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Physics QUESTION #990

Assertion (A): In Young's double slit experiment, fringes produced by red light are wider compared to blue light. Reason (R): Fringe width is directly proportional to the wavelength of light. Choose the correct option:

Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
(A) is true but (R) is false
Both (A) and (R) are true and (R) is the correct explanation of (A)
(A) is false but (R) is true✔️

Correct Answer Logic:

Fringe width $\beta = \frac{\lambda D}{d}$. Since $\lambda_{red} > \lambda_{blue}$, red fringes are wider, not closer. The assertion in the paper states red fringes are 'closer' which is false. But (R) is true. Hence (A) is false but (R) is true.

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Mathematics QUESTION #4145

Question 2

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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Agronomy QUESTION #2110

Question 3

The 'yield gap' concept in agronomy is defined as the difference between:

The yield of traditional varieties and modern high-yielding varieties under the same management
Potential yield (Yp — maximum achievable by best-adapted variety with optimal management, no biotic/abiotic stress) and actual farm yield (Ya) — quantifying the improvement possible through better agronomic management, technology adoption, and policy support without requiring new variety development✔️
The yield of irrigated crops versus rainfed crops in the same region
The maximum recorded experimental yield and the national average yield reported by FAO

Correct Answer Logic:

Yield gap analysis (van Ittersum framework): Yp = potential yield (radiation-limited in irrigated; temperature and radiation in rainfed = water-limited yield, Yw). Ya = actual farm yield. Yield gap = Yp or Yw − Ya. Globally, average Ya is 50–60% of Yp for major cereals. Closing the yield gap through improved agronomy (fertilization, pest control, irrigation timing) can double production without expanding cultivated area.

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Math (Module-1) QUESTION #5463

Question 4

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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Boilers Mechanical Engineering QUESTION #2457

Question 5

The law of conjugate gear-tooth action (the fundamental law of gearing) states that for constant angular velocity ratio, the common normal at the point of contact must:

Always pass through the center of the smaller gear (pinion)
Always intersect the line of centers at the same fixed point — the pitch point P✔️
Be parallel to the line of centers
Be perpendicular to the tooth profile at all times

Correct Answer Logic:

The fundamental law of gearing: the common normal to the mating tooth surfaces at the contact point must always pass through the pitch point P (fixed point on the line of centers).

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3539

Question 6

'Fixed Oils' differ from 'Volatile Oils' because fixed oils:

Can be saponified (made into soap)✔️
Evaporate at room temperature
Are always liquid
Do not contain fat

Correct Answer Logic:

Fixed oils are esters of fatty acids and glycerol; volatile oils are not.

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Physics QUESTION #7070

Question 7

An ideal gas is contained in an isolated closed chamber. During an adiabatic expansion, the average time between molecular collisions increases as $V^q$, where $V$ is the volume. Determine the value of $q$ in terms of $\gamma = C_p/C_v$.

$\frac{3\gamma+5}{6}$
$\frac{3\gamma-5}{6}$
$\frac{\gamma+1}{2}$✔️
$\frac{\gamma-1}{2}$

Correct Answer Logic:

Average time between collisions $\tau$ is given by $\tau = \frac{\lambda}{v_{rms}}$, where $\lambda$ is the mean free path.

1. $\lambda \propto \frac{1}{n} \propto V$ (where $n$ is number density).
2. $v_{rms} \propto \sqrt{T}$.
3. For an adiabatic process, $TV^{\gamma-1} = \text{constant}$, so $T \propto V^{1-\gamma}$ and $\sqrt{T} \propto V^{\frac{1-\gamma}{2}}$.

Therefore, $\tau \propto \frac{V}{V^{\frac{1-\gamma}{2}}} = V^{1 - \frac{1-\gamma}{2}} = V^{\frac{2-1+\gamma}{2}} = V^{\frac{\gamma+1}{2}}$.
Hence, $q = \frac{\gamma+1}{2}$.

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General Knowledge QUESTION #8647

Question 8

Which city is known as the 'City of Mosques'?

Lahore
Madina
Baghdad
Dhaka✔️

Correct Answer Logic:

Dhaka, Bangladesh is historically known as the 'City of Mosques'.

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Boilers Mechanical Engineering QUESTION #2454

Question 9

The Rayleigh (energy) method for approximating the fundamental natural frequency equates:

Maximum kinetic energy to maximum potential energy: $T_{max} = V_{max}$ giving $\omega_n^2 = k/m$✔️
Mean kinetic energy to mean potential energy
Damping energy to spring potential energy
Total energy to the product of mass and stiffness

Correct Answer Logic:

Rayleigh's method: for conservative systems in harmonic motion, maximum kinetic energy $T_{max}=\frac{1}{2}m(\omega_n X)^2$ equals maximum potential energy $V_{max}=\frac{1}{2}kX^2$. Setting $T_{max}=V_{max}$: $\omega_n^2=k/m$.

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Boilers Mechanical Engineering QUESTION #2541

Question 10

By Pappus's second theorem, the volume of a solid formed by rotating plane area $A$ through angle $2\pi$ about an external axis at centroidal distance $\bar{d}$ is:

$V=\pi\bar{d}^2 A$
$V=2\pi\bar{d}A$✔️
$V=4\pi\bar{d}A$
$V=\frac{A}{2\pi\bar{d}}$

Correct Answer Logic:

Pappus's second theorem: $V=\theta\cdot\bar{d}\cdot A$. For a full revolution ($\theta=2\pi$): $V=2\pi\bar{d}A$, where $\bar{d}$ is the distance from the area's centroid to the axis of revolution.

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General Abilities QUESTION #4618

Question 11

Solve for $x$: $x + y = 10$ and $x - y = 2$

$x = 4$
$x = 6$✔️
$x = 8$
$x = 5$

Correct Answer Logic:

Add equations: $2x = 12$, so $x = 6$

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General Knowledge QUESTION #8853

Question 12

Heat from the sun's rays is reduced by which atmospheric layer?

Oxygen
Nitrogen
Ozone layer✔️
None of these

Correct Answer Logic:

The ozone layer absorbs harmful UV radiation.

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English QUESTION #2742

Question 13

Choose the CORRECT sentence.

Each of the students have submitted their assignment.
Each of the students has submitted their assignment.✔️
Each of the students have submitted his assignment.
Each of the student has submitted their assignment.

Correct Answer Logic:

'Each' is singular and takes a singular verb. So 'has' (not 'have') is correct. The sentence should be 'Each of the students has submitted their assignment.'

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Mathematics QUESTION #6014

Question 14

How many values of $k$ allow the system of equations $(k+1)x + 8y = 4k$ and $kx + (k+3)y = 3k-1$ to have no solution?

Infinite
1✔️
2
3

Correct Answer Logic:

For no solution, the determinant of the coefficient matrix must be zero but the system must be inconsistent.

$\Delta = (k+1)(k+3) - 8k = k^2+4k+3-8k = k^2-4k+3 = (k-1)(k-3) = 0$

So $k=1$ or $k=3$. Check each:

$k=1$: Equations become $2x+8y=4$ and $x+4y=2$ — same line (infinite solutions). Not "no solution".

$k=3$: Equations become $4x+8y=12$ and $3x+6y=8$. Simplify: $x+2y=3$ and $x+2y=8/3$ — contradiction! No solution.

So exactly $\mathbf{1}$ value of $k$ gives no solution.

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Urdu QUESTION #5213

Question 15

'آم کے آم، گٹھلیوں کے دام' ضربِ مثل کا کیا مطلب ہے؟

دوہرا فائدہ✔️
دوہرا نقصان
نقصان
ان میں سے کوئی نہیں

Correct Answer Logic:

آم کے آم گٹھلیوں کے دام کا مطلب ہے ایک کام سے دوہرا فائدہ حاصل کرنا۔

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General Knowledge QUESTION #8996

Question 16

Who is the founder of the Scout Movement?

Robert Baden-Powell✔️
Lord Colin Powell
Maccollins
Nikola Tesla

Correct Answer Logic:

Baden-Powell founded the Scouting movement.

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General Ability and Fire Fighting QUESTION #5632

Question 17

Which of the following describes a 'firebreak' as a firefighting technique?

A chemical barrier sprayed ahead of a fire
A physical gap created by clearing combustible material to stop fire spread✔️
A water curtain created by hoses
A foam barrier applied around a structure

Correct Answer Logic:

A firebreak is created by physically clearing or removing combustible material (trees

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Boilers Mechanical Engineering QUESTION #4057

Question 18

'Thermal Lagging' (Insulation) is applied to steam pipes to:

Make them look thick
Reduce heat loss to the atmosphere✔️
Prevent the pipes from rusting
Increase the noise

Correct Answer Logic:

Insulation keeps the steam hot and prevents it from turning into water during transport.

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General Knowledge QUESTION #2629

Question 19

CACHE memory in a computer is best described as:

The permanent storage drive where the operating system is installed
An assigned stored location for recently or frequently accessed data, allowing faster retrieval✔️
The temporary working memory that loses all data when the computer is shut down
The memory module that stores the BIOS firmware permanently

Correct Answer Logic:

Cache is the assigned stored location for recently or frequently accessed data. It sits between the CPU and RAM and provides extremely fast access to data the CPU uses most often. On mobile apps, cache stores recently used or changed data locally for quicker access.

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Quantitative Reasoning QUESTION #7215

Question 20

Nothing (i)_____ scientists more than seeing a longstanding problem in their field solved by an outsider. If you question this (ii)_____, consider the (iii)_____ reaction of paleontologists to the hypothesis by Luis Alvarez — a physicist — and Walter Alvarez — a geologist — that dinosaurs were wiped out by a large meteor impact.

Blank (i)	Blank (ii)	Blank (iii)
A. amazes	D. exposition	G. contemptuous
B. pleases	E. objurgation	H. indifferent
C. nettles	F. observation	I. insincere

Blank (i) = amazes, Blank (ii) = exposition, Blank (iii) = contemptuous
Blank (i) = pleases, Blank (ii) = objurgation, Blank (iii) = indifferent
Blank (i) = nettles, Blank (ii) = observation, Blank (iii) = contemptuous✔️
Blank (i) = nettles, Blank (ii) = exposition, Blank (iii) = insincere

Correct Answer Logic:

This three-blank question requires understanding the tone and logic of the passage.

Blank (i): The example shows paleontologists reacted badly to outsiders solving their problem. Scientists are irritated or annoyed by this — not amazed or pleased. Nettles means to irritate or annoy, which fits perfectly.

Blank (ii): The word introduces the supporting example: “if you doubt this _____”. “Exposition” means an explanation or presentation; “objurgation” means harsh scolding (too strong a word); observation means a stated claim or remark — the most neutral and fitting choice here.

Blank (iii): Since paleontologists were annoyed that outsiders solved their problem, their reaction to the Alvarez hypothesis would be contemptuous (scornful, dismissive). “Indifferent” means uncaring (doesn’t convey negativity), and “insincere” means dishonest (unrelated).

Correct Answers: Blank (i) = C (nettles), Blank (ii) = F (observation), Blank (iii) = G (contemptuous).

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