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Physics QUESTION #394

Question 21

The cobalt is absorbed by

Bones
Skin
Liver✔️
Thyroid gland

Correct Answer Logic:

Radioactive cobalt accumulates in liver

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Civil / Architecture QUESTION #2361

Question 22

In the Finite Element Method (FEM) applied to structural analysis, the stiffness matrix $[K]$ of a structure is assembled from element stiffness matrices $[k_e]$. For a 2-node bar element of length $L$, cross-sectional area $A$, and modulus $E$, the element stiffness matrix is:

$[k_e] = \dfrac{EA}{L} \begin{bmatrix} 1 & -1 \\ -1 & 1 \end{bmatrix}$✔️
$[k_e] = \dfrac{EA}{L} \begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix}$
$[k_e] = \dfrac{EI}{L^3} \begin{bmatrix} 12 & -6L \\ -6L & 4L^2 \end{bmatrix}$
$[k_e] = \dfrac{EA}{L^2} \begin{bmatrix} 1 & -1 \\ -1 & 1 \end{bmatrix}$

Correct Answer Logic:

For a 2-node axial (bar) element with DOFs $\{u_1, u_2\}$, the element stiffness matrix derived from the principle of virtual work is $[k_e] = \dfrac{EA}{L}\begin{bmatrix}1 & -1 \\ -1 & 1\end{bmatrix}$. This is symmetric and singular (as expected for an unrestrained element). Option C is part of the Euler-Bernoulli beam element stiffness matrix (for bending DOFs).

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Mathematics QUESTION #4128

Question 23

For $\oint_{|z|=2} \frac{5z - 2}{z(z-1)} \, dz$, what is the value?

$0$
$6\pi i$
$10\pi i$✔️
$4\pi i$

Correct Answer Logic:

Residue at $z=0$: $\lim_{z \to 0} z \cdot \frac{5z-2}{z(z-1)} = \frac{-2}{-1} = 2$. Residue at $z=1$: $\lim_{z \to 1} (z-1) \cdot \frac{5z-2}{z(z-1)} = \frac{3}{1} = 3$. Sum of residues $= 5$. Integral $= 2\pi i \times 5 = 10\pi i$.

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Civil Engineering QUESTION #6572

Question 24

Alloys containing more than $2.1\%$ carbon by weight are classified as:

Steel
Cast Iron✔️
Pig Iron
Wrought Iron

Correct Answer Logic:

Carbon content defines the iron–carbon alloy type:

Steel: $0.008\% - 2.1\%$ C
Cast Iron: $> 2.1\%$ C (typically $2.1\% - 4\%$)

Cast iron is brittle and has high compressive strength.

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Urdu QUESTION #5075

Question 25

فصیلِ شب کس شاعر کی تحریر ہے؟

حفیظ جالندھری
محمد حسین آزاد
علامہ اقبال
مرزا ادیب✔️

Correct Answer Logic:

فصیلِ شب مرزا ادیب کی مشہور ادبی تصنیف ہے۔

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Mathematics QUESTION #6938

Question 26

If $\displaystyle\sum_{r=0}^{25}\left\{{}^{50}C_r \cdot {}^{50-r}C_{25-r}\right\} = K\binom{50}{25}$, find the value of $K$.

$(25)^2$
$2^{25}-1$
$2^{24}$
$2^{25}$✔️

Correct Answer Logic:

Note: ${}^{50}C_r \cdot {}^{50-r}C_{25-r} = \dfrac{50!}{r!(50-r)!} \cdot \dfrac{(50-r)!}{(25-r)!(25)!} = \dfrac{50!}{r!(25-r)!25!} = {}^{50}C_{25}\cdot{}^{25}C_r$

So the sum $= {}^{50}C_{25}\displaystyle\sum_{r=0}^{25}{}^{25}C_r = {}^{50}C_{25}\cdot 2^{25}$

Therefore $K = \mathbf{2^{25}}$.

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Contracts QUESTION #5855

Question 27

A Thief steals a laptop and sells it to an innocent Buyer. The original owner finds the Buyer and demands the laptop. Does the Buyer have good title?

Yes, because the Buyer was a 'Good Faith Purchaser for Value'.
No, a thief has 'void title' and cannot pass good title to anyone.✔️
Yes, because the laptop is a movable good.
No, unless the Buyer is a merchant.

Correct Answer Logic:

Under UCC §2-403, a person with void title (a thief) has no power to transfer title, even to a good faith purchaser.

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Mathematics QUESTION #7484

Question 28

Let N be the set of natural numbers and two functions f and g be defined as $f,g: \mathbb{N} \to \mathbb{N}$ such that $f(n) = \begin{cases} \frac{n+1}{2} & \text{if } n \text{ is odd} \\ \frac{n}{2} & \text{if } n \text{ is even} \end{cases}$ and $g(n) = n - (-1)^n$. Then fog is:

onto but not one-one
one-one but not onto
both one-one and onto✔️
neither one-one nor onto

Correct Answer Logic:

First, $g(n) = n - (-1)^n = \begin{cases} n-1 & \text{if } n \text{ is odd} \\ n+1 & \text{if } n \text{ is even} \end{cases}$. For odd n, $g(n) = n-1$ is even, and for even n, $g(n) = n+1$ is odd. Now $(f \circ g)(n) = f(g(n))$. If n is odd: $g(n) = n-1$ (even), so $f(g(n)) = \frac{n-1}{2}$. If n is even: $g(n) = n+1$ (odd), so $f(g(n)) = \frac{(n+1)+1}{2} = \frac{n+2}{2}$. For injectivity: if $(f \circ g)(n_1) = (f \circ g)(n_2)$, we need to show $n_1 = n_2$. If both are odd: $\frac{n_1-1}{2} = \frac{n_2-1}{2}$, so $n_1 = n_2$. If both even: $\frac{n_1+2}{2} = \frac{n_2+2}{2}$, so $n_1 = n_2$. If one odd and one even: $\frac{n_1-1}{2} = \frac{n_2+2}{2}$, giving $n_1 = n_2+3$, which contradicts parity. So fog is injective. For surjectivity: any $m \in \mathbb{N}$ can be written as $m = \frac{2m-1}{2}$ (from odd $n=2m-1$) or $m = \frac{2m+2}{2}$ (from even $n=2m-2$). So fog is surjective. Thus fog is bijective.

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Ability / HR / Governance / Special Education QUESTION #1796

Question 29

Which of the following is NOT listed as a component of 'corrupt and fraudulent practices' under Rule 2(f) of the PPRA Rules 2004?

Collusive practices
Coercive practices
Speculative practices✔️
Obstructive practices

Correct Answer Logic:

Rule 2(f) defines corrupt and fraudulent practices as comprising five specific categories: coercive practices, collusive practices, corrupt practices, fraudulent practices, and obstructive practices. 'Speculative practices' is not among the defined categories.

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Civil Engineering QUESTION #2116

Question 30

For a rectangular cross-section beam, the ratio of maximum shear stress to average shear stress is:

1.0
1.5✔️
2.0
1.33

Correct Answer Logic:

For a rectangular section of width $b$ and depth $d$: maximum shear stress occurs at the neutral axis $= \dfrac{3V}{2bd} = 1.5 \times \dfrac{V}{bd}$. Average shear stress $= \dfrac{V}{bd}$. Therefore ratio $= 1.5$. This is a fundamental result derived from the shear stress distribution formula $\tau = \dfrac{VQ}{Ib}$.

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Physics QUESTION #4401

Question 31

The reciprocal of the resistivity of a material is called its:

Impedance
Conductivity✔️
Admittance
Reactance

Correct Answer Logic:

Electrical conductivity $\sigma = \dfrac{1}{\rho}$ where $\rho$ is resistivity. Conductivity measures how easily a material allows electric current to flow. Its SI unit is $S\ m^{-1}$ (Siemens per metre).

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Biology QUESTION #567

Question 32

Name the class without antennae.

Arachnida✔️
Myriapoda
Insecta
Crustacea

Correct Answer Logic:

Arachnids lack antennae

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ETAG General Aptitude QUESTION #3766

Question 33

Four landmarks H1, H2, H3, and H4 are located in a park. 1) H2 and H3 are not the easternmost. 2) H2 and H3 are not the westernmost. 3) The easternmost and westernmost are not the southernmost. 4) Two landmarks are west of H2. 5) The southernmost has at least two landmarks to its east. Which landmark is the southernmost?

H1✔️
H2
H3
H4

Correct Answer Logic:

Based on logical deduction of positions, H1 is the only landmark satisfying the condition of being the southernmost with at least two hills to its east.

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Islamic Studies QUESTION #7918

Question 34

After the Hijrat to Medina, what was the first important action the Holy Prophet (SAW) took?

Built a Mosque for prayers✔️
Built his house
Created Bait-ul-mal
Raised an army

Correct Answer Logic:

After arriving in Medina, the Prophet (PBUH) first built Masjid-e-Nabawi (the Prophet's Mosque). This established a center for worship, community gathering, education, and governance. He also established brotherhood (Muakhaat) between Muhajirin and Ansar, created a written constitution (Sahifah al-Medina), and built houses adjacent to the mosque.

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Tourism & Hospitality Management QUESTION #1611

Question 35

The Tourism and Hospitality Laws course specifically covers Pakistan's 'Hotel & Restaurant Act 1976 and Rules 1978.' Under this Act, which of the following obligations is placed on hotel operators?

To submit annual financial audits to the Ministry of Tourism
To register with the relevant authority, comply with prescribed standards of accommodation and service, and adhere to regulated pricing and consumer protection requirements✔️
To provide free accommodation to government officials
To employ only locally trained hospitality staff

Correct Answer Logic:

The Hotel & Restaurant Act 1976 (covered in Module 4 of the Tourism & Hospitality Laws course) regulates the registration, classification, standards of accommodation and service, and pricing compliance of hotels and restaurants in Pakistan — forming the primary legislative framework governing hospitality operations.

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Boilers Mechanical Engineering QUESTION #4077

Question 36

'Phosphate Treatment' in a boiler helps to:

Make the water blue
Keep scale-forming minerals in a soft, non-adherent 'sludge' form✔️
Increase the pressure
Clean the exterior

Correct Answer Logic:

The sludge is then removed via the blow-down.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3347

Question 37

'Lyophilization' is a process used for:

Killing microbes with heat
Freeze-drying to preserve microbial cultures✔️
Staining slides
Testing water

Correct Answer Logic:

Water is removed under vacuum while the sample is frozen, allowing for long-term storage.

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MCQs Section QUESTION #4860

Question 38

Choose the correct synonym of "FETTER"

Rot
To restrain✔️
Make better
Enable to fly

Correct Answer Logic:

To fetter means to restrain or restrict someone with chains, or more broadly, to impose restrictions on someone's freedom of action.

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Boilers Mechanical Engineering QUESTION #2504

Question 39

The octahedral shear stress theory (von Mises criterion) for yielding states that yielding begins when:

$\sigma_{vm} = \sqrt{\sigma_1^2 + \sigma_2^2 + \sigma_3^2} \geq S_y$
$\sigma_{vm} = \sigma_1 - \sigma_3 \geq S_y$
$\sigma_{vm} = \frac{1}{\sqrt{2}}\sqrt{(\sigma_1-\sigma_2)^2+(\sigma_2-\sigma_3)^2+(\sigma_3-\sigma_1)^2} \geq S_y$✔️
$\sigma_{vm} = \frac{\sigma_1+\sigma_2+\sigma_3}{3} \geq S_y$

Correct Answer Logic:

The von Mises (distortion energy) criterion: $\sigma_{vm}=\frac{1}{\sqrt{2}}\sqrt{(\sigma_1-\sigma_2)^2+(\sigma_2-\sigma_3)^2+(\sigma_3-\sigma_1)^2}\geq S_y$.

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Chemistry QUESTION #5562

Question 40

Which of the following is an anionic detergent?

Sodium lauryl sulphate✔️
Cetyltrimethyl ammonium bromide
Glyceryl oleate
Sodium stearate

Correct Answer Logic:

Anionic detergents have a negatively charged hydrophilic head. Sodium lauryl sulphate ($CH_3(CH_2)_{11}OSO_3^- Na^+$) has an anionic sulphate group → anionic detergent. Cetyltrimethylammonium bromide has a cationic nitrogen → cationic detergent. Glyceryl oleate is a nonionic detergent. Sodium stearate ($C_{17}H_{35}COO^-Na^+$) is a soap, not a synthetic detergent.

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