Problem 1: The sum of the Residues of the complex function

F (z) = (z + 1)/((z - 4)(z - 2)) is -

Problem 2: If

U = log(x³ + y³ + z³ - 3xyz),

then

∂u/∂x + ∂u/∂y + ∂u/∂z = ?

Problem 3: The solution of the linear differential equation

(x + 10y³) dy/dx = y

is -

Problem 4: The rank of the matrix

1 1 1
1 2 3
1 4 7

is -

Problem 5: The value of _C F^→ dr^→ when F^→ = 2xyzi^{^} + x²zj^ + x²yk^ and C is a straight line joining (0, 0, 0) and (1, 1, 1) .

Problem 6: The arc of the segment cut off from the parabola x² - 8y.by the line x - 2y + 8 = 0 is ____unit.

Problem 7: x⁴ - 4x³ - 9 = 0.

Solve by Newton-Raphson method then (k + 1) step is

Problem 8: The value of ₀∫^2π cos (x) dx by using Trapezoidal method with 8 equal intervals. Compute by calculator. Then the error upto 5 significant digit is

Problem 9: In Binomial distribution the mean of variable is given as 9 and standard deviation is given as √6,then find the number trials.

Problem 10: Which of the following is not true with respect to Expectation and Variance for discrete distribution,X₁, X₂ are variables.

P) E(aX₁ + b) = aE(X₁) + b
Q) E(aX₁ + b) = E(aX₁) + b
R) V (aX₁ + bX₂) = a²V (X₁) + b²V (X₂)
S) V (aX₁ + bX₂) = V (aX₁) + V (bX₂)

Problem 11: Which of the differential equations is the equation of hyperbola

a) dy/dx = y/x, (b)dy/dx = 1/xy, (c) dy/dx = x/y, (d)dy/dx = -x/y.