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 \(3 \frac{\pi}{2}\) and \(2\pi\).\nStep 1: \(3 \frac{\pi}{2} = \frac{3\pi}{2}\) is at 270 degrees, \(2\pi\) is 360 degrees.\nStep 2: Angles between 270° and 360° lie in the 4th quadrant.\nAnswer: (d) 4\(^{th}\)\n\n3. Problem: Convert \(\pi\) radians to degrees.\nStep 1: \(\pi\) radians = 180 degrees.\nAnswer: (b) 180\(^{\circ}\)\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