Explore topic-wise InterviewSolutions in Current Affairs.

This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.

1.

Resolve `(3x+2)/(x^(2)+5x+6)` into partical fractions.A. `(7)/((x+2))+(4)/((x+3))`B. `(4)/((x+3))+(8)/((x+2))`C. `(4)/((x+3))-(7)/((x+2))`D. `(7)/((x+3))-(4)/((x+2))`

Answer» `(3x+2)/(x^(2)+5x+6)=(A)/(x+2)+(B)/(x+3)`.
Discussion
2.

Resolve `(4x+3)/(x^(3)-7x-6)` into partical fractions.A. `(1)/(4(x+1))+(3)/(4(x-3))-(1)/((x+2))`B. `(-1)/(4(x+1))+(3)/(4(x-3))+(1)/((x+2))`C. `(1)/(4(x+1))-(3)/(4(x-3))+(1)/((x+2))`D. `(1)/(4(x+1))-(3)/(4(x-3))+-(1)/(x+2)`

Answer» `(i)` Use `x^(3)-7x-6=(x+1)(x+2)(x-3)`.
`(ii) (4x+3)/(x^(3)-7x-6)=(A)/(x+1)+(B)/(x+2)+(C )/(x-1)`.
Discussion
3.

If `(x)/((x+2)(x+3))=(A)/(x+3)+(B)/(x+2)`, then `A-B` is `=`_________.A. `4`B. `5`C. `-6`D. `2`

Answer» Let `(x)/((x+2)(x+3))=(A)/(x+3)+(B)/(x+2)`
`(x)/((x+2)(x+3))=(A(x+2)+B(x+3))/((x+2)(x+3))`.
Consider `A(x+2)+B(x+3)=x`
Put `x=-3`, `-A=-3impliesA=3`
Put `x=-2`, `B=-2`
`:. A-B=3-(-2)=3+2=5`.
Discussion
4.

Resolve `(3x-5)/((x-1)^(4))` into partical fractions.A. `(1)/((x-1))+(2)/((x-1)^(2))-(3)/((x-1)^(3))+(4)/((x-1)^(4))`B. `(3)/((x-1)^(2))+(2)/((x-1)^(3))-(1)/((x-1)^(4))`C. `(3)/((x-1)^(3))+(2)/((x-1)^(4))`D. `(3)/((x-1)^(3))-(2)/((x-1)^(4))`

Answer» `(3x-5)/((x-1)^(4))=(A)/(x-1)+(B)/((x-1)^(2))+(C )/((x-1)^(3))+(D)/((x-1)^(4))`.
Discussion
5.

If `(1)/((a^(2)-bx)(b^(2)-ax))=(A)/(a^(2)-bx)+(B)/(b^(2)-bx)`, then the value of `A` and `B` respectively would be _________.A. `(b)/(b^(3)-a^(3))`, `(a)/(b^(3)-a^(3))`B. `(b)/(b^(3)-a^(3))`, `(a)/(a^(3)-a^(3))`C. `(b)/(a^(3)-b^(3))`, `(a)/(a^(3)-a^(3))`D. `(-b)/(b^(3)-a^(3))`, `(-a)/(a^(3)-a^(3))`

Answer» `(i)` Simplify LHS and RHS by taking LCM.
`(ii)` Compare the like terms and obtain the required values.
Discussion