List of top Mathematics Questions

The maximum value of the variance of a Binomial distribution with parameters \( n \) and \( p \) is:
There are two bags:
- Bag 1: 4 red, 3 black → total = 7 balls
- Bag 2: 2 red, 3 black → total = 5 balls
A bag is chosen at random and one ball is drawn. What is the probability that the ball is red?
In a lottery containing 35 tickets, exactly 10 tickets bear a prize. If a ticket is drawn at random, then the probability of not getting a prize is
A bag contains 7 green and 5 black balls. 3 balls are drawn at random one after the other. If the balls are not replaced, then the probability of all three balls being green is
Suppose that a book of 600 pages contains 40 print mistakes. Assume that these errors are randomly distributed throughout the book and the number of errors per page follows a Poisson distribution. The probability that all the 10 pages selected at random have no print mistakes is:
If X is a Poisson random variate with mean 3, then \(P(|X-3|<2)\) =
A bag contains 3 white, 2 blue and 5 red balls. One ball is drawn at random from this bag. Then, the probability that the ball drawn is not red is
If $x$ is chosen at random from the set $\{1,2,3,4\}$ and $y$ is chosen at random from the set $\{5,6,7\}$, then the probability that $xy$ will be even is
What is the probability of getting a sum of 9 when two dice are thrown?
In a binomial distribution, if:
- Number of trials $ n $
- Mean $ = 4 $
- Variance $ = 3 $
Then find: $$ 2^{32} \cdot P\left(X = \frac{n}{2}\right) $$
If \( A \) and \( B \) are two independent events such that \( P(A) = 0.3 \), \( P(B) = x \), and \( P(A \cup B) = 0.44 \), then \( x = \):
In a toy factory, the machines A, B, and C are used to manufacture 30%, 40%, and 30% of the output respectively. The probability that a toy produced by machines A, B, and C is defective is 2%, 3%, and 1% respectively. A toy is found to be defective. The probability that it was manufactured by machine B is:
If a number is chosen at random from the set \( \{1, 2, 3, \dots, 100\} \), then the probability that it is a perfect cube is:
If $ A $ and $ B $ are two events such that $ P(B) \ne 0 $ and $ P(B) \ne 1 $, then: $$ P(\bar{A} \mid B) = ? $$
A person P speaks truth in 75% cases and another person R in 80% cases. Then the probability that they likely to contradict each other in narrating the same event is
The ratio of the largest and shortest distances from the point $(2, -7)$ to the circle $x^2 + y^2 - 14x - 10y - 151 = 0$ is
For any two nonzero real numbers $a$ and $b$, if the line $\dfrac{x}{a} + \dfrac{y}{b} = 1$ is a tangent to the circle $x^2 + y^2 = 1$, then which of the following is true?
The least distance from origin to a point on the line $y = x + 3$ which lies at a distance of 2 units from $(0,3)$ is
If the centroid of a triangle with vertices \((4, p, -3), (-1, -1, 2)\) and \((3, 5, -8)\) is given by mid point of \((1, 4, -2)\) and \((q, 2, -4)\), then \(p^2+q^2 = \)
Find the radius of the circle that has the lines: $$ 3x - 4y + 4 = 0 \quad \text{and} \quad 6x - 8y - 7 = 0 $$ as its tangents.
Suppose, in triangle $\triangle ABC$, $x - y + 5 = 0$, $x + 2y = 0$ are respectively the equations of the perpendicular bisectors of the sides $AB$ and $AC$. If $A$ is $(1, -2)$, the equation of the line joining $B$ and $C$ is
If the tangent at the point $P$ on the circle $x^2 + y^2 + 6x + 6y = 2$ meets the straight line $5x - 2y + 6 = 0$ at a point $Q$ on the y-axis, then the length of $PQ$ is
A point P on a line is at a distance of 4 units from the origin (0, 0). If the line makes 60\(^\circ\) with the negative direction of the x-axis, then P is
The eccentricity of the ellipse \( 9x^2+16y^2=144 \) is
The centroid of a triangle with vertices \( (a, 1, 3), (-2, b, -5), (4, 7, c) \) lies at the origin. Find \( a^2 + b^2 + c^2 \).