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Mathematics QUESTION #6971

Question 1

Evaluate $\displaystyle\lim_{n\to\infty}\left(\dfrac{(n+1)(n+2)\cdots3n}{n^{2n}}\right)^{1/n}$

$\dfrac{27}{e^2}$✔️
$\dfrac{9}{e^2}$
$3\ln3-2$
$\dfrac{18}{e^4}$

Correct Answer Logic:

$\ln L = \lim_{n\to\infty}\dfrac{1}{n}\sum_{r=1}^{2n}\ln\!\left(1+\dfrac{r}{n}\right) = \int_0^2\ln(1+x)\,dx$

$=\left[(1+x)\ln(1+x)-(1+x)\right]_0^2 = (3\ln3-3)-(-1) = 3\ln3-2$

$L = e^{3\ln3-2} = \dfrac{27}{e^2}$

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Math Physics Chemistry Biology QUESTION #4283

Question 2

The most primitive respiratory process occurring in a living cell is:

Lactic acid fermentation
Alcoholic fermentation
Glycolysis✔️
Krebs's cycle

Correct Answer Logic:

Glycolysis is the most ancient and primitive form of cellular respiration, occurring in the cytoplasm without oxygen. It is universal among all living organisms.

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Mathematics QUESTION #4127

Question 3

Using Cauchy Residue Theorem, evaluate $\oint_{|z|=2} \frac{5z - 2}{z(z-1)} \, dz$. The poles inside are at:

$z = 0$ only
$z = 1$ only
$z = 0$ and $z = 1$✔️
No poles inside $|z| = 2$

Correct Answer Logic:

Poles at $z = 0$ and $z = 1$. Both satisfy $|z| < 2$, so both are inside the contour.

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Agronomy QUESTION #2020

Question 4

In Pakistan's seed multiplication system, which class of seed is produced directly from Breeder seed and is used to produce Registered seed?

Certified seed
Foundation seed✔️
Truthfully Labeled seed
Commercial seed

Correct Answer Logic:

The seed multiplication chain in Pakistan follows: Breeder Seed → Foundation Seed → Registered Seed → Certified Seed. Foundation seed is produced from breeder seed under strict supervision and maintains very high genetic and physical purity standards.

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Mathematics QUESTION #7435

Question 5

If the vectors $\vec{AB} = 3\hat{i} + 4\hat{k}$ and $\vec{AC} = 5\hat{i} - 2\hat{j} + 4\hat{k}$ are the sides of a triangle ABC, then the length of the median through A is:

$\sqrt{18}$
$\sqrt{72}$
$\sqrt{33}$✔️
$\sqrt{45}$

Correct Answer Logic:

The median from A goes to the midpoint M of BC. We have $\vec{AB} + \vec{BC} = \vec{AC}$, so $\vec{BC} = \vec{AC} - \vec{AB} = (5\hat{i}-2\hat{j}+4\hat{k}) - (3\hat{i}+4\hat{k}) = 2\hat{i}-2\hat{j}$. The midpoint M of BC from B is at $\frac{\vec{BC}}{2} = \hat{i}-\hat{j}$. The position of M from A is $\vec{AM} = \vec{AB} + \frac{\vec{BC}}{2} = 3\hat{i}+4\hat{k} + \hat{i}-\hat{j} = 4\hat{i}-\hat{j}+4\hat{k}$. The length is $|\vec{AM}| = \sqrt{16+1+16} = \sqrt{33}$.

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Pakistan Affairs QUESTION #9036

Question 6

The largest share of revenue receipts for the Pakistani Federal Government comes from:

General Sales Tax (GST/VAT)✔️
Income Tax
Wealth Tax
Central Excise Duty

Correct Answer Logic:

Sales tax/GST is the largest source of federal revenue.

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Paper-I (Pharmaceutics II (Industrial and Quality Control) and Pharmaceutics III (Hospital and Community Pharmacy)) QUESTION #5690

Question 7

Which equation represents the 'Alligation Alternate' method for mixing two concentrations $C_{1}$ and $C_{2}$ to get concentration $C_{m}$?

$\frac{Parts_{1}}{Parts_{2}} = \frac{|C_{2} - C_{m}|}{|C_{1} - C_{m}|}$✔️
$\frac{Parts_{1}}{Parts_{2}} = \frac{|C_{1} - C_{2}|}{C_{m}}$
$C_{1}V_{1} = C_{2}V_{2}$
$P = V \times D$

Correct Answer Logic:

Alligation alternate uses the absolute difference between the desired and available concentrations to determine mixing proportions.

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General Knowledge QUESTION #172

Question 8

The British constitution can be amended through a _______ majority.

Two-Third
Three-Fourth
One-Two
None of these✔️

Correct Answer Logic:

The UK has an uncodified constitution; it can be amended by a simple majority in Parliament.

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Planning QUESTION #4920

Question 9

In development economics, what does GDP measure?

Total government debt of a country
Total value of goods and services produced✔️
Total population density
Total development projects

Correct Answer Logic:

GDP (Gross Domestic Product) measures the total monetary value of all goods and services produced within a country's borders during a specific time period, indicating economic performance.

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General Knowledge QUESTION #4705

Question 10

Which organization is considered the world's oldest international human rights body?

Amnesty International
Freedom House
Anti-Slavery International✔️
Human Rights Watch

Correct Answer Logic:

Anti-Slavery International, founded in 1839, is the world's oldest international human rights organization, predating Amnesty International (1961) and Freedom House (1941).

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Information Technology QUESTION #1125

Question 11

Which optimization method involves minimizing the memory access count in a program?

Constant folding
Register allocation✔️
Instruction scheduling
None of these

Correct Answer Logic:

Register allocation is the process of assigning a large number of target program variables onto a small number of CPU registers to minimize slow memory accesses.

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Mathematics QUESTION #7471

Question 12

If the vectors $\vec{AB} = 3\hat{i} + 4\hat{k}$ and $\vec{AC} = 5\hat{i} - 2\hat{j} + 4\hat{k}$ are the sides of a triangle ABC, then the length of the median through A is:

$\sqrt{18}$
$\sqrt{72}$
$\sqrt{33}$✔️
$\sqrt{45}$

Correct Answer Logic:

The median from A goes to midpoint M of BC. Position vector of B from A is $\vec{AB} = 3\hat{i}+4\hat{k}$, and of C from A is $\vec{AC} = 5\hat{i}-2\hat{j}+4\hat{k}$. Midpoint M has position vector $\frac{\vec{AB}+\vec{AC}}{2} = \frac{(3\hat{i}+4\hat{k})+(5\hat{i}-2\hat{j}+4\hat{k})}{2} = \frac{8\hat{i}-2\hat{j}+8\hat{k}}{2} = 4\hat{i}-\hat{j}+4\hat{k}$. Length of median $AM = |\vec{AM}| = \sqrt{16+1+16} = \sqrt{33}$.

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Physical Education QUESTION #6813

Question 13

Which philosopher is most credited with the idea that 'a feeble body weakens the mind'?

John Locke
Rousseau✔️
Plato
Aristotle

Correct Answer Logic:

Rousseau argued in 'Emile' that a strong body is necessary to support a strong and active mind.

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Accounting Finance and Punjab Sales Tax on Services QUESTION #2556

Question 14

Under section 16C of the Punjab Sales Tax on Services Act, 2012, a registered person shall NOT be allowed to adjust input tax in a tax period in excess of what percentage of the output tax for that tax period?

Seventy percent
Eighty percent
Ninety percent✔️
One hundred percent

Correct Answer Logic:

Section 16C(1) as amended provides that a registered person shall not be allowed to adjust input tax in a tax period in excess of ninety percent of the output tax for that tax period.

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Math Physics Chemistry Biology QUESTION #808

Question 15

Which is not a calcareous material?

Clay✔️
Marble
Lime
Marine shell

Correct Answer Logic:

Calcareous materials contain calcium carbonate $(\text{CaCO}_3)$. Marble, lime, and marine shells are all calcareous. Clay is an aluminosilicate and is not calcareous.

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General Knowledge QUESTION #4474

Question 16

In 2025, conflict between Thailand and Cambodia erupted on the issue of:

Human trafficking
Boundary claims✔️
Unchecked smuggling
Ownership of a temple

Correct Answer Logic:

Thailand–Cambodia disputes historically revolve around border demarcation issues.

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Psychology QUESTION #9849

Question 17

Which of the following is NOT listed as a classification of psychoneuroses?

Phobic reactions
Conversion reactions
Neurasthenic reactions
Delusional reactions✔️

Correct Answer Logic:

Delusional reactions are characteristic of psychoses, not psychoneuroses. Classical psychoneurotic categories include phobic, conversion, neurasthenic, anxiety, and obsessive-compulsive reactions.

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Maths QUESTION #4596

Question 18

Solve: $3x - 7 = 14$

$x = 7$✔️
$x = 21$
$x = \frac{7}{3}$
$x = 3$

Correct Answer Logic:

$3x - 7 = 14 \Rightarrow 3x = 21 \Rightarrow x = 7$

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Reading and Writing (Module-1) QUESTION #10473

Question 19

The novel was criticized as -------, its plot bearing an uncomfortably close ------- to a dozen earlier bestsellers.

novel . . departure
derivative . . resemblance✔️
inventive . . contrast
groundbreaking . . deviation

Correct Answer Logic:

An unoriginal plot ('derivative') bears a close 'resemblance' to earlier works.

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Math Physics Chemistry Biology QUESTION #11431

Question 20

Which is a steroid hormone?

Insulin
Cortisol✔️
Glucagon
Thyroxine

Correct Answer Logic:

Cortisol is a glucocorticoid steroid hormone produced by the adrenal cortex. Being lipid-soluble, it crosses cell membranes and acts on nuclear receptors to regulate gene expression. Insulin and glucagon are peptide hormones (from pancreas); thyroxine is an amino acid-derived hormone — none of these are steroids.

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