List of top Mathematics Questions

If $X$ and $Y$ are two events such that $P (X | Y )=\frac{1}{2}, P(X | Y)=\frac{1}{3.} \, and \, P(X \cap Y)\frac{1}{6}$ Then, which of the following is/are correct?

Four fair dice $D_1, D_2, D_3$ and $D_4$ each having six faces numbered $1, 2, 3, 4, 5$ and $6$ are rolled simultaneously. The probability that D$_4$ shows a number appearing on one of $D_1, D_2$ and $D_3$, is

The point $P$ is the intersection of the straight line joining the points $Q(2, 3, 5)$ and $R (1, - 1, 4)$ with the plane $5x - 4y - z = 1$. If $S$ is the foot of the perpendicular drawn from the point $T (2,1, 4)$ to $QR$, then the length of the line segment $PS$ is

The equation of a plane passing through the line of intersection of the planes $x + 2y + 3z = 2$ and $x - y + z = 3$ and at a distance $\frac{2}{\sqrt 3}$ from the point $(3,1, -1)$ is

If $\overrightarrow{a} $ and $ \overrightarrow{b}$ are vectors such that $| \overrightarrow{a}+\overrightarrow{b} |=\sqrt{29}$ and $\overrightarrow{a}\times(2\widehat{i}+3\widehat{j}+4\widehat{k})=(2\widehat{i}+3\widehat{j}+4\widehat{k})\times\overrightarrow{b},$ then a possible value of $ (\overrightarrow{a}+\overrightarrow{b})(-7\widehat{i}+2\widehat{j}+3\widehat{k} is $

A ship is fitted with three engines $ E_1, E_2$ and $E_3 $ The engines function independently of each other with respective probabilities $\frac {1}{2}, \frac {1}{4}$ and $\frac{1}{4}$. For the ship to be operational at least two of its engines must function. Let $X$ denotes the event that the ship is operational and let $ X_1 , X _2 $ and $ X_ 3 $ denote, respectively the events that the engines $ E_1 , E_2$ and $E_3 $ are functioning. Which of the following is/are true?

The fixed point $P$ on the curve $ y = x^2 - 4x + 5 $ such that the tangent at $ P $ is perpendicular to the line $ x + 2y = 7 $ is given by

The value of $^{10}C_1+^{10}C_2+^{10}C_3+....+^{10}C_9 $ is

The value of $7 \log\left(\frac{16}{15} \right) +5 \log\left(\frac{25}{24}\right) + 3 \log\left(\frac{81}{80}\right) $ is equla to

Let R be the set of real numbers A = {(x, y) $\in$ R $\times$ R : y - x is an integer} is an equivalence relation on R. B = {(x, y) $\in$ R $\times$ R : x = $\alpha$y for some rational number $\alpha$} is an equivalence relation on R.

The probabilities that a student passes in Mathematics, Physics and Chemistry are m, p and c, respectively. Of these subjects, the students has a 75% chance of passing in at least one, a 50% chance of passing in at least two and a 40% chance of passing in exactly two. Which of the following relations are true

The digit in the unit's place of $7^{171} +(177)!$ is

The intercept on the line $y = x$ by the circle $x^2 + y^2 - 2x = 0$ is $AB$. Equation of the circle with $AB$ as diameter is

If the coordinates of one end of a diameter of the circle $x^2+y^2+4x-8y+5=0$, is (2,1), the coordinates of the other end is

The coordinates of the two points lying on $x + y = 4$ and at a unit distance from the straight line $4x + 3y = 10$ are

Evaluate $\int \frac{x^{2}+4}{x^{4}+16}dx.$

Evaluate $\int\limits^{3\pi/4}_{\pi/4} \frac{1}{1+cos\,x}dx$

A dice is rolled twice and the sum of the numbers appearing on them is observed to be $7$. What is the conditional probability that the number $2$ has appeared at least once ?

If $X$ is a poisson variate such that $P(X = 1) = P(X = 2)$, then $P(X=4)$ is equal to

In an equilateral triangle, the inradius, circumradius and one of the exradii are in the ratio

In how many ways 6 letters be posted in 5 different letter boxes?

If $D$ is the set of all real $x$ such that $1-e^{\left(1/ x\right)-1}$ is positive, then $D$ is equal to

The number of ways of painting the faces of a cube of six different colours is

The sum of the coefficients of $(6\,a-5\,b)^n$, where $n$ is a positive integer, is

The function $\sin \, x + \cos \, x$ is maximum when $x$ is equal to