Nios Class 10th Mathematics (211) Solved TMA English Medium | 2025-26 Solved TMA

a. A learner of class 10 was playing with number blocks and suddenly made the numbers like 1441,121,14578754 etc . She was surprised after reading the numbers. Her teacher explained her that these are called “PALINDROME NUMBERS” which are read the same whether read forwards and backwards. The teacher asked the learner to do the following. Help the learner to find out the answers: Write all Palindrome numbers less than 100. Is there any particular number which is a factor of all above formed numbers? Will the numbers formed be Rational or Irrational? b. Anil was learning the topic of Laws of Exponents. Help Anil to answer the following questions using Laws of Exponents learnt. (i) Find value of x if (ii) Simplify 2. a. Ratul and his friends were setting up a tent in their backyard. While fixing the poles, they noticed that two ropes, AB and CD, were crossing each other at point O to hold the tent firmly. To provide extra support, they tied another rope, OP, at the intersection as shown in figure. While adjusting the ropes, they started discussing the angles formed and came up with the following questions: (i) What is the value of x? (ii) What is the measure of ∠BOP? Answer the questions. b. Three friends Sushma, Salma & Saloma walk away from a fixed point in three different directions such that the path of each is equally inclined to those of the other two. (i) Find the angles which their path make with each other. (ii) Name the type of lines formed by tracing the path. 4. a. There is a door whose upper half part is made of semi opaque glass with wooden frame. The ratio of length and breadth of the upper half part is 5:3. If we subtract 0.5 feet from the breath and 1 foot from the length of the upper half part, we get the dimension of glass portion (i) Taking the length of the upper part of the door as 5x and breadth as 3x, express the length and breadth of glass portion in terms of x. (ii) Give the polynomial representing the area of the glass. Also find zeros of the polynomial obtained. b. A curious student, who was interested in prime numbers, observed three consecutive prime numbers 7, 11 and 13 — and found a special pattern in them. He named them "The Prime Trio”. (i) The learner added these three numbers together. What type of number is formed? Do all sets of three consecutive prime numbers exhibit the same property? If not, provide an example where this does not hold. (ii) The learner then experimented with a three-digit number (e.g., 157). By writing the same number again to its right, he formed a six-digit number (157157). He then divided this number by 7, 11, and 13 successively. What was the result? Create two more examples following this pattern and write your observations. b. (i) A shopkeeper used a bar graph to record the daily sales of different products and a histogram to show the age distribution of customers. Based on this, can you identify two key differences between a bar graph and a histogram? (ii) Draw a histogram for the following data. 6.a. Sketch a Rectangular shaped village say ABCD. Create a triangular area inside the village APD for girl’s education for constructing schools and colleges. Such that APD= and PDA= . Take BC as 10 km and extend DC upto a point E such that CE=BC. i. Draw the figure to represent above situation. ii. What will be measure of PAD? iii. What will be measure of BCE? iv. What will be measure of length BE? v. If APD would have been an Equilateral triangle then find whether APD BCE? Why or why not? b. Draw three different sets of two triangles of any dimensions. Check by paper cutting and overlapping methods that are they congruent triangles or not? Also check if they are similar triangles? Give reasons (why or why not). Define similar figures. Draw two circles of radius 5cm and 7cm respectively. Will they be similar? Also draw a circle of any radius and take three points A, B and C on its circumference such that the points are equidistant from each other. What will be measurement of angles formed at the centre of circle if centre O is joined with points A, B and C? 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