## Non-repeated linear factors in Denominator -Basic Level

Compared to other sections, Maths is considered to be the most scoring section. If prepared thoroughly, Maths can help students to secure a position in the exam. These questions are very important in achieving your success in Exams after 12th.

Q1. The remainder obtained when the polynomial is divided by is 1+ x + x3+x9 + x27 + x81 + x243 is divided by is x-1 is

•  3
•  5
•  7
•  11

7

Q2. If then 1/(x(x+1)(x+2)(x+3)....(x+n))=A0/(x) +A1/ (x+1)+........An/(x+n) then A,=1

•  r!(-1)/(n-r)!
•  (-1)/r!(n-r)!
•  (1)/r!(n-r)!
•  None of these

(-1)/r!(n-r)!

Q3. (x+1)/((x-1)(x-2)(x-3))=

•  (1/(x-1))+(3/(x-2))+(1/(x-3))
•  -(3/(x-1))+(1/(x-2))+(2/(x-3))
•  (1/(x-1))+(3/(x-2))+(2/(x-3))
•  None of these

(1/(x-1))+(3/(x-2))+(2/(x-3))

Q4. if (ax2+bx+c)/((x-1)(x+2)(2x+3))=(3/(x-1))+(2/(x+2))+(5/(2x+3)) ,then

•  a=5
•  b=18
•  c=22
•  None of these

c=22

Q5.  (ex+2)/ ((ex-1)(2ex-3))=(3/(ex-1))+(B/(2ex-3)) then B=

•  1
•  3
•  5
•  7

7

Q6. (3x+4)/(x2-3x+2)=(A/(x-2)-(B/(x-1)) then (A,B)=

•  (7,10)
•   (10,7)
•  (10,-7)
•  (-10,7)

(10,7)

Q7.  if (9/((x-1)(x+2)2) )=(A/(x-1))+(B/(x+2))+(C/(x+2)2 )then A-B-C=

•  3
•  -1
•  5
•  None of these

5

Q8. ((ax+b)/(3x+4))2 =(1/(3x+4))-(3/(3x+4)2) then

•  a=2
•  b=-1
•  a=3
•  b=4

a=3

Q9. (x2+13x+15)/((2x+3)(x+3)2)=

•  (1/(x+3))-(1/(2x+3))+(5/(x+3))2
•  (1/(2x+3))-(1/(x+3))+(5/(x+3))2
•  (1/(2x+3))+(1/(x+3))+(5/(x+3))2
•  (1/(2x+3))-(1/(x+3))-(5/(x+3))2

(1/(x+3))-(1/(2x+3))+(5/(x+3))2

Q10. The partial fraction of (3x3-8x2+10)/(x-1)4

•  (3/(x-1))+(1/(x-1))2+(7/(x-1))3+(5/(x-1))4
•  (3/(x-1))+(1/(x-1))2-(7/(x-1))3+(5/(x-1))4
•  (3/(x-1))+(1/(x-1))2-(7/(x-1))3+(5/(x-1))4
•  None of these

(3/(x-1))+(1/(x-1))2-(7/(x-1))3+(5/(x-1))4

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