GATE IN 2018 Question Paper (04-Feb-2018) (Shift 2)

Given $\vec{F}=\left(x^2-2y\right)\vec{i}-4yz\vec{J}+4x{z}^2\vec{k},$ the value of the line integral _C^ F.dl along the straight line C from (0, 0, 0) to (1, 1, 1) is.

Two bags A and B have equal numbers of balls. Bag A has 20% red balls 80% green balls. Bag B has 30% red balls, 60% green balls and 10% yellow balls. Contents of Bags A and B are mixed thoroughly, and a ball is randomly picked from the mixture. What is the chance that the ball picked is red?

Consider the following system of linear equations:

3x + 2ky = -2

Kx + 6y = 2

Here x and y are the unknowns and k is a real constant. The value of k for which there are infinite number of solutions is

Consider the following equations

$\frac{\partial V\left(x,y\right)}{\partial x}=p{x}^2+y^2+2xy$

$\frac{\partial V\left(x,y\right)}{\partial y}=x^2+q{y}^2+2xy$

Where p and q are constants. V (x, y) that satisfies the above equations is

In the given circuit, superposition is applied. When V₂ is set to 0 V, the current I₂ is -6 A. When V­₁ is set to 0 V, the current I₁ is +6 A. Current I₃ (in A) when both sources are applied will be (up to two decimal places) _____.