List of top Mathematics Questions

In the adjoining figure, TS is a tangent to a circle with centre O. The value of $2x^\circ$ is

For a circle with centre O and radius 5 cm, which of the following statements is true?
P: Distance between every pair of parallel tangents is 10 cm.
Q: Distance between every pair of parallel tangents must be between 5 cm and 10 cm.
R: Distance between every pair of parallel tangents is 5 cm.
S: There does not exist a point outside the circle from where length of tangent is 5 cm.

In the adjoining figure, PA and PB are tangents to a circle with centre O such that $\angle P = 90^\circ$. If $AB = 3\sqrt{2}$ cm, then the diameter of the circle is

Two coins are tossed simultaneously. The probability of getting at least one head is

Given $\triangle ABC \sim \triangle PQR$, $\angle A = 30^\circ$ and $\angle Q = 90^\circ$. The value of $(\angle R + \angle B)$ is

The distance of the point A($-3$, $-4$) from x-axis is
If the zeroes of the polynomial $ax^2 + bx + \dfrac{2a}{b}$ are reciprocal of each other, then the value of $b$ is
Which of the following quadratic equations has real and equal roots?
Which of the following cannot be the unit digit of $8^n$, where $n$ is a natural number?
$\sqrt{0.4}$ is a/an

The Statue of Unity situated in Gujarat is the world’s largest Statue which stands over a 58 m high base. As part of a project, a student constructed an inclinometer and wishes to find the height of the Statue of Unity using it. He noted the following observations from two places:
Situation – I: The angle of elevation of the top of Statue from Place A, which is $80\sqrt{3}$ m away from the base of the Statue, is found to be $60^\circ$. 
Situation – II: The angle of elevation of the top of the Statue from a Place B, which is 40 m above the ground, is found to be $30^\circ$ and the total height of the statue including the base is given to be 240 m.
Based on the given information, answer the following:

Given the vectors: \[ \mathbf{a} = i + 3j - k, \quad \mathbf{b} = 3i - j + 2k, \quad \mathbf{c} = i + 2j - 2k \] and the following information: \[ \frac{\mathbf{a} \cdot \mathbf{c}}{|\mathbf{c}|} = \frac{10}{3} \] Find the value of \( \alpha + \beta \) and the projection of \( \mathbf{a} \) on \( \mathbf{c} \).
Given that: \[ \cot \left( \frac{A + B}{2} \right) \cdot \tan \left( \frac{A - B}{2} \right) \] and the equation involving coordinates: \[ \frac{x}{2} + \frac{y}{3} + \frac{2}{6} - 1 = 0 \] Find the area of \( \Delta ABC = 2 \).
Evaluate the following integrals: \[ \int \frac{(x^4 + 1)}{x(2x + 1)^2} \, dx \] and \[ \int \frac{1}{x^4 + 5x^2 + 6} \, dx \]
Given that \( \cot \left( \frac{A+B}{2} \right) \cdot \tan \left( \frac{A-B}{2} \right) = \), and the equation \( \frac{x}{2} + \frac{y}{3} + \frac{2}{6} - 1 = 0 \), find the area of \( \Delta ABC = 2 \).
A boy tries to message his friend. Each time, the chance the message is delivered is \( \frac{1}{6} \), and the chance it fails is \( \frac{5}{6} \). He sends 6 messages. Find the probability that exactly 5 messages are delivered.
The angle between the lines whose direction cosines satisfy the equations: \[ l + m + n = 0 \quad \text{and} \quad m^2 + n^2 - l^2 = 0 \] Find the angle between the two lines.
Given the equation: \[ 81 \sin^2 x + 81 \cos^2 x = 30 \] Find the value of \( x \).
Evaluate the integral: \[ \int \frac{1}{\sin^2 2x \cdot \cos^2 2x} \, dx \]
If \( \tan(\pi \cos x) = \cot(\pi \sin x) \), then what is \( \sin \left( \frac{\pi}{2} + x \right) \)?
If \( \tan^{-1} (\sqrt{\cos \alpha}) - \cot^{-1} (\cos \alpha) = x \), then what is \( \sin \alpha \)?
Choose a randomly selected leap year, in which 52 Saturdays and 53 Sundays are to be there. Given the following probability distribution:
Find the mean and standard deviation.
There are 6 boys and 4 girls. Arrange their seating arrangement on a round table such that 2 boys and 1 girl can't sit together.
Population of Town A and B was 20,000 in 1985. In 1989, the population of Town A was 25,000, and Town B had 28,000. What will be the difference in population between the two towns in 1993?
Evaluate the limit $ \lim_{n \to \infty} \frac{6^n - 9x - 7^n + 1}{\sqrt{2} - \sqrt{11} + \cos n} $