CAT Questions

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 $$\begin{gathered} = log 33 + log 23+ log 103log10×3×22 \\ \end{gathered}$$ 

=log33 12+log 23+log 10312log(10×3×22)  

=12log 33+3 log 2+12 log103log10+log3+log22  

=32log 3 + 2 log 2 + log 10log 3 + 2 log 2 + log 10 = 32  

 Given A = log321875 and B = log2432187

B = log352187 = log321875

=> A

Therefore, A = B

Let the length of the 1st train = L mts

Speed of 1st train = 48 kmph

Now the length of the 2nd train = L/2 mts

Speed of 2nd train = 42 kmph

Let the length of the bridge = D mts

Distance = L + L/2 = 3L/2

Relative speed = 48 + 42 = 90 kmph = 90 x 5/18 = 25 m/s(opposite)

Time = 12 sec

=> 3L/2x25 = 12

=> L = 200 mts

Now it covers the bridge in 45 sec

=> distance = D + 200

Time = 45 sec

Speed = 48 x5/18 = 40/3 m/s

=> D + 200/(40/3) = 45

=> D = 600 - 200 = 400 mts

Hence, the length of the bridge = 400 mts.

A constitutional monarchy is a form of monarchical government established under a constitutional system which acknowledges an elected or hereditary monarch as head of state.

The monarchs in a constitutional monarchy had only the power that was allocated to them in the constitution of their land or republic.

The Mediterranean sea separates Europe from Africa.

Let the amount invested by saketh = RS. p

Now, that of sandeep = 20,000 x 6

saketh = 12 x p

Ratio of their earnings = 120000 : 12p = 6000 : (9000 - 6000)

=> $$\begin{gathered} 12000012p = 60003000 \\ => p= Rs. 5000 \end{gathered}$$

Hence, the amount investe by saketh  = Rs. p  = Rs. 5000.