GATE BT 2021 • Q15
MCQ • 1 Mark
Section 2: General Biotechnology
Biomolecules, enzyme kinetics
Subtopic: Fundamentals of Biomolecules, enzyme kinetics
Question Statement:
to 0.5
2
44
5
NAT
8 to 8
2
45
5
NAT
64 to 65
2
46
5
NAT
13 to 14
2
47
5
NAT
1.20 to 1.30
2
48
5
NAT
Options:
-
(A) (V3, 2Vz)
-
(B) (2, 23)
-
(C) (2V2, V3)
-
(D) (2V2, 2V2)
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2021 Q.15)**
**1. Governing Concept**:
- **Topic**: Engineering Mathematics & Polar to Cartesian Coordinates
- Polar coordinates $(r, \theta) = (4, \pi/4)$.
- Conversion to Cartesian coordinates $(x, y)$:
$x = r \cos \theta = 4 \cos\left(\frac{\pi}{4}\right) = 4 \times \frac{1}{\sqrt{2}} = \frac{4\sqrt{2}}{2} = 2\sqrt{2}$
$y = r \sin \theta = 4 \sin\left(\frac{\pi}{4}\right) = 4 \times \frac{1}{\sqrt{2}} = 2\sqrt{2}$
- Therefore:
$(x, y) = (2\sqrt{2}, 2\sqrt{2})$
**2. Option Analysis**:
- **Option (A) is INCORRECT**: Erroneous radical factors.
- **Option (B) is INCORRECT**: Corresponds to $\theta = \pi/3$.
- **Option (C) is INCORRECT**: Asymmetric coordinates; for $\theta = \pi/4$, $x$ must equal $y$.
- **Option (D) [(2√2, 2√2)] is CORRECT**: Matches $x = y = 2\sqrt{2}$.
**3. Final Answer**:
- **Correct Choice**: **D**
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