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This two-blank question requires understanding the critical tone of the passage.
Blank (i): The agency never defined “untenable risk,” leaving it without a firm standard. This absence of a standard made it open and vulnerable to outside influence. Susceptible to means vulnerable or open to — exactly right. “Unaware of” doesn’t explain the influence, and “irritated at” changes the meaning entirely.
Blank (ii): Experts reacted negatively to the agency’s poor decision. They would pan it — meaning to criticize harshly. “Complimented” is the opposite, and “overlooked” means to ignore, not to criticize.
Correct Answers: Blank (i) = A (susceptible to), Blank (ii) = E (panned).
A machine has an original cost of Rs. 19,00,000 and installation charges of Rs. 1,00,000. Its useful life is 5 years and residual value is Rs. 40,000. Using the Straight Line Method, what is the depreciation charge for the 4th year?
Total cost $= 19{,}00{,}000 + 1{,}00{,}000 = Rs.\ 20{,}00{,}000$
Depreciable amount $= 20{,}00{,}000 - 40{,}000 = Rs.\ 19{,}60{,}000$
Annual depreciation (SLM) $= \dfrac{19{,}60{,}000}{5} = Rs.\ 3{,}92{,}000$
Under the Straight Line Method, depreciation is equal every year. So the 4th year's depreciation is also Rs. 3,92,000. There is no change between years in SLM.
Evaluate $\sin^{-1}\!\left(\dfrac{12}{13}\right)-\sin^{-1}\!\left(\dfrac{3}{5}\right)$.
Let $A=\sin^{-1}(12/13)$: $\sin A=12/13,\ \cos A=5/13$.
Let $B=\sin^{-1}(3/5)$: $\sin B=3/5,\ \cos B=4/5$.
$\sin(A-B)=\sin A\cos B-\cos A\sin B=\dfrac{12}{13}\cdot\dfrac{4}{5}-\dfrac{5}{13}\cdot\dfrac{3}{5}=\dfrac{48}{65}-\dfrac{15}{65}=\dfrac{33}{65}$... Hmm, but let me check $\cos(A-B)$: $=\cos A\cos B+\sin A\sin B=\dfrac{5}{13}\cdot\dfrac{4}{5}+\dfrac{12}{13}\cdot\dfrac{3}{5}=\dfrac{20+36}{65}=\dfrac{56}{65}$.
So $A-B=\cos^{-1}(56/65)=\pi/2-\sin^{-1}(56/65)$. Answer: $\dfrac{\pi}{2}-\sin^{-1}\!\left(\dfrac{56}{65}\right)$.
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