Bihar Board Previous Year Question Papers With Solutions Class 12 Math
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 Math 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 Math 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 Math: 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 Math: Ques No 2
Let A = {1, 2, 3}, which of the following functions f: A
[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 Math: 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’ = I2 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 A2 = A, then (A + I3)3 – 7A is equal to
[BSEB Board 2018]
Options:
A. I3
B. A
C. 3A
D. I3 – 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 x2y2 = (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(2x))/(d(3x)) is
[BSEB Board 2018]
Options:
A. (2/3)x
B. 2x-1/3x-1
C. (2/3)x log32
D. (2/3)x log23
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 x2 , 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 x2 + y2 = a2 at (x1, y1) is
[BSEB Board 2018]
Options:
A. xx1 – yy1 = 0
B. xx1 + yy1 = 0
C. xx1 – yy1 = a2
D. xx1 + yy1 = a2
Solution:
Bihar Board Previous Year Question Papers With Solutions Class 12 Maths: Ques No 24
The value of
[BSEB Board 2018]
Options:
A. 5a4
B. 5x4
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. y2/2 – x2/2 = xy + c
B. x = kyex
C. x = kyex
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) = x3, 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 (x2 – y2)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 x3 – 2x2 + 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 x2 + y2 = 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.