Contents

# Bihar Board Previous Year Question Papers With Solutions Class 12 Maths

Hi students, welcome to **Amans Maths Blogs (AMB)**. On this page, you will get the Bihar Board Previous Year Question Papers With Solutions Class 12 Maths that were asked in previous year exams of BSEB (Bihar Secondary Education Board) Board. These papers was set by the examination conduction body members body of BSEB. These BSEB Board Exams Previous Year Questions Papers With Solutions helps the students to manage the time in examination hall. So If the students solve Bihar Board Previous Year Question Papers With Solutions Class 12 Maths, the students learn the time management.

## Bihar Board Previous Year Question Papers With Solutions Class 12 Maths 2018

**Time: 3 Hours 15 Minutes | Total Marks: 100**

**Instructions to the candidates:**

1. Candidates are required to give their answers in their own words as far as practicable.

2. Figures in the right hand margin indicates the full marks.

3. While answering the questions, candidates should adhere to the word limit as far as practicable.

4. 15 minutes of extra time has been allotted for the candidates to read the questions carefully.

5. This questions papers is divided into two sections- Section A and Section B.

6. In Section A, there are 50 Objective Type Questions which are compulsory, each carrying 1 marks. Darken the circle with blue/black ball pen against the correct option on OMR sheet provided to you. Do not use whitener/Liquid/Blade/Nail or OMR Paper, otherwise the result will be invalid.

7. In Section B, there are 22 short answer type questions (each carrying 2 marks), out of which any 15 questions are to be answered. Aprt from this, there are 4 Long Answer Type Questions (Each carrying 5 Marks). Each questions has an alternate option.

8. Use of any electronic device is prohibited.

**Section A: Objective Type Questions**

Question No 1 to 50 have four options, out of which only one is correct. You have to mark, you select option, on the OMR sheet.

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 1**

Let A = {5, 6}; how many binary operations can be defined on this set?

[BSEB Board 2018]

**Options:**

A. 8

B. 10

C. 16

D. 20

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 2**

Let A = {1, 2, 3}, which of the following functions f: A A does not have an inverse function?

[BSEB Board 2018]

**Options:**

A. {(1, 1), (2, 2), (3, 3)}

B. {(1, 2), (2, 1), (3, 1)}

C. {(1, 3), (3, 2), (2, 1)}

D. {(1, 2), (2, 3), (3, 1)}

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 3**

If A = {}1,2,3}, B = {6,7,8} and f: A A is a function such that f(x) = x + 5, then what type of function is f?

[BSEB Board 2018]

**Options:**

A. Into

B. One-One Onto

C. Many-One Onto

D. Constant Function

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 4**

What type of a relation is “Less Than” in the set of real numbers?

[BSEB Board 2018]

**Options:**

A. Only symmetric

B. Only Transitive

C. Only Reflexive

D. Equivalence Relation

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 5**

The value of is

[BSEB Board 2018]

**Options:**

A. 8/5

B. 12/5

C. 2/5

D. 4/5

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 6**

The value of is

[BSEB Board 2018]

**Options:**

A.

B.

C.

D. None of These

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 7**

The value of is

[BSEB Board 2018]

**Options:**

A.

B.

C.

D.

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 8**

The value of is

[BSEB Board 2018]

**Options:**

A.

B.

C.

D.

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 9**

If and then =

[BSEB Board 2018]

**Options:**

A.

B.

C.

D. None of These

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 10**

If a, b, c are in AP then the value of

[BSEB Board 2018]

**Options:**

A. 3

B. -3

C. 0

D. 1

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 11**

If 7 and 2 are two roots of the equation

then the third root is

[BSEB Board 2018]

**Options:**

A. -9

B. 14

C. 1/2

D. None of These

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 12**

If and

then the value of *x* is

[BSEB Board 2018]

**Options:**

A. 1

B.

C.

D. 0

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 13**

If

and A + A’ = I_{2} then is

[BSEB Board 2018]

**Options:**

A. Pi

B. Pi/3

C. 3Pi/2

D. Pi/6

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 14**

If A be a square matrix. Then A + A’ will be a

[BSEB Board 2018]

**Options:**

A. Symmetric Matrix

B. Skew Symmetric Matrix

C. Null Matrix

D. Unit Matrix

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 15**

If A is a matrix of order 3 x 3 such that A^{2} = A, then (A + I^{3})^{3} – 7A is equal to

[BSEB Board 2018]

**Options:**

A. I_{3}

B. A

C. 3A

D. I_{3 }– A

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 16**

Let A be a non-singular matrix of the order 2 x 2, then |adj A| =

[BSEB Board 2018]

**Options:**

A. 2|A|

B. |A|

C. |A|2

D. |A|^{3}

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 17**

The value of (d/dx)[log(sec x + tan x)] is

[BSEB Board 2018]

**Options:**

A. 1/(sec x + tan x)

B. sec x

C. tan x

D. sec x + tan x

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 18**

If x^{2}y^{2} = (x + y)^{5}, then value of (dy/dx) is

[BSEB Board 2018]

**Options:**

A. x/y

B. y/x

C. -y/x

D. -x/y

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 19**

If y = , then value of (dy/dx) is

[BSEB Board 2018]

**Options:**

A. Pi

B. 1

C. 0

D.

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 20**

The value of (d(2^{x}))/(d(3^{x})) is

[BSEB Board 2018]

**Options:**

A. (2/3)^{x}

B. 2^{x-1}/3^{x-1}

C. (2/3)^{x} log_{3}2

D. (2/3)^{x} log_{2}3

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 21**

If f(x) = sin x + cos x is minimum then value of x is

[BSEB Board 2018]

**Options:**

A. Pi/6

B. Pi/2

C. Pi/3

D. Pi/4

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 22**

If y = log cos x^{2} , then dy/dx at x = has the value is

[BSEB Board 2018]

**Options:**

A. 1

B. Pi/4

C. 0

D.

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 23**

Equation of the tangent to the curve x^{2} + y^{2} = a^{2} at (x_{1}, y_{1}) is

[BSEB Board 2018]

**Options:**

A. xx_{1} – yy_{1} = 0

B. xx_{1} + yy_{1} = 0

C. xx_{1} – yy_{1} = a^{2}

D. xx_{1} + yy_{1} = a^{2}

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 24**

The value of

[BSEB Board 2018]

**Options:**

A. 5a^{4}

B. 5x^{4}

C. 1

D. 0

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 25**

The value of

[BSEB Board 2018]

**Options:**

A. cos x + c

B. sin x + c

C. -cos x – sin x + c

D. sin (x/2) + c

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 26**

The value of

[BSEB Board 2018]

**Options:**

A. + c

B. (1/3) + c

C. + c

D. (1/3) + c

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 27**

The value of

[BSEB Board 2018]

**Options:**

A.

B.

C.

D.

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 28**

The value of

[BSEB Board 2018]

**Options:**

A.

B.

C.

D.

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 29**

If f(-x) = -f(x), then

[BSEB Board 2018]

**Options:**

A.

B. 0

C. 1

D. -1

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 30**

[BSEB Board 2018]

**Options:**

A. 1

B.

C.

D. 0

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 31**

Area between the x-axis and the curve y = sin x from x = 0 to x = Pi/2 is

[BSEB Board 2018]

**Options:**

A. 2

B. -1

C. 1

D. None of These

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 32**

[BSEB Board 2018]

**Options:**

A. 0

B. 1

C. 2

D. 1/2

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 33**

The differential equation

is of order = _______ and degree = _______.

[BSEB Board 2018]

**Options:**

A. Order = 2, Degree = 3

B. Order = 1, Degree = 2

C. Order = 2, Degree = 2

D. None of These

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 34**

Solution of the differential equation ydx – xdy = xydx is

[BSEB Board 2018]

**Options:**

A. y^{2}/2 – x^{2}/2 = xy + c

B. x = kye^{x}

C. x = kye^{x}

D. None of These

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 35**

Integrating factor (I.E.) of differential equation

[BSEB Board 2018]

**Options:**

A. log x

B. x

C. 1/x

D. None of These

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 36**

Solution of

[BSEB Board 2018]

**Options:**

A.

B.

C.

D.

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 37**

If

then the corresponding unit vectors

in the direction of

[BSEB Board 2018]

**Options:**

A.

B.

C.

D. None of These

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 38**

The direction cosines of the vectors

[BSEB Board 2018]

**Options:**

A. 3/13, 4/13, 12/13

B. 3/13, -4/13, 12/13

C. 3/Root(13), 4/Root(13), 12/Root(13)

D. 3/Root(13), -4/Root(13), 12/Root(13)

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 39**

are perpendiculars to each other then the value of x is

[BSEB Board 2018]

**Options:**

A. -2, 5

B. 2, 5

C. -2, -5

D. 2, -5

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 40**

The value of

[BSEB Board 2018]

**Options:**

A.

B. 0

C. 1

D.

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 41**

The direction cosine of y axis are

[BSEB Board 2018]

**Options:**

A. (1, 0, 1)

B. (0, 1, 0)

C. (1/Root(2), 0, 1/Root(2))

D. None of These

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 42**

The equation of the xy-planes is

[BSEB Board 2018]

**Options:**

A. x =0, y = 0

B. z = 0

C. x = y 0

D. None of These

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 43**

If two planes 2x – 4y + 3z = 5 and x + 2y + z = 12 are perpendicular to each other, then =

[BSEB Board 2018]

**Options:**

A. -2

B. 2

C. 3

D. None of These

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 44**

The distance between (4, 3, 7) and (1, -1, -5) is

[BSEB Board 2018]

**Options:**

A. 13

B. 15

C. 12

D. 5

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 45**

If A’ and B’ are independent events, then

[BSEB Board 2018]

**Options:**

A. P(A’B’) = P(A).P(B)

B. P(A’B’) = P(A’) + P(B’)

C. P(A’B’) = P(A’).P(B’)

D. P(A’B’) = P(A’) – P(B’)

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 46**

If events A and B are mutually exclusive, then

[BSEB Board 2018]

**Options:**

A. P(A B) = P(A).P(B)

B. P(A B) = 0

C. P(A B) = 1

D. P(A B) = 0

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 47**

If P(A) = 3/8, P(B) = 1/2 and P(A B) = 1/4, then P(A/B) =

[BSEB Board 2018]

**Options:**

A. 2

B. 1/2

C. 2/3

D. 3/2

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 48**

If A and B are two events such that P(A) 0 and P(B/A) = 1

[BSEB Board 2018]

**Options:**

A. B A

B. A B

C. B =

D. A B =

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 49**

[BSEB Board 2018]

**Options:**

A. log x + log(1 + Root(x)) + C

B. 2 log (1 + Root(x)) + C

C. log (1 + Root(x)) + C

D. log Root(x) + C

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 50**

Solution of

[BSEB Board 2018]

**Options:**

A. 1 – e

B. e – 1

C. e

D. 1

**Solution:**

**Section B (Non-Objective Type Questions)**

Short Answer Type Questions

Question No 1 to 22 are short answer type questions. Each question of this category carries 2 marks. Answer any fifteen (15) questions on your copy.

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 1**

Examine whether the function f: R R one-one (injective) if f is f(x) = x^{3}, x R.

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 2**

Prove that

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 3**

Prove that

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 4**

Find the value of x and y, when

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 5**

Prove that

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 6**

If

, then prove that f(x + y) = f(x).f(y).

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 7**

Find the value of x, such that

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 8**

Find dy/dx, when x = y log(xy)

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 9**

If

, then find dy/dx

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 10**

If , then find dy/dx

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 11**

Integrate

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 12**

Prove that

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 13**

Evaluate

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 14**

Solve (x^{2} – y^{2})dy/dx = 2xy

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 15**

Solve

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 16**

Prove by vector method, that the angle inscribed in a semi-circle is a right angle.

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 17**

If

are three vectors and

prove that

**Solution:**

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 17**

Find the value of p, if

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 19**

Prove by direction numbers, that the point (1, -1, 3), (2, -4, 5) and (5, -13, 11) are in a straight line.

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 20**

Find the distance of the point (4, -5, 6) from the plane

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 21**

If A and B are two independent events then prove that P(A U B) = 1 – P(A’)P(B’)

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 22**

Odds are 8 : 5 against a man, who is 55 years old, living till he is 75 and 4 : 5 against his wife who is now 48, living till she is 68. Find the probability that the couple will be alive 2 years hence.

**Long Answer Type Questions**

Question No 23 to 26 are short answer type questions. Each question of this category carries 5 marks. Each question has an alternative as ”or”. You have to answer each question or its alternative.

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 23**

Find the maximum and minimum values of x^{3} – 2x^{2} + x + 6.

**OR **

If

then prove that dy/dx = y/x

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 24**

Prove that

**OR **

Find the area of the smaller portion of the circle x^{2} + y^{2} = 4 cut off by the line x + y = 2.

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 25**

Prove by vector method, that in any triangle ABC, a/sin A = b/sin B = c/sin C.

**OR **

Show that the line joining the points (4, 7, 8), (2, 3, 4) is parallel to the line joining the points (2, 3, 10), (-2, -4, 2).

**Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 26**

Maximize Z = 7x + 3y subject to x + 2y > = 3y, x + y < = 4, x > = 0, y > = 0.

**OR **

A furniture dealer deals in only two items, table and chair. He has Rs 5000 to invest and space to store at most 60 pieces. A table costs him Rs. 250 and a chair Rs. 50. He can sell a table at a profit of Rs. 50 and a chair at a profit of Rs 15. Assuming that he can sell all the items that he buys, how should he invest his money in order that he may maximize his profit.