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Mathematics QUESTION #4145

Solve $\frac{dy}{\sqrt{1-y^2}} = \frac{dx}{\sqrt{1-x^2}}$ with $y(0) = \frac{\sqrt{3}}{2}$. What is the solution?

$\sin^{-1}(y) = \sin^{-1}(x) + \frac{\pi}{3}$
$\sin^{-1}(y) = \sin^{-1}(x) + \frac{\pi}{6}$
$y = \sin(\sin^{-1}(x) + \frac{\pi}{3})$
Both (A) and (C)✔️

Correct Answer Logic:

Integrating: $\sin^{-1}(y) = \sin^{-1}(x) + C$. At $x=0$, $y=\frac{\sqrt{3}}{2}$: $\frac{\pi}{3} = 0 + C$, so $C = \frac{\pi}{3}$. Thus $\sin^{-1}(y) = \sin^{-1}(x) + \frac{\pi}{3}$, equivalent to $y = \sin(\sin^{-1}(x) + \frac{\pi}{3})$.

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Basic Mathematics QUESTION #4583

Question 5002

In an arithmetic sequence $2, 5, 8, 11, 14$, what is the average?

$8$✔️
$7$
$40$
$6$

Correct Answer Logic:

For arithmetic sequence with odd number of terms, average = middle term = $8$

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3290

Question 5003

Which concentration of Ethyl Alcohol is most effective as a disinfectant?

$100\%$
$70\%$✔️
$30\%$
$10\%$

Correct Answer Logic:

$70\%$ alcohol is more effective than $100\%$ because water is required to denature proteins and penetrate the cell.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3115

Question 5004

Which enzyme in saliva begins the chemical digestion of carbohydrates?

Pepsin
Lipase
Amylase✔️
Trypsin

Correct Answer Logic:

Salivary amylase breaks down starches into simpler sugars.

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English QUESTION #721

Question 5005

The setting of "1984" is a dystopian superstate called:

Eurasia
Eastasia
Oceania✔️
Utopia

Correct Answer Logic:

Oceania is the totalitarian regime governed by the Party and Big Brother.

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English QUESTION #4448

Question 5006

We congratulate you ____ your achievement?

for
to
on✔️
at

Correct Answer Logic:

'Congratulate someone on something' is the standard idiomatic expression.

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Constitutional Law QUESTION #5809

Question 5007

To reduce the federal deficit, Congress passes a law that taxes the gross receipts of all state-operated lotteries at a rate of 25%. A state that uses its lottery revenue exclusively for public education sues to enjoin the tax, claiming it violates the Tenth Amendment. Is the tax constitutional?

Yes, because the tax is uniform across all states and falls within the taxing power.✔️
Yes, because the Tenth Amendment does not protect state-run commercial activities from federal taxation.
No, because the tax targets a specific state function and interferes with state sovereignty.
No, because the tax is not for the general welfare as it depletes educational funding.

Correct Answer Logic:

Under the Taxing and Spending Clause, Congress has broad power to tax. A tax is generally valid if it is geographically uniform and reasonably related to revenue production. The Tenth Amendment rarely limits federal taxes that apply to state-owned businesses unless they are uniquely discriminatory or destructive to state existence.

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English QUESTION #2710

Question 5008

What does the phrasal verb 'Call off' mean?

To cancel✔️
To shout
To visit
To postpone

Correct Answer Logic:

To 'call off' means to cancel a planned event or activity.

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Dairy Food Science and Technology QUESTION #5991

Question 5009

In dairy microbiology, 'psychrotolerant' bacteria differ from 'psychrophilic' bacteria in that:

Psychrotolerant bacteria cannot grow above $20^{\circ}\text{C}$; psychrophilic bacteria grow optimally at $20^{\circ}\text{C}$
Psychrotolerant bacteria have optimal growth above $20^{\circ}\text{C}$ but can grow slowly at refrigeration temperatures ($0\text{–}7^{\circ}\text{C}$); psychrophilic bacteria have optimal growth below $15^{\circ}\text{C}$✔️
Psychrotolerant bacteria are heat resistant; psychrophilic bacteria are not
They are identical terms used interchangeably in dairy science

Correct Answer Logic:

True psychrophiles have optimal growth $<15^{\circ}\text{C}$ and cannot grow above $20^{\circ}\text{C}$. Psychrotolerant (psychrotrophs) bacteria grow optimally at $20\text{–}30^{\circ}\text{C}$ but can also grow at refrigeration temperatures ($0\text{–}7^{\circ}\text{C}$), though slowly. Major dairy spoilage organisms ($Pseudomonas\;fluorescens$) are psychrotolerant.

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Math (Module-1) QUESTION #5478

Question 5010

In the given system of equations, a parabola $y = ax^2 + bx + c$ intersects a line. If they intersect at exactly one point $(x, y)$, what is the value of $x$?

-8
-6✔️
6
8

Correct Answer Logic:

Based on the original SAT test key, the intersection point occurs at $x = -6$.

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Paper-II (Pharmacognosy and Pharmaceutics-I) QUESTION #3596

Question 5011

'Senna' and 'Aloe' belong to which chemical class of glycosides?

Saponin Glycosides
Anthraquinone Glycosides✔️
Cardiac Glycosides
Cyanophore Glycosides

Correct Answer Logic:

Anthraquinone glycosides are well known for their stimulant laxative properties.

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Boilers Mechanical Engineering QUESTION #3990

Question 5012

A 'Safety Valve' must be set to open at a pressure:

Slightly below the working pressure
Exactly at the working pressure
Slightly above the working pressure but not exceeding the design limit✔️
Double the working pressure

Correct Answer Logic:

It acts as a relief valve to prevent the boiler from exceeding its maximum allowable working pressure (MAWP).

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Commerce QUESTION #6088

Question 5013

A company has the following reserves:

Share premium: $60,000
Revaluation reserve: $75,000
General reserve: $10,000
Retained earnings: $21,500

What is the maximum number of $1 bonus shares the company can issue?

31,500
91,500
135,000
166,500✔️

Correct Answer Logic:

A bonus issue can be made from any reserve, including capital reserves (Share Premium, Revaluation) and revenue reserves (General, Retained). Total = $60,000 + $75,000 + $10,000 + $21,500 = $166,500.

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