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 Bihar Board 12th Maths Objective Answers Chapter 9 Differential Equations

Bihar Board 12th Maths Objective Answers Chapter 9 Differential Equations

Question 1.
The order of the differential equation of all tangent lines to the parabola y = x2 is
(a) 1
(b) 2
(c) 3
(d) 4
Answer:
(a) 1

Question 2.
The differential equation of all parabolas whose axis of symmetry is along the axis of the x-axis is of order
(a) 3
(b) 1
(c) 2
(d) none of these
Answer:
(c) 2

Question 3.
The degree of the equation satisfying the relation 1+x2−−−−−√+1+y2−−−−−√=λ(1+y2−−−−−√−y1+x2−−−−−√) is
(a) 1
(b) 2
(c) 3
(d) none of these
Answer:
(a) 1

Question 4.
The degree of the differential equation (d2ydx2)2/3+4−3dydx=0 is
(a) 2
(b) 1
(c) 3
(d) none of these
Answer:
(a) 2

Question 5.
The differential equation whose solution is (x – h)2 + (y – k)2 = a2 is (a is a constant)

Answer:
(b) [1+(dydx)2]3=a2(d2ydx2)2

Question 6.
The differential equation satisfied by y = Ax + B is (A, B are parameters)
(a) x2 y1 = y
(b) xy1 + 2y2 = 0
(c) xy2 + 2y1 = 0
(d) none of these
Answer:
(c) xy2 + 2y1 = 0

Question 7.
The differential equation whose solution represents the family xy = Aeax + Be-ax

Answer:
(c) xd2ydx2+2dydx=a2xy

Question 8.
The differential equation having solution is y = 17ex + ae-x is
(a) y” – x = 0
(b) y” – y = 0
(c) y’ – y = 0
(d) y’ – x = 0
Answer:
(b) y” – y = 0

Question 9.
The solution of a differential equation is y = c1e4x + c2e3x, the differential equation is given by

Answer:
(b) dydx=1+y21+x2

Question 11.
The differential equation of all ‘Simple Harmonic Motions’ of given period 2πn is

Answer:
(b) d2xdt2+n2x=0

Question 12.
The differential equation of all parabolas whose axes are parallel to y-axis is

Answer:
(a) dydx=−c2x2

Question 13.
The differential equation of all non-horizontal lines in a plane is

Answer:
(b) d2xdy2=0

Question 14.
The differential equation of all circles which pass through the origin and whose centre lies on y-axis is

Answer:
(a) (x2−y2)dydx−2xy=0

Question 15.
The differential equation of the family of circles touching the x-axis at origin is given by

Answer:
(b) y′=2xyx2−y2

Question 16.
The differential equation representing the family of ellipses with centre at origin and foci on x-axis is given as
(a) xy’ + y = 0
(b) x2y2(y”)2 + yy’= 0
(c) xyy” + x(y’)2 – yy’ = 0
(d) None of these
Answer:
(b) x2y2(y”)2 + yy’= 0

Question 17.
The differential equation of all parabolas whose axes are along x-axis is
(a) y22+y1=0
(b) y21+y2=0
(c) y21+y1y2=0
(d) y21+yy2=0
Answer:
(d) y21+yy2=0

Question 18.
The equation of family of curves for which the length of the normal is equal to the radius vector is
(a) y2∓x2=k2
(b) y±x=k
(c) y2 = kx
(d) none of these
Answer:
(a) y2∓x2=k2

Question 19.
The solution of the differential equation dydx=x2+y2+12xy satisfying (1) = 1, is
(a) a hyperbola
(b) a circle
(c) y2 = x(1 + x) – 10
(d) (x – 2)2 + (y – 3)2 = 5xy
Answer:
(a) a hyperbola

Question 20.
Given the differential equation dydx=6x22y+cosy; y(1) = π
Mark out the correct statement.
(a) solution is y2 – sin y = -2x3 + C
(b) solution is y2 + sin y = 2x3 + C
(c) C = π2+ 2√2
(d) C = π2 + 2
Answer:
(b) solution is y2 + sin y = 2x3 + C

Question 21.
For the differential equation xdydx+2y=xydydx,
(a) order is 1 and degree is 1
(b) solutio is ln(yx2) = C – y
(c) order is 1 and degree is 2
(d) solution is ln(xy2) = C + y
Answer:
(a) order is 1 and degree is 1

Question 22.
The particular solution In(dydx) = 3x + 4y, y(0) = 0 is
(a) e3x + 3e-4y = 4
(b) 4e3x – 3e-4y = 3
(c) 3e3x + 4e4y = 7
(d) 4e3x + 3e-4y = 7
Answer:
(d) 4e3x + 3e-4y = 7

Question 23.
The solution of the differential equation

Answer:
(d) None of these

Question 25.
The solution of the differential equation

Answer:
(b) cey/2

Question 27.
If ydx – xdy + ln x dx = 0, y(1) = -1, then
(a) y + 1 + ln x = 0
(b) y + 1 + 2 ln x = 0
(c) 2(y + 1) + lnx = 0
(d) y + 1 – y ln x = 0
Answer:
(a) y + 1 + ln x = 0

Question 28.
The differential equation dydx=1−y2y−−−−√ determines a family of circle with
(a) variable radii and fixed centre (0, 1)
(b) variable radii and fixed centre (0, -1)
(c) fixed radius 1 and variable centre on x-axis
(d) fixed radius 1 and variable centre on y-axis
Answer:
(c) fixed radius 1 and variable centre on x-axis

Question 29.
If y dx + y2 dy = x dy, x ∈ R, y > 0 and y(1) = 1, then y(-3) =
(a) 3
(b) 2
(c) 1
(d) 5
Answer:
(a) 3

Question 30.
The solution of y dx + (x + x2y) dy = 0 is

Answer:
(b) −1xy+lny=c

Question 31.
If (x + y)2 dydx = a2, y = 0 when x = 0, then y = a if xa =
(a) 1
(b) tan 1
(c) tan 1 + 1
(d) tan 1 – 1
Answer:
(d) tan 1 – 1

Question 32.

Answer:
(a) ex – 1

Question 33.
If sinx dydx + y cosx = x sinx, then (y – 1) sinx =
(a) c – x sinx
(b) c + xcosx
(c) c – x cos x
(d) c + x sin x
Answer:
(c) c – x cos x

Question 34.
The solution of the differential equation

Answer:
(c) ey=x33+ex+c

Question 35.
The solution of the differential equation xdy + ydx = xydx when y(1) = 1 is

Answer:
(b) exex

Question 36.
The solution of differential equation (ey + 1) cosx dx + ey sinx dy = 0 is
(a) (ey + 1) sinx = c
(b) ex sinx = c
(c) (ex + 1) cosx = c
(d) none of these
Answer:
(a) (ey + 1) sinx = c

Question 37.
The solution of the differential equation dydx=x1+x2 is

Answer:
(a) y = e sin2x

Question 40.
The general solution of the differential equation dydx=x2y2 is
(a) x3 – y3 = c
(b) x3 + y3 = c
(c) x2 + y2 = c
(d) x2 – y2 = c
Answer:
(a) x3 – y3 = c

Question 41.
The Solution of cos(x + y) dy = dx is

Answer:
(c) √3e

Question 44.

Answer:
(d) secyx=cxy

Question 47.

Answer:
(a) xy=cey/x

Question 50.

Answer:
(c) Circle

Question 51.

Answer:
(b) c=xy+x22

Question 54.
The solution of differential equation dydx=x−yx+y is
(a) x2 – y2 + 2xy + c = 0
(b) x2 – y2 – xy + c = 0
(c) x2 – y2 + xy + c = 0
(d) x2 – y2 – 2xy + c = 0
Answer:
(d) x2 – y2 – 2xy + c = 0

Question 55.

Answer:
(c) e2+14

Question 57.

Answer:
(d) 6

Question 58.

Answer:
(d) 14

Question 61.

Answer:
(b) y=1+x2√x+cx

Question 63.

Answer:
(c) ye−3x=−e−3x(2cos2x+3sin2x)13+c

Question 64.

Answer:
(a) y=sin1x−cos1x

Question 66.
The degree of the differential equation

(a) 1
(b) 2
(c) 3
(d) not defined
Answer:
(d) not defined

Question 67.
The order and degree of the differential equation d2ydx2+(dydx)14+x15=0 respectively are
(a) 2 and not defined
(b) 2 and 2
(c) 2 and 3
(d) 3 and 3
Answer:
(a) 2 and not defined

Question 68.
The differential equation for y = A cos αx + B sin αx, where A and B are arbitrary constants is

Answer:
(c) 1−x2−−−−−√

Question 70.
Integrating factor of the differential equation dydx + y tanx – sec x = 0 is
(a) cos x
(b) sec x
(c) ecos x
(d) esec x
Answer:
(b) sec x

Question 71.
The solution of the differential equation dydx=1+y21+x2 is
(a) y = tan-1 x
(b) y – x = k(1 + xy)
(c) x = tan-1 y
(d) tan(xy) = k
Answer:
(b) y – x = k(1 + xy)

Question 72.
The solution of the differential equation cos x sin y dx + sin x cos y dy = 0 is
(a) sinxsiny=c
(b) sin x sin y = c
(c) sin x + sin y = c
(d) cos x cos y = c
Answer:
(b) sin x sin y = c

Question 73.

Answer:
(c) ey=ex2+c

Question 74.
Which of the following is the general solution of

Answer:
(a) y(1+x2)=c+tan−1x