• Volume of a sphere: (4/3) * π * r^3

  • Radius (r) = diameter/2 = 1/2 unit

  • Volume = (4/3) * π * (1/2)^3 = π/6 cubic units

• Volume of a cube: side^3 = 1 cubic unit

• Clearly, π/6 is less than 1.

So, the answer is (B) less.

The correct form for this sentence is "The unruly crowd demanded that the accused be hanged without trial." There should be 3rd form of verb

So, the answer is (A) hanged. 

• Prone means lying flat face downward.

• Prone to  means having a tendency to suffer from something.

So, the correct statements are (ii) and (iii).

The answer is (D) 

• If it rains, the field is wet. This is a conditional statement.

• Option (C) "If (i), then (ii)" contradicts the given fact. If it rains (i), the field must be wet

So, the answer is (C) 

a = 6/5 m

Area of the square = a^2 = 36/25= 1.44

Area of the equilateral triangle = (√3/4) * a^2 = (√3/4) * 1.44 ≈ 0.623 m^2

Total area of the window = Area of square + Area of triangle = 1.44 + 0.623 ≈ 2.06 m^2

Answer is (B) 

Group P has a higher mean and standard deviation than group Q. This indicates that the scores in group P are more spread out than in group Q.

Option (C) "Most students of group Q scored marks in a narrower range than students in group P" is most likely to be true based on the given information about means and standard deviations.

Answer is (C)

The paragraph mentions that critics argue that smart cities will lead to a surveillance state. This indicates a perception about smart cities.

Option (iv) "There is a perception that smart cities promote surveillance" accurately reflects this information.

So, the answer is (C) 

For the identity element x, we have a □ x = a for any a.

So, ax + (a + x) = a  ⇒ ax + x = 0 ⇒ x ( a + 1) = 0

This equation holds true for all a if x = o

The answer is (A)