Vector and tensor analysis mcqs with answers
31. The differential equation is not exact, but if
then the substitution … will work to reduce it to homogeneous form?
A. x = X + h, y = Y + k
B. x = X – h, y = Y – k
C.
D. None of these
32. (2x + y + 1)dx + (4x + 2y – 1)dy = 0 has solution.
A. -x – 2y – ln | 2x + y – 1 |= c
B. -x – 2y = ln | 2x + y – 1 | +c
C. x + 2y + ln | 2x – y – 1 |= c
D. x – 2y = ln | 2x + y + 1 | +c
33. (y² + 2xy)dx + x²dy = 0 has solution
A. | yx |= c | y + x |
B. | yx³|= c | y + 3x³|
C. | yx³|= c | y + 3x³|
D. | yx³|= c | y + 3x |
34. (x² + 3y²)dx + 2xydy = 0 has solution
A. | sin(y/x) |= cx
B. | sin(y/x) |³= cx³
C. | sin(y/x) |³= cx²
D. | sin(x/y) |= cx²
35. An expression M(x, y)dx+N(x, y)dy is called a (an) ____________ if there exists a function f(x, y) such that
A. Exact differential
B. Non exact differential
C. Homogeneous differential
D. Linear differential
Vector and tensor analysis mcqs with answers