12th Math chapter 9: full solution, notes, MCQ, & free PDF | Bihar board

12th Math chapter 9: cover all important question with new latest pattern. you can download Math chapter 9 notes & full solution as PDF format in English. below we are goin to cover chapter 9 Math class 12 Bihar board

Bihar board Math chapter 9 class 12: specially we focused on Bihar board latest pattern of Math, and on this post covered class 12th Math chapter 9 based on Bihar board. check out below to get full solutions of Math chapter 9 class 12 bihar board.

12th Math chapter 9 Bihar board with NCERT-Details & Highlights

name of content	12th Math chapter 9 full solution
content	Math objective type MCQ question with answer
name of subjects	class 12 Math
important for exam	Bihar board & other state board
pattern & Level	NCERT & State level question

12th Math chapter 9 all objective solutions – download PDF

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 thes

Answer: (a) 2

Question 5. 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 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

Answer: (b) y” – y = 0

Question 7. The differential equation of all non-horizontal 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 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 9. 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

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) y² = kx
    (d) none of these

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) y² = x(1 + x) – 10
    (d) (x – 2)² + (y – 3)² = 5xy

Answer: (a) a hyperbola

Question 12. 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 13. 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 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

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

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 x-axis
    (d) fixed radius 1 and variable centre on y-axis

Answer: (c) fixed radius 1 and variable centre on x-axis

Question 17. 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 18. 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 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

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

Answer: (a) (e^y + 1) sinx = c

Question 21. 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 22. 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 23.

Answer: (d) 6

Question 24. The degree of the differential equation

• • (a) 1
    (b) 2
    (c) 3
    (d) not defined

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

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}

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

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

Answer: (b) sin x sin y = c

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Bihar board 12th science stream subjects wise solution

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SL.N.	Subject name with solutions
01	Physics
02	Chemistry
03	Biology
04	Math
05	Hindi
06	English