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**NIOS CLASS 12TH Mathematics (311) SOLVED TMA In English Medium PDF SESSION 2023 - 24**

**Which is Applicable for March/April & October/November 2024 Examination.**

This platform provides Nios **Mathematics (311)** TMA Solved with project work for class 12th. Here you can Get Nios Solved Tutor Mark Assignment (TMA) in Good Quality which helps to achieve More and More Marks. Nios Assignment’s Answer Prepared by well Skilled and Experienced Teachers.

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**Salient Features:**

➛ This Nios Tutor Marked Assignment (TMA) is Only valid for 2023-24 Academic Session.

➛ Best Answer in PDF Format of NIOS TMA.

➛ Assignments are prepared by well experienced and Nios Experts.

➛ Answers are available in English Medium.

➛ We guide you to prepare good assignment file.

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**Note -**

➛ Total six questions are given by Nios in TMA. All questions have 2 options out of which one has to be selected. In this PDF, we have given you the answer of one option which is better so that your marks will be good.

➛ You have to write the question and answer on the A4 size sheet as given in this PDF.

➛ After writing, the page has to be scanned and made a PDF and upload on the portal of NIOS.

**TMA Questions**

**1. Answer any one out of the following questions.**

(i) Write the following sets in roster form

a) A = {x : x is an integer and –3 ≤ x < 7}

b) B = {x : x is a natural number less than 6}

**OR**

a) From the given figure, find tan P – cot R.

b) Prove that (sin4θ – cos4θ +1) cosec2θ = 2

**2. Answer any one out of the following questions.**

(a) Find the 28th term from the end of the AP 6, 9, 12, 15, 18, ..…, 102.

(b) How many 3-digits numbers are divisible by 7?

**OR**

a) The sum of some terms of a GP is 315. Its first term is 5 and the common ratio is 2.

Find the number of its terms and the last term.

b) Find the common ratio of a GP whose sum of infinite terms is 8 and its second term is

2.

**3. Answer any one out of the following questions.**

a) If z1 = 2 + 8i and z2 = 1 – i, then find |z1/z2|.

b) Suppose z = (2 – i)2

+ [(7 – 4i)/(2 + i)] – 8, express z in the form of x + iy such that x and y are real numbers.

**OR**

a) Solve the inequality x2

+ x - 28 < 2.

b) −1<4x+2<10

**4. Answer any one out of the following questions.**

a) In how many of the distinct permutations of the letters in MISSISSIPPI do the four

I’s not come together?

b) How many 5-digit telephone numbers can be constructed using the digits 0 to 9, if

each number starts with 67 and no digit appears more than once?

**OR**

a) A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of these committees would consist of 1

man and 2 women?

b) Determine the number of 5 card combinations out of a deck of 52 cards, if there is

exactly one ace in each combination.

**5. Answer any one out of the following questions.**

Prove the following by using the principle of mathematical induction for all n ∈ N:

a) 1.2 + 2.22 + 3.22 + … + n.2n = (n – 1) 2n+1 + 2

b) n (n + 1) (n + 5) is a multiple of 3

**OR**

a) Expand (x/3 + 2/y)4

b) Find the remainder when 7103 is divided by 25

c) Find the last two digits of the number (13)10

**6. Answer any one out of the following questions.**

(i) If a tyre is bought from this company, what is the probability that :

(i) it has to be substituted before 4000 km is covered?

(ii) it will last more than 9000 km?

(iii) it will need to be replaced after it has covered somewhere between 4000 km

and 14000 km?

b) Two players, Sangeet and Rashmi, play a tennis match. The probability of Sangeet

winning the match is 0.62. What is the probability that Rashmi will win the match?

c) A coin is tossed three times, consider the following events.

P: ‘No head appears’,

Q: ‘Exactly one head appears’ and

R: ‘At Least two heads appear’.

Check whether they form a set of mutually exclusive and exhaustive events.

**OR**

a) Find the range and coefficient of range of the following data.

(i) 63, 89, 98, 125, 79, 108, 117, 68

(ii) 43.5, 13.6, 18.9, 38.4, 61.4, 29.8

b) If the range and the smallest value of a set of data are 36.8 and 13.4 respectively, then find the largest value.

c) A teacher asked the students to complete 60 pages of a record note book. Eight

students have completed only 32, 35, 37, 30, 33, 36, 35 and 37 pages. Find the

standard deviation of the pages yet to be completed by them.

**NOTE- You will get the answers of all these questions after purchasing the PDF.**

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**Most Important Facts relating to TMA:**

➛ This assignment solution is based on the latest session 2023-24.

➛ The Last date of submission of this assignment is 31 January 2024 (For April examination).

➛ The Last date of submission of this assignment is 31 August 2024 (For Oct. examination).

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