TS EAMCET 2020 (Online) 11th September Evening Shift | Permutations and Combinations Question 71 | Mathematics

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

$(q+1) p!: 1$

$(q+1): 1$

$1: p$ !

$p!: q!$

TS EAMCET 2020 (Online) 11th September Morning Shift

MCQ (Single Correct Answer)

-0

$n^5-5 n^3+4 n$ is divisible by 120 is true for

all positive integers $n$

all positive integers for $n \geq 3$ only

all positive integers for $n \geq 1$ only

all positive integers for $n \geq 5$ only

TS EAMCET 2020 (Online) 11th September Morning Shift

MCQ (Single Correct Answer)

-0

The number of integers $x, y, z, w$ satisfying $x+y+z+w=25$ and $x, y, z \geq-1, w \geq 1$, is

${ }^{28} \mathrm{C}_3$

${ }^{30} \mathrm{C}_3$

${ }^{29} \mathrm{C}_3$

${ }^{31} C_3$

TS EAMCET 2020 (Online) 11th September Morning Shift

MCQ (Single Correct Answer)

-0

If 3 sisters and 8 other girls are together playing a game, then the number of ways in which all the girls are seated around a circle such that the three sisters are not seated together, is

$11!\times 8$

$8!\times 504$

$7!\times 210$

$8!\times 84$

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