Kickstart your SSLC academic year successfully with this comprehensive guide to 10th Maths 1st Mid Term Test 2026 Important 2 Marks Questions. Short-answer questions are vital for scoring high, and they typically test your core understanding of early chapters like Relations and Functions and Numbers and Sequences. This curated selection highlights the most repeated textbook problems, compulsory-type questions, and essential formulas that examiners favor. Practice these high-yield 2-mark questions to perfect your step-by-step working and secure maximum marks in your first mid-term exam!
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STD: X — MATHS
1. If B × A = {(-2, 3), (-2, 4), (0, 3), (0, 4), (3, 3), (3, 4)}, find A and B.
2. Find k if f ∘ f(k) = 5 where f(k) = 2k - 1.
3. Find A × B and B × A if A = {m, n} and B = ∅.
4. 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.
5. If A = {1, 3, 5} and B = {2, 3}, then find (i) A × B and B × A.
6. Find the value of a if g ∘ f(a) = 1 where f(x) = x2, g(x) = x - 2.
8. Given the function f : x → x2 - 5x + 6. Evaluate (i) f(-1) (ii) f(2).
9. Find the value of k, such that f ∘ g = g ∘ f where f(x) = 3x + 2, g(x) = 6x - k.
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 f : ℕ → ℕ be defined by f(x) = x2, then find the image of 1 and find the pre-image of 49.
12. If A = {2, -2, 3} and B = {1, -4}, then find A × B and B × A.
13. Find the value of k, such that f ∘ g = g ∘ f where f(x) = 3x - 2 and g(x) = 2x + k.
14. Find the value of [f(x + 2) - f(2)]/x, x ≠ 0 where f(x) = 2x + 5.
16. Let A = {1, 2, 3} and B = {x / x is a prime less than 10}. Find A × B and B × A.
17. If X = {-5, 1, 3, 4} and Y = {a, b, c}, then which of the following relations are functions from X to Y?
(i) R1 = {(-5, a), (1, a), (3, b)}
(ii) R2 = {(-5, b), (1, b), (3, a), (4, c)}
18. Represent the function f(x) = √(2x2 - 5x + 3) as a composition of two functions.
19. Show that the function f : ℕ → ℕ defined by f(x) = 2x - 1 is one-one function.
20. Show that the function f : ℕ → ℕ defined by f(m) = m2 + m + 3 is one-one function.
21. Find A × B and B × A if A = B = {p, q}.
22. If f(x) = 2x - 1 and g(x) = (x + 1)/2, show that f ∘ g = g ∘ f = x.
23. Define: Bijection.
24. 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.
25. A function f is defined by f(x) = 3 - 2x. Find x such that f(x2) = [f(x)]2.
26. A plane is flying at a speed of 500 km per hour. Express the distance 'd' travelled by the plane as function of time 't' in hours.
27. Find the value of n if 1 + 2 + 3 + ... + n = 666.
28. If 13824 = 2a × 3b, then find a and b.
29. Find the number of terms in the A.P. 3, 6, 9, 12, ..., 111.
30. Find the sum of 9 + 3 + 1 + ... + ∞.
31. 'a' and 'b' are two positive integers such that ab × ba = 800. Find 'a' and 'b'.
32. Compute x such that 104 ≡ x (mod 19).
33. Find the 12th term from the last of an A.P. -2, -4, -6, ..., -100.
34. Find the least positive value of x such that 71 ≡ x (mod 8).
35. If F1 = 1, F2 = 3 and Fn = Fn-1 + Fn-2, then find the value of F4.
36. Find the sum of 3 + 1 + 1/3 + ... + ∞.
37. What is the time 100 hours after 7 a.m.?
38. Find the 19th term of an A.P. -11, -15, -19, ...
39. Which term of an A.P. 16, 11, 6, 1, ... is -54?
40. If 1 + 2 + 3 + ... + k = 325, then find the value of 13 + 23 + 33 + ... + k3.
41. Find the sum of 1 + 8 + 27 + ... + 1000.
42. If 13 + 23 + 33 + ... + k3 = 44100, then find 1 + 2 + 3 + ... + k.
43. Find x, y and z, given the numbers x, 10, y, 24, z are in A.P.
44. If the nth term of a sequence is an = 5n/(n + 2), then find a6 and a13.
45. If d is the Highest Common Factor of 32 and 60, find x and y satisfying d = 32x + 60y.
46. Today is Tuesday. My Uncle will come after 45 days. In which day my Uncle will be coming?
47. Find the 4th term of a G.P. whose sum to infinity is 12 and first term is 8.
48. Find the least number that is divisible by the first ten natural numbers.
49. Find the sum of the following: 1 + 3 + 5 + ... upto 40 terms.
50. Find the ratio of a G.P. if its 2nd term is √6 and 6th term is 9√6.
51. Find the quotient and remainder when a is divided by b where a = 17 and b = -3.
52. Solve 8x ≡ 1 (mod 11).
53. Find the quotient and remainder when a is divided by b where a = -12 and b = 5.
54. Find the first 3 terms of a G.P. if a = 6 and r = 3.
55. If 3 + k, 18 - k, 5k + 1 are in A.P. then find k.
56. We have 34 cakes. Each box can hold 5 cakes only. How many boxes we need to pack and how many cakes are unpacked?
57. Find the sum of 16 + 17 + 18 + ... + 75.
58. Find the value of (a - b)/(b - c) if a, b, c are in G.P.
59. Find the first four terms of the sequence whose nth terms are given by an = n3 - 2.
60. Find the largest number which divides 1230 and 1926 leaving remainder 12 in each case.
61. Find the 7th term of a G.P. 729, 243, 81, ...
62. Find the sum of 3 + 6 + 9 + ... + 96.
63. Define: Euclid's Division Lemma.
64. Find the sum of the first 15 terms of the A.P. 8, 71/4, 61/2, 53/4, ...
65. Prove that two consecutive positive integers are always coprime.
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