NIOS CLASS 10TH Mathematics (211) SOLVED TMA In English Medium PDF SESSION 2024 - 25

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March/April & October/November 2025 Examinations

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Questions Covered in This PDF:

1. Answer any one of the following question.

(a) Ankur, a secondary level mathematics student, initially struggled to differentiate between
rational and irrational numbers. Through an effective explanation utilizing fractions and
decimal expansions, his sister Riya successfully clarified the distinction. Describe a possible
method Riya might have used and then apply it to classify the following numbers as rational
or irrational:
1.125, ????, 1.67676767…….,
ଶଶ

(i) How many rational numbers and irrational numbers exist between the natural numbers 1 and 2?
(ii) There is/are natural number ‘n’ such that √???? lies between 1 and 2. How many value(s) of n are possible? Represent √???? on a real number line for each such value of n, satisfying above condition.

2. Answer any one of the following question.

(a) A polygon which has equal sides and equal angles is called a regular polygon. It is found
that the interior angle of regular polygon having n sides can be calculated as:

(i) Name the simplest regular polygon and write the value of its interior angle.
(ii) Prove that the sum of the (interior) angles of a hexagon is 720o

Perform the activity whose steps are given below and answer the questions that follows it:
 Fix three nails/awl pins A, B and C on a wooden board or any surface as shown below
Take a piece of thread equal in length to BC and another piece of thread equal in length (AB + AC). Compare the lengths of the two threads.
(i) If the length corresponding to BC = x and the length corresponding to AB + AC = y Which of the following is true?
(a) x = y
(b) x > y
(c) x < y
(d) x =2 y
(ii) Based on your learning from above activity, explain in which of the following three cases, is construction of a triangle possible from the given measurements:
(a) 10 cm, 7 cm and 3 cm
(b) 7 cm, 8 cm and 16 cm
(c) 3.0 cm, 3.5 cm and 5.8 cm

3. Answer any one of the following question.

(a) (i) State Equal Intercept Theorem
(ii) A wooden ladder has parallel rungs (PA, QB and RC) as shown in figure If PQ = 3 cm, QR = 4 cm and AB = 3.5 cm find the value of AC.

b) If ABC is an equilateral triangle and AD is the median. Prove that 3AB2 = 4AD2

4. Answer any one of the following questions in about 100-150 words.

(a) (i) If the sum of the exponents of the prime factors in the prime factorisation of 31752 is a and the product of the exponents of the prime factors in the prime factorisation of 21168 is b. Find a:b.

(ii) Aman and Neha, donated Rs. x and Rs. y respectively from their pocket money, towards Prime Minister’s National Relief Fund (PMNRF). The donations made by them are represented by the following equation:

Find the total donation made by Aman and Neha towards PMNRF.

b) Alankriti want to build a cuboidal water tank which has the capacity to store water represented by the polynomial x3 + 9x2 + 26x + 24 when it is fully filled, whereas (x+4) represents the height of the tank.

(i) Identify height of the tank as a monomial, binomial or a trinomial.
(ii) Find the degree of the polynomial representing the capacity of the cuboidal tank.
(iii) Find the expression for the polynomial representing the area of the base of the cuboidal tank. Also, calculate the possible expressions for the length and breadth.
(iv) If the polynomial 3x2 + 15x + 18 represents the amount of water that leaked from the above fully filled cuboidal tank, then
(a) find the expression for the polynomial representing the volume of water left in the tank.
(b) Find the polynomial that represents the height of remaining water in the tank. [Hint: Capacity/Volume of the cuboidal tank = length X breadth X height and area of the base = length X breadth]

5. Answer any one of the following questions.

(a) (i) Comment on the location of the orthocenter of each of the triangle shown below:

(ii) Do the steps of construction in your response sheet using a ruler and pencil, then answer
the questions that follow it:
 Draw ∆????????????.
 Mark midpoint D of the side BC, join A to D.
Mark another point G on line segment AD such that AG:GD = 2:1.
 Mark midpoint E and F of side AC and AB respectively and join B to E and C to F.
(a) What is the term given to line segments AD, BE and CF?
(b) Do line segments BE and CF also passes through point G?
(c) What is the special name given to point G?

b) In a circle of radius 17 cm and centre O, PQ and RS are two parallel chords such that PQ = 16 cm and RS = 30 cm. Find the distance between the chords if
(a) The chords are on the same side of the centre of the circle.
(b) The chords are on the opposite sides of the centre of the circle.

6. Prepare any one Project out of the following projects given below:

a)Take any book (say your Mathematics Book – 1), randomly open any page of the book in such a way that the page number on the right hand side page is less than 100 and note the page number. Repeat this activity 50 times and record your reading every time, separated by a comma. (Ignore the page number which is 100 or more).
(i) Present the above raw data in the form of arrayed data.
(ii) Construct a frequency table for the data using equal class sizes and taking one class
as 0-10 (10 excluded) using tally marks.
(iii) Also construct a cumulative frequency table for the above grouped data.
(iv) Construct a histogram and a frequency polygon for the data.

b) Shown below is the histogram representing the runs scored by a cricket team in different overs. Answer the following questions based on the histogram.

(i) In which interval of overs the cricket team scored maximum runs?
(ii) In which intervals of overs the cricket team scored equal number.
(iii) Construct a grouped frequency table for the data using equal class sizes from the above histogram.
(iv) Also construct a cumulative frequency table for the above grouped data.
(v) Construct a frequency polygon for the data.

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


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- 31 January 2025 (For March/April Exam)

- 31 August 2025 (For October/November Exam)

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