Engineering Answers

The integral factor of (x²y)dx- (x³ + y³)dy = 0 is

A) -y^4

B) -1/y^4

C) y^4 D) 1/y^4

The solution of ye^{x}dx + (2y + e^{x})dy=0, y(0) = -1 is A) y = e^{x}. B) y=e^{-x} C) y = 1 D) y = -1

The particular integral value of (D² + 4)y = sin²x is

A) 1/8-x/8 sin2x

B) 1/8+x/8 Sin2x

C) 1/8-x/8 Cos2x D)1/8+x/8 Cos2x

The yp value of (D²− 3D+ 2)y = e^{3x}

A) 1/2 e^{3x}

B) e^{3x}

C) 2e^{3x}. D) 3e^{3x}

The value of 1/D²+3D (2 + 6x) =

A) x

B) x² C) 0 D) 1

Solution of (D³ - 2D² - 3D)y = 0

A) y = C1.₁e^{x} + C₂е^{-x }+ С3.e^{3x} B) y = C1e^x + C₂е^{-x} + С3.e^{-3x}

C) y = C1+C₂е^{-x} + С3.e^{3x}

D) y = C₁+C₂е^{-x} + С3e^{-3x}

If f(x, y) = 1, then the value of ∫∫R 1 dxdy gives

A) 2 * Area of the region R

B) 1/2* Area of the region

C) Area of the region R R

D) 0

If V = x²z²i-2y²z²j+ xy²zk then Curl V at (3,2,1) is

A) 20i + 14k

B)2i + 14k

C)14j+20k

D) 20i + 14j

The unit normal to the surface x² + y² + z² = 3 at (1,1,1) is A)1/√16 (2i+2j+2k) B)1/√3(i+j+ k)

C) 1/√6(i+2j+3k)

D)1/√3(i+2j+2k)

If Ø(x, y, z) = x² - y²-2²-2, then ∇Ø at (2,1,-1) is

A) 4i +2j-2k

B)4i-2j-2k

C) 4i + 2j + 2k

D)4i - 2j +2k