List of top Mathematics Questions

Find the coordinates of the points that trisect the line segment AB joining the points \( A(-1, 2) \) and \( B(2, 8) \).

Show graphically that the linear equations \( x - y = 8 \), \( 3x - 3y = 16 \) are inconsistent, i.e. it has no solution.

What do you understand by irrational number? Prove that \( 5 - 3\sqrt{2} \) is an irrational number.

Find the value of K for which the given system of equations has infinitely many solutions: \[ Kx + 3y = K-3 \quad \text{(1)} \] \[ 12x + Ky = K \quad \text{(2)} \]

Form a quadratic equation, one of whose zero is \( 2 + \sqrt{5} \) and the sum of zeros is 4.

If \( \sin A + \cos A = \sqrt{2} \), find the value of \( \sin A \cos A \).

Two coins are tossed simultaneously, what is the probability of getting at least one head?

The A.P. \( 8, 10, 12, \ldots \) has 60 terms. Find the sum of the last 20 terms.

Assertion (A): The number \(4^n\) cannot end with the digit 0, where \(n\) is a natural number.
Reason (R): A number ends with 0 if its prime factorization contains both 2 and 5.

If the mid point of a line segment joining the points \( (h, 3) \) and \( (6, 5) \) is \( (4, 4) \), then find the value of h.

Assertion (A): The tangent to a circle is a special case of the secant, when the two end points of its corresponding chord coincide.
Reason (R): A tangent to a circle is a line that intersects the circle at only one point.

If the zeroes of a quadratic polynomial \( 3x^2 - kx + 12 \) are equal, then find the value of \( k \).

Which of the following pairs of lines in a circle cannot be parallel:

The probability of a sure event is:

Area of a sector of a circle of radius 21 cm and the central angle 60° is:

The distance of the point \(P(-6, 8)\) from the origin is:

In \( \triangle ABC \), \( DE \parallel BC \) such that \( \frac{AD}{DB} = \frac{3}{5} \); if \( AC = 5.6 \, \text{cm} \), then \( AE \) is equal to:

A polynomial of degree three has:

If the product of two numbers is 2880 and their H.C.F. is 12, then the value of their L.C.M. is:

If \[ A=\begin{bmatrix}2 & 3\\3 & 5\end{bmatrix}, \] then find the value of \[ \left|A^{2025}-3A^{2024}+A^{2023}\right|. \]

In 15 days, 9 women and 15 girls can reap a field. In what time could 15 women and 16 girls reap the same field, assuming 3 women can do as much work as 4 girls?

If a train runs at 50 km/hr, it reaches 60 minutes earlier than its schedule time at its destination but if it runs at 8.33 m/s it reaches at its destination 300 minutes late, find the correct time for the train to complete its journey.

If the image of the point \( P(a,2,a) \) in the line \[ \frac{x}{2} = \frac{y+a}{1} = \frac{z}{1} \] is \( Q \) and the image of \( Q \) in the line \[ \frac{x-2b}{2} = \frac{y-a}{1} = \frac{z+2b}{-5} \] is \( P \), then \( a + b \) is equal to

If \( P \) is a point on the circle \( x^2 + y^2 = 4 \), \( Q \) is a point on the straight line \( 5x + y + 2 = 0 \) and \( x - y + 1 = 0 \) is the perpendicular bisector of \( PQ \), then 13 times the sum of abscissa of all such points \( P \) is _________.

In the given figure, a circle is centred at \((1, 2)\). The diameter of the circle is