List of top Mathematics Questions

A Circle S passes through the points of intersection of the circles \( x^2 + y^2 - 2x + 2y - 2 = 0 \) and \( x^2 + y^2 + 2x - 2y + 1 = 0 \). If the centre of this circle S lies on the line \( x - y + 6 = 0 \), then the radius of the circle S is:
The length of the tangent from a point 15 cm away from the centre of a circle of radius 9 cm is:
The value of \(p\), for which the pair of equations \(3x + 4y + 2 = 0\) and \(9x + py + 8 = 0\) represents parallel lines, is:
The value of \(\log_6 2 + \log_6 3\) is:
H.C.F. of 2023, 2024, 2025 is:
Which of the following rational number has terminating decimal?
The expression \((6 + 5\sqrt{3}) - (4 - 3\sqrt{3})\) is:
tan 9$^\circ$ - tan 27$^\circ$ - tan 63$^\circ$ + tan 81$^\circ$ =
The equations \(2x^2 + ax - 2 = 0\) and \(x^2 + x + 2a = 0\) have exactly one common root. If \(a \neq 0\), then one of the roots of the equation \(ax^2 - 4x - 2a = 0\) is:
A line \( L \) passing through the point \( P(-5,-4) \) cuts the lines \( x - y - 5 = 0 \) and \( x + 3y + 2 = 0 \) respectively at \( Q \) and \( R \) such that \[ \frac{18}{PQ} + \frac{15}{PR} = 2, \] then the slope of the line \( L \) is:
If \(\frac{2}{\sqrt{x}} = 2\) and \(\frac{4}{\sqrt{y}} = -1\), then
Which term of the A.P.: \(20, 18, 16, \dots\) is \(-80\)?
The discriminant of the quadratic equation \(3x^2 - 2x + \frac{1}{3} = 0\) is:
How many two-digit numbers are divisible by 3?
In a G.P. the 3rd term is 24 and 6th is 192, then the 10th term is:
Rainfall of a town in a week is 4 cm, 5 cm, 12 cm, 3 cm, 6 cm, 8 cm, and 4 cm, then the average rainfall per day is:
A Kiddy bank contains hundred 50 paise coins, fifty ₹1 coins, twenty ₹2 coins, and ten ₹5 coins. If one of the coins will fall out when the bank is turned upside down, what is the probability that the coin is a ₹5 coin?
From a helicopter, a person observes an object on the ground at an angle of depression of \(30^\circ\). If the helicopter is flying at a height of 500 m from the ground, then the distance between the person and the object is:
A boy observed the top of an electric pole at an angle of elevation of \(60^\circ\) when the observation point is 6 meters away from the foot of the pole, then the height of the pole is:
A chord of a circle of radius 4 cm is making an angle 60° at the centre, then the length of the chord is:
The volume of a right circular cone with radius 6 cm and height 7 cm is:
(use \(\pi = \frac{22}{7}\))
If two cubes each of volume 64 cm\(^3\) are joined end to end together, then the surface area of the resulting cuboid is:
The roots of the quadratic equation \(x^2 - 4x + 4 = 0\) are:
If the system of equations
\( 2x + 3y - z = 5 \)  
\( x + \alpha y + 3z = -4 \)  
\( 3x - y + \beta z = 7 \)  
has infinitely many solutions, then \( 13 \alpha \beta \) is equal to:  
The area of a sector, whose radius is 7 cm with the angle 72° is: