Bihar Board Solutions: Bihar Board 12th Maths VVI Objective Questions Model Set 2 in English
Bihar Board Solutions: Bihar Board 12th Maths VVI Objective Questions Model Set 2 in English
Bihar Board Solutions: Bihar Board 12th Maths VVI Objective Questions Model Set 2 in English
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Answer:
﴾b﴿ 1
Question 2.
Answer:
﴾b﴿ 1
Question 3.
Answer:
﴾b﴿ ‐2
Question 4.
Answer:
﴾c﴿ ‐1
Question 5.
Answer:
﴾d﴿ ‐﴾x3 + y3﴿2
Question 6.
Answer:
﴾c﴿ a + c = ‐1, b ∈ R
Question 7.
Answer:
﴾c﴿ − 12
Question 8.
Question 9.
﴾a﴿ continuous at x = 1
﴾b﴿ differentiable at x = 1
﴾c﴿ continuous at x = ‐3
﴾d﴿ All of these
Answer:
﴾d﴿ All of these
Question 10.
Question 10.
If f (x) = , x ≠ 0 be continuous at x = 0, then f﴾0﴿ =
√4+x−2
﴾a﴿ 1
﴾b﴿ 1
﴾c﴿ 2
﴾d﴿ 2
3
Answer:
﴾b﴿ 14
Question 11.
Moving along the x‐axis there are two points with x = 10 + 6t, x = 3 + t2. The speed
with which they are reaching from each other at the time of encounter is ﴾x is an cm and
t is in seconds﴿
﴾a﴿ 16 cm/s
﴾b﴿ 20 cm/s
﴾c﴿ 8 cm/s
﴾d﴿ 12 cm/s
Answer:
﴾c﴿ 8 cm/s
Question 12.
A particle is moving along the curve x = at2 + bt + c. If ac = b2, then particle would be
moving with uniform
﴾a﴿ rotation
﴾b﴿ velocity
﴾c﴿ acceleration
﴾d﴿ retardation
Answer:
﴾c﴿ acceleration
Question 13.
The distance ‘s’ metres covered by a body in t seconds, is given by s = 3t2 – 8t + 5. The
body will stop after
﴾a﴿ 1 s
﴾b﴿ 34 s
﴾c﴿ 4
3
s
﴾d﴿ 4 s
Answer:
﴾c﴿ 43 s
Question 14.
The position of a point in time ‘t’ is given by x = a + bt – ct2, y = at + bt2. Its
acceleration at time ‘t’ is
﴾a﴿ b – c
﴾b﴿ b + c
﴾c﴿ 2b – 2c
−−− −−−
﴾d﴿ 2√b2 + c2
Answer:
−−− −−−
﴾d﴿ 2√b2 + c2
Question 15.
The function f﴾x﴿ = log ﴾1 + x﴿ – 2x
2+x
﴾a﴿ ﴾‐1, ∞﴿
﴾b﴿ ﴾‐∞, 0﴿
﴾c﴿ ﴾‐∞, ∞﴿
﴾d﴿ None of these
Answer:
﴾a﴿ ﴾‐1, ∞﴿
Question 16.
Answer:
﴾d﴿ loge﴾10x + x10﴿ + C
Question 17.
Answer:
x
﴾a﴿
2
1 2
2 + C
3
(log 2)
Question 18.
Question 18.
Answer:
4
﴾b﴿ −
cos x
+ C
4
Question 19.
Answer:
﴾a﴿
−3
+ C
3
√sin x
Question 20.
Answer:
﴾b﴿ − 5 tan5/3 x +
3 3 11/3
tan x + C
11
Question 21.
The area bounded by the curve 2x2 + y2 = 2 is
﴾a﴿ π sq. units
﴾b﴿ √2 π sq. units
﴾c﴿ π
2
sq. units
﴾d﴿ 2π sq. units
Answer:
﴾b﴿ √2 π sq. units
Question 22.
2 2
2
+ 2
= 1
a b
Answer:
﴾c﴿ πab sq. units
Question 23.
Area of the region bounded by y = |x|, x ≤ 5 in the first quadrant is
﴾a﴿ 11
2
sq. units
﴾b﴿ 17
2
sq. units
﴾c﴿ 25
2
sq. units
﴾d﴿ 27
2
sq. units
Answer:
﴾c﴿ 25
2
sq. units
Question 24.
−− −−−−
Determine the area under the curve y 2
= √a − x
2
included between the lines x = 0
and x = a.
a
﴾a﴿ 4
πa
﴾b﴿
πa
4
2
﴾c﴿
πa
﴾a﴿ 4
πa
Question 25.
2
Question 26.
The order of the differential equation whose general solution is given by
y = ﴾C1 + C2﴿ cos﴾x + C3﴿ – C4ex+C5
Question 27.
The order of the differential equation whose general solution is given by y = ﴾A + B﴿ cos
﴾x + C﴿ + Dex is
﴾a﴿ 4
﴾b﴿ 3
﴾c﴿ 2
﴾d﴿ 1
Answer:
﴾b﴿ 3
Question 28.
Find the magnitude of vector 3^i + 2^ ^
j + 12k
﴾a﴿ √157
﴾b﴿ 4√11
﴾c﴿ √213
﴾d﴿ 9√3
Answer:
﴾a﴿ √157
Direction ﴾29﴿ : Study the given parallelogram and answer the following questions.
Question 29.
Which of the following represents equal vectors?
﴾a﴿ a, c
﴾b﴿ b, d
﴾c﴿ b, c
﴾d﴿ m, d
Answer:
﴾b﴿ b, d
Question 30.
The cosines of the angle between any two diagonals of a cube is
﴾a﴿ 13
﴾b﴿ 1
﴾c﴿ 2
﴾d﴿ 1
√3
Answer:
﴾a﴿ 13
Question 31.
Which of the following is false?
﴾a﴿ 30°, 45°, 60° can be the direction angles of a line is space.
﴾b﴿ 90°, 135°, 45° can be the direction angles of a line is space.
﴾c﴿ 120°, 60°, 45° can be the direction angles of a line in space.
﴾d﴿ 60°, 45°, 60° can be the direction angles of a line in space.
Answer:
﴾a﴿ 30°, 45°, 60° can be the direction angles of a line is space.
Question 32.
The optimal value of the objective function is attained at the points
﴾a﴿ on X‐axis
﴾b﴿ on Y‐axis
﴾c﴿ which are corner points of the feasible region
﴾d﴿ none of these
Answer:
﴾c﴿ which are corner points of the feasible region
Question 33.
Which one of the following is the order of the differential equation
2 2
?
d y dy
3 4
+ x ( ) = x
2
dx dx
﴾a﴿ 1
﴾b﴿ 2
﴾c﴿ 3
﴾d﴿ 0
Answer:
﴾b﴿ 2
Question 34.
If two events A and B area such that P﴾A
¯
﴿ = 0.3, P﴾b﴿ = 0.4 and P (B|A ∪ B
¯
) =
﴾a﴿ 21
﴾b﴿ 1
﴾c﴿ 2
﴾d﴿ 1
Answer:
﴾d﴿ 14
Question 35.
If E and F are events such that 0 < P﴾F﴿ < 1, then
﴾a﴿ P﴾E|F﴿ + P﴾Ē |F﴿ = 1
﴾b﴿ P﴾E|F﴿ + P﴾E|F¯ ﴿ = 1
﴾c﴿ P﴾Ē |F﴿+ P﴾E|F¯ ﴿ = 1
﴾d﴿ P﴾E|F¯ ﴿ + P﴾Ē |F﴿ = 0
Answer:
﴾a﴿ P﴾E|F﴿ + P﴾Ē |F﴿ = 1
Question 36.
Let R be a relation in N defined by R= {﴾1 + x, 1 + x2﴿ : x ≤ 5, x ∈ N﴿. Which of the
following is false?
﴾a﴿ R = {﴾2, 2﴿, ﴾3, 5﴿, ﴾4, 10﴿, ﴾5, 17﴿, ﴾6, 25﴿}
﴾b﴿ Domain of R = ﴾2, 3, 4, 5, 6﴿
﴾c﴿ Range of R = {2, 5, 10, 17, 26}
﴾d﴿ None of these
Answer:
﴾a﴿ R = {﴾2, 2﴿, ﴾3, 5﴿, ﴾4, 10﴿, ﴾5, 17﴿, ﴾6, 25﴿}
Question 37.
The relation R = {﴾1, 1﴿, ﴾2, 2﴿, ﴾3, 3﴿, ﴾1, 2﴿, ﴾2, 3﴿, ﴾1, 3﴿} on set A = {1, 2, 3} is
﴾a﴿ Reflexive but not symmetric
﴾b﴿ Reflexive but not transitive
﴾c﴿ Symmetric and transitive
﴾d﴿ Neither symmetric nor transitive
Answer:
﴾a﴿ Reflexive but not symmetric
Question 38.
Let P = {﴾x, y﴿ | x2 + y2 = 1, x, y ∈ R}. Then, P is
﴾a﴿ Reflexive
﴾b﴿ Symmetric
﴾c﴿ Transitive
﴾d﴿ Anti‐symmetric
Answer:
﴾b﴿ Symmetric
Question 39.
For real numbers x and y. we write xRy ⇔ x – y + √2.
﴾a﴿ Reflexive
﴾b﴿ Symmetric
﴾c﴿ Transitive
﴾d﴿ None of these
Answer:
﴾a﴿ Reflexive
Question 40.
Let L denote the set of all straight lines in a plane. Let a relation R be defined by αRβ ⇔
α ⊥ β, α, β ∈ L. Then, R is
﴾a﴿ Reflexive only
﴾b﴿ Symmetric only
﴾c﴿ Transitive only
﴾d﴿ None of these
Answer:
﴾b﴿ Symmetric only
Question 41.
Answer:
﴾b﴿ π
Question 42.
Answer:
﴾b﴿ 3
π
Question 43.
Answer:
﴾a﴿ π4
Question 44.
Answer:
﴾b﴿ 4
3π
Question 45.
Answer:
﴾d﴿ 2π
3
Question 46.
x + y 2x + z 4 7
If [ ] = [ ] , then the values of x, y, z and w respectively are
x − y 2z + w 0 10
﴾a﴿ 2, 2, 3, 4
﴾b﴿ 2, 3, 1, 2
﴾c﴿ 3, 3, 0, 1
﴾d﴿ None of these
﴾d﴿ None of these
Answer:
﴾a﴿ 2, 2, 3, 4
Question 47.
a + b 2 6 2
If [ ] = [ ] , then find the values of a and b respectively
5 ab 5 8
﴾a﴿ 2, 4
﴾b﴿ 4, 2
﴾c﴿ Both ﴾a﴿ & ﴾b﴿
﴾d﴿ None of these
Answer:
﴾c﴿ Both ﴾a﴿ & ﴾b﴿
Question 48.
For what values of x and y are the following matrices equal?
﴾a﴿ 2, 3
﴾b﴿ 3, 4
﴾c﴿ 2, 2
﴾d﴿ 3, 3
Answer:
﴾c﴿ 2, 2
Question 49.
Find the values of a, b, c and d respectively if
﴾a﴿ 1, 3, 9, 8
﴾b﴿ 1, 2, 3, 4
﴾c﴿ 1, 4, 8, 10
﴾d﴿ 1, 5, 6, 7
Answer:
﴾b﴿ 1, 2, 3, 4
Question 50.
then find the values of a, b, c, x, y and z respectively.
﴾a﴿ ‐2, ‐7, ‐1, ‐3, ‐5, 2
﴾b﴿ 2, 7, 1, 3, 5, ‐2
﴾c﴿ 1, 3, 4, 2, 8, 9
﴾d﴿ ‐1, 3, ‐2, ‐7, 4, 5
Answer:
﴾a﴿ ‐2, ‐7, ‐1, ‐3, ‐5, 2
Class 12
Bihar Board 12th Maths VVI Objective Questions Model Set 1 in English
Bihar Board 12th Maths VVI Objective Questions Model Set 3 in English
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