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2.7, , Partial fractions, , EXERCISE, The, , 3x-1, , partial fractions o (x-2) (x-3), , are, , (2), , ()-2, , -3, , 8, , (3)-2, , 8, , 4)2-3-x, , X-3, X+1, , Thepartial fractions, o125x+6, , (1)+2, , 2re, , X+3, , (3), , x+3, , 2, , 2, , 4)2243, , 3)2 x+3, , 3, , The, , partial, , fractions, , or, , 2x+3, 3x? +14x-5, , are, , () 16(3x-1), (3), , 7, , 16(3x-1), , 16(x +5), , 4. 123x+2, , (216(3x-1), , 16(x +5), , -11, , 3x +4, , 7, , 11, , 11, , (4)none of these, , B, , x, , -1, , then (A, B), , =, , (3) (10, 7), , (2) (10, 7), , (1) (7, 10), , 16(x +5), , (4) (-10, 7), , B, , -2x)q-2x) 0+3x), (1) A, X+1, , 2B =, 1+3, 1+3x then, , 1-2x, (2)2A, , B, , A, , (2x -1) (3x +1) 2x-11, , 3x+1, , 3x, , then a, , 1.(x-6)(x+a) x-6, 8., , x1, , If (2x-a)(x+2), , (1) (0, 5), , =, , (4) 8, , =, , (3) 3, , (2)-3, , (1)2, , 16A +9B, (3) 6, , (2) 5, , (1)4, , (4)-3A, , (3)3A, , (4)-2, , 2x-a, n3(5. 1) X+2 then (a, b)=, b, , (2) (5, 1), , (Radiant's)-, , (3) -5, 1), , (4) (-5, -1), -(Chapter-2)

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2.8, , -1, , 10., , x-10x+13, , (x-)&2-5x +6), , 11, 12., , x-1, , X-b, , (x-a) (X -b) x - a, (2)-2:1, (1)1:2, X-4, 2, 25x-2kx2, , k, , then, , B, X, , X-X, , (2) 2, (1) 1, Let a, b, c be such that, , =, , (3) 2, , (4) 3, , then A, 1+x, (3) 3, , (4) 4, , b, , a, , C, , d-0-20-3x)1--2, x+1, , 15., , (4) 3, , 2, , TX-3 then (a, b)=, (3) (7, 1), (2) (1, 7), , x-a) (x -3)), (1) (7, 1), , x-, , (2) b, , 1, , 10, , then, , (x +1) (x +2) (x+3), , (3) c =25, , x, , (2x-)x, , C, , (x+1)(x+2), , (x +1) (x + 2) (x +3), (1) a =, , (4) (-1, 7), , b, , x-5x +1, , 16., , then, , (3), , (2), , (1) 5, , (4)3:1, , (3) 1:3, , (2)-2, , 13. -X+6x*A, 14., , thena : b=, , I, , (1)-3, , +C=, , (4) 4, , (3) -1, , 2, , 3x, , thenA +B, , x-2X-3, , (2) 1, , (1) 0, , (4)-1, , (3), , (2) 2, , (1) 1, , =, , x-b, , 2(x a ), , x -a) (x - b), , 9, , then k, , (4), , none, , of these, , B, , +2) (x-3), (2), , (), , 2x-1, , X-3, , x+2, , A=, , -1, , (3) 25, , 50, , (4), , 27, , 4, , X, , 8., , x-a)(x-b) (x-c), , X*k+, , (1) a-b -c (2) a +b+c, (1+x)(1+2x)(1+3x) =k+, , 19. f d-x)(1-2x)(1-3x), ()k=6, (Chapter-2)-, , (2) A, , 12, , A, , B, , C, x-b + X-c, , x-a, (3) a, , +b +c, B, , then k, , =, , (4) - (a + b + c), C, , +, -x1-2x1-3x, then, (3) B= 30, , (4) C, , -20, Radiant's

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20., , (x-1) (x+2), (1) 1, , A, , 21. 1x+1 (x-1), , 23., , 10, , (3), , (4) 1, , B, , C, , (x-2)-2x)-2&-2+, (2) -1, 2 tX+1, , If, , x+2x+1, Ir +2x+3, x, , x+1? then AB, , (2)4C+1, B, , then, , 25. If (3x + 4), (1) 3, , 1, , (3) 6, , 3, , 2x+1, , then, , 3x-4, , 1, x-3, , (1)1, , b, , a +, , =, , (4) 6, , C, X+1, , (2) 3, , -3) (x+a), , (4) 0, , (3) 5, , B, , 26. R-1D(X+1) (x+2), , 27., , (4) 2C, , 3 then A+ B-C=, , 3x +4, (3x +4), (2) 4, , (1)1, , =, , (3) 3C, , (2) 3, , ax +b, , (4)-2, , C, +, , X+1, , (1)1, , then A+C, , (3) 2, , B, , A+, , (1) 4C, , 24, , X+1(x+12 then A =, , A, , (1)1, , (4) -2, , C, , (2), , 3x+X-2, +x-2, , k=, , (3) 2, B, , X-1, , (1), , ", , then, , (2)-1, 3x +4, , 22., , B, , X*k+, , D, x +2 hen 3A =, , (3) 6, , then, , X+a, , (2) 2, , (4) 9, , a, (3) 3, , (4) 4, , (3)3, , (4) 4, , k, , 28. IfA, -4, (1), 29., , If ax +b, , (2x+3), , (1) 1, , 30., , X+2, , then k=, , (2) 2, 2, , (2x+3, 2x +3, (2) 2, , then a, , +, , b, , (3) 3, , (4) 4, , X+2, , The number of partial fractions of 2(2-n s, , (1) 1, , 31., 31., , x-2, , (2)2, , (3)3, , (4) 4, , X+4, , The number, (1) 2, , of partial fractions, (2)3, , -Radiant's, , ot, , (x-4) (x+1), (3) 4, , (4) none of these, , (Chapter-2)

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32., , 1, , 42-19x, , A, , Bx +C, , (x +1) (x-2), , x2, , x+1, , (), , 33., , then A, , If, , 2x+1, , Bx+C, , (x-D(x+)-i, , (), 34., , x2+1 thenA+B+C, , (2), , 3), Bx +C, , If, , (x-a)(x, , X-ax+b, , +b), , 1, , -1, , (1)+b, , (2)2+b, , 2x+1, , 35, , A, , (x-)(x+1) x-1, (1) 2, , Bx+C, , A-B, , x+1, , C, , A, , Bx+C, , 38, , 3x+2, , If, , 39, , Ir X+1), , x+X, , If, , x+1, , Bx+C, , (Chapter-2), , 2x243 then A + C -B, (3) 3, , xx+a, , IECET 201I, , =, , (4) 5, , A), (4), , Bx +C, , 2, , x+a2 thentan!, (2), , (3), , (2+x)(1-x+x, (), , (4) 2, , (3), , 3x-1, , If, , =, , Bx +C, , x241 then sin-!, , (2), , (1), 41., , A, , A+B, , (3) 1, , (2) 2, , (), 40., , +2x+4, A, , (X+1)(2x+3), , ()0, , (4) 1, , Bx +C, , X-2, (2) 1, , (1)0, , a+b2, , (4) 8, , (3)-2, , A, , x-8, , (4), , -1, , B=F, , (2) -1, , -x-1, , 37, , =, , (3) 6, , (x-1) (x2+2) x-1x+2, (1)1, , then B, , (3) a+b, , (2) 4, , 2x+3x+4, , 36., , (4), , (3), , (2), , (2), , (4), , 2, , Bx+C, , 1-X+x2 then sin, (3) t, (4) T, , 4, , 1., , 2.

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Partial F, , LIOnS, , (X+1), 42., , Bx+C, , x+thencos, , x (x +1)x, , (2, x+3, +2)( +5), , 43., , (1)0, , 44., , 3) 4, , x+1, , (4) 2, , Cx+D, , x-x+1 then A + B+C+ D=, (3) 2, , Ax +B, , (4)-2, , Cx+D, , +X+x+kx+1 thenk=, (3) -1, , (4) 2, , x+X+, , The number of partial fractions of, (1) 1, , (2) 2, , The number of, , partial, , (1) 2, , (2) 3, , K, , 3x +5, +1, , fractions of, , (x +23, (1) 1, , s1S, , (4) 4, , x+3x+1, , -1, (x-1, , 1is, , (3) 4, , (4) 5, , B, , A, , B), x+1 +1? then (A,, (3) (2, 3), (2) -2, 3), , =, , x2+1, , (x+1, , x+5, , x+X+1, , (3) 3, , x+24x+28 Ax+B, (1) 0, , 50, , thenA+ C, , (3) -1, , (2) 1, , (1) 2, 3), 49., , +5, , (2) 1, , (1)0, , 48., , +2, , Ax +B, x+X+1, , 1f4, x+X4+1, , 45 Ir3x-2x-1, x+x+1, , 47., , Cx +D, , (2) 1, , (1) 0, , 46., , Ax + B, , 4), , Cx+D, +, , (x +1, (3) -1, , (2) 1, , (4) (3, 2), , Ex +F, , (x+1, , then, , B, , (4) 2, , k, , +2 a+2k=, (2) 2, , (3) 3, , (4) 4, , S1., , The remainderthat obtains when I + x +x'+x+ x + x + x243 is divided by x- 1 is, , 52., , (4) 7, (3) 5, Theremainder obtained when the polynomial x*-3x +9x-27 x+81 is divided by x - 3 is, , (1)0, , (2) 2, , (1) 9, , (2) 27, , Radiant', , (3) 81, , (4) 243, , (Chapter-2)

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1., , 2, , 2., , 3, , 3., , 1, , 4., , 2, , 6., , 3, , 7., , 3, , 8., , 4, , 9., , 3, , 11., , 2, , 12., , 1, , 13., , 1, , 14., , 1, , 5., , 3, , 10. 2, , (x3x, , 15. 3, , Put x, , Put x, 16., , 1, , 17., , 1, , 18. 2, , 19., , 2, , 20., , 1, , 21., , 1, , 22., , 4, , 23., , 4, , 24., , 4, , 25., , 2, , Hence, , 26. 3, , 27., , 2, , 28., , 4, , 29., , 3, , 30., , 4, , 3x, , 31., , 2, , 32., , 4, , 33., , 2, , 34., , 2, , 35., , 3, , Putx, , 36., , 2, , 37., , 2, , 38., , 2, , 39., , 1, , 40., , 3, , Put x, , 41., , 2, , 42., , 2, , 43., , 1, , 44., , 2, , 5. 3, , 46., , 2, , 47., , 2, , 48., , 4, , 49., , 2, , 52., , 3, , 51. 4, , Henc, , 50. 35, Put, , Put, Now, , Hen6., , x+, , Put, , Put, Thu, He, , Chapter-2)