1
TS EAMCET 2022 (Online) 18th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { Match the items of List-I to the items of List-II } $$

List-I List-II
(A) The number of ways of not selecting ( $n-r$ ) things from $n$ different things (I) $1+{ }^n C_1+{ }^n C_2+\ldots+{ }^n C_r$
(B) $\quad(n-r+1) \cdot{ }^n C_{r-1}$ (II) $(r+1) \cdot{ }^n C_{r+1}$
(C) The number of ways of selecting atleast ( $n-r$ ) things from $n$ different things (III) $r \cdot{ }^n \mathrm{C}$,
(D) $(n-r)\left({ }^{(n-1)} C_{r-1}+{ }^{(n-1)} C_r\right)$ (IV) $$
\begin{aligned}
& 2^n-1-n- \\
& { }^n C_2-\ldots-{ }^n C_r
\end{aligned}
$$
(V) ${ }^n C_{n-1}$
A
A B C D
V III IV II
B
A B C D
I II IV III
C
A B C D
V III I II
D
A B C D
I V IV III
2
TS EAMCET 2022 (Online) 18th July Morning Shift
MCQ (Single Correct Answer)
+1
-0
  1. If $L$ and $M$ are respectively the coefficient of $x^{-7}$ in $\left(a x+\frac{b}{x^2}\right)^{11}$ and the coefficient of $x^7$ in $\left(b x^2+\frac{a}{x^2}\right)^{11}$, then $L+M=$
A

$\frac{1}{b}\left[\right.$ coefficient of $x^{-6}$ in $\left.\left(a x+\frac{b}{x^2}\right)^{12}\right]$

B

$\frac{1}{a}\left[\right.$ coefficient of $x^{-6}$ in $\left.\left(a x^2+\frac{b}{x}\right)^{12}\right]$

C

$a\left[\right.$ coefficient of $x^{-10}$ in $\left.\left(a x+\frac{b}{x^2}\right)^{11}\right]$

D

$b\left[\right.$ coefficient of $x^4$ in $\left.\left(a x^2+\frac{b}{x}\right)^{11}\right]$

3
TS EAMCET 2022 (Online) 18th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $\frac{x^2-3 x+2}{(x-4)(x-3)^2}=\frac{A}{x-4}+\frac{B}{x-3}+\frac{C}{(x-3)^2}$ then $A+B+C=$

A

1

B

0

C

-1

D

5

4
TS EAMCET 2022 (Online) 18th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $\frac{x^2+3}{\left(x^2+1\right)\left(x^2+2\right)}=\frac{A x+B}{x^2+1}+\frac{C x+D}{x^2+2}$ then $A+B+C+D=$

A

3

B

2

C

0

D

1

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