List of top Mathematics Questions

If four dice are thrown simultaneously, then the probability that none of the dice shows the number 1 on its face, is:
The range of a random variable \( X \) is \( \{0, 1, 2\} \). If \( P(X=0) = 3C^3 \), \( P(X=1) = 4C-10C^2 \), and \( P(X=2) = 5C-1 \), then the value of \( C \) is:
A bag contains 12 two rupee coins, 7 one rupee coins and 4 fifty paise coins. If three coins are selected at random, then the probability that the sum of the values of the three coins is not an integral multiple of a rupee is
If A and B simultaneously toss one coin each every time, each 50 times, then the probability of not getting a tail on both the coins is:
A bag contains 10 similar balls, of which 4 are blue and 6 are red. Three balls are taken at random from the bag one after the other without replacement. The probability that all the three balls drawn are red is:
One out of 9 ships is likely to sink when they are set on sail. When 6 ships are set on sail, the probability that exactly 3 of them will not arrive safely is:
If $ X $ is a random variable with the probability distribution \[ P(X = k) = \frac{(k+1)c}{2^k}, \quad k = 0, 1, 2, ..., \] then $ P(X \geq 3) $ is:
Probability that missing card is not a spade, given two drawn cards are spades?
From a collection of eight cards numbered 1 to 8, if two cards are drawn at random, one after the other with replacement, then the probability that the product of numbers that appear on the cards is a perfect square is:
If $X_1, X_2, ..., X_n$ are $n$ independent events such that $P(X_r) = \frac{1}{r+1}$, for $r=1, 2, ..., n$, then the probability that none of the $n$ events occur is
If the mean and varian of a binomial variable $X$ are 2 and 1 respectively, then $P(X>1) = $
It is observed that there will be 25 blood specimens of normal persons, if 100 blood samples are tested. If 10 specimens are sent to a laboratory for testing, then the probability of having at least two specimens of normal persons is:
If a cubical die is thrown, then the mean and variance of the random variable \( X \), giving the number on the face that shows up, are respectively:
Let \(A\) and \(B\) be two independent events of a random experiment. If the probability that both \(A\) and \(B\) occur is \(\frac{1}{6}\) and the probability that neither of them occurs is \(\frac{1}{3}\), then the probability of occurrence of \(A\) is:
The probability that a non-leap year contains 53 Sundays is
In a committee of 25 members, each member is proficient either in Mathematics or in Statistics or in both. If 19 of them are proficient in Mathematics and 16 of them are proficient in Statistics, then the probability that a person selected at random from the committee is proficient in both is
The minimum value of the function $f(x)=\int\limits_0^2 e^{|x-t|} d t$ is :
The equation of the pair of tangents drawn from the point \( (1, 1) \) to the circle \( x^2 + y^2 + 2x + 2y + 1 = 0 \) is:
The point $ P(2, 1) $ is translated to a point $ Q $ parallel to the line $ L: x - y - 4 = 0 $ by $ 2\sqrt{5} $ units. If the point $ Q $ lies in the third quadrant, then the equation of the line passing through $ Q $ and perpendicular to $ L $ is:
A ray of light incident along a line meets another line $7x - y + 1 = 0$ at the point $(0,1)$ and is then reflected along the line $y + 2x = 1$. Then the equation of the line of inciden is
If $(2,3)$ is the vertex and $(3,2)$ is the focus of a parabola, then its equation is
Let the points $P_1(\frac{\pi}{4}), P_2(\frac{3\pi}{4}), P_3(\frac{5\pi}{4}), P_4(\frac{7\pi}{4})$ lie on the hyperbola $\frac{x^2}{9} - \frac{y^2}{16} = 1$. Then they form:
The polar of a point with respect to the circle \( x^2 + y^2 - 10x + 12y - 3 = 0 \), which is not a tangent and not a chord of contact, is:
If \( t \in \mathbb{R} \setminus \{-1\} \), then the locus of the point \[ \left( \frac{3at}{1 + t^3}, \frac{3at^2}{1 + t^3} \right) \] is:
If A(2,3) and B(2,-3) are two points, then the equation of the locus of a point $P$ such that $PA + PB = 8$ is