Square Root, Ratio and Proportion percentage
Workshop Calculation and Science, Module-2
Q1: What is the square root of 529?
- 13
- 23
- 33
- 43
Show Calculation
\[ \sqrt{529} = \sqrt{23 × 23} = 23 \]
Q2: What is the square root of 0.017?
- 0.001
- 0.13
- 0.00001
- 0.000001
Show Calculation
\[ \sqrt{0.017} \approx 0.130 \]
Q3: What is the definition of ratio?
- Relation of two quantities of the same kind
- Relation of two quantities of different kind
- Equality between two ratios
- Inequality between two ratios
Q4: What is the ratio of 4 kg to 800 grams?
- 5 : 1
- 4 : 8
- 8 : 4
- 2 : 4
Show Calculation
\[ 4\ \text{kg} = 4000\ \text{g} \quad \Rightarrow \quad \frac{4000}{800} = 5 : 1 \]
Q5: What percentage of 80 is 20?
- 80%
- 40%
- 25%
- 20%
Show Calculation
\[ \frac{20}{80} \times 100 = 25\% \]
Q6: How much is 8% of 40 kg?
- 2.2 kg
- 3.2 kg
- 4.2 kg
- 5.2 kg
Show Calculation
\[ 40 \times \frac{8}{100} = 3.2\ \text{kg} \]
Q7: Convert 52% into fraction
- \(\frac{9}{25}\)
- \(\frac{11}{25}\)
- \(\frac{13}{25}\)
- \(\frac{17}{25}\)
Show Calculation
\[ \frac{52}{100} = \frac{13}{25} \]
Q8: Convert 0.456 decimal fraction into percentage
- 45.6%
- 4.56%
- 0.456%
- 0.0456%
Show Calculation
\[ 0.456 \times 100 = 45.6\% \]
Q9: What is the \('x'\) value for \(x^2 + 6^2 = 10^2\)?
- 4
- 6
- 8
- 10
Show Calculation
\[ x^2 + 36 = 100 \Rightarrow x^2 = 100-36 = 64 \] \[\Rightarrow x = \sqrt{8 × 8} = 8 \]
Q10: What is the square root of decimal number 550.37?
- 21.26
- 22.26
- 22.46
- 23.46
Show Calculation
\[ \sqrt{550.37} \approx 23.46 \]
Q11: What is the value of \(\sqrt{8} + \sqrt{18} - 2\sqrt{2}\)?
- 2.24
- 3.24
- 4.24
- 5.24
Show Calculation
\[ \sqrt{8} + \sqrt{18} - 2\sqrt{2} = 2\sqrt{2} + 3\sqrt{2} - 2\sqrt{2}\] \[= 3\sqrt{2} \approx 4.24 \]
Q12: What is the side AB if AC = 10 cm and BC = 6 cm?
- 8 cm
- 6 cm
- 5 cm
- 4 cm
Show Calculation
\[ AB = \sqrt{AC^2 - BC^2} = \sqrt{10^2 - 6^2} \] \[= \sqrt{100 - 36} = \sqrt{64} = 8\ \text{cm} \]
Q13: What is the side AB if BC = 15 cm and AC = 9 cm?
- 4 cm
- 8 cm
- 10 cm
- 12 cm
Show Calculation
\[ AB = \sqrt{BC^2 - AC^2} = \sqrt{15^2 - 9^2} \] \[= \sqrt{225 - 81} = \sqrt{144} = 12\ \text{cm} \]
Q14: What is the value of side AC if AB = 7 cm and BC = 5 cm?
- 8.2 cm
- 8.6 cm
- 8.4 cm
- 8.1 cm
Show Calculation
\[ AC = \sqrt{AB^2 + BC^2} = \sqrt{7^2 + 5^2} \] \[= \sqrt{49 + 25} = \sqrt{74} \approx 8.6\ \text{cm} \]
Q15: What is the length L₂, if total length (L) is 2.75 metres and L₁ : L₂ = 2 : 3?
- 1.1 metre
- 1.25 metre
- 1.65 metre
- 1.75 metre
Show Calculation
\[ \text{Total parts} = 2 + 3 = 5, \] \[\quad L_2 = \frac{3}{5} \times 2.75 = 1.65\ \text{metres} \]
Q16: How many days a mechanic takes to assemble 64 machines if he assembles 8 machines in 3 days?
- 20 days
- 22 days
- 24 days
- 26 days
Show Calculation
\[ \text{If 8 machines take 3 days}, \] \[\quad 1\ \text{machine takes } \frac{3}{8}\ \text{days} \] \[ \Rightarrow 64 \times \frac{3}{8} = 24\ \text{days} \]
Q17: What will be the RPM of smaller gear if a 180 mm dia meshes with 60 mm dia gear and the bigger gear makes 60 RPM?
- 120 RPM
- 140 RPM
- 160 RPM
- 180 RPM
Show Calculation
\[ \text{RPM}_{\text{small}} = \frac{180}{60} \times 60 = 180\ \text{RPM} \]
Q18: What is the percentage of copper if the casting weight is 42.3 kg copper and 2.7 kg tin?
- 92%
- 94%
- 96%
- 98%
Show Calculation
\[ \text{Total} = 42.3 + 2.7 = 45,\] \[\quad \frac{42.3}{45} \times 100 = 94\% \]
Q19: A motorcycle tyre is sold for ₹300. What is the purchase price if 25% profit is added?
- ₹200
- ₹220
- ₹240
- ₹260
Show Calculation
\[\text{Selling Price}= \text{Cost Price} + 25\%\ \text{of Cost Price} \] \[\Rightarrow 1.25x = 300 \Rightarrow x = \frac{300}{1.25} = 240 \]
Q20: What is the decimal fraction of conversion of 18.5%?
- 0.185
- 0.175
- 0.165
- 0.195
Show Calculation
\[ 18.5\% = \frac{18.5}{100} = 0.185 \]