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The coefficient of $Z^5$ corresponds to $n+2=5\Rightarrow n=3$: coefficient $=\dfrac{3^3}{3!}=\dfrac{27}{6}=\dfrac{9}{2}$. Verify: $\dfrac{27}{6}=\dfrac{9}{2}$ — both options 1 and 2 are the same value. The coefficient is $\dfrac{9}{2}$.

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Commerce QUESTION #1211

Question 2604

In a sales mix decision, the product with the highest contribution margin per unit should be:

Sold exclusively, regardless of customer demand.
Prioritized when resources are constrained.✔️
Avoided to reduce risk.
Discounted to maximize revenue.

Correct Answer Logic:

When resources (such as machine hours or materials) are constrained, products should be ranked by contribution margin per unit of the limiting factor (not just per unit). The product yielding the highest contribution margin per scarce resource should be prioritized to maximize total contribution and profit. Selling exclusively ignores demand and other constraints.

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Reading and Writing (Module-1) QUESTION #5411

Question 2605

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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Mathematics QUESTION #1305

Question 2606

The Trapezoidal Rule for $n$ equally spaced points with step size $h$ is:

$\dfrac{h}{2}(y_0+2y_1+\cdots+2y_{n-1}+y_n)$✔️
$\dfrac{h}{3}(y_0+4y_1+2y_2+\cdots+y_n)$
$h(y_0+y_1+\cdots+y_n)$
$\dfrac{h}{2}(y_0+y_n)$

Correct Answer Logic:

The Trapezoidal Rule approximates $\int_a^b f(x)\,dx\approx\dfrac{h}{2}[f(x_0)+2f(x_1)+2f(x_2)+\cdots+2f(x_{n-1})+f(x_n)]$. This gives the first and last function values weight 1 and all interior values weight 2.

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Urdu QUESTION #5112

Question 2607

مسدسِ حالی کس بحر میں لکھی گئی ہے؟

بحرِ ہزج✔️
بحرِ متدارک
بحرِ کامل
بحرِ رمل

Correct Answer Logic:

مسدسِ حالی بحرِ ہزج میں لکھی گئی ہے۔

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Pakistan Affairs QUESTION #591

Question 2608

Band i Matram', was part of a Hindi novel:

Verdict on India
Anand Math✔️
Mirat al Aroos
None of These

Correct Answer Logic:

It is a poem from Bankim Chandra Chattopadhyay's 1882 novel Anandamath.

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Reading and Writing (Module-1) QUESTION #5361

Question 2609

Climate models suggest that while total rain in the US West might stay the same, it will likely happen in fewer but heavier storms. Scientist Geeta Persad simulated how this would impact aquifers and irrigation. The study found that fewer rain events would lead to more dry days and more irrigation, though this impact depends heavily on the current precipitation levels of the area. Which choice best describes data from the table that support Persad and her colleagues' conclusion?

If baseline precipitation is somewhat concentrated, the amount of water being used for irrigation will increase 0.4% for surface water and 0.9% for groundwater, whereas the amount of water entering aquifers will increase 11.0% if baseline precipitation is evenly distributed.
If baseline precipitation is somewhat concentrated, water use for irrigation will increase only slightly, whereas it will increase 9.0% for surface water and 7.9% for groundwater if baseline precipitation is evenly distributed.✔️
If baseline precipitation is somewhat concentrated, the amount of water entering aquifers will increase 4.9%, while the amount being used for irrigation will increase 0.4% for surface water and 0.9% for groundwater.
If baseline precipitation is somewhat concentrated, water use for irrigation will decline by a small amount, whereas it will increase 11.0% for surface water and 9.0% for groundwater if baseline precipitation is evenly distributed.

Correct Answer Logic:

The conclusion states that irrigation needs are 'highly sensitive' to baseline distribution. Option B contrasts the small 0.4%-0.9% increase (concentrated baseline) with the much larger 9.0%-7.9% increase (even baseline).

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Basic Mathematics QUESTION #2879

Question 2610

The average weight of 3 boys is $40$ kg. If the weights of two are $35$ kg and $42$ kg, find the third.

40 kg
43 kg✔️
45 kg
38 kg

Correct Answer Logic:

Total weight $= 3 \times 40 = 120$. Third boy $= 120 - (35 + 42) = 43$ kg.

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Commerce QUESTION #1202

Question 2611

Which financial statement is unique to public sector accounting?

Statement of Financial Performance
Statement of Cash Flows
Appropriation Account✔️
Statement of Changes in Equity

Correct Answer Logic:

The Appropriation Account is unique to public sector (government) accounting. It shows how the government's budget has been allocated and spent across various ministries and departments. It accounts for voted grants and actual expenditures, showing the utilization of appropriated funds.

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Chemistry QUESTION #1435

Question 2612

In glycolysis, the enzyme hexokinase catalyzes the conversion of:

Glucose to glucose-6-phosphate✔️
Pyruvate to lactate
Fructose-6-phosphate to fructose-1,6-bisphosphate
None of these

Correct Answer Logic:

Hexokinase is the first enzyme of glycolysis. It catalyzes the phosphorylation of glucose using ATP: $\text{Glucose} + \text{ATP} \xrightarrow{\text{hexokinase}} \text{Glucose-6-phosphate} + \text{ADP}$. This irreversible step traps glucose inside the cell. Phosphofructokinase-1 catalyzes the conversion of fructose-6-phosphate to fructose-1,6-bisphosphate.

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Physics QUESTION #1048

Question 2613

In a certain camera, four identical thin convex lenses are arranged axially in contact. Power and magnification compared to individual lens (power $p$, magnification $m$):

4p and $m^4$✔️
p^4 and $m^4$
4p and 4m
p^4 and 4m

Correct Answer Logic:

Power of lenses in contact adds: $P_{total}=4p$. For magnification: lenses in contact act as one system, but if we consider each lens magnifying, total magnification $= m\times m\times m\times m = m^4$. Answer: 4p and $m^4$.

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English QUESTION #2690

Question 2614

Choose the grammatically correct sentence:

Each of the students have finished.
Each of the students has finished.✔️
Each of the students are finished.
Each of the students were finished.

Correct Answer Logic:

'Each' is a singular pronoun and requires a singular verb 'has' regardless of the plural noun 'students'.

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General Knowledge QUESTION #2617

Question 2615

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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Basic Mathematics QUESTION #2813

Question 2616

If the price of an item is increased by $25\%$ and then decreased by $20\%$, what is the net percentage change?

0%✔️
5% increase
5% decrease
No change

Correct Answer Logic:

Let original price $= 100$. After $25\%$ increase: $125$. After $20\%$ decrease: $125 \times 0.80 = 100$. Net change $= 0\%$. The item returns to its original price.

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Reading and Writing (Module-1) QUESTION #5432

Question 2617

Cats can judge unseen people's positions by voice. Researchers measured surprise via ear and head movements when cats heard owners' voices from one or two speakers. How did researchers determine cats' surprise level?

They watched ear and head movements.✔️
They examined reaction to a stranger's voice.
They studied physical interaction with owner.
They tracked how each cat moved around the room.

Correct Answer Logic:

The text explicitly states "measuring cats' levels of surprise based on their ear and head movements."

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3303

Question 2618

The 'BCG' vaccine is used to provide protection against:

Hepatitis B
Tuberculosis✔️
Polio
Tetanus

Correct Answer Logic:

Bacillus Calmette-Guérin (BCG) is an attenuated strain of *Mycobacterium bovis*.

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Mathematics QUESTION #1266

Question 2619

For $f(x,y)=xy-2x$ on the triangular region with vertices $(0,0)$, $(4,0)$, $(0,4)$, the absolute minimum value is:

$-8$✔️
$0$
$-4$
$4$

Correct Answer Logic:

On boundary edge from $(0,0)$ to $(4,0)$ ($y=0$): $f=-2x$, minimum at $x=4$: $f=-8$. Interior critical point: $f_x=y-2=0\Rightarrow y=2$; $f_y=x=0\Rightarrow x=0$, giving $f(0,2)=0$. Checking all boundaries, the absolute minimum is $-8$ at $(4,0)$.

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General Science and Ability QUESTION #193

Question 2620

The process of preserving meat by stewing in a covered earthenware jug is called:

Burial
Jugging✔️
Curing
None of these

Correct Answer Logic:

Jugging is a traditional method of slow-cooking meat inside a tightly sealed jug.

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