The probability distribution of a ramdom variable X is: P(X=x)=caseskx^2,& x=1,2,3\\2kx,&x=4,5,6\\0,&otherwisecases Where K is a constant Match List-I with List-II, List-I, List-II, (A) k, (I) 7/22, (B) P(X ≥ 4), (II) 1/44, (C) P(X < 4), (III) 95/22, (D) E[X], (IV) 15/22, Choose the correct answer from the options given below: Option 1: (A) - (I), (B) - (II), (C) - (IV), (D) - (III) Option 2: (A) - (IV), (B) - (I), (C) - (II), (D) - (III) Option 3: (A) - (II), (B) - (IV), (C) - (I), (D) - (III) Option 4: (A) - (III), (B) - (IV), (C) - (I), (D) - (II)

Answer: (A) - (II), (B) - (IV), (C) - (I), (D) - (III). Solution: Solution Coming Soon

Algebra

Probability

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The probability distribution of a ramdom variable $X$ is:

$P(X=x)=\begin{cases}kx^2,& x=1,2,3\\2kx,&x=4,5,6\\0,&\text{otherwise}\end{cases}$ Where $K$ is a constant

Match List-I with List-II

List-I List-II
(A) $k$ (I) 7/22
(B) $P(X \geq 4)$ (II) 1/44
(C) $P(X < 4)$ (III) 95/22
(D) $E[X]$ (IV) 15/22

Choose the correct answer from the options given below:

List-I	List-II
(A) $k$	(I) 7/22
(B) $P(X \geq 4)$	(II) 1/44
(C) $P(X < 4)$	(III) 95/22
(D) $E[X]$	(IV) 15/22

(A) - (I), (B) - (II), (C) - (IV), (D) - (III)

(A) - (IV), (B) - (I), (C) - (II), (D) - (III)

(A) - (II), (B) - (IV), (C) - (I), (D) - (III)

(A) - (III), (B) - (IV), (C) - (I), (D) - (II)

✅ Correct Option: 3

Solution Coming Soon

2023: 30 May Shift 3

The mean number of heads in two tosses of a coin is :

2026: 12 May Shift 2

A bag contains 4 balls. Let E be an event in which two balls are drawn at random and found to be white, then

Match List-I with List-II

List-I	List-II
(A) Probability that all balls are white	(I) $\dfrac{1}{6}$
(B) Probability of drawing 2 white ball at random given that there are 3 white ball	(II) $\dfrac{3}{5}$
(C) P(E)	(III) $\dfrac{1}{2}$
(D) Probability of drawing 2 white ball at random given that there is only 2 white ball	(IV) $\dfrac{5}{9}$

Choose the correct answer from the options given below:

2025: 22 May Shift 1

Probability that a man speaks truth is $\frac{3}{4}$ . He throws a die and reports that it is a six. The probability that it is actually a six is

2025: 27 May Shift 1

It is given that 3% of items manufactured by an industry are defective. The probability that a packet of 250 items contains one defective item is: [Given: $e^{-7.5} \approx 0.000553$ ]

2025: 14 May Shift 1

Match List-I with List-II

Let A & B are two events such that P(A)=0.8, P(B)=0.5, P(B|A)=0.4

List-I	List-II
(A) $P(A \cap B)$	(I) 0.2
(B) $P(A \mid B)$	(II) 0.32
(C) $P(A \cup B)$	(III) 0.64
(D) $P(A')$	(IV) 0.98

Choose the correct answer from the options given below:

2025: 3 June Shift 1

60% members of a committee favour a certain proposal and 40% members oppose the proposal. A member is selected and let the random variable X = 0 if he opposes and X = 1 if he is in favour. Then the variance of the random variable X is

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