NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.5 (Limits and Derivatives)
NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.5 contains all the questions with detailed solutions. Students are advised to solve these questions for better understanding of the concepts in exercise 13.5.
Krati Saraswat21 Feb, 2024
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NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.5 (Limits and Derivatives)
NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.5 Limits and Derivatives is prepared by academic team of Physics Wallah. We have prepared NCERT Solutions for all exercise of chapter 13. Below is step by step solutions to all questions given in the NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.5 of Limits and Derivatives.NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.1
NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.5 (Limits and Derivatives) Overview
NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.5 cover several important topics. It is highly recommended for students to review each topic thoroughly in order to gain a comprehensive understanding of the concepts taught in the chapter and make optimal use of the provided solutions. These solutions are the result of dedicated efforts by the Physics Wallah teachers aimed at assisting students in grasping the concepts covered in this chapter. By going through and practicing these solutions, the objective is for students to achieve excellent results in their exams effortlessly.NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.5
Solve The Following Questions of NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.5
Question 1. A die is thrown 6 times. If ‘getting an odd number’ is a success, what is the probability of: (i) 5 successes? (ii) at least 5 successes? (iii) at most 5 successes? Solution : The repeated tosses of a die are Bernoulli trials. Let X denote the number of successes of getting odd numbers in an experiment of 6 trials. Probability of getting an odd number in a single throw of a die is, p - 3/6 = 1/2 q = 1 - p = 1/2 X has a binomial distribution.
NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.2
Question 2. A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of two successes. Solution : The repeated tosses of a pair of dice are Bernoulli trials. Let X denote the number of times of getting doublets in an experiment of throwing two dice simultaneously four times. Probability of getting doublets in a single throw of the pair of dice is
NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.3
Question 3. There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item? Solution : Let X denote the number of defective items in a sample of 10 items drawn successively. Since the drawing is done with replacement, the trials are Bernoulli trials.
NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.4
Question 4. Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that: (i) all the five cards are spade? (ii) only 3 cards are spades? (iii) none is spade? Solution : Let X represent the number of spade cards among the five cards drawn. Since the drawing of card is with replacement, the trials are Bernoulli trials. In a well shuffled deck of 52 cards, there are 13 spade cards.
NCERT Solutions for Class 12 Maths Chapter 13 Miscellaneous Exercise
Question 5. The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs. Solution : Let X represent the number of bulbs that will fuse after 150 days of use in an experiment of 5 trials. The trials are Bernoulli trials. It is given that, p = 0.05
Question
6. A bag consists of 10 balls each marked with one of the digits 0 to 9. If four balls are drawn successively with replacement from the bag, what is the probability that none is marked with the digit 0?
Solution :
Let X denote the number of balls marked with the digit 0 among the 4 balls drawn.
Since the balls are drawn with replacement, the trials are Bernoulli trials.
X has a binomial distribution with
n
= 4 and p = 1/10
Question
7. In an examination, 20 questions of true-false are asked. Suppose a student tosses a fair coin to determine his answer to each question. If the coin falls heads, he answers ‘true’, if it falls tails, he answers ‘false’. Find the probability that he answers at least 12 questions correctly.
Solution :
Let X represent the number of correctly answered questions out of 20 questions.
The repeated tosses of a coin are Bernoulli trails. Since “head” on a coin represents the true answer and “tail” represents the false answer, the correctly answered questions are Bernoulli trials.
Question
8. Suppose X has a binomial distribution B(6,1/2) Show that X = 3 is the most likely outcome.
(Hint: P(X = 3) is the maximum among all P ( x i ), x i = 0, 1, 2, 3, 4, 5, 6)
Solution : X is the random variable whose binomial distribution is B(6,1/2). Therefore, n = 6 and p = 1/2
Therefore, P (X = 3) is maximum.
Question
9. On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?
Solution :
The repeated guessing of correct answers from multiple choice questions are Bernoulli trials. Let X represent the number of correct answers by guessing in the set of 5 multiple choice questions.
Probability of getting a correct answer is,
p
= 1/3
Question
10. A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is 1/100 What is the probability that he will win a prize:
(a) at least once
(b) exactly once
(c) at least twice?
Solution :
Let X represent the number of winning prizes in 50 lotteries. The trials are Bernoulli trials.
Clearly, X has a binomial distribution with
n
= 50 and p = 1/100
Question
11. Find the probability of getting 5 exactly twice in 7 throws of a die.
Solution :
The repeated tossing of a die are Bernoulli trials. Let X represent the number of times of getting 5 in 7 throws of the die.
Probability of getting 5 in a single throw of the die,
p
= 1/6
Question
12. Find the probability of throwing at most 2 sixes in 6 throws of a single die.
Solution :
The repeated tossing of the die are Bernoulli trials. Let X represent the number of times of getting sixes in 6 throws of the die.
Probability of getting six in a single throw of die,
p
= 1/6
Let A represents the favourable event i.e., 6
Question
13. It is known that 10% of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles 9 are defective?
Solution :
The repeated selections of articles in a random sample space are Bernoulli trails. Let X denote the number of times of selecting defective articles in a random sample space of 12 articles.
Clearly, X has a binomial distribution with
n
= 12 and
p
= 10% = 10/100 = 1/10
In each of the following, choose the correct answer:
Question 14. Binomial distribution is given this name because: (A) This distribution was evolved by James binomial. (B) Each trial has only two outcomes. Namely success and failure. (C) Its probability function is obtained by general of binomial expansion. (D) It is obtained by combining two distributions. Solution: option (C) is correct. Question 15. In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is:
(D) None of these
Solution :
The repeated selection of students who are swimmers are Bernoulli trials. Let X denote the number of students, out of 5 students, who are swimmers.
Probability of students who are not swimmers,
q
= 1/5
Therefore, option (A) is correct.
NCERT Solutions For Class 12 Maths Chapter 13 Exercise 13.5 FAQs
How can NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.5 help in exam preparation?
These solutions provide detailed explanations and step-by-step solutions to all the exercises in Exercise 13.5. By referring to these solutions, students can understand the concepts thoroughly and prepare effectively for exams.
What is the significance of studying Limits and Derivatives in Class 12 Maths?
Understanding Limits and Derivatives is fundamental in calculus and lays the groundwork for various mathematical concepts and applications. It helps in analyzing functions, determining rates of change, and solving optimization problems.
Where can I find NCERT Solutions for Class 12 Maths Chapter "Limits and Derivatives"?
NCERT Solutions for Class 12 Maths Chapter "Limits and Derivatives" are available on Physics Wallah.
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