NIOS CLASS 12TH Mathematics (311) SOLVED TMA In English Medium PDF SESSION 2024 - 25

Which is Applicable for March/April & October/November 2025 Examination.

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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.

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TMA Questions

1. Answer any one out of the following questions.

(i) In a joint family of 30 members, 10 members like only red colour. 15 members like only blue
colour. 2 members like both the colours. If
R = set of family members who like Red colour,
B = set of family members who like Blue colour.
(i) How can the set of family members who like Red colour only be represented in terms of sets R and B?
(ii) How can the set of family members who like Blue colour only be represented in terms of sets R and B?
(iii) Find the number of members who neither like red colour nor blue colour.
(iv) Draw a Venn diagram for the situation.

b) Whether the following function is even or odd? Also find the domain of the function.

2. Answer any one out of the following questions.

(a) Find the roots of the quadratic equation x2 + 2x + 4 = 0. Also represent the roots of the quadratic equation on an argand plane
(b) Verify the following statement, using the principle of mathematical induction for all n ∈ 𝑵 : 1+2+3+…………..+n = ௡(௡ାଵ)

3. Answer any one out of the following questions.

a) IRs. 1000 is deposited at compound interest at 10 % per annum. The amount of money in the account at the end of any year can be calculated by the relation given below: ,where A is amount, P is principal deposited, R is rate of interest per annum and n is time duration (in years) for which the principal is invested.
(i) Find the amount at the end of 1st, 2nd and 3rd year.
(ii) Show that the sequence of amount in the account at the end of each year forms a geometric progression

b) Aadarsh, Babil and Charanjeet were playing a game in which they have to place rice grains on a 3 X 3 checkerboards consisting of 9 squares, each having a number from 1 to 9 written on it, as shown below.
Aadarsh arranged the rice grains on each square such that the number of rice grains is equal to the number written on the squares. i.e. He put one (1) grain on the square marked "1", two
(2) grains on the square marked "2", and so on.
Babil arranged the rice grains on each square such that the number of rice grains is equal to the square of the number written on the squares. i.e. He put one grain (= 12) on the square
marked "1", four (= 22) grains on the square marked "2", and so on.
Charanjeet arranged the rice grains on each square such that the numberof rice grains isequal to the cube of the number written on thesquares. i.e. He put one (= 13) grain on thesquare marked "1", eight (= 23) grains on the square marked "2", and so on.
Find the ratio of the total number of rice grains arranged on the checkerboard by Aadarsh, Babil and Charanjeet, respectively

4. Answer any one out of the following questions.

a) I (i) Prove that: = 𝑡𝑎𝑛2𝑥
(ii) Find the general value of '𝜃 ' satisfying: 4cos2𝜃 = 3

Arun saw few dogs on the street shivering with cold in the winters. He decided to build a small triangular shed for them (one end of the shed as shown in figure). He has rods of length 2.45 m, 1.80 m and 2.2 m using which he made the shed frame. Find the angles (∠A,∠B,∠C) to which the sticks are arranged with one another to form the triangular frame as shown in the figure.
Also verify sine formula for this triangle.

5. Answer any one out of the following questions.

a) (i) There are 5 railway stations between how many different tickets need to be printed in order between any two stations.
(ii) Out of 3 boys and 7 girls, a committee of 5 has to be formed. In how many ways can thisbe done if the committee must have
(a) exactly 2 girl.
(b) at least 2 girls.
(i) In the expansion of (1+a)n if the coefficients of three consecutive terms are in A.P., then Prove that n+2 is a perfect square.
(ii) Solve the inequality: x2+5x+10 < 4

6. Answer any one out of the following questions.

a) There are thirteen cards in each of the four suits in a regular 52-card deck: clubs (♣), diamonds (♦), hearts (♥), and spades (♠). The printing of hearts and diamonds is done with Red ink whereas that of clubs and spades is done in black ink. All the suits consist of three face cards—the King, Queen, and Jack—having reversible (or double-headed) pictures. There are ten more cards in each suit, ranging from one (the Ace) to ten.
(i) If a card is selected from a well shuffled deck of 52 cards, what is the probability of drawing
(a) a club ?
(b) a black king ?
(c) a queen of spade ?
(d) a red spade?
(ii) A card is drawn from a pack of 52 cards so that each card is equally likely to be selected. Check whether the following events are independent?
Event A : the card drawn is a diamond
Event B : the card drawn is a queen
(iii) A card from a pack of 52 playing cards is lost. From the remaining cards of the pack, three cards are drawn at random (without replacement) and are found to be all clubs. Find the probability of the lost card being a club.

Air Quality Index (AQI)
b) Government organizations have created a parameter called air quality index (AQI) to show the public how polluted the air is now or is expected to get in the future. The AQI increases along with air pollution levels and the corresponding public health risk. Poor air quality generally impacts children, the elderly, and people with respiratory or cardiovascular conditions first. Governmental organizations typically advise citizens to limit their outdoor physical activity or perhaps stay indoors entirely when the Air Quality Index (AQI) is high.

To present status of the air quality and its effects on human health, the following description categories have been adopted Monthly AQI of two different cities A and B have been given in the following table. Based on the table and above information answer the following questions:

(i) What is the range of the data of AQI for city – A and city – B?
(ii) Calculate the mean of the data of AQI for city – A and city – B?
(iii) Based on the mean AQI levels over the year, which city has cleaner air?
(iv) Find the variance and standard deviation of the AQI data for city – A and city – B?
(v) Which city A or B shows greater variablility in AQI levels?

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