**Bihar Board Maths Sample Papers for Class 12**

**(General Instructions) :**

a) All Questions are compulsory

b) There is No negative marking for any wrong answer.

c) Questions are in two sections

**Directions to questions 1 to 10: choose the correct answer .**

**1. Which of the following is a null set?**

(a) {x : IxI = 4, x ∈ N}

(b) {x : x2 + 2x + 1 = 0, x ∈ R}

(c) {x : IxI < 1, x ∈ N}

(d) None of these

*answer- c*

2. **The number of non-empty subset of the set {a, b, c, d} is**

(a) 16

(b) 18

(c) 15

(d) 19

*answer- c*

**3. If A, B and C are non-empty subsets of a set then (A –B) ∪ (B- A) equals**.

(a) (A ∩ B) ∪ (A ∪ B)

(b) (A ∪ B) – (A ∩ B)

(c) A – (A ∩ B)

(d) (A ∪ B) – B

*answer- b*

**4. Let X be a non- empty set containing n elements. Then what is the number of relation on X ?**

(a) *2*

(b) 2*n*

(c) *2²n*

(d) n²

*answer- a*

**5. The range of the function f(x) = 2 – 3x, x ∈ R, x > 0 is**

(a) [-∞, 2]
(b) [+∞, 2]
(c) (-∞, 2)

(d) (-∞, 2]

*answer- c*

**6. If A = {1, 2, 3} and B = {3, 8} then (A ∪ B) x (A ∩ B) is**

(a) {(3, 1), (3, 2), (3, 3), (3, 8)}

(b) {(1, 3), (2, 3), (3, 3), (8, 3)}

(c) {(1, 2)}, (2, 2), (3, 3), (8, 8)}

(d) {(8, 3), (8, 2), (8, 1), (8, 8)}

*answer- b*

**7. The value of tan22 ½° is:**

(a) +√2 −1

(b) –√2 −1

(c) − √2 +1

(d) none of these

*answer- a*

**8. The general solution of equation tanθ= cotα is:**

(a) θ= nΠ + Π/2 – α

(b) θ= nΠ – Π/2 + α

(c) θ= nΠ + Π/2 + α

* *(d) θ= nΠ – Π/2 – α

*answer- a*

**9. Which of the following is correct?**

(a) 6 + i > 8 – i

(b) 6 + i > 4 – i

(c) 6 + i > 4 + 2i

(d) none of these

*answer- d*

**10. If z is any non-zero complex number then arg(z) + arg( z ) is equal to:**

(a) 0

(b) Π / 2

(c) Π

(d) 3Π / 2

*answer- a*

**11. Im(z) is equal to (Im(z):**

(a) ½ (z+ z̅) i

(b) ½ (z – z̅)

(c) ½(z̅ – z)i

(d) none of these

*answer- c*

**12. If 9P5 + 5. 9P4 = 10P4 then:**

(a) 4

(b)5

(c) 9

(d) 10

*answer- d*

**13. A polygon has 44 diagonals. The number of sides is**

(a) 9

(b) 8

(c) 7

(d) 11

*answer- d*

**15. 1+ ½ +¼ +1/8 +…….is to ∞**

(a) 1

(b) 2

(c)½

(d) none of these

*answer- b*

**16. The x- axis divide the line segment joining the points (2, -3) and (5, 6) is**

(a) 1 : 2

(b) 2 : 1

(c) 1 : 3

(d) none of these

*answer- a*

**17. The point of intersection of the lines 3x – 2y – 8 = 0 and 5x + 4y – 6 = 0 is**

(a) (2, -1)

(b) (2, 1)

(c) (-2, 1)

(d) (-2, -1)

*answer- a*

**18. The length of perpendicular from point (1, -2, -5) to the yz – plane is**

(a) -5

(b) -2

(c) 1

(d) 5

*answer- c*

**19. If f(x) = 1/ x f’(x) is equal to**

(a) 0

(b) 1/ –

*x*

(c) 1/ x²

(d) 1

*answer- c*

**20. The contra positive of (p ∨ q) → r is:**

(a) r → (p ∨ q)

(b) ∼ r → ∼ (p ∨ q)

(c) ∼ r → (∼ p ∧ ∼ q)

(d) p → (p ∨ r)

*answer- b*

*Instructions : ***Q. No. 21 to 25 ****In the following questions there are two statements. Statement-I follows Statements-II. You have to go through these statements and mark your answer from the given questions. 5 × 2 = 10**

(a) If both the statement are correct and statement II is the correct explanation of statement I.

(b) If both statements are correct but statement II is not the correct explanation of statement I

(c) Statement I is correct but statement II is wrong.

(d) Statement I is wrong but statement II is correct.

**21. **Statement I : sinx + cos ax periodic for all a ∈ R

Statement II : sin x, cos ax are periodic functions.

*answer- a*

**22.** Statement I : In any triangle ABC, the minimum value of *r *is 9

Statement II : A.M. ≥ G.M.

*answer- c*

**23.** Statement I : 7 is an irrational number

Statement II : An irrational number is non-terminating and non- repeating decimal.

*answer- a*

**24. **Statement I : 1, 3, 5, ……….. (2n – 1) > nn ; n ∈ N

Statement II : The sum of the first n natural numbers is equal to n2.

*answer- b*

**25. **Statement I : The relation R in a set A = {1, 2, 3, …….. 14} defined by

R = {(x, y) : 3x – y = 0} have the domain {1, 2, 3, 4} and

R = {3, 6, 9, 12}

Statement II : Domain & Range of the relation R is respectively the set of all first & second entries of the distinct ordered pair of the relation.

*answer- d*

*Instructions ***: Question No. 26 to 28 In the following question there may be more than**

**one correct answer. You have to choose the correct options. ****(1 x 3 = 3)**

**26. If z1, z2 are two complex number then**

(a) Iz1 + z2I ≤ Iz1I + Iz2I

(b) Iz1 – z2I ≥ Iz1I – Iz2I

(c) Iz1 + z2I ≥ Iz1I Iz2I

(d) Iz1 – z2I ≤ Iz1 + z2I

*answer- b, c*

**27. If nC4, nC5 and nC6 are in A.P. then n is:**

(a) 8

(b) 9

(c) 14

(d) 7

*answer- c,d*

**28. If (1+x)²n = a0 + a1x + a2x² + ……. + a2nx²n then**

(a) a0 + a2 + a4 + …….. = ½ (a0 + a1 + a2 + a3 + ……….

(b) an+1 < an

(c) an-3 = an+1

(d) none of these

*answer- a,d*