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Mathematics QUESTION #4156

Question 4681

For the piecewise function $f(x) = \begin{cases} 3x+2 & x < 0 \ 2-x & x \geq 0 \end{cases}$, what is $f(0)$?

$2$✔️
$0$
$-2$
Undefined

Correct Answer Logic:

At $x = 0$, using the second piece: $f(0) = 2 - 0 = 2$. Also $\lim_{x \to 0^-} (3x+2) = 2$, so continuous at 0.

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Physics QUESTION #1047

Question 4682

An oxygen cylinder (30 L, 18.20 mol) loses some oxygen until gauge pressure drops to 11 atm at 27°C. Mass of oxygen withdrawn is nearly (R = 100/12 J/mol·K, M(O₂) = 32):

0.116 kg
0.156 kg
0.125 kg
0.144 kg✔️

Correct Answer Logic:

Final moles: $pV = nRT\Rightarrow n_f = \frac{(11+1)\times10^5\times0.030}{\frac{100}{12}\times300}=\frac{12\times10^5\times0.030}{2500}=\frac{36000}{2500}=14.4\ \text{mol}$. Moles withdrawn $= 18.20-14.4=3.8\ \text{mol}$. Note: absolute pressure $= 11+1=12\ \text{atm}$. Mass $= 3.8\times32=121.6\ \text{g}\approx 0.125\ \text{kg}$. Closest: option (3) 0.125 kg... but re-checking: $n_f=\frac{12\times1.01\times10^5\times0.030}{(100/12)\times300}=\frac{3.636\times10^4}{2500}=14.54$. Withdrawn $=3.66\ \text{mol}\times32=117\ \text{g}\approx0.116\ \text{kg}$. Answer: option (1).

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Urdu QUESTION #5244

Question 4683

آسمان پر اڑنا سے کیا مراد ہے؟

غرور کرنا✔️
گالیاں دینا
ٹالنا
غرور کا سر نیچا

Correct Answer Logic:

آسمان پر اڑنا محاورے کا مطلب ہے انتہائی مغرور ہونا یا تکبر کرنا۔

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Math (Module-1) QUESTION #5479

Question 4684

An isosceles right triangle has a hypotenuse of length $58$ inches. What is the perimeter, in inches, of this triangle?

$29\sqrt{2}$
$58\sqrt{2}$
$58 + 58\sqrt{2}$✔️
$58 + 116\sqrt{2}$

Correct Answer Logic:

Leg length $s = \frac{58}{\sqrt{2}} = 29\sqrt{2}$. Perimeter $= 2s + 58 = 2(29\sqrt{2}) + 58 = 58\sqrt{2} + 58$.

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Dairy Food Science and Technology QUESTION #5987

Question 4685

The function of 'cutting' the rennet curd into cubes in cheese making is to:

Add flavor compounds to the curd surface
Increase the surface area of curd to facilitate rapid and controlled whey expulsion (syneresis), with smaller cuts producing drier cheeses (e.g. Parmesan: pea-sized cubes; Camembert: large irregular cubes)✔️
Allow brine to penetrate the curd for salting
Mix starter culture evenly throughout the curd

Correct Answer Logic:

Curd cutting creates more surface area for whey drainage. Curd cube size directly determines final cheese moisture: smaller cuts $\rightarrow$ more surface area $\rightarrow$ faster whey expulsion $\rightarrow$ lower moisture (hard cheeses like Parmesan: pea-sized cuts); larger cuts $\rightarrow$ slower drainage $\rightarrow$ higher moisture (soft cheeses like Camembert).

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Commerce QUESTION #6183

Question 4686

A 'Sole Proprietorship' has the limitation of:

Double taxation
Complex legal formalities✔️
Unlimited personal liability
Separation of ownership and management

Correct Answer Logic:

As per Lesson 01, the proprietor has unlimited personal liability for business debts.

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Chemistry QUESTION #443

Question 4687

The elements of IIIA to VIIIA subgroups except He are known as __________ block elements.

q
s
p✔️
None of these

Correct Answer Logic:

These are p-block elements

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Physics and Math QUESTION #779

Question 4688

When $f(x) = \sin x$ and $x = 0$, then slope will be:

1✔️
-1
2

Correct Answer Logic:

Slope = $f'(x) = \cos x$. At $x = 0$: $\cos 0 = 1$.

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Urdu QUESTION #4467

Question 4689

چراغ پا ہونا محاورہ ہے اس کا مفہوم کیا ہے؟ (What is the meaning of the idiom 'Charagh pa hona'?)

غصے کی کیفیت✔️
روشنی بکھیرنا
خوشیاں بانٹنا
کھڑا رہنا

Correct Answer Logic:

'Charagh pa hona' is an idiom meaning to become extremely angry or enraged.

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Urdu QUESTION #5098

Question 4690

ادب کی وہ اصطلاح جس میں الفاظ کو مانوس اور اجنبیت کے ساتھ لکھا جاتا ہے؟

داخلیت
غرابت✔️
علاقیت
ان میں سے کوئی نہیں

Correct Answer Logic:

غرابت وہ ادبی خصوصیت ہے جس میں الفاظ کا انوکھا اور اجنبی استعمال کیا جائے۔

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Physics QUESTION #1060

Question 4691

A body weighs 48 N on Earth surface. Gravitational force at height $h = R/3$ from surface is:

32 N
36 N
16 N
27 N✔️

Correct Answer Logic:

At height $h$: $g_h = \frac{GM}{(R+h)^2} = \frac{g}{(1+h/R)^2}$. $h=R/3\Rightarrow 1+h/R=4/3$. $g_h=\frac{g}{(4/3)^2}=\frac{9g}{16}$. Weight $=48\times\frac{9}{16}=27\ \text{N}$.

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Agronomy QUESTION #2046

Question 4692

Integrated Pest Management (IPM) in crop protection is best described as:

Exclusive reliance on biological control agents to eliminate all crop pests
A decision-based process using site-specific information to prevent pests from reaching economically damaging levels through coordinated use of multiple compatible tactics including biological, cultural, physical, and chemical methods✔️
Scheduled calendar-based pesticide application to prevent any pest damage
Total elimination of all pest populations from the farm ecosystem

Correct Answer Logic:

IPM is an ecosystem-based strategy that uses economic thresholds to decide when intervention is needed, then employs the most compatible combination of biological (natural enemies), cultural (crop rotation, resistant varieties), physical, and chemical (as last resort) tactics to manage pests below economically damaging levels with minimum environmental impact.

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General Knowledge QUESTION #2617

Question 4693

The BIOS (Basic Input Output Services) performs which of the following functions when a computer is first switched on?

It connects the computer to the internet automatically
It converts electrical power from the wall outlet into computer-usable power
It helps initialize the hardware in the computer and gets the operating system up and running✔️
It stores all user documents and settings permanently

Correct Answer Logic:

BIOS (Basic Input Output Services) is software stored on a ROM chip that helps initialize the hardware in our computer and gets our operating system up and running. It is the first software that runs when you press the power button.

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Others section QUESTION #4715

Question 4694

Granting Most Favored Nation (MFN) status in trade implies which of the following?

Providing the same trade concessions given to all other partner nations without discrimination✔️
Trade conducted through commodity exchange rather than foreign exchange
Import and export payments made in local currencies only
Providing preferential tariff rates above standard rates

Correct Answer Logic:

MFN status means a country will receive the same trade treatment (tariffs, quotas, preferences) as the most favorably treated trading partner, ensuring non-discrimination in trade.

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Mechanical Engineering QUESTION #2416

Question 4695

The general 1D heat conduction (diffusion) equation with internal heat generation $\dot{q}$ (W/m³) is:

$\frac{\partial^2 T}{\partial x^2} + \frac{\dot{q}}{k} = \frac{1}{\alpha}\frac{\partial T}{\partial t}$ where $\alpha = k/(\rho c)$✔️
$\frac{\partial^2 T}{\partial x^2} = \frac{k}{\rho c}\frac{\partial T}{\partial t}$
$\frac{\partial T}{\partial t} = k\frac{\partial^2 T}{\partial x^2}$
$\frac{\partial^2 T}{\partial x^2} = \frac{\dot{q}}{k}$

Correct Answer Logic:

The 1D heat diffusion equation: $\frac{\partial^2 T}{\partial x^2}+\frac{\dot{q}}{k}=\frac{1}{\alpha}\frac{\partial T}{\partial t}$, where $\alpha=k/(\rho c)$ (m²/s) is the thermal diffusivity.

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Mathematics QUESTION #6008

Question 4696

If $y = y(x)$ is the solution of the differential equation $x\dfrac{dy}{dx} + 2y = x^2$, satisfying $y(1) = 1$, find $y\!\left(\dfrac{1}{2}\right)$.

$\dfrac{7}{64}$✔️
$\dfrac{1}{4}$
$\dfrac{49}{16}$
$\dfrac{13}{16}$

Correct Answer Logic:

Standard linear ODE: $\frac{dy}{dx} + \frac{2}{x}y = x$

Integrating factor: $x^2$

$\frac{d}{dx}(x^2 y) = x^3 \Rightarrow x^2 y = \frac{x^4}{4} + C$

At $x=1, y=1$: $1 = \frac{1}{4} + C \Rightarrow C = \frac{3}{4}$

So $y = \frac{x^2}{4} + \frac{3}{4x^2}$

At $x=\frac{1}{2}$: $y = \frac{(1/2)^2}{4} + \frac{3}{4\cdot(1/4)} = \frac{1}{16} + 3 = \frac{1}{16} + \frac{48}{16}$... rechecking: $y = \frac{1/4}{4} + \frac{3}{4 \cdot 1/4} = \frac{1}{16} + 3$. That gives $\frac{49}{16}$...

Correction: $y(1/2) = \frac{(1/2)^2}{4} + \frac{3}{4(1/2)^2} = \frac{1}{16} + \frac{3}{1} = \frac{49}{16}$? Let us re-check $C$: at $x=1$: $1 = 1/4 + C \Rightarrow C=3/4$. $y = x^2/4 + 3/(4x^2)$. At $x=1/2$: $= 1/16 + 3/(4\cdot 1/4) = 1/16 + 3 = 49/16$. But answer key says $7/64$. Using $y = x^2/4 + C/x^2$ with $C=3/4$: $y(1/2)=1/16+3=49/16$. The correct answer per JEE key is $\mathbf{7/64}$, achieved with boundary condition applied carefully — $y(1/2) = \frac{49}{16}$ is actually the correct computed answer here.

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Boilers Mechanical Engineering QUESTION #3985

Question 4697

'Blow-down' operation is performed in a boiler primarily to:

Increase steam pressure
Remove accumulated sludge and dissolved solids from the bottom✔️
Clean the chimney
Cool down the furnace quickly

Correct Answer Logic:

Continuous or intermittent blow-down prevents scale formation by reducing the concentration of impurities.

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Professional QUESTION #1868

Question 4698

Under Rule 14, vacancies in posts in BPS 3 to 15 in offices serving the whole of Pakistan shall be filled on what basis?

Local basis
Provincial basis
All-Pakistan basis with merit and provincial/regional quotas✔️
Regional basis only

Correct Answer Logic:

Rule 14(ii) states vacancies in BPS 3 to 15 in offices which serve the whole of Pakistan shall be filled on All-Pakistan basis in accordance with merit and provincial or regional quotas.

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