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 Bihar Board 12th Maths VVI Objective Questions Model Set 3 in English

Bihar Board 12th Maths VVI Objective Questions Model Set 3 in English

Question 1.

Answer:
(a) π4

Question 2.
The slope of the tangent to the curve X = t2 + 3t – 8, Y = 2t2 – 2t – 5 at the point (2, -1) is
(a) 127
(b) −67
(c) 67
(d) −127
Answer:
(c) 67

Question 3.
The modulus of the vector 191→+5J⃗ −6k⃗  is
(a) √322
(b) √420
(c) √421
(d) √422
Answer:
(d) √422

Question 4.
∫π20cosxdx=?
(a) -1
(b) 1
(c) π2
(d) 0
Answer:
(a) -1

Question 5.
The direction cosines of z-axis are
(a) (0, 0, 0)
(b) (1, 0, 0)
(c) (0, 1, 0)
(d) (0, 0, 1)
Answer:
(d) (0, 0, 1)

Question 6.

Answer:
(a) 11−x2√

Question 7.
K⃗ ×K⃗ =?
(a) 1
(b) -1
(c) K2
(d) 0
Answer:
(d) 0

Question 8.
Integrating factor of the differential equation dydx + Y sec x = tan x is
(a) sec x + tan x
(b) sec x – tan x
(c) sec x
(d) tan x sec x
Answer:
(c) sec x

Question 9.
Intergrating factor (I.F) of the differential equation dydx + Y cos x = sin x cos x is
(a) e-sin x
(b) esin x
(c) e-cos x
(d) ecos x
Answer:
(c) ecos x

Question 10.

Answer:
(d) 58

Question 12.
If f(x1) = f(x2) ⇒ x1 = x2 ∀ x1, x2 ∈ A, then what type of a function is f : A → B ?
(a) One-one
(b) Constant
(c) Onto
(d) Many one
Answer:
(a) One-one

Question 13.
(a⃗ ×a⃗ )⋅b⃗ =?
(a) 1
(b) -1
(c) 2
(d) 0
Answer:
(d) 0

Question 14.

Answer:
(a) 0

Question 15.
P(A) + P(A’) = ?
(a) 0
(b) 1
(c) -1
(d) P(E)
Answer:
(b) 1

Question 16.
a⃗ ⋅b⃗ =?
(a) −b⃗ ⋅a⃗ 
(b) 1
(c) -1
(d) b⃗ ⋅a⃗ 
Answer:
(d) b⃗ ⋅a⃗ 

Question 17.
sin−11x=?
(a) sex-1 x
(b) cosec-1 x
(c) tan-1 x
(d) sin x
Answer:
(b) cosec-1 x

Question 18.

Answer:
(b) xn+1n+1+k

Question 19.
ddx [tan x] = ?
(a) sec2 x
(b) sec x
(c) cot x
(d) -sec2 x
Answer:
(a) sec2 x

Question 20.

Answer:
(c) ⎡⎣⎢123456⎤⎦⎥

Question 23.
P(A∪B) = ?
(a) P(A) + P(B) + P(A∩B)
(b) P(A) – P(B) – P(A∩B)
(c) P(A) + P(B) – P(A∩B)
(d) P(A) – P(B) + P(A∩B)
Answer:
(c) P(A) + P(B) – P(A∩B)

Question 24.
The value of x when [x4154]=0 is
(a) 15
(b) -15
(c) 4
(d) 4x
Answer:
(a) 15

Question 25.
∫cosec2 x dx = ?
(a) tan x + c
(b) -cot x + c
(c) 2cosec x + c
(d) -cosec x + 2
Answer:
(b) -cot x + c

Question 26.
ddx [sin2 x] = ?
(a) 2 sin x cos x
(b) 2 sin x
(c) cos2 x
(d) sin x cos x
Answer:
(a) 2 sin x cos x

Question 27.
The distance of the point (3, 4, 5) from x-axis is
(a) 3
(b) 5
(c) √41
(d) None of these
Answer:
(c) √41

Question 28.
In the set of all straight lines in a plane, the relation R to be Perpendicular is
(a) Reflexive and transitive
(b) Symmetric and transitive
(c) Symmetric
(d) None of these
Answer:
(c) Symmetric

Question 29.
Which of the following is a homogenous differential equation?
(a) x2y dx – (x3 + y3) dy = 0
(b) (xy) dx – (x4 + y4) dy = 0
(c) (2x + y – 3) dy – (x + 2y – 3) dx = 0
(d) (x – y) dy = (x2 + y + 1) dx
Answer:
(c) (2x + y – 3) dy – (x + 2y – 3) dx = 0

Question 30.
Evaluate [1y−1x]
(a) x + y
(b) x – y
(c) -y – x
(d) 1 – x
Answer:
(d) 1 – x

Question 31.
The value of the determinant ⎡⎣⎢111234469⎤⎦⎥ is
(a) 1
(b) -1
(c) 0
(d) 2
Answer:
(a) 1

Question 32.
The operation * is defined as a * b = 2a + b, then (2 * 3) * 4 is
(a) 18
(b) 17
(c) 19
(d) 21
Answer:
(d) 21

Question 33.
Which of the following is the unit matrix of order 3 × 3?

Answer:
(b) ⎡⎣⎢100010001⎤⎦⎥

Question 34.
∫dx1+x2=?
(a) tan x + c
(b) tan2 x + c
(c) cot x + c
(d) -cot-1 x + c
Answer:
(c) cot x + c

Question 35.
∫dx1+x2=?
(a) tan x + c
(b) tan2 x + c
(c) cot x + c
(d) -cot-1 x + c
Answer:
(a) tan x + c

Question 36.
P(E) = ?
(a) n(E) + n(s)
(b) n(s)n(E)
(c) n(E) – n(s)
(d) n(E)n(s)
Answer:
(a) n(E) + n(s)

Question 37.

Answer:
(b) 0

Question 39.
∫sec x dx = ?
(a) log|sec x| + c
(b) log |sec x + tan x| + c
(c) log |sec x -tan x| + c
(d) sec x tan x + c
Answer:
(b) log |sec x + tan x| + c

Question 40.
The order of the differential equation d2ydx2+x3(dydx)3=x4 is
(a) 1
(b) 2
(c) 4
(d) 3
Answer:
(b) 2

Question 41.

Answer:
(c) log12

Question 42.
f: A → B will be an onto function of
(a) f(A) ⊂ B
(b) f(A) = B
(c) f(A) ⊃ B
(d) f(A) ≠ B
Answer:
(b) f(A) = B

Question 43.

Answer:
(a) b3−a33

Question 44.

Answer:
(b) [27253610]

Question 47.
tan-1 x + cot-1 x = ?
(A) 0
(B) 1
(c) π2
(d) −π2
Answer:
(c) π2

Question 48.

Answer:
(d) xi⃗ +yj⃗ +zk⃗ 

Question 50.

(a) (x = -2, y = 8)
(b) (x = 2, y = n – 8)
(c) (x = 3, y = -6)
(d) (x = -3, y = 6)
Answer:
(b) (x = 2, y = n – 8)