1
TS EAMCET 2020 (Online) 11th September Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $x^4+x^2+1=0$, then $\frac{\alpha^3+\beta^3+\gamma^3+\delta^3}{\alpha^6+\beta^6+\gamma^6+\delta^6}=$

A

0

B

1

C

-1

D

$\frac{1}{2}$

2
TS EAMCET 2020 (Online) 11th September Evening Shift
MCQ (Single Correct Answer)
+1
-0

For $n=1,2,3, \ldots .50$, let

$$ A=\left\{a_n / a_n=\left\{\begin{array}{ll} (-1)^{\frac{n}{2}}\left(\frac{n}{2}\right), & \text { if } n \text { is even } \\ (-1)^{\frac{n-1}{2}}\left(\frac{n-1}{2}\right), & \text { if } n \text { is odd } \end{array}\right\}\right\} $$

and $B$ is the set of all distinct elements of $A$. The number of permutations all the elements of set $B$ such that even integers are in increasing order, is

A

$\frac{26!}{12!}$

B

$\frac{49!}{12!13!}$

C

$\frac{50!}{24!26!}$

D

$\frac{26!}{13!12!}$

3
TS EAMCET 2020 (Online) 11th September Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $\alpha$ represents the number of arrangements of $p$ men and $q$ women in a row such that all men are together and $\beta$ represents the number of circular arrangements of the same people with the same condition, then $\alpha: \beta$ is

A

$(q+1) p!: 1$

B

$(q+1): 1$

C

$1: p$ !

D

$p!: q!$

4
TS EAMCET 2020 (Online) 11th September Evening Shift
MCQ (Single Correct Answer)
+1
-0

If ${ }^n C_0,{ }^n C_1,{ }^n C_2, \ldots,{ }^n C_n$ respectively are the binomial coefficients in the expansion of $(1+x)^n$, then when $n=10, \sum_{r=1}^{10}{ }^n C_r \cdot r(r-4)=$

A

5120

B

7680

C

20480

D

28160

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