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Mathematics QUESTION #1333

A power series solution $y=\sum_{n=0}^\infty a_n x^n$ to an ODE converges in a neighbourhood of an ordinary point $x_0$ up to the distance to the nearest:

Irregular singular point
Singular point✔️
Ordinary point
Boundary point

Correct Answer Logic:

By the theorem on power series solutions, if $x_0$ is an ordinary point of the ODE, the power series solution converges in the interval \(|x-x_0|

Uploaded by: Fani Warraich

Psychology QUESTION #9905

Question 2

In Thurston's method of attitude scaling, the key factor is the use of:

Numbers
Judges✔️
Reinforcement
Positive and negative items

Correct Answer Logic:

In Thurston's equal-appearing interval method, the critical element is a panel of judges who evaluate attitude statements and place them on an 11-point scale from unfavourable to favourable. Median judge ratings determine each item's scale value.

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General Knowledge QUESTION #8827

Question 3

The epic 'Talism-e-Hoshruba' was originally composed by which author?

Ibn-e-Insha
Mumtaz Mufti
Muhammad Husain Jah✔️
Musharraf Ali Farooqi

Correct Answer Logic:

Muhammad Husain Jah wrote this Urdu epic.

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Dairy Food Science and Technology QUESTION #6002

Question 4

In a continuous butter-making machine (e.g. Fritz machine) compared to the traditional batch churn, the main advantages are:

Batch churn produces better flavor; continuous machine is only faster
Continuous machines offer higher throughput, better process control, more uniform butter composition (fat $\approx 80\%$, moisture $\leq 16\%$), and easier CIP while eliminating the need for batch washing steps✔️
Batch churns produce butter with higher fat content
Continuous machines cannot handle cream with fat content $>35\%$

Correct Answer Logic:

Continuous butter-making machines (Fritz/Westfalia) operate at high throughput (up to $10{,}000\;\text{kg/hr}$) with: consistent butter composition; automated process control; integrated pasteurization and standardization of cream; better CIP capability; and elimination of batch-to-batch variation. They have largely replaced batch churns in modern dairy plants.

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Reading and Writing (Module-1) QUESTION #5411

Question 5

In many of her landscape paintings from the 1970s and 1980s, Lebanese American artist Etel Adnan worked to capture the essence of California's fog-shrouded Mount Tamalpais region through abstraction, using splotches of color to represent the area's features. Interestingly, the triangle representing the mountain itself _______ among the few defined figures in her paintings. Which choice completes the text so that it conforms to the conventions of Standard English?

are
have been
were
is✔️

Correct Answer Logic:

Singular verb 'is' agrees with the singular subject 'the triangle.'

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3319

Question 6

'Tetanus' is caused by an anaerobic bacterium called:

*Clostridium tetani*✔️
*Bacillus anthracis*
*Vibrio cholerae*
*Bordetella pertussis*

Correct Answer Logic:

It produces a potent neurotoxin that causes muscle stiffness (lockjaw).

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Mathematics QUESTION #6947

Question 7

Let $A=\begin{pmatrix}i&-i\\-i&i\end{pmatrix}$ where $i=\sqrt{-1}$. The system $A^8\begin{pmatrix}x\\y\end{pmatrix}=\begin{pmatrix}8\\64\end{pmatrix}$ has:

Exactly two solutions
No solution✔️
A unique solution
Infinitely many solutions

Correct Answer Logic:

$A = \begin{pmatrix}i&-i\\-i&i\end{pmatrix}$. Note $\det(A) = i^2-i^2=0$, so $A$ is singular.

$A^2$: compute $(A)^2$. Row1·Col1: $i(i)+(-i)(-i)=-1+(-1)=-2i$... Let's compute: $A^2_{11}=i\cdot i+(-i)(-i)=i^2+i^2=-1-1=-2$. So $A^2 = -2A$... check: $A^2 = -2\begin{pmatrix}i&-i\\-i&i\end{pmatrix}$.

Therefore $A^8 = (-2)^4 A^4 = 16(A^2)^2=16\cdot4A^2=64\cdot(-2A)=-128A$.

Wait: $A^2=-2A \Rightarrow A^4=4A^2=-8A \Rightarrow A^8=-8A^4... $ Correctly: $A^8=(-2)^7A = -128A$.

$-128A\begin{pmatrix}x\\y\end{pmatrix}=\begin{pmatrix}8\\64\end{pmatrix}$. Since $\det(A)=0$, check consistency. The equations are linearly dependent but RHS $(8,64)$ is not in column space of $A$. Hence no solution.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3345

Question 8

'Anaerobes' cannot grow in the presence of oxygen because they lack:

DNA
Cell walls
Enzymes like Superoxide Dismutase and Catalase✔️
Ribosomes

Correct Answer Logic:

These enzymes are needed to neutralize toxic oxygen byproducts.

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Disaster Management QUESTION #6534

Question 9

In the context of Pakistan's disaster landscape, what makes GLOFs particularly challenging compared to other flood hazards?

They occur in populated areas
They combine remote occurrence locations, rapid onset, limited monitoring infrastructure, and high destructive potential✔️
They affect larger areas
They happen more frequently

Correct Answer Logic:

Section 5.5 identifies GLOFs as climate-driven hazards requiring specific focus. Their challenges include remote mountain locations, rapid onset leaving little warning time, limited monitoring infrastructure in northern areas, and potentially catastrophic downstream impacts, requiring specialized early warning and community preparedness.

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English QUESTION #4460

Question 10

Which of the following sentence is CORRECT?

Why industry and academia should collaborate to work on their programs?
Why academia and industry should work to collaborate on their programs?
Why industry and academia should work for the collaboration on their programs?
None of these✔️

Correct Answer Logic:

All options are incorrect because they are structured as statements rather than questions. A correct question would be: 'Why should industry and academia collaborate...?'

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Physics QUESTION #1061

Question 11

An unpolarized light beam is incident on medium of refractive index 1.73 at Brewster's angle. Then:

Both reflected and transmitted light are perfectly polarized at 60° and 30°
Transmitted light is completely polarized with refraction angle close to 30°
Reflected light is completely polarized and angle of reflection is close to 60°✔️
Reflected light is partially polarized and angle of reflection is close to 30°

Correct Answer Logic:

Brewster's angle: $\tan\theta_B=n=1.73\approx\sqrt{3}\Rightarrow\theta_B=60°$. At Brewster's angle, reflected light is completely polarized (in the plane perpendicular to incidence). Angle of reflection $=60°$. Transmitted light is partially polarized (not completely). Answer: option (3).

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CISA QUESTION #1757

Question 12

Which category of BPR risks is most likely to emerge during the design phase?

Transition risk, skill risk, financial risk
Management risk, technical risk, HR risk
Technical risk, detection risk, audit risk
Scope risk, skill risk, political risk✔️

Correct Answer Logic:

The primary risks during the BPR design phase are improper scope definition, lack of required skills, political resistance from stakeholders, and insufficient management support — collectively categorized as scope risk, skill risk, and political risk.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3282

Question 13

Fungi that are unicellular and reproduce by 'Budding' are called:

Molds
Yeasts✔️
Mushrooms
Algae

Correct Answer Logic:

Yeasts like *Saccharomyces* are single-celled fungi that reproduce via budding.

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Physics QUESTION #7854

Question 14

Centripetal force for car in circular path is provided by:

Inertia
Mass pull
Engine power
Friction between tyres and road✔️

Correct Answer Logic:

Friction provides the necessary centripetal force.

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Accounting & Finance QUESTION #1215

Question 15

Internal check is carried on by:

Staff specially appointed for the purpose
Internal auditor
Supervisor of the staff
Members of the staff✔️

Correct Answer Logic:

Internal check is a system where the accounting and other operations of a business are so organized that the work of one member of staff is automatically checked by another member in the normal course of their duties. It is carried out by members of the staff themselves as part of their routine work — not by a separately appointed person.

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Chemistry QUESTION #5555

Question 16

The hybridisation of Xe in $XeOF_4$ and the number of lone pairs on Xe are respectively:

$sp^3d^2$ and 1✔️
$sp^3d$ and 2
$sp^3d^2$ and 2
$sp^3d$ and 1

Correct Answer Logic:

In $XeOF_4$: Xe has 8 valence electrons. Bonds: 1 double bond to O + 4 single bonds to F = 5 bond pairs. Lone pairs on Xe = 1. Total electron pairs = 6 → $sp^3d^2$ hybridisation. Shape is square pyramidal. So hybridisation = $sp^3d^2$ and lone pairs = 1.

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Paper-II (Pharmacology and Social Behaviour, Law & Ethics and Computer Sciences) QUESTION #5772

Question 17

Captopril lowers blood pressure by inhibiting the conversion of:

Angiotensin II to I
Angiotensin I to II✔️
Bradykinin to inactive metabolites
Renin to Angiotensinogen

Correct Answer Logic:

ACE inhibitors block the conversion to the potent vasoconstrictor Angiotensin II.

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Planning QUESTION #5007

Question 18

Which zoning technique allows density bonuses in exchange for public amenities?

Euclidean zoning
Performance zoning
Incentive zoning✔️
Floating zones

Correct Answer Logic:

Incentive zoning offers developers increased density, height, or FAR in exchange for providing public benefits (parks, affordable housing, transit improvements), balancing private development rights with public amenity provision—widely used in major cities like New York.

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Civil Engineering QUESTION #6568

Question 19

In differential levelling, the back sight (BS) reading on a benchmark of RL $500\,\text{m}$ is $2.685\,\text{m}$ and the fore sight (FS) reading on a new point is $1.345\,\text{m}$. The RL of the new point is:

502.685 m
501.340 m✔️
501.345 m
504.030 m

Correct Answer Logic:

Height of Instrument $= 500 + 2.685 = 502.685\,\text{m}$. RL of point $= 502.685 - 1.345 = 501.340\,\text{m}$.

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Verbal Reasoning QUESTION #70

Question 20

A box contains 5 red, 3 blue, and 2 green balls. Two balls are drawn at random without replacement.

1/5
7/15
17/45✔️
8/15

Correct Answer Logic:

Total balls = 10

Use complement method:

P(at least one green)

= 1 − P(no green)

Balls without green = 8

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