The Laplace transform F(s) of the function f(t) = cos (at), where a is constant, is _____________.
Options:
(A) 2
22
s
sa
(B) 22
a
sa
(C) 22
s
sa
(D) 22
s
sa
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2016 Q.24)**
**1. Governing Concept & Question Classification**:
- **Section**: BT
- **Question Type**: **MCQ** (1 Mark)
- **Topic**: Biochemistry / Enzyme Kinetics (Patterns of Enzyme Inhibition)
**2. Detailed Step-by-Step Analysis**:
- Let us evaluate each statement concerning classical enzyme inhibition kinetics:
- **Statement A**: *In competitive inhibition, substrate and inhibitor compete for the same active site of an enzyme.* This is **TRUE**. Competitive inhibitors are structural analogs of the substrate that bind reversibly to the free enzyme's active site.
- **Statement B**: *Addition of a large amount of substrate to an enzyme cannot overcome uncompetitive inhibition.* This is **TRUE**. In uncompetitive inhibition, the inhibitor binds exclusively to the enzyme-substrate ($ES$) complex ($ESI$). Increasing $[S]$ actually increases the concentration of $ES$, facilitating more inhibitor binding; hence, high $[S]$ cannot restore $V_{\max}$.
- **Statement C**: *Competitive inhibition cannot be overcome by addition of large amount of substrate.* This is **FALSE / NOT TRUE**. Because the substrate and competitive inhibitor compete mutually for the same binding site, adding a sufficiently high excess of substrate ($[S] \to \infty$) outcompetes the inhibitor, driving all enzyme molecules into the $ES$ form and fully restoring maximum velocity ($V_{\max}^{\text{apparent}} = V_{\max}$).
- **Statement D**: *A non-competitive inhibitor binds to a site other than the catalytic site.* This is **TRUE** (allosteric site).
- Therefore, the statement that is **NOT true** is **Statement C**.
- **Option-by-Option Evaluation**:
- **Option (A) [TRUE/NOT ANSWER]**: Accurately describes competitive binding.
- **Option (B) [TRUE/NOT ANSWER]**: Accurately states that uncompetitive inhibition cannot be reversed by excess substrate.
- **Option (C) [FALSE STATEMENT / CORRECT OPTION]**: Falsely claims competitive inhibition cannot be overcome by high substrate; competitive inhibition is famously reversible by high $[S]$.
- **Option (D) [TRUE/NOT ANSWER]**: Accurately describes allosteric non-competitive binding.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **C**
- **Scoring Criteria**: +1.0 Mark (Negative marking: -0.33 marks).
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