GATE Questions

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Let A, B, C be the respective events of solving the problem and A , B, C be the respective events of not solving the problem. Then A, B, C are independent event

∴A, B, C are independent events

Now,  P(A) = 1/2 , P(B) = 1/3 and P(C)=1/4

 PA=12, PB=23, PC= 34

∴ P( none  solves the problem) = P(not A) and (not B) and (not C)  

                  = PA∩B∩C 

                  = PAPBPC         ∵ A, B, C are Independent                       

                  =  12×23×34  

                  = 14  

Hence, P(the problem will be solved) = 1 - P(none solves the problem) 

                = 1-14= 3/4

Given expression = (45 x 750/100) - (25 x 480/100) = (337.50 - 120) = 217.50

52.5% of 800 + 30.5% of 2800 = ? + 87.30

420 + 854 - 87.30 = ?

1274 - 87.30 = ?

? = 1186.70

ten = 3(number of letters)
nine = 4(number of letters)
sixty = 5(number of letters)
ninety = 6(number of letters)
seventy = 7(number of letters)
sixtysix = 8(number of letters)
ninetysix=96(number of letters)

Then, likwise choose the number which has 9 letters in its Spelling.

From all the hints given, 

only 042 satisfies and it unlocks the key.

In chemical nomenclature, the IUPAC nomenclature of organic chemistry is a systematic method of naming organic chemical compounds as recommended by the International Union of Pure and Applied Chemistry (IUPAC).

Given Equation is 

Mg + O2 → MgO

Balancing the Chemical Equation is nothing but Conservation of Matter. As Matter is Neither created nor Destroyed, it must be conserved.

Here we have 1 Mg and 2 O on the left side and 1 Mg and 1 O on the right side

To balance that, add 1 Mg on the left side so that it becomes 2 Mg and 2 O on the left side

i.e,

2 Mg + O2 → 2 MgO

Here it has 2 Mg & 2 O on the left side and 2 Mg and 2 O on the right side and the Chemical equation is Balanced.

Here the series follows the pattern that, product of succesive prime numbers i.e,

 2 × 3 = 6

 3 × 5 = 15

 5 × 7 = 35

 7 × 11 = 77

 11 × 13 = 143

 13 × 17 = 221

 17 × 19 = 323

So here in place of 77 the number 63 is written.

So the wrong number is 63.