10th Maths 1st Mid Term Important 2 Mark Questions 2026

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Important sums for MID TERM EXAM - 2026

10th Standard — Mathematics (English Medium)

2 Marks

1. If A = {1, 3, 5} and B = {2, 3} then
(i) find A × B and B × A
(ii) Is A × B = B × A? If not why?
(iii) Show that n(A × B) = n(B × A) = n(A) × n(B)

2. Find A × B, A × A and B × A
(i) A = {2, -2, 3} and B = {1, -4}
(ii) A = B = {p, q}

3. Let A = {1, 2, 3} and B = {x | x is a prime number less than 10}. Find A × B and B × A.

4. If B × A = {(-2, 3), (-2, 4), (0, 3), (0, 4), (3, 3), (3, 4)}, find A and B.

5. The arrow diagram shows a relationship between the sets P and Q. Write the relation in:
(i) Set builder form
(ii) Roster form
(iii) What is the domain and range of R?

→

6. Let A = {1, 2, 3, 4, ..., 45} and R be the relation defined as "is square of a number" on A. Write R as a subset of A × A. Also, find the domain and range of R.

7. A Relation R is given by the set {(x, y) | y = x + 3, x ∈ {0, 1, 2, 3, 4, 5}}. Determine its domain and range.

8. Let f = {(x, y) | x, y ∈ ℕ and y = 2x} be a relation on ℕ. Find the domain, co-domain and range. Is this relation a function?

9. Let A = {1, 2, 3}, B = {4, 5, 6, 7} and f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. Show that f is one-one but not onto function.

10. If A = {-2, -1, 0, 1, 2} and f : A → B is an onto function defined by f(x) = x² + x + 1 then find B.

11. Let f be a function from ℝ to ℝ defined by f(x) = 3x - 5. Find the values of a and b given that (a, 4) and (1, b) belong to f.

12. Find k if f ∘ f(k) = 5 where f(k) = 2k - 1.

13. Is 7 × 5 × 3 × 2 + 3 a composite number? Justify your answer.

14. 'a' and 'b' are two positive integers such that a^b × b^a = 800. Find 'a' and 'b'.

15. If m, n are natural numbers, for what values of m, does 2ⁿ × 5^m ends in 5?

16. If 13824 = 2^a × 3^b then find a and b.

17. Find the number of terms in the A.P. 3, 6, 9, 12, ..., 111.

18. Find the 19th term of an A.P. -11, -15, -19, ...