12th Standard CBSE Syllabus & Materials
12th Standard CBSE
CBSE 12th Biology Sexual Reproduction in Flowering Plants Important Questions And Answers Study Material - QB365 Set B
NEW12th Standard CBSE
CBSE 12th Biology Sexual Reproduction in Flowering Plants Important Questions And Answers Study Material - QB365 Set A
NEW12th Standard CBSE
CBSE 12th Biology Sexual Reproduction in Flowering Plants Assertion and Reason Study Material - QB365 Set D
NEW12th Standard CBSE
CBSE 12th Biology Sexual Reproduction in Flowering Plants Assertion and Reason Study Material - QB365 Set C
NEW12th Standard CBSE
CBSE 12th Biology Sexual Reproduction in Flowering Plants Assertion and Reason Study Material - QB365 Set B
NEW12th Standard CBSE
CBSE 12th Biology Sexual Reproduction in Flowering Plants Assertion and Reason Study Material - QB365 Set A
Published on: 02/11/2025
Download CBSE Class 12th Standard CBSE Maths question papers, sample papers, important questions, and previous year solved papers in PDF format. Get free study materials, NCERT solutions, and exam preparation resources for Class 12th Standard CBSE Maths
Questions + Answers key
Take MCQ Maths Test
1.
An urn contains 6 balls of which two are red and four are black. Two balls are drawn at random. Probability that they are of the different colours is
\(\frac{2}{5}\)
\(\frac{1}{15}\)
\(\frac{8}{15}\)
\(\frac{4}{15}\)
2.
If A and B are two events such that P(A) =0.2, P(B) =0.4 and P(A U B) = 0.5, then value of P(A /B) is?
0.1
0.25
0.5
0.08
3.
From the set {1, 2, 3, 4, 5}, two numbers a and b (a \(\neq\) b) are chosen at random. The probability that \(\frac{a}{b}\) is an integer, is
\(\frac{1}{3}\)
\(\frac{1}{4}\)
\(\frac{1}{2}\)
\(\frac{3}{5}\)
4.
A bag contains 3 white, 4 black and 2 red balls, If 2 balls are drawn at random (without replacement), then the probability that both the balls are white, is
\(\frac{1}{18}\)
\(\frac{1}{36}\)
\(\frac{1}{12}\)
\(\frac{1}{24}\)
5.
Three dice are thrown simultaneously. The probability of obtaining a total score of 5 is
\(\frac{5}{216}\)
\(\frac{1}{6}\)
\(\frac{1}{36}\)
\(\frac{1}{49}\)
6.
A card is picked at random from a pack of 52 playing cards, Given that the picked card is a queen, the pobability of this card to be a card of spade is
\(\frac{1}{3}\)
\(\frac{4}{13}\)
\(\frac{1}{4}\)
\(\frac{1}{2}\)
7.
A die is thrown once, Let A be the event that the number obtained is greater than 3, Let B be the event that the number obtained is less than 5, Then, P(AUB) is
\(\frac{2}{5}\)
\(\frac{3}{5}\)
0
1
8.
A problem in Mathematics is given to three students whose chances of solving it are \(\frac{1}{2}, \frac{1}{3}, \frac{1}{4},\) respectively. If the events of their solving the problem are independent,then the probability that the problem will be solved, is
\(\frac{1}{4}\)
\(\frac{1}{3}\)
\(\frac{1}{2}\)
\(\frac{3}{4}\)
9.
For any two events A and B, if \(P(\bar{A})=\frac{1}{2}, P(\bar{B})=\frac{2}{3}\) and \(P(A \cap B)=\frac{1}{4}\), then \(P\left(\frac{\bar{A}}{\bar{B}}\right)\)equals to
\(\frac{3}{8}\)
\(\frac{5}{8}\)
\(\frac{1}{8}\)
\(\frac{1}{4}\)
10.
Five fair coins are tossed simultaneously. The probability of the events that atleast one head comes up is
\(\frac{27}{32}\)
\(\frac{5}{32}\)
\(\frac{31}{32}\)
\(\frac{1}{32}\)
11.
The probability that A speaks the truth is \(\frac{4}{5}\)and that of B speaking the truth is \(\frac{3}{4}\). The probability that they contradict each other in stating the same fact is
\(\frac{7}{20}\)
\(\frac{1}{5}\)
\(\frac{3}{20}\)
\(\frac{4}{5}\)
12.
If the sum of numbers obtained on throwing a pair of dice is 9, then the probability that number obtained on one of the dice is 4, is
\(\frac{1}{9}\)
\(\frac{4}{9}\)
\(\frac{1}{18}\)
\(\frac{1}{2}\)
13.
For two events A and B, if P(A) = 0.4, P(B) = 0.8 and P(B/A) = 0.6, then P(AUB) is equal to
0.24
0.3
0.48
0.96
14.
The events E and F are independent. If P (E)=0.3 and P(EUF) = 0.5, then P(E/F) - P(F/E) equals to
\(\frac{1}{7}\)
\(\frac{2}{7}\)
\(\frac{3}{35}\)
\(\frac{1}{70}\)
15.
If \(P(A \cap B)=\frac{1}{8}\) and \(P(\bar{A})=\frac{3}{4} \text {, then } P\left(\frac{B}{A}\right)\) is equal to
\(\frac{1}{2}\)
\(\frac{1}{3}\)
\(\frac{1}{6}\)
\(\frac{2}{3}\)
16.
If A and B are events such that \(P\left(\frac{A}{B}\right)=P\left(\frac{B}{A}\right) \neq 0 \text {, }\), then
\(A \subset B, \text { but } A \neq B\)
A = B
\(A \cap B=\phi\)
P(A) = P(B)
17.
A bag A contains 3 white, 2 red balls and a bag B contains 4 white and 5 red balls. One ball is drawn at random from one of the bags and is found to be red, then the probability that it was drawn from bag B is
\(\frac{27}{43}\)
\(\frac{20}{43}\)
\(\frac{25}{43}\)
none of these
18.
If P(A) = 0.3, P(B) = 0.5 and P(A/B) = 0.4, then P(B/A) is
\(-\frac{2}{3}\)
\(\frac{2}{3}\)
\(\frac{3}{5}\)
none of these
19.
A bag contains 5 red, 6 blue and 4 black balls. Three balls are drawn from the bag. Then the probability that none of them is red, is
\(\frac{24}{91}\)
\(\frac{2}{91}\)
\(\frac{6}{35}\)
none of these
20.
Bag A contains 3 red and 5 black balls and bag B contains 2 red and 4 black balls. A ball is drawn from one of the bags. The probability that ball drawn is red is
\(\frac{17}{24}\)
\(\frac{17}{48}\)
\(\frac{3}{8}\)
\(\frac{1}{3}\)
21.
A pair of dice is thrown and it is known that the second dice always exhibits an odd number. Then the probability that the sum obtained on two dice is 7, is
\(\frac{1}{6}\)
\(\frac{5}{6}\)
\(\frac{1}{2}\)
none of these
22.
The probability of A, Band C solving a problem are \(\frac{1}{2}, \frac{1}{3} \text { and } \frac{1}{4}\) respectively. Then the probability that the problem will be solved is
\(\frac{1}{2}\)
\(\frac{3}{4}\)
\(\frac{1}{4}\)
none of these
23.
If events A and B are independent, p(A) = 0.35, p(A\(\cup\)B) = 0.60 then P(B) is
0.25
0
0.95
none of these
24.
Two events A and B are said to be independent if
\(P(A \cup B)=P(A) P(B)\)
\(P(A \cap B)=0\)
\(P(A \cap B)=P(A) P(B)\)
none of these
25.
If a die is thrown and a card is selected at random from a deck of 52 playing cards, then the probability of getting an even number on the die and a spade card is
\(\frac{1}{2}\)
\(\frac{1}{4}\)
\(\frac{1}{8}\)
\(\frac{3}{4}\)
26.
If two events are independent, then
they must be mutually exclusive
the sum of their probabilities must be equal to 1
Both (a) and (b) are correct
None ofthe above is correct
27.
A flashlight has 8 batteries out of which 3 are dead. If two batteries are selected without replacement and tested, then probability that both are dead is
\(\frac{33}{56}\)
\(\frac{9}{64}\)
\(\frac{1}{14}\)
\(\frac{3}{28}\)
28.
IfA and B are two events such that \(A \subset B\) and \(P(B) \neq 0\), then which of the following is correct?
\(P\left(\frac{B}{A}\right)=\frac{P(A)}{P(B)}\)
\(P\left(\frac{A}{B}\right)
\(P\left(\frac{A}{B}\right) \geq P(A)\)
None of these
29.
If 3 A and B are two events such that \(P(B)=\frac{3}{5}\),\(P(A / B)=\frac{1}{2} \text { and } P(A \cup B)=\frac{4}{5}\) then P(A) equals
\(\frac{3}{10}\)
\(\frac{1}{5}\)
\(\frac{1}{2}\)
\(\frac{3}{5}\)
30.
If A and B are events such that \(P\left(\frac{A}{B}\right)=P\left(\frac{B}{A}\right)\) then
\(A \subset B \text { but } A \neq B\)
A=B
\(A \cap B=\phi\)
p(A) = PCB
31.
The variance of random variable \(X \text { i.e., } \sigma_{x}^{2}\) or Var(X) is equal to
\(E\left(X^{2}\right)+\left[E\left(X^{2}\right)\right]^{2}\)
\(E(X)-\left[E\left(X^{2}\right)\right]\)
\(E\left(X^{2}\right)-[E(X)]^{2}\)
None of these
32.
The mean of the number obtained on throwing a die having written 1on three faces, 2 on two faces and 5 on one face is
1
2
5
\(\frac{8}{3}\)
33.
For the following probability distribution.
\(\begin{array}{c|c|c|c|c|c}
\hline \mathbf{X} & -4 & -3 & -2 & -1 & 0 \\
\hline \boldsymbol{P}(\boldsymbol{X}) & 0.1 & 0.2 & 0.3 & 0.2 & 0.2 \\
\hline
\end{array}\)
E(X) is equal to
0
-1
-2
-1.8
34.
Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed 6 times. Then the possible values of X are
0, 1, 3, 5
0, 1, 2, 3
0, 1, 2, 4
0, 2, 4, 6
35.
If E1,E2, ...En constitute a partition of sample space S and A is any event of non -zero probability, then P(EJ A) is equal to
\(\frac{P\left(E_{i}\right) P\left(A / E_{i}\right)}{\sum_{j=1}^{n} P\left(E_{j}\right) P\left(A / E_{j}\right)} \text { for any } i=1,2,3, \ldots, n\)
\(\frac{P\left(E_{i}\right) P\left(E_{i} / A\right)}{\sum_{j=1}^{n} P\left(E_{j}\right) P\left(A / E_{j}\right)} \text { for any } i=1,2,3, \ldots, n\)
\(\frac{P\left(E_{i}\right) P\left(E_{i} / A\right)}{P(A)} \text { for any } i=1,2,3, \ldots, n\)
None of the above
36.
Let {El, E2,..., E3} be a partition of the sample space S and A be any event associated with S then
\(P(A)=P\left(E_{1}\right) P\left(A / E_{1}\right)+P\left(E_{2}\right) P\left(A / E_{2}\right)+\ldots +P\left(E_{n}\right) P\left(A / E_{n}\right) \)
\(P(A)=\sum_{1=1}^{n} P\left(E_{j}\right) P\left(A / E_{j}\right)\)
Both (a) and (b)
None of these
37.
The events \(E_{1}, E_{2}, \ldots, E_{n}\) represent a partition of the sample space S, if
\(E_{i} \cap E_{j}=\phi, i \neq j, i, j=1,2,3, \ldots, n\)
\(E_{1} \cup E_{2} \cup \ldots \cup E_{n}=S\)
\(P\left(E_{i}\right)>0 \text { for all } i=1,2,3, \ldots, n\)
All of the above
38.
Two events A and B are said to be independent, if
A and B are mutually exclusive
\(P\left(A^{\prime} \cap B^{\prime}\right)=[1-P(A)][1-P(B)]\)
\(P(A)=P(B)\)
P(A) + P(B) = 1
39.
If three mutually independent events are A, B andC, then
\(P(A \cap B)=P(A) \cdot P(B) ; P(A \cap C)=P(A) \cdot P(C)\)
\(P(B \cap C)=P(B) \cdot P(C)\)
\(P(A \cap B \cap C)=P(A) \cdot P(B) \cdot P(C)\)
All of the above
40.
Four cards are successively drawn without replacement from a deck of 52 playing cards. The probability that all the four cards are king is.
\(\frac{1}{270721}\)
\(\frac{1}{270722}\)
\(\frac{1}{270724}\)
\(\frac{1}{270725}\)
41.
By rule of multiplication of probability \(P(E \cap F)\) is equal to
P(E)· P(F / E)
P(F)· P(E / F)
Both (a) and (b)
None of these
42.
If \(P(A)=0.4, P(B)=0.8 \text { and } P(B / A)=0.6\) then \(P(A \cup B)\) is equal to
0.24
0.3
0.48
0.96
43.
If \(P(A)=\frac{3}{10}, P(B)=\frac{2}{5} \text { and } P(A \cup B)=\frac{3}{5}\), then
\(\frac{1}{4}\)
\(\frac{1}{3}\)
\(\frac{5}{12}\)
\(\frac{7}{12}\)
44.
If \(P(\dot{A})=\frac{4}{5} \text { and } P(A \cap B)=\frac{7}{10}\) , then P(B/ A) is
\(\frac{1}{10}\)
\(\frac{1}{8}\)
\(\frac{7}{8}\)
\(\frac{17}{20}\)
45.
A and B are any two events such that P(A) + P(B) – P(A and B) = P(A), then
P(B|A) = 1
P(A|B) = 1
P(B|A) = 0
P(A|B) = 0
46.
If P(A|B) > P(A), then which of the following is correct
P(B|A) < P(B)
P(A ∩ B) < P(A) . P(B)
P(B|A) > P(B)
P(B|A) = P(B)
47.
If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1, then
A ⊂ B
B ⊂ A
B = Φ
A = Φ
48.
The probability that a student is not a swimmer is \(\frac { 1 }{ 5 } \). Then the probability that out of five students, four are swimmers is
\(_{ }^{ 5 }{ { C }_{ 4 } }{ \left( \frac { 4 }{ 5 } \right) }^{ 4 }\frac { 1 }{ 5 } \)
\({ \left( \frac { 4 }{ 5 } \right) }^{ 4 }\frac { 1 }{ 5 } \)
\(_{ }^{ 5 }{ { C }_{ 1 }\frac { 1 }{ 5 } }{ \left( \frac { 4 }{ 5 } \right) }^{ 4 }\)
None of these
49.
In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is
10–1
\({ \left( \frac { 1 }{ 2 } \right) }^{ 5 }\)
\({ \left( \frac { 9 }{ 2 } \right) }^{ 5 }\)
\(\frac { 9 }{ 10 } \)
50.
Suppose that two cards are drawn at random from a deck of cards. Let X be the number of aces obtained. Then the value of E(X) is
\(\frac{37}{221}\)
\(\frac{5}{13}\)
\(\frac{1}{13}\)
\(\frac{2}{13}\)
51.
The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is
1
2
5
\(\frac83\)
52.
If A and B are two events such that A ⊂ B and P(B) ≠ 0, then which of the following is correct?
\(P(A|B)=\frac { P(B) }{ P(A) } \)
P(A|B) < P(A)
P(A|B) ≥ P(A)
None of these
53.
Probability that A speaks truth is \(\frac45\). A coin is tossed. A reports that a head appears. The probability that actually there was head is ____.
\(\frac45\)
\(\frac12\)
\(\frac15\)
\(\frac25\)
54.
Two events A and B will be independent, if ______.
A and B are mutually exclusive
P(A'B') = [1 – P(A)] [1 – P(B)]
P(A) = P(B)
P(A) + P(B) = 1
55.
The probability of obtaining an even prime number on each die, when a pair of dice is rolled is _____.
0
\(\frac13\)
\(\frac{1}{12}\)
\(\frac{1}{36}\)
56.
If A and B are events such that P(A|B) = P(B|A), then _____.
A ⊂ B but A ≠ B
A = B
A ∩ B = Φ
P(A) = P(B)
57.
If P(A) = \(\frac12\), P(B) = 0, then P(A|B) is ______.
0
\(\frac12\)
not defined
1
58.
The probability distribution of the discrete variable X is given as:
| X | 2 | 3 | 4 | 5 |
| P(X) | \(\frac{5}{k}\) | \(\frac{7}{k}\) | \(\frac{9}{5}\) | \(\frac{11}{k}\) |
The value of k is
8
16
32
48
59.
Three balls are drawn from a bag containing 2 red and 5 black balls, if the random variable X represents the number of red balls drawn, then X can take values
0, 1, 2
0, 1, 2, 3
0
1, 2
60.
Two dice are thrown once. If it is known that the sum of the numbers on the dice was less than 6 the probability of getting a sum 3 is
\(\frac{1}{18}\)
\(\frac{5}{18}\)
\(\frac15\)
\(\frac25\)
61.
If P(A ∩ B) = 70% and P(B) = 85%, then P(A/B) is equal to
\(\frac{14}{17}\)
\(\frac{17}{20}\)
\(\frac78\)
\(\frac18\)
62.
Let A and B be two given independent events such that P(A) =p and P(B) = q and P(exactly one of A, B) = \(\frac23\), then value of 3p + 3q – 6pq is
2
-2
4
-4
63.
Let A and B be two given events such that P(A) = 0.6, P(B) = 0.2 and P(A/B) = 0.5. Then P(A’/B’) is
\(\frac { 1 }{ 10 } \)
\(\frac { 3 }{ 10 } \)
\(\frac { 3 }{ 8 } \)
\(\frac { 3 }{ 8 } \)
64.
Two coins are tossed once.
Assertion (A) If E : tail appears on one coin and F : one coin shows head, then P(E/F) is 1.
Reason (R) If E : no tail appears and F : no head appears, then P(E/F) is 0.
(a) Both A and R are correct; R is the correct explanation of A
(b) Both A and R are correct; R is not the correct explanation of A
(c) A is correct; R is incorrect
(d) R is correct; A is incorrect
65.
Assertion (A) If P(A) = \(\frac{3}{5}\)and P(B)=\(\frac{1}{5}\), then P(A\(\cap\)B), if A and B are independent events, is \(\frac{3}{25}\).
Reason (R) Two cards are drawn at random and without replacement from a pack of 52 playing cards. Then, the probability that both the cards are 25 black, is \(\frac{25}{102}\).
(a) Both A and R are correct; R is the correct explanation of A
(b) Both A and R are correct; R is not the correct explanation of A
(c) A is correct; R is incorrect
(d) R is correct; A is incorrect
66.
Assertion (A) Two coins are tossed simultaneously. The probability of getting two heads, if it is known that at least one head comes up, is \(\frac{1}{3}\).
Reason (R) Let E and F be two events with a random experiment, then \(P(F / E)=\frac{P(E \cap F)}{P(E)} \text {. }\)
(a) Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
(b) Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
(c) Assetion is correct but Reason is incorrect.
(d) Both Assertion and Reason are incorrect.
67.
Consider the following statements
Assertion: Let A and B be two independent events. Then P(A\(\cap\)B) = P(A) + P (B)
Reason: Three events A, B, and C are said to be independent, if P(A\(\cap\)B\(\cap\)C) = P(A)P(B)P(C).
(a) Assertion is correct, Reason is correct; Reason is a correct explanation for assertion.
(b) Assertion is correct, Reason is correct; Reason is not a correct explanation for Assertion
(c) Assertion is correct, Reason is incorrect
(d) Assertion is incorrect, Reason is correct.
68.
Consider the two events E and F which are associated with the sample space of a random experiment.
Assertion: P(E/F)=\(\frac{n(E\cap F)}{n(F)}\)
Reason: P(E/F) = \(\frac{P(E\cap F)}{P(F)}\)
(a) Assertion is correct, Reason is correct; Reason is a correct explanation for assertion.
(b) Assertion is correct, Reason is correct; Reason is not a correct explanation for Assertion
(c) Assertion is correct, Reason is incorrect
(d) Assertion is incorrect, Reason is correct.
69.
Assertion: For a binomial distribution B(n, p),
Mean > Variance
Reason: Probability is less than or equal to 1
(a) Assertion is correct, Reason is correct; Reason is a correct explanation for assertion.
(b) Assertion is correct, Reason is correct; Reason is not a correct explanation for Assertion
(c) Assertion is correct, Reason is incorrect
(d) Assertion is incorrect, Reason is correct.
70.
Assertion: Consider the experiment of drawing a card from a deck of 52 playing cards, in which the elementary events are assumed to be equally likely.
If E and F denote the events the card drawn is a spade and the card drawn is an ace respectively. then P(E / F) = \(\frac{1}{4}\)and P(F / E) = \(\frac{1}{13}\)
Reason: E and F are two events such that the probability of occurrence of one of them is not affected by occurrence of the other. Such events are called independent events.
(a) Assertion is correct, Reason is correct; Reason is a correct explanation for assertion.
(b) Assertion is correct, Reason is correct; Reason is not a correct explanation for Assertion
(c) Assertion is correct, Reason is incorrect
(d) Assertion is incorrect, Reason is correct.
71.
Assertion: The mean of a random variable X is also called the expectation of X, denoted by E(X).
Reason: The mean or expectation of a random variable X is not sum of the products of all possible values of X by their respective probabilities.
(a) Assertion is correct, Reason is correct; Reason is a correct explanation for assertion.
(b) Assertion is correct, Reason is correct; Reason is not a correct explanation for Assertion
(c) Assertion is correct, Reason is incorrect
(d) Assertion is incorrect, Reason is correct.
72.
Let A and B be two events associated with an experiment such that
P(A\(\cap\)B) = P(A)P(B)
Assertion: P(A | B) = P(A) and P(B | A) = P(B)
Reason: P(A \(\cup\)B) = P(A) + P(B)
(a) Assertion is correct, Reason is correct; Reason is a correct explanation for assertion.
(b) Assertion is correct, Reason is correct; Reason is not a correct explanation for Assertion
(c) Assertion is correct, Reason is incorrect
(d) Assertion is incorrect, Reason is correct.
1.
(c)
\(\frac{8}{15}\)
2.
(b)
0.25
3.
(c)
\(\frac{1}{2}\)
4.
(c)
\(\frac{1}{12}\)
5.
(c)
\(\frac{1}{36}\)
6.
(c)
\(\frac{1}{4}\)
7.
(d)
1
8.
(d)
\(\frac{3}{4}\)
9.
(b)
\(\frac{5}{8}\)
10.
(c)
\(\frac{31}{32}\)
11.
(a)
\(\frac{7}{20}\)
12.
(d)
\(\frac{1}{2}\)
13.
(d)
0.96
14.
(d)
\(\frac{1}{70}\)
15.
(a)
\(\frac{1}{2}\)
16.
(d)
P(A) = P(B)
17.
(c)
\(\frac{25}{43}\)
18.
(b)
\(\frac{2}{3}\)
19.
(a)
\(\frac{24}{91}\)
20.
(b)
\(\frac{17}{48}\)
21.
(a)
\(\frac{1}{6}\)
22.
(b)
\(\frac{3}{4}\)
23.
(d)
none of these
24.
(c)
\(P(A \cap B)=P(A) P(B)\)
25.
(c)
\(\frac{1}{8}\)
26.
(d)
None ofthe above is correct
27.
(d)
\(\frac{3}{28}\)
28.
(c)
\(P\left(\frac{A}{B}\right) \geq P(A)\)
29.
(c)
\(\frac{1}{2}\)
30.
(d)
p(A) = PCB
31.
(c)
\(E\left(X^{2}\right)-[E(X)]^{2}\)
32.
(b)
2
33.
(d)
-1.8
34.
(d)
0, 2, 4, 6
35.
(a)
\(\frac{P\left(E_{i}\right) P\left(A / E_{i}\right)}{\sum_{j=1}^{n} P\left(E_{j}\right) P\left(A / E_{j}\right)} \text { for any } i=1,2,3, \ldots, n\)
36.
(c)
Both (a) and (b)
37.
(d)
All of the above
38.
(b)
\(P\left(A^{\prime} \cap B^{\prime}\right)=[1-P(A)][1-P(B)]\)
39.
(d)
All of the above
40.
(d)
\(\frac{1}{270725}\)
41.
(c)
Both (a) and (b)
42.
(d)
0.96
43.
(d)
\(\frac{7}{12}\)
44.
(c)
\(\frac{7}{8}\)
45.
(b)
P(A|B) = 1
46.
(c)
P(B|A) > P(B)
47.
(a)
A ⊂ B
48.
(a)
\(_{ }^{ 5 }{ { C }_{ 4 } }{ \left( \frac { 4 }{ 5 } \right) }^{ 4 }\frac { 1 }{ 5 } \)
49.
(c)
\({ \left( \frac { 9 }{ 2 } \right) }^{ 5 }\)
50.
(d)
\(\frac{2}{13}\)
51.
(b)
2
52.
(c)
P(A|B) ≥ P(A)
53.
(a)
\(\frac45\)
54.
(b)
P(A'B') = [1 – P(A)] [1 – P(B)]
55.
(d)
\(\frac{1}{36}\)
56.
(d)
P(A) = P(B)
57.
(c)
not defined
58.
As ΣP(X) = 1
\(\Rightarrow \frac { 5 }{ k } +\frac { 7 }{ k } +\frac { 9 }{ k } +\frac { 11 }{ k } =1\)
\(\Rightarrow k=32\)
59.
As there are 2 red balls, so maximum ’ red balls can be 2.
60.
As favourable cases for sum less than 6 are 10 and favourable for a total of 3 is 2.
61.
As P(A/B) = \(\frac { P(A\cap B) }{ P(B) } \)
= \(\frac{70}{100}\times \frac{100}{85}=\frac{14}{17}\)
62.
As P(A) P\(\overline { B } \) + P\(\overline { A} \) P(B) = \(\frac { 2 }{ 3 } \)
⇒ p.(1-q) + (1 - q) q=\(\frac { 2 }{ 3 } \)
⇒ p - pq + q - pq = \(\frac { 2 }{ 3 } \)
⇒ 3p + 3q - 6 pq = 2
63.
As, \(P(A/B)=\frac { P(A\cap B) }{ P(B) } \)
\(\Rightarrow P(A\cap B)=0.5\times 0.2=0.1\)
\(P(A'/B')=\frac { P(A'\cap B') }{ P(B') } \)
\(=\frac { 1-P(A\cup B) }{ 1-P(B) } =\frac { 3 }{ 8 } \)
64.
(b) Both A and R are correct; R is not the correct explanation of A
65.
(b) Both A and R are correct; R is not the correct explanation of A
66.
(a) If two coins are tossed simultaneously, then sample space is given by
S = {(H, H), (H, T), (T, H), (T, T)}
Now, let A be the event of getting two heads.
\(\therefore \quad P(A)=\frac{1}{4}\)
and B be the event of getting atleast one head.
\(\therefore \quad P(B)=\frac{3}{4}\)
Thus, \(P\left(\frac{A}{B}\right)=\frac{P(A \cap B)}{P(B)}=\frac{1 / 4}{3 / 4}=\frac{1}{4} \times \frac{4}{3}=\frac{1}{3}\)
Hence, Assertion is true.
Reason is also true.
67.
(d) Assertion is incorrect, Reason is correct.
68.
(a) Assertion is correct, Reason is correct; Reason is a correct explanation for assertion.
69.
(a) Assertion is correct, Reason is correct; Reason is a correct explanation for assertion.
70.
(a) Assertion is correct, Reason is correct; Reason is a correct explanation for assertion.
71.
(c) Assertion is correct, Reason is incorrect
72.
(c) Assertion is correct, Reason is incorrect
12th Standard CBSE Syllabus & Materials
12th Standard CBSE
CBSE 12th Standard Biology Sexual Reproduction in Flowering Plants Sample Question Papers Study Material - QB365 Set 1
NEW12th Standard CBSE
CBSE 12th Chemistry d- and f- Block Elements Important Questions And Answers Study Material - QB365 Set B
NEW12th Standard CBSE
CBSE 12th Chemistry d- and f- Block Elements Important Questions And Answers Study Material - QB365 Set A
NEW12th Standard CBSE
CBSE 12th Chemistry Chemical Kinetics Important Questions And Answers Study Material - QB365 Set B
NCERT Books
Syllabus
Exam Pattern
Sample Question Papers
Previous year Question Papers
Important Notes
MCQ Practice test
NCERT Exemplers
Case study Questions
Image Based Questions
Passage based Questions
HOT Questions
Value Based Questions
Model Questions Papers
NCERT ( Book Back ) Questions
Assertion and Reason
Important Questions And Answers
CBSE 12th Standard CBSE Subjects
CBSE Standards
