12th Mathematics - Book Back Answers - Chapter 11 - English Medium Guides

  

 

Plus Two / 12th Mathematics - Book Back Answers - Chapter 11 - English Medium

Tamil Nadu Board 12th Standard Mathematics - Chapter 11: Book Back Answers and Solutions

    This post covers the book back answers and solutions for Chapter 11 from the Tamil Nadu State Board 12th Standard Mathematics textbook. These detailed answers have been carefully prepared by our expert teachers at KalviTips.com.

    We have explained each answer in a simple, easy-to-understand format, highlighting important points step by step under the relevant subtopics. Students are advised to read and memorize these subtopics thoroughly. Once you understand the main concepts, you’ll be able to connect other related points with real-life examples and confidently present them in your tests and exams.

    By going through this material, you’ll gain a strong understanding of Chapter 11 along with the corresponding book back questions and answers (PDF format).

Question Types Covered:

• 1 Mark Questions: Choose the correct answer, Fill in the blanks, Identify the correct statement, Match the following 
• 2 Mark Questions: Answer briefly 
• 3, 4, and 5 Mark Questions: Answer in detail

All answers are presented in a clear and student-friendly manner, focusing on key points to help you score full marks.

All the best, Class 12 students! Prepare well and aim for top scores. Thank you!

 

I. Multiple Choice Questions

1. Let X be random variable with probability density function
f(x)={$\left\{\begin{array}{ll}\frac{\mathbf{2}}{{\mathit{x}}^{\mathbf{3}}}& \mathit{x}\mathbf{\ge }\mathbf{1}\\ \mathbf{0}& \mathit{x}\mathbf{<}\mathbf{1}\end{array}\right.$
Which of the following statement is correct?
(1) both mean and variance exist 
(2) mean exists but variance does not exist
(3) both mean and variance do not exist 
(4) variance exists but Mean does not exist.
Answer Key:
(2) mean exists but variance does not exist

 
2. A rod of length 2l is broken into two pieces at random. The probability density function of
the shorter of the two pieces is
f(x)=$\left\{\begin{array}{l}\frac{\mathbf{\{}}{}\end{array}\right.$$\left\{\begin{array}{ll}\frac{\mathbf{1}}{\mathit{l}}& \mathbf{0}\mathbf{<}\mathit{x}\mathbf{<}\mathit{l}\\ \mathbf{0}& \mathit{l}\mathbf{\le }\mathit{x}\mathbf{<}\mathbf{2}\mathit{l}\end{array}\right.$
The mean and variance of the shorter of the two pieces are respectively
(1) $\frac{\mathit{l}}{\mathbf{2}}\mathbf{,}\mathbf{ }\frac{{\mathit{l}}^{\mathbf{2}}}{\mathbf{3}}$
(2) $\frac{\mathit{l}}{\mathbf{2}}\mathbf{,}\mathbf{ }\frac{{\mathit{l}}^{\mathbf{2}}}{\mathbf{6}}$
(3) $\mathit{l}\mathbf{,}\mathbf{ }\frac{{\mathit{l}}^{\mathbf{2}}}{\mathbf{12}}$
(4) $\frac{\mathit{l}}{\mathbf{2}}\mathbf{,}\mathbf{ }\frac{{\mathit{l}}^{\mathbf{2}}}{\mathbf{12}}$
Answer Key:
(4) $\frac{\mathit{l}}{\mathbf{2}}\mathbf{,}\mathbf{ }\frac{{\mathit{l}}^{\mathbf{2}}}{\mathbf{12}}$

$\frac{\mathbf{ }}{}$
3. Consider a game where the player tosses a six-sided fair die. If the face that comes up is 6, the
player wins ₹36, otherwise he loses ₹ k² , where k is the face that comes up k = {1, 2, 3, 4, 5}.
The expected amount to win at this game in ₹ is
(1) $\frac{\mathbf{19}}{\mathbf{6}}$
(2) -$\frac{\mathbf{19}}{\mathbf{6}}$

(3) $\frac{\mathbf{3}}{\mathbf{2}}$
(4) -$\frac{\mathbf{3}}{\mathbf{2}}$
Answer Key:
(2) -$\frac{\mathbf{19}}{\mathbf{6}}$

$\frac{\mathbf{ }}{}$
4. A pair of dice numbered 1, 2, 3, 4, 5, 6 of a six-sided die and 1, 2, 3, 4 of a four-sided die is rolled and the sum is determined. Let the random variable X denote this sum. Then the number of elements in the inverse image of 7 is
(1) 1 
(2) 2 
(3) 3 
(4) 4
Answer Key:
(4) 4

 
5. A random variable X has binomial distribution with n = 25 and p = 0.8 then standard deviation of X is
(1) 6 
(2) 4 
(3) 3 
(4) 2
Answer Key:
(4) 2

 
6. Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed n times. Then the possible values of X are
(1) i+2n, i = 0,1,2...n 
(2) 2i–n, i = 0,1,2...n 
(3) n–i, i = 0,1,2...n 
(4) 2i+2n, i = 0,1,2...n
Answer Key:
(2) 2i–n, i = 0,1,2...n

 
7. If the function f (x) = $\frac{\mathbf{1}}{\mathbf{12}}$ for a < x < b , represents a probability density function of a
continuous random variable X, then which of the following cannot be the value of a and b?
(1) 0 and 12 
(2) 5 and 17 
(3) 7 and 19 
(4) 16 and 24
Answer Key:
(4) 16 and 24

 
8. Four buses carrying 160 students from the same school arrive at a football stadium. The buses
carry, respectively, 42, 36, 34, and 48 students. One of the students is randomly selected. Let
X denote the number of students that were on the bus carrying the randomly selected student.
One of the 4 bus drivers is also randomly selected. Let Y denote the number of students on
that bus.
Then E(X) and E(Y) respectively are
(1) 50, 40 
(2) 40,50 
(3) 40.75, 40 
(4) 41, 41
Answer Key:
(3) 40.75, 40 

 
9. Two coins are to be flipped. The first coin will land on heads with probability 0.6, the second
with Probability 0.5. Assume that the results of the flips are independent, and let X equal the
total number of heads that result. The value of E(X) is
(1) 0.11 
(2) 1.1 
(3)11 
(4)1
Answer Key:
(2) 1.1 

 
10. On a multiple-choice exam with 3 possible destructives for each of the 5 questions, the
probability that a student will get 4 or more correct answers just by guessing is
(1) $\frac{\mathbf{11}}{\mathbf{243}}$
(2) $\frac{\mathbf{3}}{\mathbf{8}}$
(3) $\frac{\mathbf{1}}{\mathbf{243}}$
(4) $\frac{\mathbf{5}}{\mathbf{243}}$
Answer Key:
(1) $\frac{\mathbf{11}}{\mathbf{243}}$

$\frac{\mathbf{ }}{}$
11. If P(X = 0) = 1 − P(X = 1). If E(X) = 3Var(X), then P(X = 0) is
(1) $\frac{\mathbf{2}}{\mathbf{3}}$
(2) 
(3) $\frac{\mathbf{1}}{\mathbf{5}}$
(4) $\frac{\mathbf{1}}{\mathbf{3}}$
Answer Key:
(4) $\frac{\mathbf{1}}{\mathbf{3}}$

$\frac{\mathbf{ }}{}$
12. If X is a binomial random variable with expected value 6 and variance 2.4, then P(X = 5) is
(1)⁶⁴

(2)$$¹⁰

(3)⁴⁶

(4)⁵⁵
Answer Key:
(4)⁵⁵

 
13. The random variable X has the probability density function
$\left\{\begin{array}{l}\mathit{\{}\end{array}\right.$$\left\{\begin{array}{ll}\mathit{a}\mathit{x}\mathbf{+}\mathit{b}& \mathbf{0}\mathbf{<}\mathit{x}\mathbf{<}\mathbf{1}\\ \mathbf{0}& \mathit{o}\mathit{t}\mathit{h}\mathit{e}\mathit{r}\mathit{w}\mathit{i}\mathit{s}\mathit{e}\end{array}\right.$
and E(X ) = $\frac{\mathbf{7}}{\mathbf{12}}$, then a and b are respectively
(1) 1 and $\frac{\mathbf{1}}{\mathbf{2}}$
(2) $\frac{\mathbf{1}}{\mathbf{2 }}$and 1
(3 2 and 1
(4) 1 and 2
Answer Key:
(1) 1 and $\frac{\mathbf{1}}{\mathbf{2}}$

$\frac{\mathbf{ }}{}$
14. Suppose that X takes on one of the values 0, 1, and 2. If for some constant k,
P(X = i) = k P(X = i −1) for i = 1, 2 and P(X = 0) =$\frac{\mathbf{1}}{\mathbf{7}}$, then the value of k is
(1) 1 
(2) 2 
(3) 3 
(4) 4
Answer Key:
(2) 2

 
15. Which of the following is a discrete random variable?
I. The number of cars crossing a particular signal in a day.
II. The number of customers in a queue to buy train tickets at a moment.
III. The time taken to complete a telephone call.
(1) I and II 
(2) II only 
(3) III only 
(4) II and III
Answer Key:
(1) I and II

 
16. If f(x)=$\left\{\begin{array}{l}\mathbf{\{}\end{array}\right.$$\left\{\begin{array}{ll}\mathbf{2}\mathit{x}& \mathbf{0}\mathbf{\le }\mathit{x}\mathbf{\le }\mathit{a}\\ \mathbf{0}& \mathit{o}\mathit{t}\mathit{h}\mathit{e}\mathit{r}\mathit{w}\mathit{i}\mathit{s}\mathit{e}\end{array}\right.$ is a probability density function of a random variable, then the value of a is
(1) 1 
(2) 2 
(3) 3 
(4) 4
Answer Key:
(1) 1 

 
17. The probability mass function of a random variable is defined as:

x	-2	-1	0	1	2
F(x)	k	2k	3k	4k	5k

Then E(X ) is equal to:
(1) $\frac{\mathbf{1}}{\mathbf{15}}$
(2) $\frac{\mathbf{1}}{\mathbf{10}}$
(3) $\frac{\mathbf{1}}{\mathbf{3}}$
(4) $\frac{\mathbf{2}}{\mathbf{3}}$
Answer Key:
(4) $\frac{\mathbf{2}}{\mathbf{3}}$

$\frac{\mathbf{ }}{}$
18. Let X have a Bernoulli distribution with mean 0.4, then the variance of (2X–3) is
(1) 0.24 
(2) 0.48 
(3) 0.6 
(4) 0.96
Answer Key:
(4) 0.96

 
19. If in 6 trials, X is a binomial variable which follows the relation 9P(X=4) = P(X=2), then the
probability of success is
(1)0.125 
(2) 0.25 
(3) 0.375 
(4) 0.75
Answer Key:
(2) 0.25

 
20. A computer salesperson knows from his past experience that he sells computers to one in
every twenty customers who enter the showroom. What is the probability that he will sell a
computer to exactly two of the next three customers?
(1) $\frac{\mathbf{57}}{{\mathbf{20}}^{\mathbf{3}}}$
(2) $\frac{\mathbf{57}}{{\mathbf{20}}^{\mathbf{2}}}$
(3) $\frac{{\mathbf{19}}^{\mathbf{3}}}{{\mathbf{20}}^{\mathbf{3}}}$
(4) $\frac{\mathbf{57}}{\mathbf{20}}$
Answer Key:
(2) $\frac{\mathbf{57}}{{\mathbf{20}}^{\mathbf{2}}}$

 

II.Short Answer Questions.

12th Mathematics

III. Long Answer Questions.

12th Mathematics

IV. Exercise.

12th Mathematics