The expression  (A+B)³ = A³ + 3A²B + 3AB² + B³, a plain algebraic identity, is possible for 2 square matrices if and only if AB = BA, i.e., the multiplication should be commutative in this case.  

AB = [1  1 \ 1  0][a  b \ c  d] = [a+c    b+d \ a   b]

and

BA = [a  b \ c  d][1  1\ 1  0] = [a+b  a \ c+d  c]

Thus, b = c and a = b + d

|(b+c)/(a-d)| = |2b/(b+d-d)| = 2

Correct answer is option D

Case 1 : Exactly one digit repeated twice --

eg AABCD     Words= 10C1 X 9C3 X {5!/2!} =50400

Case 2 : Exactly one digit repeated thrice --

eg AAABC     Words= 10C1 X 9C2 X {5!/3!}= 7200

Case 3 : Exactly one digit repeated four times --

eg AAAAB     Words= 10C1 X 9C1 X {5!/4!}= 450

Case 4 : Exactly one digit repeated five times --

eg AAAAA     Words= 10C1 X {5!/5!}= 10

Case 5 : Exactly two digits repeated two times each --

eg AABBC     Words= 10C2 X 8C1 X {5!/(2! 2!)}= 10800

Case 6 : Exactly two digits repeated one of them twice and the other thrice --

eg AAABB     Words= 10C1 X 9C1 X {5!/(2! 3!)}= 900

FINAL ANSWER= Sum of all cases= 69760

density of water = 1g/ml

mass of 18ml of water = densityx volume =( 1g/ml)*(18ml) = 18g

no. of mol of water = 18g/18g/mol = 1 mol

1molecule of water contain 8 electrons

1mol of water contain 8*(6.02x1023)

= 48.16x1023

In order to find the locus of the centres of the circles intersecting the given circles we subtract the equations of the two circles.On subtracting them we get 8x-12y+5=0.This is a linear equation in x and y.Therefore locus is a straight line.

Option C as Mg and O will exchange their valency which is 2 and 3 respectively

Hard work , persevearence, mock tests, good guide.

150 m/s

The compound has 49.3% carbon, 6.84% hydrogen, and remaining is oxygen, which is 43.86%, As these elements have relative atomic weight (roughly) of 12, 1 and 16 respectively. Their ratios in the compound is C:H:O = (49.3/12) : (6.84/1) : (43.86/16) = 4.108: 6.84: 2.74, and dividing by lowest number 2.74, we get C:H:O = 1.5: 2.5 :1 = 3:5:2, Therefore the empirical formula is C3H5O2 and molecular formula is (C3H5O2)*n , So, molecular weight (12*3 + 1* 5 + 2* 16) *n = 73n, As, vapour density is 73, Molecular weight is 2* 73 =146 and Hence, 73n = 146, implies n =2, Therefore, Molecular formula is C6H10O4. And Option D is the correct answer.

Answer C