CAT Questions

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Probability of atleast one failure
= 1 - no failure > 31/32
= 1 - P5 > 31/32
=  P5<1/32
= p < 1/2
Also p > 0
Hence p lies in [0,1/2].

P( only one of them will be selected) = p[(E and not F) or (F and not E)] 

 = PE∩F∪F∩E 

= PEPF+PFPE

 =17×45+15×67=27

Let a, b and c be the amounts invested in schemes X, Y and Z respectively. Then,

As we know:

Simple interest (S.I.) = PTR/100

(a × 10 × 1/100) + (b × 12 × 1/100) + (c × 15 × 1/100) = 3200

= 10a + 12b + 15c = 320000 .........(1)

Now, c = 240% of b = 12b/5 .........(2)

And, c = 150% of a = 3a/2 => a = 2/3 c = (2 × 12)b/(3 × 5) = 8b/5 .......(3)

From (1), (2) and (3), we have

16b + 12b + 36b = 320000 => 64b = 320000 => b = 5000

∴ Sum invested in Scheme Y = Rs.5000.

We know that 1 yard = 3 feet. 

A yardstick which is used for measurement has 3 feet long but it cannot walk.

There are different colors that are used for different signs on the maps. The typical color standard for topographic maps depicts contours in brown, bodies of water in blue, boundaries in black, and grids and roads in red. Topographic maps may use different colors to represent area features.

Black represents man-made objects or cultural features like roads, bridges, borders, etc...