TS ICET 23rd May 2019 Shift-1

given that 

$$x = \frac{2\sqrt{2} + \sqrt{7}}{2\sqrt{2} - \sqrt{7}}$$ 

then 1\x = $$\frac{2\sqrt{2} - \sqrt{7}}{2\sqrt{2} - \sqrt{7}}$$

then x - 1\x = 8 + 7 - 15 + 2 $$\times$$ 4 $$\sqrt{14}$$

then $$8\sqrt{14}$$ Answer

given that 

$$2^{45}$$\5 = 2 $$\times$$ $$2^{44}$$\5 = 2$$\times$$ $$2^{4}$$ $$\times$$ $$2^{11}$$ \5 

$$2^{4}$$ $$\times$$ $$2^{11}$$ \5  = 1 

then 

2 is the remainder Answer 

Setup the equation for determining the number of factors or divisors. 

The equation is= d(n)  =  (a + 1)(b + 1)(c + 1)(d + 1)

Where d(n) is equal to the number of divisors of the number and a, b, etc. are equal to the exponents of the prime factorization.

Now substitute the letters in the equation with the the exponents of your prime factorization and then solve to calculate the total number of divisors.

12,600 = 23 x 32 x 52 x 71
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
d(12600) = (3 + 1)(2 + 1)(2 + 1)(1 + 1)
d(12600) = (4)(3)(3)(2)
d(12600) = 72   Answer 

let the numbers are $$N_{1}$$and $$N_{2} = 210

then we know that 

$$N_{1}$$ $$\times$$ $$N_{2}$$ = G.C.D $$\times$$ LCM 

put the value 

$$N_{1}$$ $$\times$$  = ( 42 $$\times$$ 1260)\210

$$N_{1}$$ $$\times$$ = 252   Answer

we know the G.C.D. of 28 and 49 is = 7 

then we have given 

28x + 49y = 7 

but trial and error we have  

28.2-49 = 7

7 = 7  

X = 2 and y= -1 Answer 

given that 

= $$0.\overline{6} + 0.\overline{7} + 0.\overline{8}$$

= (6/9) + (7/9) + (8/9)

= 21/9

7/3 Answer 

given that 

= $$8\left[24 - \left\{25 - (17 - \overline{4 + 7}) + 5 \right\} + 2\right] $$  

= $$8\left[24 - \left\{25 - (17 - 9) + 5 \right\} + 2\right] $$

= 8[24 - {25 - 1} + 2 ]  

= 8[24 - 24 + 2] 

= 8$$\times$$2

= 16  Answer 

we knoe the valeu of $$\sqrt{2}$$ = 1.414 , $$\sqrt{3}$$ = 1.7304 ,   $$\sqrt{5}$$ = 2.23606 put the value we get the sequence d,c,b,a  Answer 

we know that the value of $$\sqrt{5}$$ = 2.23606 , $$\sqrt{6}$$ = 2.4494 , $$\sqrt{11}$$ = 3.3166  then we get 

$$6\sqrt{5}$$ > 4$$\sqrt{11}$$> 5 $$\sqrt{6}$$   Answer  

let the original price of the onion is X Rs 

then reduced price is =  X - 25X\400 = 15X\16 

it means now he able to buy 16 kg instead of 15 kg due to reduction 

so the original price is = 120\15 = 8 Rs\kg Answer