Question : A number, when divided by 729, gives a remainder of 56. What will we get as a remainder if the same number is divided by 27?

Option 1: 4

Option 2: 2

Option 3: 0

Option 4: 1

Question : If $x^2-\sqrt{7} x+1=0$, then $\left(x^3+x^{-3}\right)=?$

Option 1: $4 \sqrt{7}$

Option 2: $3 \sqrt{7}$

Option 3: $10 \sqrt{7}$

Option 4: $7 \sqrt{7}$

Question : When a number is successively divided by 3, 4, and 7, the remainder obtained is 2, 3, and 5 respectively. What will be the remainder when 42 divides the same number?

Option 1: 41

Option 2: 30

Option 3: 29

Option 4: 31

Question : When a number is successively divided by 3, 4 and 7, the remainder obtained are 2, 3 and 5, respectively. What will be the remainder when 84 divides the same number?

Option 1: 71

Option 2: 30

Option 3: 48

Option 4: 53

Question : If $x^2+\frac{1}{x^2}=\frac{7}{4}$ for $x>0$; then what is the value of $x+\frac{1}{x}$?

Option 1: $2$

Option 2: $\frac{\sqrt{15}}{2}$

Option 3: $\sqrt{5}$

Option 4: $\sqrt{3}$