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1. What is the next term in the sequence: 2, 4, 8, 16, ___?

1. A) 20 B) 24 C) 32 D) 30
   ✅ Correct Answer: C) 32
   🟢 Explanation: Har term ko 2 se multiply kiya gaya hai → 16 × 2 = 32

2. The 5th term in the sequence 3, 6, 9, 12, ___ is:

1. A) 15 B) 18 C) 21 D) 24
   ✅ Correct Answer: C) 21
   🟢 Explanation: Har term mein +3 ho raha hai → 12 + 3 = 15 (lekin 5th term: 3 + 4×3 = 15)

🚫 Correction: Answer should be A) 15, not 21.

3. Which sequence is arithmetic?

1. A) 2, 4, 8, 16 B) 3, 6, 9, 12 C) 5, 25, 125 D) 10, 100, 1000
   ✅ Correct Answer: B)
   🟢 Explanation: Arithmetic sequence mein har term ka difference same hota hai → Yahan +3

4. Common difference in the sequence 7, 10, 13, 16 is:

1. A) 2 B) 3 C) 4 D) 5
   ✅ Correct Answer: B) 3
   🟢 Explanation: 10 – 7 = 3, 13 – 10 = 3 → Common difference = 3

5. What is the formula for the nth term of the sequence: 2, 4, 6, 8…?

8. A) 2n B) n + 2 C) n × 2 D) All of these
   ✅ Correct Answer: D) All of these
   🟢 Explanation: 2, 4, 6, 8… ka nth term 2n hai → 2×1 = 2, 2×2 = 4, etc. n × 2 bhi same hai.

6. The pattern rule for the sequence 1, 4, 9, 16, 25 is:

9. A) Multiply by 2 B) Square of natural numbers C) Add 2 D) None
   ✅ Correct Answer: B)
   🟢 Explanation: 1² = 1, 2² = 4, 3² = 9… → Ye squares hain

7. 10th term of the arithmetic sequence 2, 5, 8,… is:

1. A) 30 B) 29 C) 28 D) 31
   ✅ Correct Answer: B) 29
   🟢 Explanation: nth term = a + (n – 1)d → 2 + (10 – 1)×3 = 2 + 27 = 29

8. In a geometric sequence, each term is obtained by:

1. A) Addition B) Multiplication C) Subtraction D) Division
   ✅ Correct Answer: B)
   🟢 Explanation: Geometric sequence mein har term previous term se multiply hoti hai

9. If nth term = 3n + 2, then 5th term is:

1. A) 15 B) 17 C) 12 D) 18
   ✅ Correct Answer: B) 17
   🟢 Explanation: 3×5 + 2 = 15 + 2 = 17

10. Which of the following is NOT a pattern?

1. A) 2, 4, 8, 16 B) 3, 5, 10, 17 C) 1, 1, 2, 3, 5, 8 D) 2, 4, 6, 9
   ✅ Correct Answer: B)
   🟢 Explanation: Is sequence ka koi clear rule follow nahi ho raha — no arithmetic or geometric pattern

11. If first term = 4 and common ratio = 2, find the 3rd term:

1. A) 8 B) 10 C) 16 D) 20
   ✅ Correct Answer: C) 16
   🟢 Explanation: Geometric: 4, 8, 16 → 3rd term = 4 × 2 × 2 = 16

12. Fibonacci sequence starts from:

8. A) 0, 1 B) 1, 1 C) 2, 3 D) 5, 8
   ✅ Correct Answer: A)
   🟢 Explanation: Standard Fibonacci starts from 0, 1 → Next terms: 1, 2, 3, 5, 8…

Sub-domain 2: Expansion and Factorisation

13. The expanded form of (a + b)² is:

1. A) a² + b² B) a² + 2ab + b² C) a² – 2ab + b² D) None
   ✅ Correct Answer: B)
   🟢 Explanation: Identity: (a + b)² = a² + 2ab + b² → Standard expansion formula.

14. (x + 3)(x – 3) = ?

1. A) x² – 9 B) x² + 9 C) x² – 6x + 9 D) x² + 6x + 9
   ✅ Correct Answer: A)
   🟢 Explanation: Identity: (a + b)(a – b) = a² – b² → x² – 3² = x² – 9

15. (2x + 1)² = ?

1. A) 4x² + 1 B) 4x² + 4x + 1 C) 4x² + 2x + 1 D) None
   ✅ Correct Answer: B)
   🟢 Explanation: (2x + 1)² = (2x)² + 2×2x×1 + 1² = 4x² + 4x + 1

16. Factor of x² – 9 is:

1. A) (x – 3)(x + 3) B) (x – 9)(x + 1) C) (x – 1)(x + 9) D) None
   ✅ Correct Answer: A)
   🟢 Explanation: x² – 9 = x² – 3² → Difference of squares identity

17. What is the result of (x + 5)²?

1. A) x² + 10x + 25 B) x² + 25 C) x² + 5x + 25 D) None
   ✅ Correct Answer: A)
   🟢 Explanation: Identity: (a + b)² = a² + 2ab + b² → x² + 2×5x + 25 = x² + 10x + 25

18. Factor of x² + 5x + 6 is:

1. A) (x + 2)(x + 3) B) (x – 2)(x + 3) C) (x + 1)(x + 6) D) (x + 2)(x – 3)
   ✅ Correct Answer: A)
   🟢 Explanation: 2 × 3 = 6 and 2 + 3 = 5 → Factors are x + 2 and x + 3

19. (a + b)(a – b) = ?

1. A) a² – b² B) a² + 2ab + b² C) a² + b² D) None
   ✅ Correct Answer: A)
   🟢 Explanation: Difference of squares identity → a² – b²

20. Which is a perfect square trinomial?

1. A) x² + 4x + 4 B) x² + 5x + 6 C) x² – 9 D) None
   ✅ Correct Answer: A)
   🟢 Explanation: x² + 4x + 4 = (x + 2)² → Perfect square trinomial

21. Which is factor of x² + 3x – 10?

1. A) (x – 5)(x + 2) B) (x + 5)(x – 2) C) (x + 3)(x + 3) D) None
   ✅ Correct Answer: B)
   🟢 Explanation: +5 and -2 multiply to -10, add to +3 → (x + 5)(x – 2)

22. Expansion of (x – 2)(x – 3):

1. A) x² + 5x + 6 B) x² – 5x + 6 C) x² – x – 6 D) x² + x – 6
   ✅ Correct Answer: B)
   🟢 Explanation: x² – 3x – 2x + 6 = x² – 5x + 6

23. Factor of x² – 16:

1. A) (x + 4)² B) (x – 4)(x + 4) C) (x + 8)(x – 2) D) None
   ✅ Correct Answer: B)
   🟢 Explanation: x² – 16 = x² – 4² → Difference of squares

24. What is (a – b)²?

1. A) a² – b² B) a² – 2ab + b² C) a² + 2ab + b² D) a² + b²
   ✅ Correct Answer: B)
   🟢 Explanation: Identity: (a – b)² = a² – 2ab + b²

Sub-domain 3: Linear Equations and Inequalities

27. Solve: x + 5 = 10

1. A) 5 B) 10 C) 15 D) 0
   ✅ Correct Answer: A) 5
   🟢 Explanation: Subtract 5 from both sides: x = 10 − 5 = 5

28. Solve: 2x = 8

1. A) 2 B) 4 C) 6 D) 8
   ✅ Correct Answer: B) 4
   🟢 Explanation: Divide both sides by 2: x = 8 ÷ 2 = 4

29. x − 3 = 7, then x = ?

1. A) 5 B) 7 C) 10 D) 12
   ✅ Correct Answer: C) 10
   🟢 Explanation: Add 3 to both sides: x = 7 + 3 = 10

30. x ÷ 2 = 6, then x = ?

1. A) 8 B) 12 C) 3 D) 6
   ✅ Correct Answer: B) 12
   🟢 Explanation: Multiply both sides by 2: x = 6 × 2 = 12

31. Which of the following is a linear equation?

1. A) x² + 2 = 5 B) x + 2 = 5 C) 2x² = 9 D) x³ = 27
   ✅ Correct Answer: B)
   🟢 Explanation: Linear equations have no exponents higher than 1 → only x

32. 3x − 4 = 5 → x = ?

1. A) 1 B) 3 C) 5 D) 6
   ✅ Correct Answer: B) 3
   🟢 Explanation:
   Add 4: 3x = 9
   Divide by 3: x = 3

33. 5x = 2x + 9 → x = ?

1. A) 2 B) 3 C) 5 D) 6
   ✅ Correct Answer: B) 3
   🟢 Explanation:
   5x − 2x = 9 → 3x = 9 → x = 3

34. Inequality symbol for “greater than or equal to”:

1. A) < B) > C) ≥ D) ≤
   ✅ Correct Answer: C)
   🟢 Explanation: The symbol ≥ means “greater than or equal to”

35. Which of these is NOT a solution of x < 5?

1. A) 1 B) 3 C) 6 D) 0
   ✅ Correct Answer: C) 6
   🟢 Explanation: x < 5 means values less than 5 — 6 is not valid

36. Solve: 2x − 1 = 7

1. A) 3 B) 4 C) 5 D) 6
   ✅ Correct Answer: C) 5
   🟢 Explanation:
   2x = 7 + 1 = 8 → x = 8 ÷ 2 = 5

37. Linear equation with variable on both sides:

1. A) x = 2 B) 2x + 3 = x + 5 C) x + 1 = 5 D) 2x = 4
   ✅ Correct Answer: B)
   🟢 Explanation: Variable on both sides (x on LHS and RHS)

38. What is the solution of: 4x + 2 = 14

1. A) 2 B) 3 C) 4 D) 5
   ✅ Correct Answer: B) 3
   🟢 Explanation:
   4x = 14 − 2 = 12 → x = 12 ÷ 4 = 3

39. If 3(x − 1) = 12, x = ?

1. A) 4 B) 5 C) 3 D) 6
   ✅ Correct Answer: B) 5
   🟢 Explanation:
   3(x − 1) = 12 → x − 1 = 4 → x = 5

40. x ÷ 4 + 3 = 5 → x = ?

1. A) 6 B) 8 C) 4 D) 2
   ✅ Correct Answer: B) 8
   🟢 Explanation:
   x/4 = 5 − 3 = 2 → x = 2 × 4 = 8