CAT Questions

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100C10 + 90C20 + 70C30 + 40C40 = 100!10!x20!x30!x40!

4 x 27 x 3125 = 22 × 33 × 55 ;

8 x 9 x 25 x 7 = 23 × 32 × 52 × 7

16 x 81 x 5 x 11 x 49 = 24 × 34 × 5 × 11 × 72

H.C.F = 22 × 32 × 5 = 180.

Sony and her brother's age sum is 31
Let Sony's mother's age be 'x'.
Now the conditions given for both of their ages related to their mom is
1/5(x-15) + 3/5(x-10) = 31
x-15 + 3x-30 = 155
4x-45 = 155
4x = 200
x = 50
So, Mother's age = 50.

Cross verification : 15 years ago age = 35 => Sony age = 7
10 years ago age = 40 => bro age = 24

Sum = 24 + 7 = 31.

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

6M + 3B = 4(1M + 1B)
6M + 3B = 4M + 4B
2M = 1B

M/B = 1/2

Volume of cuboid = (24 x 9 x 8) cm = 1728 cu.cm
Volume of small cube = (3 x 3 x 3) cm = 27 cu.cm

So, No. of small cubes formed = 1728/27 = 64.

They walked and did this.

It was never specified that the boat was at sea. Since this logic is observed by them to tackle situation.

Succus Entericus is the alkaline secretion produced by glands in the wall of the duodenum, consisting of water, mucoproteins, and hydrogencarbonate ions.

Succus Entericus is secreted by Crypts of Lieberkuhn.

It helps to counteract the highly acidic and proteolytic chyme entering the small intestine from the stomach, and thus protects the duodenum from damage.