1
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 $\left.\left(a x^2+\frac{b}{x}\right)^{11}\right]$

2
TS EAMCET 2020 (Online) 14th September Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $x$ is so small that all terms containing $x^2$ and higher powers of $x$ can be neglected, then the approximate value of $\frac{\left(1+\frac{2 x}{3}\right)^{-4}(4+5 x)^{1 / 2}}{(9+x)^{3 / 2}}$, when $x=\frac{6}{371}$, is

A

$\frac{1}{27}$

B

$\frac{29}{378}$

C

$\frac{3}{27}$

D

$\frac{1}{14}$

3
TS EAMCET 2020 (Online) 14th September Evening Shift
MCQ (Single Correct Answer)
+1
-0

The sum of the coefficients of $x^{-3 / 2}$ and $x^3$ in the expansion of $\sqrt{3+x}+\sqrt{5+x}$ when $3 < x< 5$, is

A
$$ =\frac{-18+3(5)^{-5 / 2}}{8} $$
B

$\frac{5^{-5 / 2}-18}{16}$

C

$\frac{-6+\sqrt{5}}{6}$

D

$\frac{5-\sqrt{6}}{6}$

4
TS EAMCET 2020 (Online) 14th September Morning Shift
MCQ (Single Correct Answer)
+1
-0

$p, q$ are two prime numbers. For $n=p q$, if the expansion $\left(\sqrt[4]{x^{-5}}+2 \sqrt[5]{x^5}\right)^n$ contains non-zero coefficient of $x^{-n}$ and $x^0$, then the least value of such $n$ is

A

82

B

41

C

123

D

62

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