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There are five problems in this assignment. Answer all the problems.

problem 1:  (i) Find the complex conjugate of (3+5i)/(1+2i)

(ii) Differentiate (sin x)x w.r.t. x.

(iii) Find all the seventh roots of (3+4i).

problem 2:    (i)  Find the equation of the line joining the points (-, 6, - 3) and (7, - 6, 3).

(ii) Find the equation of the sphere, which contains the circle

x2 + y2 + z2 = 18  , 3x + 3y + 3z = 11 and passes through the origin.

problem 3:  (i) Find lim 1+x2/x2

x → ∞

(ii) Compute the area bounded by y2 = 9x and x2 = 9y

(iii) Evaluate:  ∫tan-1 x dx

problem 4: Use the Cauchy - Schwarz inequality to solve x3 -  25x2 -   4x + 100 = 0, given that all its roots are rational.

problem 5:  (i) Find the perimeter of the cord r = a (1 + cos θ)

(ii) Find all the seventh roots of (3+4i).

• Category:- Math
• Reference No.:- M92335

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