CAT QUANT NUMBER SYSTEM 9

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Question 1:

The integers 573921 and 575713 when divided by a 3 digit number leave the same remainder. What is that 3 digit number?

Question 2:

Find the remainder when $\left(3^{41} +7^{ 41}\right)$  is divided by 13

Question 3:

In a division problem, product of quotient and the remainder is 24 while their sum is 10 . If the divisor is 5 then dividend is :

Question 4:

$X=$ remainder when $(1 !+2 !+3 !+\ldots+100 !)$ is divided by $15 .$ Find $X$

Question 5:

Let $n !=1 \times 2 \times 3 \times \ldots \times n$ for integer $n$ greater than or equal to $1$. 

If $P=1 !+(2 \times 2 !)+(3 \times 3 !)+\ldots . .+(12 \times 12 !)$, then $(P+3)$ when divided by $13 !$ leaves a remainder of:

Question 6:

The remainder when $\left(29^{ 29}\right)^{29} $ is divided by 9 is

Question 7:

Which least natural number when added to $7^{84} $ gives a resulting number that is divisible by 11

Question 8:

If $\mathrm{N}=\left(24^{3}+25^{3}+26^{3}+27^{3}\right)$, then $\mathrm{N}$ divided by 102 leaves a remainder of?

Question 9:

Given a number, $\mathrm{N}=55^{5}+17^{5}-72^{5}$, then which of the following is true?

Question 10:

Find the remainder when $(7 ! \times 6 !+8 ! \times  7 !)$ is divided by $9 !$