JEE Mathematics Differential Equations MCQs Set D

Question: The differential equation whose solution is y = A sin x + B cos x, is

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

Question: y = ae^mx + be^-mx satisfies which of the following differential equations?

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: If x = sint, y = cos pt, then

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:

is a solution of which of the following differential equation?

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: Family of curves y = e^x ( A cos x + B sin x), represents the differential equation

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

Question:

• a) x⁴ y₂ + y = 0
• b) x² y₂ + y = 0
• c) xy₂ - y = 0
• d) x⁴y₂ - y = 0

Answer: x⁴ y₂ + y = 0

Question: Solution of the equation (e^x +1) ydy = ( y +1)e^x dx is

• a) c ( y +1)(e^x +1) = e^y
• b) c ( y +1)(e^x -1)- e^y = 0
• c)  c( y +1)(e^x -1)+ e^y = 0
• d) None of these

Answer: c ( y +1)(e^x +1) = e^y

Question:

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

Question:

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

Question:

• a)

  

• b)

  

• c) (1+ x² )^3/2 + (1+ y² )^3/2 = c
• d) None of these

Answer:

Question: Solution of (x + y -1)dx + (2x + 2y - 3)dy = 0 is

• a) 2 y + x + log(x + y - 2) = c
• b) 2y + 2x + log(x + y - 2) = c
• c) y + 2x + log(x + y - 2) = c
• d) y + x + log(x + y - 2) = c

Answer: 2 y + x + log(x + y - 2) = c

Question: The solution of the differential equation

• a) None of these
• b) (x + y)² = a²x + c
• c) (x + y)² = 2a²x + c
• d) Both

Answer: None of these

Question: The degree of the differential equation y = Ax + A³ is :

• a) 3
• b) 4
• c) 2
• d) 1

Answer: 3

Question: The order and degree of the differential equation

• a) 2 and 1
• b) 1 and 2
• c) 1 and 1
• d) 2 and 2

Answer: 2 and 1

Question: The solution of the differential equation

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: The degree of the differential equation

• a) 2
• b) 1
• c) 3
• d) 6

Answer: 2

Question: The differential equation for which sin^–1x + sin^–1y = c is given by:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: The differential equation representing a family of circles touching the y-axis at the origin is :

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: The elimination of constants A, B and C from y = A + Bx – Ce^–x leads the differential equation

• a) y" + y"' = 0
• b) y' + e^x = 0
• c) y" – y"' = 0
• d) y" + e^x = 0

Answer: y" + y"' = 0

Question: The family of curves represented by the differential equation

• a) x cos y = constant
• b) log (x cos y) = x
• c) cos y = log x
• d) x cos y = log x

Answer: x cos y = constant

Question: The differential equation of y = Ae^2x + Be^–2x is

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

Question: The differential equation representing the family of curves y² = 2c (x + √c ) , where c is a positive parameter, is of

(1) order 1    (2) order 2
(3) degree 3 (4) degree 4

• a) 1 and 3 are correct
• b) 1 and 2 are correct
• c) 1, 2 and 3 are correct
• d) 2 and 4 are correct

Answer: 1 and 3 are correct

Question:

• a) 1, 2 and 3 are correct
• b) 2 and 4 are correct
• c) 1 and 2 are correct
• d) 1 and 3 are correct

Answer: 1, 2 and 3 are correct

Question: Solution of the differential equation

(1) y + e^–x = k (2) y – e^–x = k
(3) y – e^x = k (4) y + e^x = k

• a) 1 and 3 are correct
• b) 1 and 2 are correct
• c) 1, 2 and 3 are correct
• d) 2 and 4 are correct

Answer: 1 and 3 are correct

Question: Differential equation dy/dx= f (x).g(y) can be solved by separating variable as dy/g(y)= f (x) dx

The equation of the curve passing through the point (1, 0) and satisfies the differential equation (1 + y²) dx – xy dy = 0, is

• a) x² – y² = 1
• b) x² – y² = 2
• c) x² + y² = 1
• d) x² + y² = 2

Answer: x² – y² = 1

Question: Differential equation dy/dx= f (x).g(y) can be solved by separating variable as dy/g(y)= f (x) dx Solution of the differential equation

• a) tan^–1 y + sin^–1x = c
• b) tan^–1 x + sin^–1y = c
• c) tan^–1 y . sin^–1x = c
• d) tan^–1 y – sin^–1x = c

Answer: tan^–1 y + sin^–1x = c

Question: Differential equation dy/dx= f (x).g(y) can be solved by separating variable as dy/g(y)= f (x) dx If dy/dx = 1 + x + y + xy and y (–1) = 0, then y =

• a)

  

• b)

  

• c) ln (1 + x) – 1
• d) 1 + x

Answer:

Question:

Statement-1 : The equation of the curve through the point (1, 0) which satisfies differential equation (1 + y²) dx – xy dy = 0 is x² – y² = 1.

Statement-2 : D.E. dy/dx = f (x) . g (y) can be solved by separating variables as dy/g(y)=f (x) dx

• a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
• b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• c) Statement -1 is False, Statement-2 is True.
• d) Statement -1 is True, Statement-2 is False.

Answer: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Question:

Statement-1 : The differential equation of all circles in a plane must be of order 3.
Statement-2 : There is only one circle passing through three noncollinear points.

• a) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• b) Statement -1 is False, Statement-2 is True.
• c) Statement -1 is True, Statement-2 is False.
• d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Answer: Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

Question:

Statement-1 : The equation of the curve passing through (3, 9) which satisfies differential equation

Statement-2 : The solution of differential equation

• a) Statement -1 is True, Statement-2 is False.
• b) Statement -1 is False, Statement-2 is True.
• c) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Answer: Statement -1 is True, Statement-2 is False.

Question: Solution of differential equation

is

• a) x² + y² = px³
• b) x² + y³ = px²
• c) x³ + y² = px²
• d) None of these

Answer: x² + y² = px³

Question: The solution of the equation dy/dx= x/2y-x is

• a) (x - y)(x + 2y)² = c
• b) y = (2y - x) + c
• c) y = x + c
• d) None of these

Answer: (x - y)(x + 2y)² = c

Question: The solution of the equation

• a)

  

• b) y = log y +1
• c) y = xy + c
• d) None of these

Answer:

Question:

• a) y² + 2xy - x² = c
• b) y² - 2xy - x² = c
• c) y² + 2xy + x² = c
• d) y² - 2xy + x² = c

Answer: y² + 2xy - x² = c

Question: The solution of ye^-x/y dx -(xe^-x/y + y³)dy = 0 is

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: The solution of the differential equation.

ydx + (x + x² y)dy = 0 is

• a)

  

• b)

  

• c)

  

• d) log y = cx

Answer:

Question: Solution of the differential equation, ydx - xdy + xy² dx = 0 is

• a) 2x + x² y = λy
• b) 2y + y² x = λy
• c) 2y - y²x = λy
• d) None of these

Answer: 2x + x² y = λy

Question: y+x²=dy/dx has the solution

• a) y + x² + 2x + 2 = ce^x
• b) y + x + x² + 2 = ce^2x
• c) y + x + 2x² + 2 = ce^x
• d) y² + x + x² + 2 = ce^x

Answer: y + x² + 2x + 2 = ce^x

Question: Integrating factor of the differential equation

• a) ( √x)^{log x}
• b) x^{log x}
• c) ( √e)^{log x}
• d) None of these

Answer: ( √x)^{log x}

Question: The slope of a curve at any point is the reciprocal of twice the ordinate at the point and it passes through the point (4, 3), then equation of the curve is

• a) y² = x + 5
• b) x² = y + 5
• c) y² = x - 5
• d) x² = y -5

Answer: y² = x + 5

Question: The elimination of the arbitrary constant m from the equation y = e^mx gives the differential equation:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: Solution of the differential equation x²y–x³ dy/dx=y⁴ cos x, when y(0) = 1 is :

• a) x³ = 3 y³ sin x
• b) none of these
• c) x³ ≠ y³ sin x
• d) y³ = 3x³ sin x

Answer: x³ = 3 y³ sin x

Question: The general solution of the differential equation (x + y) dx + xdy = 0 is :

• a) x² + 2xy = c
• b) x² + y² = c
• c) 2x² – y² = c
• d) y² = c

Answer: x² + 2xy = c

Question:  The solution of differential equation

is :

• a) y = 1 + ce^–x
• b) y = x + ce^–x
• c) y = 1– ce^–x
• d) y = x – ce^–x

Answer: y = 1 + ce^–x

Question:

• a) sin x + c₁ x + c₂
• b) cos x + c₁ x + c₂
• c) tan x + c₁x + c₂
• d) log sin x +c₁ x + c₂

Answer: sin x + c₁ x + c₂

Question:

• a) 2 cos (xy) + x^–2 = c
• b) 2 sin (xy) + x^–2 = c
• c) 2 cos (xy) + y^–2 = c
• d) 2 sin (xy) + y^–2 = c

Answer: 2 cos (xy) + x^–2 = c

Question: The rate of increase of bacteria in a certain culture is proportional to the number present. If it doubles in 5 hours then in 25 hours, its number would be

• a) 32 times the original
• b) 8 times the original
• c) 16 times the original
• d) 64 times the original

Answer: 32 times the original

Question: The solution of the equation,

is:

• a) y sec² x = sec x + c
• b) y sec x = tan x + c
• c) y = sec x + c sec² x
• d) none of these

Answer: y sec² x = sec x + c

Question:

• a) sec x
• b) cos x
• c) sin x
• d) tan x

Answer: sec x

Question: The solution of x dy – y dx + x² e^x dx = 0 is :

• a)

  

• b)

  

• c) x + e^y = c
• d) y + e^x = c

Answer:

Question: The solution of the differential equation.

• a) y = sin x
• b) y = sin x – cos x
• c) y = cos x
• d) y = sin x + cos x

Answer: y = sin x

Question:

• a) 1 and 2 are correct
• b) 1 and 3 are correct
• c) 1, 2 and 3 are correct
• d) 2 and 4 are correct

Answer: 1 and 2 are correct

Question: Given a function ‘g’ which has a derivative g '(x) for every real x and satisfies g'(0) = 2 and g (x + y) = e^y g(x) + e^x g(y) for all x and y then

• a) 1, 2 and 3 are correct
• b) 1 and 2 are correct
• c) 2 and 4 are correct
• d) 1 and 3 are correct

Answer: 1, 2 and 3 are correct

Question: The curve for which the area of the triangle formed by the x-axis, the tangent line and radius vector of the point of tangency is equal to a² is

• a) 1 and 3 are correct
• b) 1 and 2 are correct
• c) 1, 2 and 3 are correct
• d) 2 and 4 are correct

Answer: 1 and 3 are correct

Question:

Statement 1 : The differential equation y³ dy + (x + y²) dx = 0 becomes homogeneous if we put y² = t.
Statement 2 : All differential equation of first order first degree becomes homogeneous, if we put y = tx.

• a) Statement -1 is True, Statement-2 is False.
• b) Statement -1 is False, Statement-2 is True.
• c) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Answer: Statement -1 is True, Statement-2 is False.

Question:

• a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
• b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• c) Statement -1 is False, Statement-2 is True.
• d) Statement -1 is True, Statement-2 is False.

Answer: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Question:

• a) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• b) Statement -1 is False, Statement-2 is True.
• c) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
• d) Statement -1 is True, Statement-2 is False.

Answer: Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.