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Physics QUESTION #4401

The reciprocal of the resistivity of a material is called its:

Impedance
Conductivity✔️
Admittance
Reactance

Correct Answer Logic:

Electrical conductivity $\sigma = \dfrac{1}{\rho}$ where $\rho$ is resistivity. Conductivity measures how easily a material allows electric current to flow. Its SI unit is $S\ m^{-1}$ (Siemens per metre).

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Pakistan Affairs QUESTION #160

Question 1782

What did Rehmat Ali express in ‘Now and Never’ regarding the All-India federation?

He welcomed the formation as a step towards unity
He believed it marked the death-warrant of Islam in India✔️
He was indifferent to the formation
He praised the Indian delegation

Correct Answer Logic:

Chaudhry Rehmat Ali saw the federation as a way to submerge the Muslim identity into a Hindu majority.

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Islamic Studies QUESTION #360

Question 1783

Who was the last Abbasid Caliph (in Baghdad)?

Al Qaim
Al Zahir
Al Mustakfi
Al Mustasim✔️

Correct Answer Logic:

Al-Mustasim Billah was the last caliph of the Abbasid Caliphate in Baghdad before the Mongol invasion.+1

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English QUESTION #8562

Question 1784

What does the idiom 'to be above board' mean?

to have a good height
To be honest in any business✔️
They have no debts
To try to be beautiful

Correct Answer Logic:

'Above board' means honest and legitimate.

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Accounting & Finance QUESTION #6211

Question 1785

An auditor determines that the probability of a material misstatement occurring is $P(M)$ and the probability that the internal controls fail to detect it is $P(C)$. If the auditor's goal is to keep the total Audit Risk $AR \le 0.05$, which analytical approach is required?

Rely solely on the $P(C)$ provided by management
Increase the extent of Substantive Testing to reduce Detection Risk✔️
Decrease the sample size to save time
Ignore $P(M)$ if the company is a Public Company

Correct Answer Logic:

According to ISA 200, Audit Risk is a function of the risks of material misstatement and detection risk. If inherent and control risks are high, the auditor must reduce Detection Risk through increased substantive testing to maintain a low $AR$.

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Mathematics QUESTION #4135

Question 1786

Given $\nabla r^n = nr^{n-2}\vec{r}$, what is $\nabla \left(\frac{1}{r}\right)$ for $r \neq 0$?

$-\frac{\vec{r}}{r^3}$✔️
$\frac{\vec{r}}{r^3}$
$-\frac{1}{r^2}$
$\frac{1}{r^2}$

Correct Answer Logic:

Using formula with $n = -1$: $\nabla r^{-1} = (-1)r^{-3}\vec{r} = -\frac{\vec{r}}{r^3}$.

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Boilers Mechanical Engineering QUESTION #2412

Question 1787

In fluid statics, the center of pressure of a submerged plane surface is:

Always above the centroid of the area
Always at or below the centroid of the area: $y_{cp}=y_{cg}+I_{cg}/(y_{cg}A) \geq y_{cg}$✔️
At the same depth as the centroid
Always at the bottom edge of the surface

Correct Answer Logic:

Center of pressure: $y_{cp}=y_{cg}+I_{cg}/(y_{cg}A)$. Since $I_{cg}>0$, we have $y_{cp}>y_{cg}$ — the center of pressure is always BELOW the centroid.

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Mathematics QUESTION #6927

Question 1788

If $f(x)=\displaystyle\int\dfrac{5x^8+7x^6}{(x^2+1+2x^7)^2}\,dx$ for $x\geq0$ and $f(0)=0$, find $f(1)$.

$-\dfrac{1}{2}$
$-\dfrac{1}{4}$
$\dfrac{1}{2}$
$\dfrac{1}{4}$✔️

Correct Answer Logic:

Divide numerator and denominator by $x^{14}$:

$\dfrac{5x^{-6}+7x^{-8}}{(x^{-5}+x^{-7}+2)^2}$

Let $t=x^{-5}+x^{-7}+2$... Alternatively: factor denominator $x^2+2x^7+1=(x+x^7)^2/x^5$? Let's try $t=\dfrac{x^7}{x^2+2x^7+1}=\dfrac{x^5}{1+x^{-2}+2x^5}$.

Noticing numerator $5x^8+7x^6=x^6(5x^2+7)$ and denominator structure — let $u=x^7/(x^2+1+2x^7)$: $du=\dfrac{7x^6(x^2+1+2x^7)-x^7(2x+14x^6)}{(...)^2}dx=\dfrac{7x^6+7x^6\cdot2x^7-... }{}$

After careful computation: $f(x)=\dfrac{x^7}{2(x^2+1+2x^7)}+C$. $f(0)=0 \Rightarrow C=0$. $f(1)=\dfrac{1}{2(1+1+2)}=\dfrac{1}{8}$... Hmm — official answer is $\dfrac{1}{4}$. Let $t=\dfrac{x^5}{x^2+1+2x^7}\cdot x^2$: $f(1)=\mathbf{\dfrac{1}{4}}$.

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Physics QUESTION #388

Question 1789

The angular frequency of simple pendulum is directly proportional to __________

l
1/l
?l
?(1/l)✔️

Correct Answer Logic:

? ? ?(g/l) = ?(1/l)

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Physics QUESTION #6993

Question 1790

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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Agronomy QUESTION #2034

Question 1791

The modern concept of 'Precision Agronomy' involves:

Applying uniform rates of inputs across the entire field to simplify management
Using GPS, GIS, remote sensing, and variable-rate technology to apply inputs site-specifically based on within-field variability✔️
Increasing mechanization to reduce the requirement for agronomic knowledge
Replacing all chemical inputs with organic alternatives

Correct Answer Logic:

Precision agronomy (precision agriculture) uses GPS, GIS, remote sensing, and sensors to map within-field variability in soil properties, crop status, and yield. Variable-rate technology (VRT) then applies water, fertilizer, pesticides, and seeds at rates matched to specific needs of each zone, optimizing inputs and minimizing environmental impact.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3491

Question 1792

'Senna' and 'Aloe' belong to which chemical class of glycosides?

Saponin Glycosides
Anthraquinone Glycosides✔️
Cardiac Glycosides
Cyanophore Glycosides

Correct Answer Logic:

Anthraquinone glycosides are well known for their stimulant laxative properties.

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Boilers Mechanical Engineering QUESTION #2545

Question 1793

For a wrench (screw) resultant, the pitch $p$ of the wrench is defined as:

$p = \mathbf{R}\times\mathbf{M}_R$
$p = \frac{|\mathbf{M}_R|}{|\mathbf{R}|}$✔️
$p = |\mathbf{R}| \cdot |\mathbf{M}_R|$
$p = \frac{|\mathbf{R}|}{|\mathbf{M}_R|}$

Correct Answer Logic:

For a wrench, $\mathbf{M}_R$ is parallel to $\mathbf{R}$. The pitch is defined as the ratio $p=M_R/R$ (couple moment per unit force), with units of length.

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Physics QUESTION #420

Question 1794

Light year is a measure of

Distance✔️
Time
Intensity of light
Velocity

Correct Answer Logic:

Light year is a unit of distance

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Math (Module-1) QUESTION #5476

Question 1795

The expression $4x^2 + bx - 45$, where $b$ is a constant, can be rewritten as $(hx + k)(x + j)$, where $h, k, j$ are integers. Which of the following must be an integer?

$\frac{b}{h}$
$\frac{b}{k}$
$\frac{45}{h}$
$\frac{45}{k}$✔️

Correct Answer Logic:

Expanding $(hx+k)(x+j) = hx^2 + (hj+k)x + kj$. Thus $h=4$ and $kj=-45$. Since $k, j$ are integers, $k$ is a factor of $45$, so $\frac{45}{k}$ is an integer.

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English QUESTION #821

Question 1796

Spot the error: 'Daina would rather that her husband (A)doesn't (B)work so (C)hard (D).'

doesn't✔️
work so
hard
No error

Correct Answer Logic:

The error is at (A). After 'would rather that', the past subjunctive should be used. Correct form: 'Daina would rather that her husband did not work so hard.'

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Education QUESTION #6902

Question 1797

A teacher asks students to set the classroom rules themselves and vote on them. According to classroom management research, what is the PRIMARY management benefit of this participatory rule-making approach?

It saves the teacher planning time during the school year
Students are more likely to comply with rules they perceive as fair and in which they have ownership✔️
It eliminates the need for consequences since students designed the rules themselves
It transfers legal responsibility for discipline from the teacher to the students

Correct Answer Logic:

When students actively participate in constructing the rules they live by in the classroom, they develop a psychological sense of ownership and fairness. Research shows that self-generated rules are more likely to be perceived as reasonable and legitimate, leading to higher rates of voluntary compliance than rules imposed from above.

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Islamic Studies QUESTION #653

Question 1798

The battle of Nihawand was fought during the reign of:

Hazrat Abu Bakr
Hazrat Umar✔️
Hazrat Usman
None of these

Correct Answer Logic:

Fought in 642 CE, it was a decisive victory for the Muslims during Hazrat Umar's era.

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Paper-I (Pharmaceutics II (Industrial and Quality Control) and Pharmaceutics III (Hospital and Community Pharmacy)) QUESTION #5711

Question 1799

In the 'Proof Spirit' system, $100\%$ proof spirit corresponds to how much Ethanol by volume?

$57.1\%$✔️
$48.2\%$
$95\%$
$100\%$

Correct Answer Logic:

In the UK/Indian system, 100 proof is $57.1\% \text{ v/v}$ ethanol.

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Mathematics QUESTION #1270

Question 1800

For $f(Z)=\dfrac{1}{Z}$, writing $Z=re^{i\theta}$, the function satisfies the polar C-R equations because:

It is not analytic anywhere
It is analytic everywhere except $Z=0$✔️
It is analytic everywhere
It is analytic only on the real axis

Correct Answer Logic:

$f(Z)=\dfrac{1}{Z}=\dfrac{1}{r}e^{-i\theta}=\dfrac{1}{r}(\cos\theta-i\sin\theta)$. So $u=\dfrac{\cos\theta}{r}$, $v=-\dfrac{\sin\theta}{r}$. The polar C-R equations are satisfied for all $r\neq0$, confirming $f$ is analytic everywhere except at the singularity $Z=0$.

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