Answer: Option A

Explanation:
2/5 = 0.4, 3/8 = 0.375,
4/9 = 0.44, 5/13 = 0.385 and 6/11 = 0.55 
So, 3/8 So, the fourth fraction is = 4/9

Answer: Option B

Explanation:
Given expression
= 1/(2 × 3) + 1/(3 × 4) + 1/(4 × 5) + ...... + 1/(21 × 22)
= (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + ..........
= (1/21 - 1/22) = 1/2 - 1/22 = 10/22 = 5/11
Thus, least fraction to be added = 1 - 5/11 = 6/11

Answer: Option A

Explanation:
Required fraction = 45/(24 × 60) = 1/32

Answer: Option B

Explanation:
a = x/(x - 1) = 1 + 1/(x - 1) = 1 + b
  a > b

Answer: Option C

Explanation:
Given, x^y = 196 14²
=> x = 14
and y = 2
then, (x - 1)^{y - 1} = (14 - 1)^{2 - 1} = 13

Answer: Option D

Explanation:
x/2 = y/4 = z/6 = k, Then x = 2k, y = 4k and z = 6k.
Now, (x + y + z)/z = (2k + 4k + 6k)/6k = 12k/6k = 2

Answer: Option B

Explanation:
If x = y
=> 3 - t = 4t + 13 
=> 5t = -10 => t = -2

Answer: Option C

Explanation:
Given, (4x + y)/(x + 4y) = 2/3 
=> 3(4x + y) = 2(x + 4y)
=> 2x = y 
.: (x + 4y)/(4x + y) = x + 4(2x)/(4x + 2x) = 9x/6x = 3/2

Answer: Option A

Explanation:
The given expression is of the form
= [(a + b)² - (a - b)²]/ab = [(a² + b² + 2ab) - (a² + b² - 2ab)]/ab
= (a² + b² + 2ab - a² - b² + 2ab)/ab = 4ab/ab = 4
=> [(176 + 124)² - (176 - 124)²]/176 × 124 = 4

Answer: Option B

Explanation:
Using the algebraic expression
(a + b + c)² = a² + b ² + c ² + 2(ab + bc + ca)
=> 2(ab + bc + ca) = (a + b + c)² - (a² + b² + c²)
=> ab + bc + ca = (a + b + c)² - (a² + b² + c²)/2
.: xy + yz + zx = (x + y + z)² = (x² + y² + z²)/2
=(6² - 14)/2 = (36 - 14)/2 = 11