Partial Differential Equation MCQ - 1 - IIT JAM MCQ

1

2

0

none of these

1

2

3

none of these

The dependent variable and its derivatives should be of second order

Each coefficient depends only on the independent variable

Each coefficient does not depend on the independent variable

The dependent variable and its derivatives should not be of same order

linear

Quasi linear

semi linear

non linear

Φ (x, y) = X(x) + Y(y)

Φ (x, y) = X(x) - Y(y)

Φ (x, y) = X(x) / Y(y)

Φ (x, y) = X(x)Y(y)

Charpit's equation 

Lagrange's equation

Bernoulli's equation

Clairut's equation

φ(x + y + z, x² + y² + z²) = 0 

φ(xyz, x + y + z) = 0

φ(xyz,x² + y² + z²) = 0

φ(x² - y² - z², x - y - z ) = 0

x² + y²- z² - 2x + 4z = 0

x² + y² - z² - 2x + 8z = 0

x² + y² + z² - 2x + 16z = 0

x² + y² + z² - 2x + 8z = 0

z = ax + by + sin ab

z = ax + by — sin ab

z = ax + y + sin b

z = x + b y — sin a

f(x² + y² + z²,xy + z ) = 0 

f(x² + y² - z²,x y + z ) = 0 

f(x² - y^2- z²,xy + z) = 0 

f(x² + y² + z²,xy - z ) = 0

z = ax + cos x 

z = ax + sin x  

z = ax + sinx 

z = ax + cos x 

Only (i) and (ii) true

Only (ii) and (iv) are true

(ii), (iii) and (iv) are true

All are true

x² + y² - yz - x + z = 

x² + y² - xz - y + z = 1

x² + y² — xy — x + z = 

y²+ z² — xy + z — x = l

xy + 2y² + x² = 3xy²

yz + 2xy + xz = 3xyz

xz + 2xz + xy = 3xyz

None of these

Only (i) , (ii) are correct

Only (ii) and (iii) correct

(i) and (iii) are correct

all are correct