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 Bihar Board 12th Maths VVI Objective Questions Model Set 2 in English

Bihar Board 12th Maths VVI Objective Questions Model Set 2 in English

Question 1.

Answer:
(b) 1

Question 2.

Answer:
(b) 1

Question 3.

Answer:
(d) -(x3 + y3)2

Question 6.

(a) continuous at every x except x = 0
(b) discontinuous at every x except x = 0
(c) continuous everywhere
(d) discontinuous everywhere
Answer:
(b) discontinuous at every x except x = 0

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.
If f(x)=4+x√−2x, x ≠ 0 be continuous at x = 0, then f(0) =
(a) 12
(b) 14
(c) 2
(d) 32
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) 43 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) 2b2+c2−−−−−−√
Answer:
(d) 2b2+c2−−−−−−√

Question 15.
The function f(x) = log (1 + x) – 2x2+x
(a) (-1, ∞)
(b) (-∞, 0)
(c) (-∞, ∞)
(d) None of these
Answer:
(a) (-1, ∞)

Question 16.

Answer:
(d) loge(10x + x10) + C

Question 17.

Answer:
(a) −3sinx√3+C

Question 20.

Answer:
(b) −35tan5/3x+311tan11/3x+C

Question 21.
The area bounded by the curve 2x2 + y2 = 2 is
(a) π sq. units
(b) √2 π sq. units
(c) π2 sq. units
(d) 2π sq. units
Answer:
(b) √2 π sq. units

Question 22.
Area of the ellipse x2a2+y2b2=1 is
(a) 4πab sq. units
(b) 2πab sq. units
(c) πab sq. units
(d) πab2 sq. units
Answer:
(c) πab sq. units

Question 23.
Area of the region bounded by y = |x|, x ≤ 5 in the first quadrant is
(a) 112 sq. units
(b) 172 sq. units
(c) 252 sq. units
(d) 272 sq. units
Answer:
(c) 252 sq. units

Question 24.
Determine the area under the curve y=a2−x2−−−−−−√ included between the lines x = 0 and x = a.
(a) πaa4
(b) πa34
(c) πa28
(d) None of these
Answer:
(a) πaa4

Question 25.
The area enclosed by curve x225+y216=1 is
(a) 10π sq. units
(b) 20π sq. units
(c) 5π sq. units
(d) 4π sq. units
Answer:
(b) 20π sq. units

Question 26.
The order of the differential equation whose general solution is given by
y = (C1 + C2) cos(x + C3) – C4ex+C5
where C1, C2, C3, C4, C5 are arbitrary constant, is
(a) 5
(b) 4
(c) 3
(d) 2
Answer:
(c) 3

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 3i^+2j^+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) 12
(c) 23
(d) 13√
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 d2ydx2+x3(dydx)2=x4?
(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) 12
(b) 13
(c) 25
(d) 14
Answer:
(d) 14

Question 35.
If E and F are events such that 0 < P(F) < 1, then
(a) P(E|F) + P(E¯|F) = 1
(b) P(E|F) + P(E|F¯) = 1
(c) P(E¯|F)+ P(E|F¯) = 1
(d) P(E|F¯) + P(E¯|F) = 0
Answer:
(a) P(E|F) + P(E¯|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) π3

Question 42.

Answer:
(d) 2π3

Question 46.
If [x+yx−y2x+z2z+w]=[40710], then the values of x, y, z and w respectively are
(a) 2, 2, 3, 4
(b) 2, 3, 1, 2
(c) 3, 3, 0, 1
(d) None of these
Answer:
(a) 2, 2, 3, 4

Question 47.
If [a+b52ab]=[6528], then find the values of a and b respectively
(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