Bihar Board 12th Maths Objective Important Questions Part 2 in English

Bihar Board 12th Maths Objective Important Questions Part 2 in English

BSEB 12th Maths Objective Important Questions Part 2 in English

Question 1.
The total revenue in rupees Received from the sale of u unit of a product is given by R(x) = 3x² + 36x + 5, the marginal revenue, when x = 15 is :
(a) 115
(b) 96
(c) 90
(d) 126
Answer:
(d) 126

Question 2.
The interval in which y = x² . e^-x is increasing is :
(a) (-∞, ∞)
(b) (-2,0)
(c) (2 ∞)
(d) (0,2)
Answer:
(d) (0,2)

Question 3.
The liney – x + 1 is a tangent to the curve y² = 4x at the point:
(a) (1,2)
(b) (2, 1)
(c) (1, -2)
(d) (-1, 2)
Answer:
(a) (1,2)

Question 4.
If f(x) = 3x² + 15x + 5, then the approximate value of f(3.02) is :
(a) 47.66
(b) 57.66
(c) 67.66
(d) 77.66
Answer:
(d) 77.66

Question 5.
The approximate change in the volume of a cube of side x metres caused by increasing the side by 3% is :
(a) 0.06 x³m³
(b) 0.6 x³m³
(c) 0.09 x³m³
(d) 0.9 x³m³
Answer:
(c) 0.09 x³m³

Question 6.
The point on the curve x² = 2y which is nearest to the point (0,5) is : V
(a) (2√2,4)
(b) (2√2,0)
(c) (0,0)
(d) (2,2)
Answer:
(a) (2√2,4)

Question 7.
Cylindrical thank of radius 10m is being filled with what at the rate of 314 cubic metre pertions. Then the depth of the sheat is increasing at of the role of:
(a) 1 m³/h
(b) 0.1 m³/m
(c) 1.1
(d) 5 cdt
Answer:
(a) 1 m³/h

Question 8.
The lihe y = mx + I is a tangent to the curve y² = 4x in the value of m is:
(a) 1
(b) 2
(c) 3
(d) 1/2
Answer:
(a) 1

Question 9.
The normal at the point (1,1) on the curve 2y + x2 = 3 is :
(a) x + y = 0
(b) x – y = 0
(c) x + y + 1 = 0
(d) x – y = 0
Answer:
(b) x – y = 0

Question 10.
The normal to the curve x² = 4y passing (1,2) is :
(a) x + y = 3
(b) x – t = 3
(c) y ÷ y = 1
(d) x – y = 1
Answer:
(a) x + y = 3

Question 11.
On which of the following intervals is the function f given by f(x) = x¹⁰⁰ + sin x – 1 Strictly decreasing ?
(a) (0,1)
(b) (π/2, π)
(c) (0, π/2)
(d) None
Answer:
(d) None

Question 12.
∫ e^xsec x (1 + tan x)dx equals :
(a) e^x cosx + c
(b) e^xsecx + c
(c) e^xsinx + c
(d) e^x + tanx + c
Answer:
(b) e^xsecx + c

Question 13.
Area lying in the first quaotrant and bounded by the circle x² + y² = 4 and the lines (x = 0) and x = 2 is to :
(a) π
(b) π/2
(c) π/3
(d) π/4
Answer:
(a) π

Question 14.
Smaller area enclosed by the circle x² + y² = 4 and the line x +y = 2 is;
(a) 2(π-2)
(b) π – 2
(c) 2π – 1
(d) 2(π + 2)
Answer:
(b) π – 2

Question 15.
The number of arbitrary constants in the general solution of a differential equation of fourth order are.
(a) 0
(b) 2
(c) 3
(d) 4
Answer:
(d) 4

Question 16.
The number of arbitrary constants in the particular solution of a differential equation of third order are :
(a) 3
(b) 2
(c) 1
(d) 0
Answer:
(d) 0

Question 17.
Which of the following differential equations has y =x as one crits particular solution ?

Answer:
(c)

Question 18.
Which of the following is a homogeneous differential equation :
(a) (4x + 6y + 5) dy – |3y + 2x + 4| dx = 0
(b) (xy) dx – (x³ + y³) dy = 0
(c) (x³ + 2y²)dx + 2xydy = 0
(d) y²dx + (x² – xy – y³)dy = 0
Answer:
(d) y²dx + (x² – xy – y³)dy = 0

Question 19.
The general solution of the differential equation
e^xdy + (ye^x +2x)dx = 0 is :
(a) xe^x + x² = c
(b) xe^y + y² = c
(c) ye^x + x² = c
(d) ye^y + x² = c
Answer:
(c) ye^x + x² = c

Question 20.
The planes 2x – y + 4z = 5 and Sx – 2.5y + 10z = 6 are :
(a) perpendicular
(b) parallel
(c) intersect y-axis
(d) passes through (0, 0, 5/4)
Answer:
(b) parallel

Question 21.
Distance between the two planes 2x + 3 y +-4z = 4 and 4x + 6y + 8x = 12 is
(a) 2 units
(b) 4 units
(c) 8 units
(d) 9 units
Answer:
(d) 9 units

Question 22.
The solution set of the in equation 2x + y > 5 is :
(a) half plane that contains the origin
(b) open half plane not containing the origin
(c) when xy-plane except the reints lying on the live 2x + y = 5
(d) none of these
Answer:
(b) open half plane not containing the origin

Question 23.
Which of the following is not a convex set ?
(a) {(x, y)/2x + 5y < 7}
(b) {(x,y)/x² + y² ≤ 4} .
(c) {x/ |x| = 5}
(d) {(x,y)/3x² + 2y ≤ b
Answer:
(c) {x/ |x| = 5}

Question 24.
The reints of which the maximum value of x + y. Subject to the constraints x + 2y ≤ 70, 2x + y ≤ 95,x,y ≥ 0 is obtained is :
(a) (30,25)
(b) (20,35)
(c) (35,20)
(d) (40,15)
Answer:
(d) (40,15)

Question 25.
Objective function of a LPP is :
(a) a constraint
(b) a function to be optimized
(c) a relation b/w the variables
(d) none of these
Answer:
(b) a function to be optimized

Question 26.
If Aand B are two events such that P(A) ≠ 0 and P(B/A) = then :
(a ) A⊂B
(b ) B⊂A
(c) B = Φ
(d) A = Φ
Answer”
(a ) A⊂B

Question 27.
If P(B/A)>P(A) then which of the following is correct:
(a) P(B / A) < P(B)
(b) P(AnB) < P(A) P(B) (c) P(B/ A) > P(B)
(d) P(B/A) = P(B)
Answer:
(c) P(B/ A) > P(B)

Question 28.
Two events A and B will be independent, if:
(a) A and B are mutually exclusive
(b) P(A’B’)=[1-P(A)][1-P(B)]
(c )P(A) = P(B)
(d) P(A) + P(B) = 1
Answer:
(b) P(A’B’)=[1-P(A)][1-P(B)]

Question 29.
If A and B are any two events such that P(A) + P(B) – P (A and B) = P(A), the ;
(a) P(B/A) = 1
(b) P(A/B) = 1
(c) P(B/A) = 0
(d) P(A/B) = 0
Answer:
(b) P(A/B) = 1

Question 30.
The mean of the numbers of obtained on throwing a die having written. I on three facems, 2 on two faces and 5 on one face is :
(a) 1
(b) 2
(c) 5
(d) 8/3
Answer:
(b) 2

Question 31.
dy – dx = y – x hindi
(a) y + x = k
(b) y – x = k
(c) y/x = k
(d) xy = k
Answer:
(b) y – x = k