Solve `((1-i)x+3i)/(2+i)+((3+2i)y+i)/(2-i)=-i "where" x, y, in R.`

Find points on the curve (x^(2))/(4) + (y^(2))/(25) = 1 at which the tangents are (i) Parallel to X-axis. (ii) Parallel to Y-axis.

Express in the form ((I+i)^2)/(3-i)

Solve the equation z^3=i

Check which of the following function is onto and into. (i) f :X rarr Y, given by f(x) = 3x, where X = {0, 1, 2 and Y = {0,3,6). (ii) f: Z rarr Z, given by f(x) = 3x + 2, (Z = set of integers).

Match column I with column II and select the correct answer from the given codes. {:(Column I, Column II),(A."Recombinant DNA",(i)"Chilled ethanol"),(B."Precipitation of DNA",(ii)DNA "staining"),(C."Transposons",(iii)"Jumping genes"),(D."Ethidium bromide",(iv)"Genetic engineering"):} 1) A − ( i v ) , B − ( i ) , C − ( i i i ) , D − ( i i ) 2) A − ( i ) , B − ( i i i ) , C − ( i i ) , D − ( i v ) 3) A − ( i i ) , B − ( i ) , C − ( i i i ) , D − ( i v ) 4) A − ( i v ) , B − ( i i ) , C − ( i ) , D − ( i i i )

If the function f:R to R is given by f(x)=(x+3)/(3) and g:R to R is given g(x)=2x-3 , then find (i) fog (ii) gof. Is f^(-1)=g ?

Express in the form a+ib:(3+5i)/(2-3i)

Match column I (enzyme) with column II (characteristic/activity) and select the correct answer from the given codes, {:(Column I,Column II),(A."Taq DNA polymerase",(i)"Cleaves the ends of linear DNA"),(B."Exonuclease",(ii)"Breakdown of fungal cell wall"),(C."Protease",(iii)"Stable above" 90^(@)C),(D."Chitinase",(iv)"Made only by eukaryotic cells"),(,(v)"Degradation of proteins"):} 1) A − ( i i i ) , B − ( i v ) , C − ( i ) , D − ( i i ) 2) A − ( i v ) , B − ( i i i ) , C − ( i ) , D − ( i i ) 3) A − ( i i ) , B − ( i ) , C − ( v ) , D − ( i i i ) 4) A − ( i i i ) , B − ( i ) , C − ( v ) , D − ( i i )