List of top Mathematics Questions on Probability asked in MHT CET

Four persons can hit a target correctly with probabilities $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}$ and $\frac{1}{5}$ respectively. If all hit at the target independently, then the probability that the target would be hit, is:

What is the probability of an impossible event?

\( \int \sqrt{x^2 + 3x} dx = \)}

\( \int \frac{x}{1+x^4} dx = \)}

A random variable X has following p.d.f. \( f(x) = kx(1 - x), 0 \le x \le 1 \) and \( P(x>a) = \frac{20}{27} \), then \( a = \)}

Consider the statements given by following
(A) If 4+3 = 8, then 5+3=9
(B) If 6 + 4 = 10, then moon is flat
(C) If both (A) and (B) are true, then 5 + 6 = 17
Then which of the following statement is correct?

The solution of $\frac{dy}{dx} = (x + y)^2$ is

The differential equation of all straight lines passing through the point \( (1, -1) \) is

Three numbers are chosen at random from numbers 1 to 20. The probability that they are consecutive is

If $A = \begin{bmatrix} 1 & \tan x \\ -\tan x & 1 \end{bmatrix}$, then $A^T A^{-1} =$}

If two numbers $p$ and $q$ are chosen randomly from the set $\{1, 2, 3, 4\}$, one by one, with replacement, then the probability of getting $p^2 \ge 4q$ is

A random variable $X$ has the following probability distribution

then the value of $P(1 \le X < 4 \mid X \le 2) =$

Two cards are drawn simultaneously from a well shuffled pack of 52 cards. If X is the random variable of getting queens, then the value of $2 E(X) + 3 E(X^2)$ for the number of queens is

If $m_1$ and $m_2$ are the slopes of the lines represented by $ax^2 + 2hxy + by^2 = 0$ satisfying the condition $16\text{h}^2 = 25\text{ab}$, then

For $\text{n} \in \mathbb{N}$ if $y = \text{a}x^{\text{n}+1} + \text{b}x^{-\text{n}}$, then $x^2 \frac{\text{d}^2 y}{\text{d}x^2} =$

If $4 \sin^{-1} x + \cos^{-1} x = \pi$ then $x =$

For \(N \in \mathbb{N}, \frac{d^n}{dx^n} (\log x) =\)

A coin is tossed until one head appears or a tail appears \(4\) times in succession. The probability distribution of the number of tosses is

Three numbers are chosen at random from numbers 1 to 20. The probability that they are consecutive is

The solution of $\frac{dy}{dx} = (x + y)^2$ is

The differential equation of all straight lines passing through the point \( (1, -1) \) is

If $f(x) = \begin{cases} \frac{1-\cos 4x}{x^2} & , \text{if } x<0 \\ a & , \text{if } x = 0 \\ \frac{(16+\sqrt{x})^{\frac{1}{2}}-4}{\sqrt{x}} & , \text{if } x>0 \end{cases}$ is continuous at $x = 0$, then a =}

If p : switch $S_1$ is closed, q : switch $S_2$ is closed, r : switch $S_3$ closed, then the symbolic form of the following switching circuit is equivalent to

The equations of the tangents to the circle $x^2 + y^2 = 36$ which are perpendicular to the line $5x + y = 2$, are

If matrix $A = \frac{1}{11} \begin{bmatrix} -1 & 7 & -24 \\ 2 & a & 4 \\ 2 & -3 & 15 \end{bmatrix}$ and $A^{-1} = \begin{bmatrix} 3 & 3 & 4 \\ 2 & -3 & 4 \\ b & -1 & c \end{bmatrix}$, then the values of $a, b, c$ respectively are ..............