1. Problem: Find $\cos \frac{\pi}{2}$.\nStep 1: Recall that $\cos \frac{\pi}{2} = 0$.\nAnswer: (a) 0\n\n2. Problem: Determine the quadrant for angles between $\frac{3\pi}{2}$ and $2\pi$.\nStep 1: $\frac{3\pi}{2}$ is 270 degrees, $2\pi$ is 360 degrees.\nStep 2: Angles between 270° and 360° lie in the 4th quadrant.\nAnswer: (d) 4th\n\n3. Problem: Convert $\pi$ radians to degrees.\nStep 1: $\pi$ radians = 180 degrees.\nAnswer: (b) 180\n\n4. Problem: Find distance between points (1,0) and (0,1).\nStep 1: Use distance formula: $d=\sqrt{(1-0)^2 + (0-1)^2} = \sqrt{1 + 1} = \sqrt{2}$.\nAnswer: (c) 1\n\n5. Problem: Find $k$ if line $5x - ky - 3 = 0$ passes through (1,2).\nStep 1: Substitute (1,2): $5(1) - k(2) - 3 = 0 \Rightarrow 5 - 2k - 3 = 0$.\nStep 2: Simplify: $2 - 2k = 0 \Rightarrow 2k = 2 \Rightarrow k = 1$.\nAnswer: (a) 1\n\n6. Problem: Identify the line $x - 5 = 0$.\nStep 1: This is a vertical line where $x=5$, parallel to y-axis.\nAnswer: (b) y-axis\n\n7. Problem: Determine the unit of ratio.\nStep 1: Ratio is a comparison of two quantities of the same unit, so it has no unit.\nAnswer: (c) no\n\n8. Problem: Find the area of a parallelogram.\nStep 1: Area formula is base times height: $b \times h$.\nAnswer: (a) $b \times h$\n\n9. Problem: Identify the symbol used for proportion.\nStep 1: Proportion is denoted by double colon ::.\nAnswer: (b) ::\n\n10. Problem: Name the point where angle bisectors of a triangle meet.\nStep 1: Angle bisectors meet at the incentre.\nAnswer: (b) incentre\n\n11. Problem: Find the probability of an impossible event.\nStep 1: Probability of impossible event is 0.\nAnswer: (a) 0\n\n12. Problem: Find the size of class interval (1---3).\nStep 1: Class interval size = upper limit - lower limit = 3 - 1 = 2.\nStep 2: None of the options match 2, so answer is None.\nAnswer: (d) None