CAT Questions

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The first letter moves three steps forward. The second letter moves two steps forward. The third letter moves three steps forward.

We have : ( a + b + c) / 3 = M   or (a + b + c) = 3M.

Now. a+b+c2=3M2=9M2 .

<=>a2+b2+c2+2ab+bc+ca=9M2

a2+b2+c2=9M2 ,(ab+bc+ca=0)     

Required mean =a2+b2+c23=9M23=3M2 .

350 days = (350/7=50 weeks) i.e  No odd days,

 So it will be a Saturday.

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Herein the given sequence, 4, 2, 1, 0.5, 0.25, 0.125,...

Common Ratio r = 2/4 = 1/2 = 0.5/1 = 0.25/0.5 = 0.125/0.25 == 0.5.

110% of S.P. = Rs. 616

S.P. = (616 x 100)/110 = Rs. 560

C.P = (110 x 560)/112 = Rs. 500

A red ball can be drawn in two mutually exclusive ways

 (i) Selecting bag I and then drawing a red ball from it.

(ii) Selecting bag II and then drawing a red ball from it.

Let E1, E2 and A denote the events defined as follows:

E1 = selecting bag I,

E2 = selecting bag II

A = drawing a red ball

Since one of the two bags is selected randomly, therefore 

P(E1) = 1/2  and  P(E2) = 1/2

Now, PAE1 = Probability of drawing a red ball when the first bag has been selected = 4/7

  PAE2  = Probability of drawing a red ball when the second bag has been selected = 2/6

 Using the law of total probability, we have 

 P(red ball) = P(A) = PE1×PAE1+PE2×PAE2 

                          = 12×47+12×26=1942