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NCERT Solutions for class 12 Maths | Chapter 9 - Differential Equations

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Free download in PDF Class 12 Maths Chapter 9 Differential Equations Multiple Choice Questions and Answers for Board, JEE, NEET, AIIMS, JIPMER, IIT-JEE, AIEE and other competitive exams. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. These short solved questions or quizzes are provided by Gkseries. These will help the students for preparation of their examination./p>

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(1)
[A]
[B]
[C]
[D]
Answer:
(2) The solution of the differential equation cos x sin y dx + sin x cos y dy = 0 is
[A] sinx/siny=c
[B] sin x sin y = c
[C] sin x + sin y = c
[D] cos x cos y = c
Answer: sin x sin y = c

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(3) The solution of the differential equation is
[A] y = tan-1 x
[B] y – x = k(1 + xy)
[C] x = tan-1 y
[D] tan(xy) = k
Answer: y – x = k(1 + xy)
(4) The differential equation satisfied by y = A/x + B is (A, B are parameters)
[A] x2 y1 = y
[B] xy1 + 2y2 = 0
[C] xy2 + 2y1 = 0
[D] none of these
Answer: xy2 + 2y1 = 0
(5) The differential equation whose solution is (x – h)2 + (y – k)2 = a2 is (a is a constant)
[A]
[B]
[C]
[D] None of these
Answer:
(6) The degree of the differential equation
[A] 2
[B] 1
[C] 3
[D] none of these
Answer: 2
(7) The degree of the equation satisfying the relation

[A] 1
[B] 2
[C] 3
[D] None of these
Answer: 1
(8) 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: 2
(9) Given the differential equation

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: solution is y2 + sin y = 2x3 + C
(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: y2∓x2=k2
(11) The differential equation of all parabolas whose axes are along x-axis is
[A]
[B]
[C]
[D]
Answer:
(12) 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: x2y2(y”)2 + yy’= 0
(13) The differential equation of the family of circles touching the x-axis at origin is given by
[A]
[B]
[C]
[D] None of these
Answer:
(14) The differential equation of all circles which pass through the origin and whose centre lies on y-axis is
[A]
[B]
[C]
[D]
Answer:
(15)
[A]
[B]
[C]
[D]
Answer:
(16)
[A] π/3
[B] π/4
[C] π/6
[D] π/12
Answer: π/12
(17)
[A]
[B]
[C]
[D]
Answer:
(18) The differential equation of all parabolas whose axes are parallel to y-axis is
[A]
[B]
[C]
[D]
Answer:
(19) 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: (ey + 1) sinx = c
(20) If sinx dy/dx + 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 – x cos x

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