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Physics and Math QUESTION #772

Question 2521

If $y = \sqrt{a^2 + x^2}$, then $\dfrac{dy}{dx} = ?$

$\dfrac{x}{\sqrt{a^2 + x^2}}$✔️
$\dfrac{\sqrt{a^2 + x^2}}{x}$
$x\sqrt{a^2 - x^2}$
None

Correct Answer Logic:

Using chain rule: $\dfrac{dy}{dx} = \dfrac{1}{2\sqrt{a^2+x^2}} \cdot 2x = \dfrac{x}{\sqrt{a^2+x^2}}$.

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Dairy Food Science and Technology QUESTION #5884

Question 2522

The Maillard reaction in milk products is accelerated by:

Low temperature and low $\text{pH}$
Reducing sugars (lactose) reacting with amino groups at high temperatures and $\text{pH}\; 6\text{–}8$✔️
Fat oxidation at refrigeration temperatures
Calcium precipitation during UHT treatment

Correct Answer Logic:

The Maillard reaction involves nucleophilic addition of amino groups (lysine $\varepsilon$-amino groups) to the carbonyl group of reducing sugars (lactose). It is promoted by elevated temperature, reduced $a_w$, and neutral to alkaline $\text{pH}$, causing browning and flavor changes in UHT milk and milk powder.

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Verbal Reasoning QUESTION #8180

Question 2523

A fabric store sells material at \$8.00 per yard, but only in whole-yard increments. Each of 3 curtains requires 1.6 yards of fabric, and all the fabric is bought as one continuous piece. What is the total purchase cost?

$\$40.00$✔️
$\$38.40$
$\$24.00$
$\$16.00$

Correct Answer Logic:

Total fabric needed: $3 \times 1.6 = 4.8$ yards.

Since fabric is sold only in whole-yard increments, you must purchase $5$ full yards (round up from 4.8).

Total cost $= 5 \times \$8.00 = \mathbf{\$40.00}$.

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Quantitative Reasoning QUESTION #8135

Question 2524

Given the overwhelming flood of information delivered by the mass media, the only practical way to stay current with the news is to rely on _______ accounts.

synoptic✔️
sensational
copious
lurid

Correct Answer Logic:

With too much information available, one needs condensed coverage. Synoptic means providing a brief general overview — exactly what's needed. 'Abridged' is the synonym pair in the original. 'Sensational' means exaggerated/dramatic. 'Copious' means abundant — which would make the flood of information worse. 'Lurid' means shocking/graphic.

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Chemistry QUESTION #7186

Question 2525

One gram of a metal carbonate ($M_{2}CO_{3}$) reacts with an excess of $HCl$ to produce $0.01186 \text{ moles}$ of $CO_{2}$. Calculate the molar mass of $M_{2}CO_{3}$ in $\text{g mol}^{-1}$.

$84.3$✔️
$118.6$
$11.86$
$1186$

Correct Answer Logic:

The reaction is $M_{2}CO_{3} + 2HCl \rightarrow 2MCl + H_{2}O + CO_{2}$:

From stoichiometry, $1 \text{ mole}$ of $M_{2}CO_{3}$ produces $1 \text{ mole}$ of $CO_{2}$.
Moles of $M_{2}CO_{3} = \text{Moles of } CO_{2} = 0.01186$.
Molar Mass = $\text{Mass} / \text{Moles} = 1 \text{ g} / 0.01186 \approx 84.3 \text{ g/mol}$.

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General Knowledge QUESTION #265

Question 2526

The recent escalation in Palestinian-Israel Conflict occurred on:

6 October 2023
7 October 2023✔️
8 October 2023
None of these

Correct Answer Logic:

The escalation began with a major attack on October 7, 2023.+1

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Civil Engineering QUESTION #2117

Question 2527

According to Euler's theory, the critical buckling load for a column with both ends pinned (hinged) is $P_{cr} = \dfrac{\pi^2 EI}{L^2}$. For the same column with one end fixed and other end free, the critical load becomes:

The same $\dfrac{\pi^2 EI}{L^2}$
$\dfrac{2\pi^2 EI}{L^2}$
$\dfrac{\pi^2 EI}{4L^2}$✔️
$\dfrac{4\pi^2 EI}{L^2}$

Correct Answer Logic:

Effective length $L_e$ for different end conditions: both pinned $= L$; one fixed one free $= 2L$. Euler's formula $P_{cr} = \dfrac{\pi^2 EI}{L_e^2}$. For fixed-free: $P_{cr} = \dfrac{\pi^2 EI}{(2L)^2} = \dfrac{\pi^2 EI}{4L^2}$. This is the minimum possible buckling load — the fixed-free condition is the least stable of all standard end conditions.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3427

Question 2528

'Denaturation' of a protein involves the loss of its:

Primary structure only
Tertiary and Secondary structure (Biological activity)✔️
Amino acids
Color

Correct Answer Logic:

Heat, acids, or heavy metals can cause a protein to unfold and stop functioning.

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Paper-II (Pharmacology and Social Behaviour, Law & Ethics and Computer Sciences) QUESTION #5767

Question 2529

Benzodiazepines exert anxiolytic effects by modulating:

Dopamine
GABA✔️
Serotonin
Acetylcholine

Correct Answer Logic:

Benzodiazepines enhance GABAergic transmission at GABA-A receptors.

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Boilers Mechanical Engineering QUESTION #2469

Question 2530

The wear load $F_w$ on a gear tooth (Buckingham equation) depends on which key gear geometry parameter related to the smaller gear?

$F_w \propto r_g^2$ (gear pitch radius squared)
$F_w = d_p B K Q$ where $d_p$ is the PINION pitch diameter✔️
$F_w \propto N_p/N_g$ (tooth ratio)
$F_w \propto P_d^2$ (diametral pitch squared)

Correct Answer Logic:

Buckingham's wear load: $F_w=d_p B K Q$, where $d_p$ is the pinion pitch diameter, $B$ is face width, $K$ is the stress-fatigue factor, and $Q=2N_g/(N_p+N_g)$ is the ratio factor.

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Chemistry QUESTION #4357

Question 2531

Which set of quantum numbers is NOT allowed for an electron?

$n=2,\ l=1,\ m=0,\ s=+\frac{1}{2}$
$n=3,\ l=0,\ m=0,\ s=-\frac{1}{2}$
$n=2,\ l=2,\ m=1,\ s=+\frac{1}{2}$✔️
$n=1,\ l=0,\ m=0,\ s=+\frac{1}{2}$

Correct Answer Logic:

For $n=2$, the allowed values of $l$ are $0$ and $1$ only (since $l$ ranges from $0$ to $n-1$). Having $l=2$ when $n=2$ is not allowed, making this set invalid.

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Urdu QUESTION #5046

Question 2532

حیاتِ سعدی کس نے لکھی ہے؟

الطاف حسین حالی
سر سید احمد خان
مولانا شبلی نعمانی✔️
ان میں سے کوئی نہیں

Correct Answer Logic:

حیاتِ سعدی مولانا شبلی نعمانی کی تصنیف ہے جو شیخ سعدی شیرازی کی سوانح عمری پر مبنی ہے۔

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Pakistan Affairs QUESTION #612

Question 2533

Which Indian plan provided a three-tiered constitutional structure before 1947?

Simon Commission
Crips Commission
Lord Wavell Plan
None of these✔️

Correct Answer Logic:

The Cabinet Mission Plan of 1946 proposed the three-tiered structure (provinces, groups, and center) .

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Chemistry QUESTION #7354

Question 2534

A ball of mass 0.66 kg moves at 100 m/s. The de Broglie wavelength associated with it (given $h = 6.6 \times 10^{-34}$ Js) will be:

$6.6 \times 10^{-34}$ m
$1.0 \times 10^{-35}$ m✔️
$1.0 \times 10^{-32}$ m
$6.6 \times 10^{-32}$ m

Correct Answer Logic:

de Broglie formula: $\lambda = \dfrac{h}{mv}$

$\lambda = \dfrac{6.6 \times 10^{-34}}{0.66 \times 100} = \dfrac{6.6 \times 10^{-34}}{66} = 1.0 \times 10^{-35}$ m

This wavelength is vanishingly small, which is why macroscopic objects do not show observable wave behaviour — confirming why quantum effects are only relevant at the atomic/subatomic scale.

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Math (Module-1) QUESTION #5463

Question 2535

Nasir bought $9$ identical storage bins. He used a $\$63$ coupon off the total price. After the coupon, the total was $\$27$. What was the original price of one bin?

9
10✔️
11
12

Correct Answer Logic:

Let $p$ be the price per bin. $9p - 63 = 27 \implies 9p = 90 \implies p = 10$.

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Chemistry QUESTION #451

Question 2536

Osmotic pressure of a solution is __________ property.

Obligative
Fractional
Colligative✔️
Automated

Correct Answer Logic:

Osmotic pressure is a colligative property

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Chemistry QUESTION #1073

Question 2537

Which of the following aqueous solutions will exhibit the highest boiling point?

$0.01\text{M}\ \text{Na}_2\text{SO}_4$✔️
$0.015\text{M}\ \text{C}_6\text{H}_{12}\text{O}_6$
$0.01\text{M}\ \text{Urea}$
$0.01\text{M}\ \text{KNO}_3$

Correct Answer Logic:

Boiling point elevation $\propto i \times m$ (van't Hoff factor $\times$ molality). Na$_2$SO$_4$: $i=3$, effective molality $=0.03$. Glucose: $i=1$, $=0.015$. Urea: $i=1$, $=0.01$. KNO$_3$: $i=2$, $=0.02$. Highest: $0.01\text{M}\ \text{Na}_2\text{SO}_4$ with effective particles $=0.03$.

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