CAT QUANT NUMBER SYSTEM 8

Attempt now to get your rank among 2 students!

Question 1:

What is the remainder when $\left[(1 !)^{3} +(2 !)^{3} +(3 !)^{3} +(4 !)^{3} +(5 !)^{3} +\right.$ $\left..+(999 !)^{3} \right]$ is divided by 5

Question 2:

Three numbers leave remainders of 43,47 and 49 on division by $N$. The sum of the three numbers leaves a remainder 9 on division by N. What are the values $\mathrm{N}$ can take?

Question 3:

$\mathrm{N}^{2}$ leaves a remainder of 1 when divided by 24 . What are the possible remainders we can get if we divide $\mathrm{N}$ by $12 ?$

Question 4:

What is the remainder when $48^{45} $ is divided by $35 ?$

Question 5:

Consider a large number $N=1234567891011121314 \ldots \ldots . .979899100 .$ What is the remainder when first 100 digits of $\mathrm{N}$ is divided by 9 ?

Question 6:

What is the remainder when we divide $3^{90}+5^{90}$ by $34 ?$

Question 7:

A prime number $\mathrm{p}$ greater than 100 leaves a remainder $\mathrm{q}$ on division by 28. How many values can q take?

Question 8:

How many positive integers are there from 0 to 1000 that leave a remainder of 3 on division by 7 and a remainder of 2 on division by 4 ?

Question 9:

N leaves a remainder of 4 when divided by 33 , what are the possible remainders when $\mathrm{N}$ is divided by 55 ?

Question 10:

A number leaves a remainder 3 on division by 14 , and leaves a remainder $\mathrm{k}$ on division by 35 . How many possible values can $\mathrm{k}$ take?