GATE Questions

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4 x 27 x 3125 = 22 × 33 × 55 ;

8 x 9 x 25 x 7 = 23 × 32 × 52 × 7

16 x 81 x 5 x 11 x 49 = 24 × 34 × 5 × 11 × 72

H.C.F = 22 × 32 × 5 = 180.

Length of the first carpet = (1.44)(6) = 8.64 cm

Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)

= 51.84(1.4)(5/4) sq m = (12.96)(7) sq m

Cost of the second carpet = (45)(12.96 x 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs. 4082.40

Let the length of each train be x mts.

Then, distance covered = 2x mts.

Relative speed = 36 - 26 = 10 km/hr.

= 10 x 5/18 = 25/9 m/sec.

2x/36 = 25/9 => x = 50 mts.

100C10 + 90C20 + 70C30 + 40C40 = 100!10!x20!x30!x40!

Let the principle be Rs. P
As the amount double itself the interest is Rs. P too
So P = P x r x 15/100
=> r = 100/15 = 20/3 % = 6.66 %.

Given that If Theresa's daughter is my daughter's mother

It has 2 ways of Answers such that it depends on the sex of me. That is Male or Female.

1) If I am a Male :

My daughter's mother is my wife.

My wife is Teresa's daughter

=> I am Teresa's Son-in-law.

2) If I am a Female :

My daughter's mother is myself.

Myself Teresa's daughter.

=> I am Teresa's Daughter.

But in the given options only Son-in-law is available and daughter is not given.

So, Son-in-law is correct.

A Christian Priest wears cassock while a Graduate wears gown.

Hence, Cassock : Priest :: Gown : Graduate.

Let p = Rs. 100.

Then, S.I is Rs. 50 and time = 5 years. 

∴ R = 100×50100×5= 10% p.a.

Now, p = Rs. 12,000 , T = 3 years and R = 10% p.a.

C.I. = Rs. 12000×1+101003-1= Rs. 3972