Write the following in Hindu-Arabic numerals:
(i)` bar(I V) C D X L I V`
(ii) ` bar(V I)C K X L I X`
(iii)` bar(I X)C C C X C I`
(iv) `bar( L X)X I X`

Write the following in Hindu Arabic numerals: (i)DCXCVII (ii) KCIX (iii) KKKCDVI (iv) """C K X X I" (V) "X I" D C C(vi) D X I I"

Write the following in the expanded form: (i) (a b+b c+c a)^2 (ii) (x/y+y/z+z/x)^2

Convert the following polar coordinates to its equivalent Cartesian coordinates. (i) ( i i ) (iii)2,pi)( i v ) (v) (ii) ( v i ) (vii)(( v i i i ) (ix)sqrt(( x )2( x i ))( x i i ) , (xiii)pi/( x i v )6( x v ) (xvi) (xvii))( x v i i i ) (xix) (iii) ( x x ) (xxi)(( x x i i ) (xxiii)-3,-( x x i v )pi/( x x v )6( x x v i ) (xxvii) (xxviii))( x x i x ) (xxx)

Convert the following points from polar coordinates to the corresponding Cartesian coordinates. (i) ( i i ) (iii)(( i v ) (v)2, (vi)pi/( v i i )3( v i i i ) (ix) (x))( x i ) (xii) (ii) ( x i i i ) (xiv)(( x v ) (xvi)0, (xvii)pi/( x v i i i )2( x i x ) (xx) (xxi))( x x i i ) (xxiii) (iii) ( x x i v ) (xxv)(( x x v i ) (xxvii)-sqrt(( x x v i i i )2( x x i x ))( x x x ) , (xxxi)pi/( x x x i i )4( x x x i i i ) (xxxiv) (xxxv))( x x x v i ) (xxxvii)

Find the derivative of the following functions:(i) sin x cos x (ii) sec x (iii) 5 sec x + 4 cos x (iv) cos e c x (v) 3 cot x + 5 cos e c x

Which of the following is/are not carrectly mathched pairs ? (a) (ii) and (iii) (b) (i) and (iv) (c) (v) only (d) (ii) only

Convert the following Cartesian coordinates to the corresponding polar coordinates using positive r and negative rdot (i) ( i i ) (iii)(( i v ) (v)-1,1( v i ))( v i i ) (viii) (ii) ( i x ) (x)(( x i ) (xii)2,-3( x i i i ))( x i v ) (xv)

Number of four-digit numbers of the form N=a b c d which satisfy following three conditions (i) ( i i ) (iii) 4000lt=N<6000 (iv) (v) (vi) ( v i i ) N (viii) (ix) is a multiple of 5 (x) ( x i ) (xii)3lt=b

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 )

Write the numerical coefficient of each of the following: (i) 7a b c (ii) -2x^3y^2z