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Mathematics QUESTION #4150

What is the general solution of $y'' - 3y' + 2y = 0$?

$y = c_1e^x + c_2e^{2x}$✔️
$y = c_1e^{-x} + c_2e^{-2x}$
$y = c_1\cos(x) + c_2\sin(x)$
$y = e^x(c_1 + c_2x)$

Correct Answer Logic:

Characteristic: $r^2 - 3r + 2 = 0 \Rightarrow (r-1)(r-2) = 0 \Rightarrow r = 1, 2$. General solution: $y = c_1e^x + c_2e^{2x}$.

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Ability / HR / Governance / Special Education QUESTION #1879

Question 3742

What is the precise legal definition of 'misconduct' under Rule 2(4) of GS E&D Rules 1973?

Only conduct contrary to Government Servants (Conduct) Rules 1964
Conduct prejudicial to good order or service discipline OR contrary to Conduct Rules 1964 OR unbecoming of an officer and gentleman including use of political influence✔️
Any act of corruption or subversion
Disobedience of lawful orders of a superior

Correct Answer Logic:

Rule 2(4) gives a composite definition: conduct prejudicial to good order/service discipline OR contrary to GS Conduct Rules 1964 OR unbecoming of an officer and gentleman — and specifically includes attempts to bring political/outside influence.

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Nursing QUESTION #9159

Question 3743

The Infant Mortality Rate (IMR) formula is:
\\text{IMR} = \\frac{\\text{Deaths of infants under 1 year}}{?} \\times 1000
What is the correct denominator?

Total population
Total deaths in the year
Number of live births in the same year✔️
Number of children under 5 years

Correct Answer Logic:

The Infant Mortality Rate (IMR) is calculated as:

\\text{IMR} = \\frac{\\text{Deaths under 1 year of age}}{\\text{Number of live births in the same period}} \\times 1000

IMR is one of the most sensitive indicators of population health status and socioeconomic development. Pakistan's IMR is approximately 55–60 per 1,000 live births, which remains higher than the SDG target. Community health nurses play a crucial role in reducing IMR through vaccination, nutrition counseling, and antenatal/postnatal care.

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General Science and Ability QUESTION #253

Question 3744

The isotopes of any element contain equal number of:

Protons✔️
Neutrons
Both electrons and protons
None of these

Correct Answer Logic:

Isotopes are atoms of the same element with the same number of protons but different neutrons.+1

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Statistics QUESTION #1982

Question 3745

The partial correlation coefficient $r_{12.3}$ between $X_1$ and $X_2$ after eliminating the linear effect of $X_3$ is computed as the simple correlation between:

$X_1$ and $X_2$ directly
The residuals $X_{1.3}$ and $X_{2.3}$ from their respective regressions on $X_3$✔️
The standardized values of $X_1$ and $X_2$
The ranked values of $X_1$ and $X_2$

Correct Answer Logic:

The partial correlation $r_{12.3}$ is defined as the Pearson correlation between the residuals $X_{1.3} = X_1 - \hat{X}_{1|X_3}$ and $X_{2.3} = X_2 - \hat{X}_{2|X_3}$. This removes the linear influence of $X_3$ from both $X_1$ and $X_2$ before computing their correlation.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3215

Question 3746

'Diabetes Insipidus' is a condition caused by the deficiency of:

Insulin
Glucagon
ADH✔️
Oxytocin

Correct Answer Logic:

Lack of ADH leads to the production of large volumes of very dilute urine.

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Physics QUESTION #400

Question 3747

A watch maker uses __________ to repair the watches.

Telescope
Convex mirror
Convex lens✔️
Concave lens

Correct Answer Logic:

Convex lens acts as magnifying glass

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General Knowledge QUESTION #4480

Question 3748

_____ authored the book “Prisoner of Geography”.

Tim Marshall✔️
Henry Kissinger
Samuel P. Huntington
None of these

Correct Answer Logic:

Tim Marshall wrote 'Prisoners of Geography'.

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Ability / HR / Governance / Special Education QUESTION #1803

Question 3749

Rule 35 requires procuring agencies to announce the final bid evaluation report at least how many days prior to the award of a procurement contract?

Seven days
Ten days
Fifteen days✔️
Twenty-one days

Correct Answer Logic:

Rule 35 (as substituted via S.R.O. 834(I)/2021) mandates that the procuring agency announce the result of bid evaluation in the form of a final evaluation report, with justification for acceptance or rejection, at least fifteen days prior to awarding the procurement contract.

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Physics QUESTION #7093

Question 3750

A particle starts at $(2, 4)$ at $t=0$ with velocity $(5\hat{i}+4\hat{j})$. Constant acceleration is $(4\hat{i}+4\hat{j})$. Find its distance from the origin at $t=2\text{ s}$.

15 m
$20\sqrt{2}\text{ m}$✔️
5 m
$10\sqrt{2}\text{ m}$

Correct Answer Logic:

Using $\vec{s} = \vec{r}_0 + \vec{u}t + \frac{1}{2}\vec{a}t^2$:

$x = 2 + 5(2) + \frac{1}{2}(4)(2^2) = 2 + 10 + 8 = 20$
$y = 4 + 4(2) + \frac{1}{2}(4)(2^2) = 4 + 8 + 8 = 20$
Distance from origin $D = \sqrt{20^2 + 20^2} = 20\sqrt{2}\text{ m}$.

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Physics QUESTION #7839

Question 3751

Magnetic field inside a solenoid is:

Along its axis✔️
Circular around wires
Strongest at ends
Zero when current flows

Correct Answer Logic:

Inside ideal solenoid, field is uniform and parallel to axis.

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The Constitution of Pakistan QUESTION #9349

Question 3752

Which Article, added by the 26th Amendment 2024, explicitly restricts High Courts from exercising suo motu jurisdiction?

Article 199(1A)✔️
Article 202A
Article 175A
Article 203A

Correct Answer Logic:

Article 199(1A), inserted by the 26th Amendment, provides that the High Court 'shall not make an order or give direction or make a declaration on its own or in the nature of suo motu exercise of jurisdiction beyond the contents of any application filed under clause (1).' This was a significant curtailment of judicial initiative.

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Physics QUESTION #1037

Question 3753

A uniform rod of mass 20 kg and length 5 m leans against a smooth wall at $60°$. Friction force from the floor is (Take $g=10\ \text{m/s}^2$):

200 N
$200\sqrt{3}\ \text{N}$
100 N✔️
$100\sqrt{3}\ \text{N}$

Correct Answer Logic:

Taking torques about the contact point on the floor. The angle with the wall is $60°$, so angle with floor is $30°$. Normal from wall (horizontal) $\times L\sin30° = mg\times\frac{L}{2}\cos30°$. Wait — using torque about foot: $N_w\cdot L\sin30° = mg\cdot\frac{L}{2}\cos30°\Rightarrow N_w = \frac{mg\cos30°}{2\sin30°} = \frac{20\times10\times\frac{\sqrt{3}}{2}}{2\times\frac{1}{2}}=100\sqrt{3}$. Friction $= N_w = 100\sqrt{3}\approx173\ \text{N}$. Answer: $100\sqrt{3}\ \text{N}$.

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Chemistry QUESTION #7354

Question 3754

A ball of mass 0.66 kg moves at 100 m/s. The de Broglie wavelength associated with it (given $h = 6.6 \times 10^{-34}$ Js) will be:

$6.6 \times 10^{-34}$ m
$1.0 \times 10^{-35}$ m✔️
$1.0 \times 10^{-32}$ m
$6.6 \times 10^{-32}$ m

Correct Answer Logic:

de Broglie formula: $\lambda = \dfrac{h}{mv}$

$\lambda = \dfrac{6.6 \times 10^{-34}}{0.66 \times 100} = \dfrac{6.6 \times 10^{-34}}{66} = 1.0 \times 10^{-35}$ m

This wavelength is vanishingly small, which is why macroscopic objects do not show observable wave behaviour — confirming why quantum effects are only relevant at the atomic/subatomic scale.

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Islamic Studies QUESTION #7927

Question 3755

Which Surah was first revealed?

Al-Annam
Al-Fateha
Al-baqarah
None of these✔️

Correct Answer Logic:

Surah Al-Alaq was the first Surah revealed, specifically its first five verses. The revelation began with 'Iqra' (Read) in the Cave of Hira in 610 CE. Since 'Al-Alaq' is not among the given options, the answer is 'None of these.' Al-Alaq means 'The Clot' and emphasizes knowledge and learning.

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MCQs Section QUESTION #4856

Question 3756

Choose the word nearly opposite in meaning to "LARCENY"

Appropriation
Peculation
Purloining
Indemnification✔️

Correct Answer Logic:

Larceny means the unlawful taking of someone's property; theft. Its antonym is 'indemnification,' meaning compensation for harm or loss — the opposite of taking something illegally.

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Chemistry QUESTION #5523

Question 3757

Identify the reaction that is NOT part of the ozone layer depletion mechanism in the stratosphere.

$CF_2Cl_2(g) \xrightarrow{hv} \cdot Cl(g) + \cdot CF_2Cl(g)$
$Cl\dot{O}(g) + O(g) \rightarrow \cdot Cl(g) + O_2(g)$
$CH_4 + 2O_3 \rightarrow 3\,CH_2{=}O + 3H_2O$✔️
$HOCl(g) \xrightarrow{hv} \cdot OH(g) + \cdot Cl(g)$

Correct Answer Logic:

The ozone depletion cycle involves: (A) CFCs releasing Cl radicals under UV, (B) ClO reacting with O atom to regenerate Cl radical (chain propagation), (D) HOCl photolysis to give OH and Cl radicals — all are real steps. Option (C), the reaction of $CH_4$ with $O_3$ to give formaldehyde and water, is NOT a recognized step in stratospheric ozone depletion chemistry.

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Education QUESTION #6917

Question 3758

A teacher at the start of the year establishes that students who arrive late must sign below a line on a class sign-in sheet that is passed around at the beginning of each lesson. What classroom management principle does this MOST directly embody?

Punitive consequence administration for non-compliant students
Systematic routine-building that reduces 'dead time' and administrative disruption to instructional flow✔️
Assertive Discipline's negative consequence tier for attendance violations
Behavior modification through contingency contracting for chronic latecomers

Correct Answer Logic:

Establishing predictable administrative routines — such as sign-in procedures — reduces the amount of instructional time consumed by attendance management. This is a foundational principle of effective classroom management: routines should automate administrative tasks so that teachers can focus maximum time on instruction and students remain on-task from the moment they enter.

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Accounting & Finance QUESTION #6094

Question 3759

P Limited produces chairs at $70 each. It receives a special order for 1,000 chairs with padded seats. This requires $6,000 in extra materials, 500 extra labour hours at $15/hour, and $2,000 extra overheads. What is the total cost of this batch?

$13,500
$15,500
$83,500
$85,500✔️

Correct Answer Logic:

1. Base cost = 1,000 $\times$ $70 = $70,000.
2. Extra materials = $6,000.
3. Extra labour = 500 $\times$ $15 = $7,500.
4. Extra overheads = $2,000.
Total = $70,000 + $6,000 + $7,500 + $2,000 = $85,500.

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Physics QUESTION #6993

Question 3760

A parallel plate capacitor (area $6\ \text{cm}^2$, separation $3\ \text{mm}$) has its gap filled with three dielectric slabs of equal thickness placed side-by-side (not stacked), with $K_1=10$, $K_2=12$, $K_3=14$. What single dielectric constant $K$ gives the same capacitance when it fully fills the capacitor?

4
14
12✔️
36

Correct Answer Logic:

The three slabs are placed side-by-side (parallel combination), each occupying one-third of the area $A/3$ and the full separation $d$.

Total capacitance:

$C = \frac{\varepsilon_0 (A/3)}{d}(K_1 + K_2 + K_3) = \frac{\varepsilon_0 A}{3d}(10+12+14) = \frac{36\varepsilon_0 A}{3d} = \frac{12\varepsilon_0 A}{d}$

For a single dielectric $K$:

$C = \frac{K\varepsilon_0 A}{d}$

$\Rightarrow K = 12$

The equivalent dielectric constant is simply the arithmetic mean: $(10+12+14)/3 = 12$.

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