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Mathematics
QUESTION #7443
Question 7281
If \(m\) is the A.M. of two distinct real numbers \(\ell\) and \(n\) (\(\ell, n > 1\)) and \(G_1, G_2\) and \(G_3\) are three geometric means between \(\ell\) and \(n\), then \(G_1^4 + 2G_2^4 + G_3^4\) equals:
Correct Answer Logic:
We have \(m = \frac{\ell+n}{2}\). For three geometric means between \(\ell\) and \(n\), we have \(\ell, G_1, G_2, G_3, n\) in G.P. The common ratio is \(r = (\frac{n}{\ell})^{1/4}\). Thus \(G_1 = \ell r = \ell(\frac{n}{\ell})^{1/4}\), \(G_2 = \ell r^2 = \ell\sqrt{\frac{n}{\ell}} = \sqrt{\ell n}\), \(G_3 = \ell r^3 = \ell(\frac{n}{\ell})^{3/4}\). We get \(G_2^2 = \ell n\) and \(G_1 \cdot G_3 = \ell^2 r^4 = \ell n\). Therefore \(G_1^4 + 2G_2^4 + G_3^4 = (G_1^2)^2 + 2(\ell n)^2 + (G_3^2)^2\). Using \(G_1^2 + G_3^2 = (\ell r)^2 + (\ell r^3)^2 = \ell^2 r^2(1+r^4) = \ell^2(\frac{n}{\ell})^{1/2}(1+\frac{n}{\ell}) = \ell n^{1/2}(\frac{\ell+n}{\ell}) = n^{1/2}(\ell+n)\). After careful calculation, the answer is \(4\ell m^2 n\).
Uploaded by: Fani Warraich
English
QUESTION #2659
Question 7282
Convert to indirect: 'He said, "What a beautiful scene!"'
Correct Answer Logic:
Exclamatory sentences use 'exclaimed with joy/wonder' and change 'What a...' to 'very'.
Uploaded by: Fani Warraich
Paper-II (Pharmacognosy and Pharmaceutics-I)
QUESTION #3653
Question 7283
Which of the following is a 'Purgative' drug?
Correct Answer Logic:
Senna contains anthraquinones that stimulate bowel movement.
Uploaded by: Fani Warraich
Pakistan Affairs
QUESTION #9039
Question 7284
In which constitution was Pakistan officially declared the 'Islamic Republic of Pakistan'?
Correct Answer Logic:
The 1956 Constitution declared Pakistan an Islamic republic.
Uploaded by: Fani Warraich
Paper-I (Anatomy/Physiology and Biochemistry/Microbiology)
QUESTION #3511
Question 7285
'Organoleptic' evaluation of a drug refers to evaluation by:
Correct Answer Logic:
It is the simplest method using sight, smell, and touch.
Uploaded by: Fani Warraich
Paper-I (Anatomy/Physiology and Biochemistry/Microbiology)
QUESTION #3392
Question 7286
The process of copying DNA into 'mRNA' is called:
Correct Answer Logic:
Transcription occurs in the nucleus before the mRNA travels to the ribosome.
Uploaded by: Fani Warraich
Boilers Mechanical Engineering
QUESTION #4082
Question 7287
'Boiler Log Book' is a legal and technical record used to:
Correct Answer Logic:
In the event of an accident, the log book is the first thing investigators look at.
Uploaded by: Fani Warraich
Molecular Biology / Bioinformatics / Biochemistry
QUESTION #11122
Question 7288
During one complete turn of the Krebs (citric acid) cycle, the direct (substrate-level) ATP production per glucose molecule is:
Correct Answer Logic:
The Krebs cycle produces 2 ATP per glucose molecule via substrate-level phosphorylation (1 GTP per acetyl-CoA turn Γ 2 turns per glucose = 2 GTP/ATP). The cycle primarily produces electron carriers: 6 NADH and 2 FADHβ per glucose, which generate ~20β22 ATP via oxidative phosphorylation in the ETC. Total aerobic ATP yield per glucose is ~30β32 ATP. The question asks specifically for direct ATP production in the Krebs cycle itself, which is 2.
Uploaded by: Fani Warraich
Correct Answer Logic:
Social competence theory identifies early, sustained human interaction as foundational to a child's social-emotional thriving. Children who lack adequate interpersonal connection may fail to thrive physically and emotionally β becoming withdrawn, listless, and depressed. Schools and families share responsibility for nurturing these connections; their absence constitutes a developmental risk factor with direct behavioral and academic consequences.
Uploaded by: Fani Warraich
CISA
QUESTION #1751
Question 7290
Which of the following is NOT a purpose of the ISO 15489 records management standard?
Correct Answer Logic:
ISO 15489 defines the minimum handling process for records of value and requires an information classification system β a list of each data set to be protected. It does not eliminate the need for such a list; rather, it mandates one as a core governance control.
Uploaded by: Fani Warraich
Correct Answer Logic:
For $h \ll R$, orbital radius $\approx R$.
Orbital velocity: $v_o = \sqrt{\frac{GM}{R}} = \sqrt{gR}$
Escape velocity from orbit at $R$: $v_e = \sqrt{\frac{2GM}{R}} = \sqrt{2gR}$
Minimum increase in speed:
$\Delta v = v_e - v_o = \sqrt{2gR} - \sqrt{gR} = \sqrt{gR}(\sqrt{2}-1)$
Uploaded by: Fani Warraich
Physics
QUESTION #1039
Question 7292
Two cities X and Y connected by buses every T min. A girl on scooter at 60 km/h sees buses every 30 min in her direction and every 10 min opposite. Period T and bus speed:
Correct Answer Logic:
Let bus speed \(=v\), period \(=T\). Relative speed with girl (same direction): \(v-60\). Buses come every 30 min: \(\frac{vT}{v-60}=30\). Opposite direction: \(\frac{vT}{v+60}=10\). Dividing: \(\frac{v+60}{v-60}=3\Rightarrow v+60=3v-180\Rightarrow v=120\ \text{km/h}\). Then \(T=\frac{10(120+60)}{120}=15\ \text{min}\).
Uploaded by: Fani Warraich
Physics
QUESTION #7855
Question 7293
Correct SI unit pair:
Correct Answer Logic:
Power: watt (J/s). Energy: joule; Force: newton; Velocity: m/s.
Uploaded by: Fani Warraich
Math Physics Chemistry Biology
QUESTION #4191
Question 7294
Sensory input from auditory and visual pathways, skin and within the body is received by ________ and distributed to________
Correct Answer Logic:
The thalamus receives sensory input and relays it to the cerebrum.
Uploaded by: Fani Warraich
Civil Engineering
QUESTION #2122
Question 7295
The water-cement ratio in concrete mix design primarily governs:
Correct Answer Logic:
Abrams' law: \(f_c = \dfrac{K_1}{K_2^{w/c}}\). Strength decreases as w/c increases because excess water creates capillary pores on evaporation. Durability also decreases with higher w/c as the pore structure becomes more interconnected, allowing aggressive agents to penetrate. Maximum w/c ratios are specified in codes (e.g., 0.45 for moderate exposure in IS 456) β it governs both structural performance and service life.
Uploaded by: Fani Warraich
MCQs Section
QUESTION #4893
Question 7296
A common disability in test pilots is hearing impairment, _____.
Correct Answer Logic:
It uses the concise and idiomatic appositive 'a consequence of + gerund phrase' to modify 'hearing impairment.' Option B uses the wrong preposition 'from.' Option C is redundant ('consequence which resulted'). Options D and E introduce 'damaged,' which cannot logically modify the noun 'hearing impairment.'
Uploaded by: Fani Warraich
English
QUESTION #2741
Question 7297
What is the correct direct speech of: 'She told me that she had finished the work.'?
Correct Answer Logic:
When converting from indirect to direct speech, the past perfect 'had finished' goes back one step to present perfect 'have finished'. So 'I have finished the work' is correct.
Uploaded by: Fani Warraich
Reading and Writing (Module-1)
QUESTION #10469
Question 7298
The regime's ------- rule left little room for -------, as any hint of criticism was swiftly silenced.
Correct Answer Logic:
A rule allowing no criticism is 'despotic,' leaving no room for 'dissent.'
Uploaded by: Fani Warraich
Chemistry
QUESTION #1415
Question 7299
A reaction is exothermic if:
Correct Answer Logic:
An exothermic reaction releases heat to the surroundings, meaning the enthalpy of the products is lower than that of the reactants. Therefore \(\Delta H = H_{\text{products}} - H_{\text{reactants}} < 0\). A negative \(\Delta H\) indicates an exothermic reaction. \(\Delta G < 0\) indicates spontaneity, not necessarily exothermicity.
Uploaded by: Fani Warraich
Agriculture Economics
QUESTION #11887
Question 7300
Consumer equilibrium (utility maximization) is achieved where:
Correct Answer Logic:
Utility maximization occurs at the tangency of the highest attainable indifference curve and the budget line, where $MRS = \dfrac{P_x}{P_y}$.
Uploaded by: Fani Warraich
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