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Professional
QUESTION #1839
Question 4921
Under Section 13(1), a civil servant shall retire from service on completing how many years of service qualifying for pension, if directed by the competent authority in the public interest?
Correct Answer Logic:
Section 13(1)(i) as substituted by Ordinance No. XXXIV of 2001 provides that a civil servant shall retire on such date after completing twenty years of service qualifying for pension or other retirement benefits as the competent authority may, in public interest, direct. In the absence of such direction, retirement occurs at age sixty under clause (ii).
Uploaded by: Fani Warraich
Correct Answer Logic:
First find direction vectors of \(L_1\) and \(L_2\). For \(L_1\), cross product of normals \((2,-2,3)\) and \((1,-1,1)\) gives \(\vec{d_1} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 2 & -2 & 3 \\ 1 & -1 & 1 \end{vmatrix} = \hat{i}(-2+3) - \hat{j}(2-3) + \hat{k}(-2+2) = \hat{i} + \hat{j}\), or \((1,1,0)\). For \(L_2\), cross product of \((1,2,-1)\) and \((3,-1,2)\) gives \(\vec{d_2} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 1 & 2 & -1 \\ 3 & -1 & 2 \end{vmatrix} = \hat{i}(4-1) - \hat{j}(2+3) + \hat{k}(-1-6) = 3\hat{i} - 5\hat{j} - 7\hat{k}\), or \((3,-5,-7)\). Find a point on each line, then find the normal to the plane containing both lines by cross product of direction vectors. This is a lengthy calculation. The distance formula gives \(\frac{1}{2\sqrt{2}}\).
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General Knowledge
QUESTION #8262
Question 4923
Which of the following individuals is recognized as one of the pioneers who helped create the internet?
Correct Answer Logic:
Vinton Cerf is widely known as one of the 'fathers of the internet' for his work on TCP/IP.
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Home Economics
QUESTION #6235
Question 4924
The first step in the management process is:
Correct Answer Logic:
Planning involves setting goals and determining the course of action to achieve them.
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Correct Answer Logic:
Both the control and experimental groups increased performance regardless of lighting changes. Mayo concluded that productivity was driven by social factors โ morale, group belonging, managerial attention. For public administration, this shifted focus from mechanical efficiency (Classical School) to the human and social dimensions of organizational life.
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Verbal Reasoning
QUESTION #8095
Question 4926
In the figure above, each of the four squares has sides of length $x$. If $\triangle PQR$ is formed by joining the centers of three of the squares, what is the perimeter of $\triangle PQR$ in terms of $x$?
Correct Answer Logic:
Each square has side length $x$, so the center of each square is at distance $\frac{x}{2}$ from each edge.
From the arrangement:
- $P$ is the center of the top-left square at $\left(\frac{x}{2}, \frac{x}{2}\right)$
- $Q$ is the center of the top-right square at $\left(\frac{3x}{2}, \frac{x}{2}\right)$
- $R$ is the center of the bottom-right square at $\left(\frac{3x}{2}, \frac{3x}{2}\right)$
Distances:
- $PQ = x$ (horizontal distance between adjacent centers)
- $QR = x$ (vertical distance between adjacent centers)
- $PR = \sqrt{x^2 + x^2} = x\sqrt{2}$ (diagonal)
Perimeter $= PQ + QR + PR = x + x + x\sqrt{2} = 2x + x\sqrt{2}$
Uploaded by: Fani Warraich
Chemistry
QUESTION #5564
Question 4928
Which of the following compounds will behave as a reducing sugar in an aqueous KOH solution? (A free hemiacetal/anomeric โOH is required for reducing sugar property)
Correct Answer Logic:
A reducing sugar must have a free anomeric โOH (hemiacetal) that can open to give an aldehyde/ketone form. Option A shows a furanose ring with a free โOH at the anomeric carbon, which can open and reduce. Options B and C have the anomeric โOH blocked as an ether or ester (non-reducing). Option D also has a blocked anomeric position.
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English
QUESTION #7638
Question 4929
Change the voice: When will you buy a car?
Correct Answer Logic:
In interrogative sentences, when changing to passive voice, the question word remains at the beginning. The structure is: Question word + will + object + be + past participle + by + subject. Therefore, 'When will you buy' becomes 'When will be bought by you'.
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Pakistan Affairs
QUESTION #608
Question 4930
Whose behaviour disheartened M.A. Jinnah, leading him to decide to stay away from India?
Correct Answer Logic:
Jinnah was disillusioned by the overall political atmosphere, specifically after the 1928 Nehru Report and the Lucknow Pact's failure .
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Mathematics
QUESTION #7441
Question 4931
The number of points, having both coordinates as integers, that lie in the interior of the triangle with vertices (0, 0), (0, 41) and (41, 0), is:
Correct Answer Logic:
Using Pick's theorem: Area = \(I + \frac{B}{2} - 1\), where I is interior points and B is boundary points. The triangle has area \(\frac{1}{2} \times 41 \times 41 = \frac{1681}{2}\). Boundary points: on the x-axis from (1,0) to (40,0) are 40 points, on y-axis from (0,1) to (0,40) are 40 points, vertices are 3 points, and on hypotenuse \(x+y=41\) from (1,40) to (40,1) are 39 points. Total B = 40+40+3+39 = 122. But actually the vertices shouldn't be counted separately. Let me recalculate: B = 40 + 40 + 39 + 3 = 122. Using Pick's theorem: \(\frac{1681}{2} = I + \frac{122}{2} - 1\), so \(I = \frac{1681}{2} - 61 + 1 = \frac{1681 - 120}{2} = \frac{1561}{2}\). This doesn't give an integer, so let me use the direct formula. For a triangle with vertices at \((0,0), (a,0), (0,a)\), interior lattice points = \(\frac{(a-1)(a-2)}{2} + (a-1) = \frac{(a-1)a}{2} - 1\). Wait, the correct formula for this specific right triangle is \(\frac{(41-1)(41-2)}{2} = \frac{40 \times 39}{2} = 780\).
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Physics
QUESTION #383
Question 4933
In LED when an electron combines with a __________ during forward bias conduction
Home Economics
QUESTION #6247
Question 4934
A 'Flashcard' is an example of which type of extension aid?
Correct Answer Logic:
Visual aids rely on sight to convey information or reinforce a message.
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General Knowledge
QUESTION #4816
Question 4935
The theory proposing that a single dominant power (hegemon) can maintain global stability is called?
Correct Answer Logic:
Hegemonic Stability Theory, developed by economists and IR scholars, argues that a dominant state (hegemon) is necessary to maintain a stable international economic and political order.
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Egnlish
QUESTION #722
Question 4936
In Wordsworth's "Tintern Abbey," the "still sad music of humanity" refers to:
Correct Answer Logic:
It reflects the poet's mature understanding of the interconnectedness of human experience and sorrow.
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Biology
QUESTION #7262
Question 4937
Thermococcus, Methanococcus and Methanobacterium exemplify:
Correct Answer Logic:
These three organisms are all Archaebacteria. Their chromatin contains histone-like proteins homologous to eukaryotic core histones (H3 and H4 homologs), which is a unique feature of archaea among prokaryotes. This partly explains why archaea are considered more closely related to eukaryotes in the three-domain classification.
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English
QUESTION #2699
Question 4938
Where should a semicolon be used?
Correct Answer Logic:
A semicolon joins two closely related independent clauses without a coordinating conjunction.
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Biology Zoology Botany
QUESTION #1357
Question 4939
Which organelle is involved in modifying, sorting, and packaging proteins for secretion?
Correct Answer Logic:
The Golgi apparatus (Golgi complex) is the cell's main processing and distribution centre for proteins and lipids. Proteins synthesised in the rough endoplasmic reticulum are transported to the Golgi where they are modified (glycosylation, phosphorylation), sorted, and packaged into vesicles for secretion, delivery to lysosomes, or incorporation into the plasma membrane.
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General Knowledge
QUESTION #8721
Question 4940
The playground for playing baseball is called:
Correct Answer Logic:
A baseball field is often called a diamond due to its shape.
Uploaded by: Fani Warraich
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