TS ICET 20th August 2021 Shift-1

$$\frac{1}{\sqrt{18}+3}+\frac{1}{\sqrt{27}+\sqrt{18}}+\frac{1}{\sqrt{36}+\sqrt{27}}+...+\frac{1}{\sqrt{900}+\sqrt{891}} =$$

If $$2^{2}$$ divides 19!, then the largest positive integer k is

The remainder when $$(48)^{5}$$ is divided by 5 is

What is the least number that should be subtracted from 5337 to make it a perfect square?

If the LCM and the GCD of two positive integers are 4641 and 21 respectively, and if one of the numbers is greater than 300 then the other number is

The product of two natural numbers is 17. Then, the sum of the reciprocals of their squares is _______

If the numerator of a fraction is increased by 2 and the denominator is increased by 3, the fraction becomes $$\frac{7}{9}$$ and if both the numerator as well as the denominator are increased by 1, the fraction betomes $$\frac{4}{5}$$. What is the original fraction?

If the fraction $$\frac{19}{21}, \frac{21}{25}, \frac{25}{29}, \frac{29}{31}$$ and $$\frac{31}{37}$$ are arranged in the ascending order, then the largest fraction is

The ascending order of the following rational numbers is

$$A = \frac{4}{9};B = \frac{7}{12};C = \frac{3}{7};D = \frac{8}{15};E = \frac{1}{2}$$

The price of petrol is increased by 40%. By how much percent should a citizen reduce his purchase so as not to increase his expenditure?