the points $(-1, -3)$ and $(x, 9)$ is 13 units, then find the values of $x$.
Find two consecutive odd positive integers, sum of whose squares is 290.
Prove that in two concentric circles, the chord of the larger circle which touches the smaller circle is bisected at the point of contact.
Capsule is a combination of:
If the mean and mode of some data are 32 and 35 respectively, then its median will be:
If two dice are tossed together, then the probability of getting the sum of numbers on both the dice as 10 is:
When a die is thrown once, the probability of getting an even number will be:
The volume of a cube is 1331 cm$^3$. Find its each side.
The value of $\dfrac{\sin 27^\circ}{\cos 63^\circ}$ will be:
If $\cos A = \dfrac{\sqrt{3}}{2}$, then the value of $\sin 2A$ will be:
The value of $\dfrac{1 + \tan^2 A}{1 + \cot^2 A}$ will be:
$\sin 2A = 2 \sin A$ is true when $A$ is equal to:
The area of a quadrant of a circle whose circumference is 22 cm will be:
The solution of a pair of linear equations $x + 2y + 5 = 0$ and $-3x - 6y + 1 = 0$ will be:
Common difference for the Arithmetic Progression (AP): $-5, -1, 3, 7, \ldots$ will be: