Class 11th Maths September Exam 2025

 Class 11th Maths September Exam 2025

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MATHEMATICS

Time: 3 hrs      Class: 11th      Max Marks: 80

NOTE: All questions are compulsory

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SECTION – A

Q1 (MCQs)

1. Set A ={Ø, 3, {5, Ø}, 2, {2}, {5}}. Which one of the following is incorrect?
   A) 2 ∈ A    B) {2} ⊂ A    C) {5} ⊂ A    D) Ø ⊂ A

2. n(A×B) = n(B×A) if
   A) n(A)=n(B)    B) A=B    C) P×Q=Q×P    D) All of these

3. The value of sin 18000 is
   A) 2    B) -1    C) 0    D) 1

4. The set of all irrational numbers between √2 and √5 is
   A) Infinite set    B) Null set    C) Finite set    D) None

5. The domain of signum function $y = \frac{|x|}{x}$ is
   A) 0    B) R    C) R – {0}    D) None

6. If sinx = -a/b then cosecx is
   A) a/b    B) b/a    C) -b/a    D) -ab

7. The conjugate of 2i is
   A) -2i    B) -2    C) 2    D) -i

8. If 3x – 4x < -2 then
   A) x > 2    B) x < 2    C) x < -2    D) None

9. There are 25 multiple-choice questions with 4 options. The total number of ways to tick options if answer is not known is
   A) 100    B) 254    C) 50    D) 425

10. The value of i^-35 is
    A) 1    B) 0    C) -i    D) i

11. For n ≥ 2, n! can be written as
    A) (n-1)!    B) n(n-1)    C) n(n-1)(n-2)    D) n(n-1)(n-2)!

12. The value of tan 150° is
    A) 2+√2    B) 2–√3    C) √3+1    D) None

13. The total number of terms in the expansion of (a+b)^n is
    A) n-1    B) n+1    C) n^2    D) 2n

14. nC1 - nC0 is
    A) n-1    B) n    C) 0    D) 2n

15. If Z = 3+4i then |Z| is
    A) 5    B) 0    C) 25    D) None

16. The value of 4i – 3i is
    A) 1    B) 18    C) 17    D) 28

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Q2 (True/False)

1. A set of even prime numbers is a singleton set.

2. Every function is said to be a relation.

3. The range of sinx is (-1,1).

4. If -2 is added to both sides of inequality y < -2 then it becomes 2-y > -4.

5. The conjugate of (3+i)(3–i) is a complex number.

6. 4C2 + 4C1 = 5C2.

7. If r=n then nCr = n.

8. 1/2i can be written as -i.

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Q3 (Fill in the blanks)

1. Total subsets of A if n(A)=4 is _______.

2. The range of |x| is _______.

3. The period of sin(3π/2) is _______.

4. Solution set of 4x+3 < 6x+7 is _______.

5. The value of 0! is _______.

6. The value of i^4 + i^6 + i^-4 + i^-6 is _______.

7. If nC2 = nC3 then nC5 = _______.

8. If Z1 = x+(3x–4y)i = Z2=3+xi then x+y = _______.

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SECTION – B

Q1. Express (-5i)(1/8 i) in a+ib form.

Q2. Solve 30x < 200 when (i) x ∈ N, (ii) x ∈ Z.
Or Solve the inequality $7 ≤ \frac{3x+11}{2} ≤ 11$.

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Q3. If 1/6! + 1/7! = x/8!, find x.

Q4. How many 3-digit numbers are formed using digits 1–9 if no digit is repeated?
Or How many chords can be drawn through 21 points on a circle?

Q5. Find the multiplicative inverse of √5 + 3i.
Or If $\frac{a+ib}{a-ib} = x+iy$, prove that x²+y²=1.

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SECTION – C

Q1. Prove that sin²6x – sin²4x = sin2x·sin10x.
Or Prove that 3sin(π/6)sec(π/3) – 4sin(5π/6)cot(π/4) = 1.

Q2. Find the domain and range of √(9–x²).

Q3. In how many distinct permutations of the letters in MISSISSIPPI do the 4 I’s not come together?
Or Find the number of 5-card combinations from a deck of 52 cards with exactly one king.

Q4. Expand (x²+3/x)^4.
Or Compute (99)^5.

Q5. Find all pairs of consecutive odd natural numbers >10 whose sum <40.

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SECTION – D

Q1. If tanx = 3/4, π < x < 3π/2, find sin(x/2), cos(x/2), tan(x/2).
Or Show that tan3x·tan2x·tanx = tan3x – tan2x – tanx.

Q2. A={3,5,7,9,11}, B={7,9,11,13}, C={11,13,15}, D={7,8,9,10}. Find:

1. B ∩ C

2. A ∩ C ∩ D

3. A ∩ (B ∪ C)

4. A ∩ (B ∪ D)

5. (A ∩ B) ∩ (B ∪ C)

6. (A ∪ D) ∩ (B ∪ C)

OR

Q2(A) Let A={1,2,3,4,6}, relation R={(a,b)∈A×A | b is divisible by a}.

1. Write R in roster form.

2. Find range & domain of R.
   (B) If P={1,2}, form P×P×P.

Q3. In how many ways can letters of PERMUTATIONS be arranged if:

1. Word starts with P and ends with S

2. Vowels are together

3. There are 4 letters between P and S

Or A group has 4 girls & 7 boys. In how many ways can a team of 5 be formed if:

1. No girls

2. At least one boy & one girl

3. At least 3 girls

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