Reading Mode - Questions

Mathematics QUESTION #7450

If the lines $\frac{x-2}{1} = \frac{y-3}{1} = \frac{z-4}{-k}$ and $\frac{x-1}{k} = \frac{y-4}{2} = \frac{z-5}{1}$ are coplanar, then k can have:

any value
exactly one value
exactly two values✔️
exactly three values

Correct Answer Logic:

For two lines to be coplanar, the scalar triple product of their direction ratios and the vector joining points on the lines must be zero. The direction ratios are $(1, 1, -k)$ and $(k, 2, 1)$. A point on the first line is $(2, 3, 4)$ and on the second is $(1, 4, 5)$. The vector joining them is $(-1, 1, 1)$. Setting up the determinant: $\begin{vmatrix} -1 & 1 & 1 \\ 1 & 1 & -k \\ k & 2 & 1 \end{vmatrix} = 0$. Expanding: $-1(1+2k) - 1(1+k^2) + 1(2-k) = 0$, which simplifies to $k^2 + 3k = 0$, giving $k = 0$ or $k = -3$. Thus, k has exactly two values.

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Math Physics Chemistry Biology QUESTION #813

Question 6622

A single chloride free radical can destroy how many ozone molecules?

100
10,000
100,000✔️
10

Correct Answer Logic:

A single chlorine free radical can catalytically destroy up to $100{,}000$ ozone molecules through a chain reaction mechanism in the stratosphere.

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General Knowledge QUESTION #4818

Question 6623

The concept explaining how individually rational self-interested behavior can lead to destructive collective outcomes is known as?

Tragedy of the Commons✔️
Population implosion
Carrying capacity
Prisoner's dilemma

Correct Answer Logic:

The Tragedy of the Commons, a concept developed by Garrett Hardin in 1968, explains how individuals acting in their own self-interest can deplete shared resources, leading to collective harm despite individual rationality.

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Paper-II (Pharmacognosy and Pharmaceutics-I) QUESTION #3631

Question 6624

'Tinctures' are alcoholic or hydro-alcoholic extractions of:

Minerals only
Crude drugs (plant or animal material)✔️
Synthetic powders
Pure water

Correct Answer Logic:

Tinctures are common liquid forms of herbal medicines.

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Pakistan Affairs QUESTION #285

Question 6625

Why Arab rule could not extend beyond Sindh and Multan?

Geographical barriers and rigid terrain
Strong resistance from local rulers✔️
Lack of interest in territorial expansion
Internal conflicts among the Arabs

Correct Answer Logic:

Strong resistance from local Hindu dynasties like the Gurjara-Pratiharas halted further Arab expansion.+1

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English QUESTION #7554

Question 6626

Translate into English: میں جانتا تھا کہ وہ وعدہ پورا نہیں کرے گا۔

I knew that he won’t keep his promise.
I knew that he would not keep his promise.✔️
I was knowing that he will not keep his promise.
I know he doesn’t keep his promise.

Correct Answer Logic:

The Urdu uses past tense "جانتا تھا" (knew) and future-in-past "کرے گا" (would not keep). Option B correctly uses "knew" + "would not keep."

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General Abilities QUESTION #4552

Question 6627

A shirt costs Rs.$50$ after a $20\%$ discount. What was the original price?

Rs.$60$
Rs.$62.5$✔️
Rs.$70$
Rs.$40$

Correct Answer Logic:

If discounted price = original $\times (1 - 0.20)$, then $50 = \text{original} \times 0.8$. Original = $\frac{50}{0.8} = 62.5$

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Paper-II (Pharmacognosy and Pharmaceutics-I) QUESTION #3654

Question 6628

The 'Stomata' are tiny pores mostly found on:

Roots
Stems
Leaves✔️
Seeds

Correct Answer Logic:

Stomata are used for gas exchange and transpiration.

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Logical Reasoning QUESTION #3959

Question 6629

Select the pair with a similar relationship: OBSTRUCTION : BUOY

construction : building✔️
boy : girl
danger : red light
iceberg : titanic

Correct Answer Logic:

2

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Planning QUESTION #5015

Question 6630

What does the Gini Coefficient measure in urban economics?

Population density
Income inequality✔️
Housing prices
Transportation costs

Correct Answer Logic:

The Gini Coefficient (0-1 scale) measures income/wealth inequality. 0 represents perfect equality; 1 represents maximum inequality. Values above 0.4 indicate high inequality. Calculated from the Lorenz curve: $G = \frac{A}{A+B}$ where A is area between Lorenz curve and equality line.

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Accounting & Finance QUESTION #6059

Question 6631

A machine has an original cost of Rs. 19,00,000 and installation charges of Rs. 1,00,000. Its useful life is 5 years and residual value is Rs. 40,000. Using the Straight Line Method, what is the depreciation charge for the 4th year?

Rs. 372,000
Rs. 400,000
Rs. 392,000✔️
Rs. 352,000

Correct Answer Logic:

Total cost $= 19{,}00{,}000 + 1{,}00{,}000 = Rs.\ 20{,}00{,}000$

Depreciable amount $= 20{,}00{,}000 - 40{,}000 = Rs.\ 19{,}60{,}000$

Annual depreciation (SLM) $= \dfrac{19{,}60{,}000}{5} = Rs.\ 3{,}92{,}000$

Under the Straight Line Method, depreciation is equal every year. So the 4th year's depreciation is also Rs. 3,92,000. There is no change between years in SLM.

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Reading and Writing (Module-1) QUESTION #5419

Question 6632

In 2019, researcher Patricia Jurado Gonzalez and food historian Nawal Nasrallah prepared a stew from a 4,000-year-old recipe found on a Mesopotamian clay tablet. When they tasted the dish, known as pašrūtum ("unwinding"), they found that it had a mild taste and inspired a sense of calm. _______ the researchers, knowing that dishes were sometimes named after their intended effects, theorized that the dish's name, "unwinding," referred to its function: to help ancient diners relax. Which choice completes the text with the most logical transition?

Therefore,✔️
Alternately,
Nevertheless,
Likewise,

Correct Answer Logic:

'Therefore' signals that the theory about the name's meaning is a logical conclusion based on the calming effect they observed.

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Planning QUESTION #4971

Question 6633

If a city's population grows from 500,000 to 800,000 over 20 years, what is the annual compound growth rate?

2.3%✔️
2.4%
2.5%
3.0%

Correct Answer Logic:

Using the compound growth formula: $r = \left(\frac{P_t}{P_0}\right)^{1/t} - 1 = \left(\frac{800000}{500000}\right)^{1/20} - 1 = (1.6)^{0.05} - 1 = 0.0237$ or approximately 2.37%, closest to 2.3%.

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General Knowledge QUESTION #2616

Question 6634

An SSD (Solid State Drive) differs from an HDD primarily because:

An SSD uses a spinning platter to store data, making it slower
An SSD uses electronic flash memory with no moving parts, making it faster and more durable✔️
An SSD requires a constant internet connection to store data
An SSD can only store temporary data and loses it when powered off

Correct Answer Logic:

An SSD (Solid State Drive) uses electronic flash memory chips with no moving parts. This makes SSDs significantly faster, quieter, more shock-resistant, and more energy-efficient than traditional HDDs which rely on spinning platters and mechanical arms.

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