GATE Questions

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It won't requires that much solving.

Here given the increase in weekly collection by Rs. 1,05,000

That is this increase denotes for all 7 days.

=> Gross Collection increase per day = Rs. 1,05,0007 = Rs. 15,000

Hence, the gross collection increase per day = Rs. 15,000.

The 8 letters can be written in 8! ways.
n(S) = 8!
Let E be the event that the letters b,c,d,e always come together when the first 8 alphabets are written down.
Now the letters a, (bcde), f, g and h can be arranged in 5! ways.
The letters b,c,d and e can be arranged themselves in 4! ways.
n(E) = 5! x 4!
Now, the required P(E) = n(E)/n(S) = 5! x 4!/8! = 1/14
Hence the answer is 1/14. 

1001 A N means 1001 Arabian Nights.

These are same as 12 S of the Z, 64 S on a C, 19 C in CB, 8 S on SS, ...

Here all the given compounds have both ionic and covalent bonds.

NaNO3 - In Sodium nitrate, Nitrate is covalently bonded as nitrogen is bonded with 3 oxygen atoms. And this nitrate is ionically bonded with sodium.

CaSO4 - In Calcium sulphate, sulphate is covalently bonded as sulphur is bonded with 4 oxygen atoms. And this sulphate is ionically bonded with calcium.

NH4Cl - In Ammonium chloride, ammonium is covalently bonded as nitrogen is bonded with 4 hydrogen atoms. And this ammonium is ionically bonded with chlorine.

Let the total quantity of gold be p kgs.

According to the question,

50% of p + 25% of p + 12.5% of p = 130900

87.5% of p = 130900

p = 130900 x 100/87.5  = 149600 kgs.

Therefore, the initial gold quantity that king has = p = 149600 kgs.

      It is a case of shifting as given below:

      1  2  3  4  5                    2  1  3  5  4

      O  F  T  E  N   →  F  O  T  N  E

---------------------------------------------------------------------------

       1  2  3  4  5                   5  4  3  1  2

1.    H  E  A  R  T       →      T  R  A  H  E    

2.    O  P  E  N  S  →  S  N  E  O  P

        1  2  3  4  5         2  1  3  5  4

3.    R  I  S  K  Y  →   I  R  S  Y  K

4.    F  I  R  S  T  →   I  F  R  S  T

Hence option 3 is correct.

Let, Distance between A and B = d

Distance travelled by P while it meets Q = d + 11

Distance travelled by Q while it meets P = d – 11

Distance travelled by Q while it meets R = d + 9

Distance travelled by R while it meets Q = d – 9

Here the ratio of speeds of P & Q => SP : SQ = d + 11 : d – 11

The ratio of speeds of Q & R => SQ : SR = d + 9 : d – 9

But given Ratio of speeds of P & R => P : R = 3 : 2

 SPSR = SPSQxSQSR = d+11d+9d-11d-9

=> d+11d+9d-11d-9 = 3/2

=>  d = 1, 99

=> d = 99 satisfies.

Therefore, Distance between A and B = 99

In geometry, we can define plane as a flat surface with no thickness.

The surface extends with no ends.

A plane does not have any edges even if we draw it on paper with edges, it does't mean it has edges.

Hence, A plane is an undefined term because it is described generally, not using a formal definition.