List of top Mathematics Questions

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

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

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.

Find the volume of a hemisphere with radius 7 cm.

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.

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.

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

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:

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

The probability of a sure event is:

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

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 \[ \left|A^{2025}-3A^{2024}+A^{2023}\right|. \]

Average age of a nuclear family of 4 members, five years ago was 12 years. On including age of the boy from neighbourhood, the present average age is 15 years. What is the present age of the boy from the neighbourhood?

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.

The half of the average value of three number is 20. The second number is thrice the third number and first number is twice the second number. What is the sum of smallest and largest number?

In the figure given above, \(\triangle ABC \sim \triangle XYZ\), then find the values of \(x\) and \(y\).

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

Assertion (A) : If probability of happening of an event is \(0.2p\), \(p>0\), then \(p\) can't be more than 5.
Reason (R) : \(P(\bar{E}) = 1 - P(E)\) for an event \(E\).

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

If three vectors are given as shown. If the angle between vectors \( \vec{p} \) and \( \vec{q} \) is \( \theta \), where \[ \cos \theta = \frac{1}{\sqrt{3}}, \quad |\vec{p}| = 2\sqrt{3}, \quad |\vec{q}| = 2, \] then find the value of \[ \left| \vec{p} \times (\vec{q} - 3\vec{r}) \right|^{2} - 3|\vec{r}|^{2}. \]

If \( \int_0^1 4 \cot^{-1}(1 - 2x + 4x^2) dx = a \tan^{-1}(2) - b \ln(5) \), where \( a, b \in \mathbb{N} \), then \( (2a + b) \) is equal to _________.