List of top Mathematics Questions

For what value of ‘m’, pair of equations \( x - 2y = 3 \) and \( 3x + my = 1 \) will have a unique solution?
For which value of \( k \), there will be an infinite number of solutions for the pair of linear equations \( x + ky = 1 \) and \( kx + y = k^2 \)?
If \( \frac{1}{x^2 - 2} = \frac{1}{7} \), then the value of \( x \) will be:
The solution of \( 2x + 3y = 18 \); \( x - 2y = 2 \) will be:
If roots of the equation \( 3x^2 - 12x + k = 0 \) are equal, then the value of \( k \) will be:
Which one is a pair of co-prime numbers?
When the angle of elevation of the sun becomes \( \theta \) from \( \varphi \), then the shadow of a pillar standing on the horizontal ground is increased by \( \alpha \) metres. Find the length of the pillar.
A cylindrical bucket of 32 cm height and 18 cm base radius is full of sand. This bucket is emptied on the ground and a conical mound of sand is formed. If the height of this mound is 24 cm, then find its radius and slant height.
In a journey of 300 km, if a person travels 60 km by train and the rest of the distance by bus, then it takes 4 hours in all. If he travels 100 km by train and the rest of the distance by bus, then it takes 10 minutes more. Find the speed of the train and the bus respectively.
Solve the following pair of equations: \[ \frac{5}{x - 1} + \frac{1}{y - 2} = \frac{7}{4}, \] \[ \frac{6}{x - 1} - \frac{2}{y - 2} = \frac{1}{2}. \]
An arc of a circle of radius 21 cm subtends an angle of 60° at the centre. Find the area of the sector formed by the arc and the area of the segment formed by the corresponding chord.
The sum of the powers of prime factors in prime factorization of 144 is:
By observing from the top of a multi-storeyed building, the angle of depression of the top and bottom of a 4 m high building are \( 30^\circ \) and \( 45^\circ \) respectively. Find the height of the multi-storeyed building and the distance between both the buildings.
The product of the age of Punita 2 years ago and her age after 4 years from now is 1 year more than twice her present age. Find her present age.
Prove that \( \sqrt{2} \) is an irrational number.
Given that HCF(255, 867) = 51, find the value of LCM(255, 867).
In a right triangle \( ABC \), angle \( B \) is a right angle and \( BD \) is perpendicular on \( AC \). Prove that: \( AB^2 = AC \cdot AD \).
Solve the following equation: \[ \frac{1}{x} - \frac{1}{x-2} = 3, \quad x \neq 0, 2. \]
Find two positive even consecutive numbers, the sum of whose squares is 340.
Find the median of the following frequency distribution:
Construct a triangle of sides 4 cm, 5 cm, and 6 cm, and again construct another corresponding triangle whose sides are \( \frac{2}{3} \) of the corresponding sides of the previous triangle.
Find the mode from the following table:
The mean and median of a frequency distribution are 26.1 and 25.8 respectively. The value of mode for the distribution will be :
The distance between the points \( (2, y) \) and \( (10, 3) \) is 10 units. Find the value of \( y \).
The measure of central tendency is :