CAT Questions

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We know that,

$$\begin{gathered} i2 = -1 \\ i3 = i2 x i = -1 x i = -i \\ i4 = i2 x i2 = -1 x -1 = 1 \\ Hence, i233 =i4 x 58 + 1 = i232 x i1 = 1 x i = i \end{gathered}$$

Let the Oranges be 'O', Bananas be 'B' and Apples be 'A'

From the given data,

2O + 3B + 4A = 15 ...... (I)

3O + 2B + A = 10 ..... (II)

On adding (I) and (II),

5O + 5B + 5A = 25

O + B + A = 5

4O + 4B + 4A = 20.

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

Screws weight = 90x100 = 9000gms
bolts weight = 100 x 150 = 15000gms
weight = screws + bolts => 24000 gms =>24 kg
Given entire box weight = 35.5kg
empty box = entire box weight - weight => 35.5kg - 24kg => 11.5kg
so the empty box is 11.5kg.

Here total parts of milk and water in the solution is 6+2 = 8 parts.

1part = 640/8 = 80

old mixture contains 6parts of milk and 2 parts of water(6:2).

To get new mixture containing half milk and half water, add 4parts of water to the old mixture then 6:(2+4) to make the ratio same.

i.e, 4 x 80 = 320 ml.

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.

Porcupine is a rodent and mildew is a fungus.

Hence, Porcupine : Rodent :: Mildew : Fungus.

N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305)

= H.C.F. of 3360, 2240 and 5600 = 1120.

Sum of digits in N = ( 1 + 1 + 2 + 0 ) = 4