TS ICET 30th September 2020 Shift-1

The positive square root of $$14 + 6\sqrt{15}$$ is

The remainder when $$3^{45}$$ is divided by 6 is

The number of positive divisors of $$n = 311^{2} \times 373^{3} \times 307^{4}$$ is

The GCD of 3240, 3600 and $$x$$ is 36 and the LCM of these three number is
$$2^{4} \times 3^{5} \times 5^{2} \times 7^{2}$$ then $$\sqrt{6x}=$$

Three bicycles are fitted with wheels that can make 6, 5 and 10 revolutions per minute respectively. One spoke on each wheel is painted blue. All three bicycles start moving at the same time, and the poke of the wheels painted blue is in the same position for all 3 bicycles. After how much time, will all the three wheels be a1igned in the same manner as they were at the starting? ( in seconds)

The number of rational numbers in the expansion of  $$\left(\sqrt[3]{25} + \frac{1}{\sqrt[4]{10}}\right)^{20}$$ is

The rational number that represents the recurring decimal number $$0.2\overline{34}$$ is

Six persons A, B, C, D, E and F are of different heights. No two among them, are of same height. It is also known that

i) A is taller than B but shorter than C
ii) Dis taller than E who is in turn is taller than F
iii) F is taller than A

Who is the shortest?

If the following fractions are arranged in descending order (of their magnitudes), the
middle one is

$$\frac{2}{3}, \frac{5}{7}, \frac{9}{13}, \frac{9}{14}, \frac{7}{9}$$

In a school 75% are girl, and the boys are 625 in number. The total student strength in the school is