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Substitute $y=4-x$ into $f=xy-2x$: $f=x(4-x)-2x=4x-x^2-2x=-x^2+2x$. Maximizing: $f'=-2x+2=0\Rightarrow x=1$, giving $f(1,3)=-1+2=1$. This is a candidate for absolute extremum.

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Biology QUESTION #7269

Question 6

Nitrogen fixation in root nodules of Alnus is brought about by:

Frankia✔️
Azorhizobium
Bradyrhizobium
Clostridium

Correct Answer Logic:

Frankia is a filamentous actinomycete that forms nitrogen-fixing root nodules (actinorhizal nodules) in non-leguminous plants like Alnus (alder), Casuarina, and Ceanothus. Rhizobium and Bradyrhizobium nodulate legumes; Azorhizobium is stem-nodulating; Clostridium is a free-living anaerobic nitrogen fixer.

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Paper-II (Pharmacognosy and Pharmaceutics-I) QUESTION #3657

Question 7

A drug that kills or expels intestinal worms is called an:

Antipyretic
Anthelmintic✔️
Analgesic
Antiemetic

Correct Answer Logic:

Drugs like Santonin are anthelmintics.

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General Abilities QUESTION #7661

Question 8

In an Arithmetic Progression, if $a_1 = 28$, $d = -4$, $n = 7$, then $a_n$ is:

$4$✔️
$5$
$3$
None of these

Correct Answer Logic:

Using the formula $a_n = a_1 + (n-1)d$, we have: $a_7 = 28 + (7-1)(-4) = 28 + 6(-4) = 28 - 24 = 4$. Therefore, the 7th term of this arithmetic progression is 4.

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General Abilities QUESTION #2868

Question 9

Simplify the fraction to its lowest terms: $\frac{48}{72}$

$\frac{4}{6}$
$\frac{2}{3}$✔️
$\frac{12}{18}$
$\frac{8}{12}$

Correct Answer Logic:

The HCF of $48$ and $72$ is $24$. Dividing both by $24$ gives $\frac{2}{3}$.

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Mathematics QUESTION #6037

Question 10

Find a value of $\theta$ for which $\dfrac{2+3i\sin\theta}{1-2i\sin\theta}$ is purely imaginary.

$\dfrac{\pi}{6}$
$\sin^{-1}\!\left(\dfrac{\sqrt{3}}{4}\right)$
$\sin^{-1}\!\left(\dfrac{1}{\sqrt{3}}\right)$✔️
$\dfrac{\pi}{3}$

Correct Answer Logic:

Multiply numerator and denominator by the conjugate of the denominator $(1+2i\sin\theta)$:

Numerator real part: $(2+3i\sin\theta)(1+2i\sin\theta)$ real part $= 2-6\sin^2\theta$

For purely imaginary, the real part must be zero: $2-6\sin^2\theta=0\Rightarrow\sin^2\theta=\frac{1}{3}\Rightarrow\sin\theta=\frac{1}{\sqrt{3}}$

Therefore $\theta=\sin^{-1}\!\left(\dfrac{1}{\sqrt{3}}\right)$

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CISA QUESTION #1765

Question 11

Which of the following would NOT be classified as a control failure?

Using a policy that has no detective mechanism to identify violations
Modifying an ineffective procedure outside of change control
Testing to determine how many policy violations have occurred✔️
Implementing a policy or standard without defining consequences for non-compliance

Correct Answer Logic:

Testing to discover policy violations is an example of a detective control in action — it is not a control failure. All other options represent failures because they lack detection, bypass change control, or implement controls without enforcement mechanisms.

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HR and Management QUESTION #6431

Question 12

In strategic HRM, matching people and organizations suggests that HR strategies contribute most to firm performance when they:

Attract the highest number of applicants
Attract and retain employees who best fit the firm's culture and business objectives✔️
Minimize recruitment and training costs
Focus exclusively on technical skills

Correct Answer Logic:

Research shows HR strategies contribute most to firm performance when used to attract and retain the type of employee who best fits the firm's culture and overall business objectives. For example, fast-growth firms perform better with risk-taking managers, while mature firms need different managerial traits.

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Civil Engineering QUESTION #2127

Question 13

Manning's equation for open channel flow is $V = \dfrac{1}{n} R^{2/3} S^{1/2}$. The Manning's roughness coefficient $n$ for a clean, straight natural river channel is approximately in the range:

0.008–0.010
0.011–0.014
0.025–0.035✔️
0.050–0.080

Correct Answer Logic:

Manning's $n$ values: smooth concrete 0.011–0.013; clean, straight natural channel 0.025–0.033; winding natural channel with some pools 0.035–0.050; very weedy/brushy channels 0.075–0.150. A clean, straight natural river typically has $n \approx 0.025–0.035$. These values are critical for flood routing, channel design, and backwater curve computations in hydraulic engineering.

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General Abilities QUESTION #7973

Question 14

$0.26 \div 100 = ?$

0.0026✔️
0.026
26
0.00026

Correct Answer Logic:

$0.26 \div 100 = 0.0026$ (move the decimal point 2 places to the left)

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Academic/Professional (Social Sciences) QUESTION #6505

Question 15

In sociology, 'Deviance' is defined as:

Criminal behavior only
Behavior that violates social norms✔️
Mental illness
Genius-level intelligence

Correct Answer Logic:

Deviance covers any behavior, belief, or condition that violates significant social norms in the society.

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Therapeutics and Patient Care QUESTION #3899

Question 16

What is the most clinically important advantage of angiotensin II receptor blockers (ARBs) over ACE inhibitors in terms of tolerability?

There is a decreased incidence of hyperkalaemia
They are less likely to cause adverse effects such as dizziness
There is a reduced incidence of cough✔️
They do not interact with non-steroidal anti-inflammatory medications

Correct Answer Logic:

ACE inhibitors cause a dry persistent cough in up to $20\%$ of patients by increasing bradykinin levels. ARBs do not inhibit ACE and therefore have a significantly lower incidence of cough.

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English QUESTION #8494

Question 17

Select the word SIMILAR in meaning to: NASCENT

Threat
Purpose
Quality
Emerging✔️

Correct Answer Logic:

Nascent means just coming into existence; emerging.

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Paper-II (Pharmacology and Social Behaviour, Law & Ethics and Computer Sciences) QUESTION #5756

Question 18

Which enzyme is permanently inactivated by organophosphate compounds like Echothiophate?

Monoamine Oxidase
Angiotensin Converting Enzyme
Acetylcholinesterase✔️
Carbonic Anhydrase

Correct Answer Logic:

Echothiophate is an organophosphate that covalently binds and permanently inactivates acetylcholinesterase.

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Therapeutics and Patient Care QUESTION #3888

Question 19

A 50-year-old male treated for pitting oedema of the ankles subsequently develops gynaecomastia and erectile dysfunction. Which diuretic is most likely responsible for these endocrine adverse effects?

Hydrochlorothiazide
Furosemide
Spironolactone✔️
Triamterene

Correct Answer Logic:

Spironolactone is a mineralocorticoid antagonist with anti-androgenic effects. Its adverse effects include gynaecomastia, menstrual irregularities, and erectile dysfunction.

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English QUESTION #2707

Question 20

Choose the correct pair word: 'The ___ of the school is very strict.'

Principle
Principal✔️
Prince
Priest

Correct Answer Logic:

'Principal' refers to the head of an institution; 'principle' refers to a fundamental truth.

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