Question 1. The order of the differential equation of all tangent lines to the parabola y = x^{2} is

 (a) 1
(b) 2
(c) 3
(d) 4
 (a) 1
Answer: (a) 1
Question 2. The differential equation of all parabolas whose axis of symmetry is along the axis of the xaxis is of order

 (a) 3
(b) 1
(c) 2
(d) none of these
 (a) 3
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
 (a) 1
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 thes
 (a) 2
Answer: (a) 2
Question 5. The differential equation satisfied by y = Ax + B is (A, B are parameters)

 (a) x^{2} y_{1} = y
(b) xy_{1} + 2y_{2} = 0
(c) xy_{2} + 2y_{1} = 0
(d) none of these
 (a) x^{2} y_{1} = y
Answer: (c) xy_{2} + 2y_{1} = 0
Question 6. The differential equation having solution is y = 17e^{x} + ae^{x} is

 (a) y” – x = 0
(b) y” – y = 0
(c) y’ – y = 0
(d) y’ – x = 0
 (a) y” – x = 0
Answer: (b) y” – y = 0
Question 7. The differential equation of all nonhorizontal lines in a plane is
Answer: (b) d2xdy2=0
Question 8. The differential equation representing the family of ellipses with centre at origin and foci on xaxis is given as

 (a) xy’ + y = 0
(b) x^{2}y^{2}(y”)^{2} + yy’= 0
(c) xyy” + x(y’)^{2} – yy’ = 0
(d) None of these
 (a) xy’ + y = 0
Answer: (b) x^{2}y^{2}(y”)^{2} + yy’= 0
Question 9. The differential equation of all parabolas whose axes are along xaxis is

 (a) y22+y1=0
(b) y21+y2=0
(c) y21+y1y2=0
(d) y21+yy2=0
 (a) y22+y1=0
Answer: (d) y21+yy2=0
Bhar Board 12th math chapter 9 most mcq solution
Question 10. 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) y^{2} = kx
(d) none of these
 (a) y2∓x2=k2
Answer: (a) y2∓x2=k2
Question 11. The solution of the differential equation dydx=x2+y2+12xy satisfying (1) = 1, is

 (a) a hyperbola
(b) a circle
(c) y^{2} = x(1 + x) – 10
(d) (x – 2)^{2} + (y – 3)^{2} = 5xy
 (a) a hyperbola
Answer: (a) a hyperbola
Question 12. Given the differential equation dydx=6x22y+cosy; y(1) = π
Mark out the correct statement.

 (a) solution is y^{2} – sin y = 2x^{3} + C
(b) solution is y^{2} + sin y = 2x^{3} + C
(c) C = π^{2}+ 2√2
(d) C = π^{2} + 2
 (a) solution is y^{2} – sin y = 2x^{3} + C
Answer: (b) solution is y^{2} + sin y = 2x^{3} + C
Question 13. For the differential equation xdydx+2y=xydydx,

 (a) order is 1 and degree is 1
(b) solutio is ln(yx^{2}) = C – y
(c) order is 1 and degree is 2
(d) solution is ln(xy^{2}) = C + y
 (a) order is 1 and degree is 1
Answer: (a) order is 1 and degree is 1
Question 14. The particular solution In(dydx) = 3x + 4y, y(0) = 0 is

 (a) e^{3x} + 3e^{4y} = 4
(b) 4e^{3x} – 3e^{4y} = 3
(c) 3e^{3x} + 4e^{4y} = 7
(d) 4e^{3x} + 3e^{4y} = 7
 (a) e^{3x} + 3e^{4y} = 4
Answer: (d) 4e^{3x} + 3e^{4y} = 7

 Question 15. 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
 Question 15. If ydx – xdy + ln x dx = 0, y(1) = 1, then
Answer: (a) y + 1 + ln x = 0

 Question 16. 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 xaxis
(d) fixed radius 1 and variable centre on yaxis
 Question 16. The differential equation dydx=1−y2y−−−−√ determines a family of circle with
Answer: (c) fixed radius 1 and variable centre on xaxis
Question 17. If y dx + y^{2} dy = x dy, x ∈ R, y > 0 and y(1) = 1, then y(3) =

 (a) 3
(b) 2
(c) 1
(d) 5
 (a) 3
Answer: (a) 3
Question 18. If (x + y)^{2} dydx = a^{2}, y = 0 when x = 0, then y = a if xa =

 (a) 1
(b) tan 1
(c) tan 1 + 1
(d) tan 1 – 1
 (a) 1
Answer: (d) tan 1 – 1
Question 19. 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
 (a) c – x sinx
Answer: (c) c – x cos x
BSEB 12th math chapter 9 objective solution
Question 20. The solution of differential equation (e^{y} + 1) cosx dx + e^{y} sinx dy = 0 is

 (a) (e^{y} + 1) sinx = c
(b) e^{x} sinx = c
(c) (e^{x} + 1) cosx = c
(d) none of these
 (a) (e^{y} + 1) sinx = c
Answer: (a) (e^{y} + 1) sinx = c
Question 21. The general solution of the differential equation dydx=x2y2 is

 (a) x^{3} – y^{3} = c
(b) x^{3} + y^{3} = c
(c) x^{2} + y^{2} = c
(d) x^{2} – y^{2} = c
 (a) x^{3} – y^{3} = c
Answer: (a) x^{3} – y^{3} = c
Question 22. The solution of differential equation dydx=x−yx+y is

 (a) x^{2} – y^{2} + 2xy + c = 0
(b) x^{2} – y^{2} – xy + c = 0
(c) x^{2} – y^{2} + xy + c = 0
(d) x^{2} – y^{2} – 2xy + c = 0
 (a) x^{2} – y^{2} + 2xy + c = 0
Answer: (d) x^{2} – y^{2} – 2xy + c = 0
Question 23.
Answer: (d) 6
Question 24. The degree of the differential equation

 (a) 1
(b) 2
(c) 3
(d) not defined
 (a) 1
Answer: (d) not defined
Question 25. 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
 (a) 2 and not defined
Answer: (a) 2 and not defined
Question 26. Integrating factor of the differential equation dydx + y tanx – sec x = 0 is

 (a) cos x
(b) sec x
(c) e^{cos x}
(d) e^{sec x}
 (a) cos x
Answer: (b) sec x
Question 27. 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
 (a) y = tan^{1} x
Answer: (b) y – x = k(1 + xy)
Question 28. 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
 (a) sinxsiny=c
Answer: (b) sin x sin y = c
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