AIEEE Questions

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Let the radii of the smaller and the larger circles be 's' m and 'l' m respectively.  

 2πs = 264 and 2πl = 352  

 s = 2642π and l = 3522π   

Difference between the areas =πl2-πs2   

  = π1762π2-1322π2 

  = 1762π-1322π  

  = (176 - 132)(176 + 132) / π  

  = (44 x 308) / (22/7) = 4312 sq.m

As we know we have 10 letter and 10 different address and one more information given that exactly 9 letter will at the correct address....so the remaining one letter automatically reach to their correct address
P(E) = favorable outcomes /total outcomes
Here favorable outcomes are '0'.
So probability is '0'.

Let the number of students in classes A, B and C be P, Q and R respectively.
Then, total score of A = 83P, total score of B = 76Q, total score of C = 85R.
Also given that,
(83P + 76Q) / (P + Q) = 79
=>4P = 3Q.
(76Q + 85R)/(Q + R) = 81
=>4R = 5Q,
=>Q = 4P/3 and R = 5P/3
Therefore, average score of A, B, C = ( 83P + 76Q + 85R ) / (P + Q + R) = 978/12 = 81.5

Angle between hands of a clock

When the minute hand is behind the hour hand, the angle between the two hands at M minutes past H 'o clock

=> 30H-M5+M2 degrees

Here H = 4, M = 15 and the minute hand is behind the hour hand.

Hence the angle

 = 30[4-(15/5)]+15/2 = 30(1)+7.5 = 37.5 degrees

Since he is telling about the thing that had happened in past.

Given (2a + 3b)/(5a - 3b) = 23/5
=> 10a + 15b = 115a - 69b
=> 105a = 84b => 5a = 4b
a/b = 4/5 => a=4 & b=5
=> bxa = 5x4 = 20.

Let the first number be x and the second number be y.

Given

5% of x = (25% of y) + y

=> 5x/100 = 5y/4

=> x = 25y ......(1)

and also given that, x - y = 96

=> x = 96 + y .....(2)

From (1)&(2)

25y = 96 + y

=> 24y = 96

=> y = 4

From (1)

x = 96 + 4 = 100

Hence, the numbers are 100 & 4.