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Pitch is the centre-to-centre spacing of rivets along the direction of force. Gauge is the perpendicular spacing; diagonal pitch is the distance between rivets in adjacent rows; margin is the edge distance.

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Mathematics QUESTION #1314

Question 2484

The Fourier series of a function $f(x)$ on $(-\pi,\pi)$ is given by $f(x)=\dfrac{a_0}{2}+\sum_{n=1}^\infty(a_n\cos nx+b_n\sin nx)$. The coefficient $a_0$ is:

$\dfrac{1}{\pi}\int_{-\pi}^{\pi}f(x)\,dx$✔️
$\dfrac{2}{\pi}\int_{-\pi}^{\pi}f(x)\,dx$
$\int_{-\pi}^{\pi}f(x)\,dx$
$\dfrac{1}{2\pi}\int_{-\pi}^{\pi}f(x)\,dx$

Correct Answer Logic:

$a_0=\dfrac{1}{\pi}\int_{-\pi}^{\pi}f(x)\,dx$. Then $a_n=\dfrac{1}{\pi}\int_{-\pi}^{\pi}f(x)\cos nx\,dx$ and $b_n=\dfrac{1}{\pi}\int_{-\pi}^{\pi}f(x)\sin nx\,dx$. The constant term in the series is $\dfrac{a_0}{2}$.

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English QUESTION #2790

Question 2485

Which is the CORRECTLY SPELLED word?

Occured
Occurred✔️
Ocurred
Occurrd

Correct Answer Logic:

The correct spelling is 'Occurred' — the final consonant 'r' is doubled before adding '-ed' because the stress is on the last syllable. Rule: double the final consonant when the syllable is stressed.

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Physical Education QUESTION #6807

Question 2486

A Subject Specialist implementing 'Pragmatism' in Physical Education would most likely prioritize:

Strict adherence to historical sports rules
Activities that solve social problems and encourage democratic cooperation✔️
Individual isolation and solitary meditation
The memorization of physiological terminology

Correct Answer Logic:

Pragmatism emphasizes 'learning by doing' and the social utility of activities in a community setting.

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Civil Engineering QUESTION #6651

Question 2487

The 'Modular Ratio' ($n$) is defined as the ratio of:

Yield strength of steel to concrete strength
Modulus of elasticity of steel to concrete✔️
Area of steel to area of concrete
Depth of steel to depth of concrete

Correct Answer Logic:

$n = E_s / E_c$. It is used in the transformed section method to analyze RC members under service loads.

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Paper-II (Pharmacology and Social Behaviour, Law & Ethics and Computer Sciences) QUESTION #5758

Question 2488

Which drug is used as a 'prophylactic' agent for motion sickness during short journeys?

Atropine✔️
Prazosin
Propranolol
Cimetidine

Correct Answer Logic:

Atropine (or related antimuscarinics) is effective for preventing motion sickness.

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English QUESTION #4449

Question 2489

His application for a visa was turned ____ by the consulate.

out
over
down✔️
aside

Correct Answer Logic:

To 'turn down' means to reject or refuse an application or offer.

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Mathematics QUESTION #7443

Question 2490

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:

$4\ell^2 mn$
$4\ell m^2n$✔️
$4\ell mn^2$
$4\ell^2m^2n^2$

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 $4\ell m^2 n$.

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Urdu QUESTION #5054

Question 2491

علامہ اقبال نے قانون اور PhD کے علاوہ کون سی ڈگری یورپ سے لی؟

ایم اے✔️
بی اے
ایم فل
ان میں سے کوئی نہیں

Correct Answer Logic:

علامہ اقبال نے یورپ میں قانون کی ڈگری لی، پھر میونخ یونیورسٹی سے PhD کی اور کیمبرج سے ایم اے کی ڈگری حاصل کی۔

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Ability / HR / Governance / Special Education QUESTION #1859

Question 2492

What type of appointment is made for vacancies occurring for less than six months under Rule 8-B(4)?

Acting charge appointment
Regular appointment
Current charge appointment✔️
Ad hoc appointment

Correct Answer Logic:

Rule 8-B(4) states against vacancies occurring for less than six months, current charge appointment may be made according to orders issued from time to time.

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Islamic Studies QUESTION #632

Question 2493

The basic obligatory action of Hajj is:

Wuquf-e-Arafat✔️
Rami
Tawaf-e-Ziyarat
None of these

Correct Answer Logic:

Wuquf (standing) at Arafat is the most essential pillar of Hajj.

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Civil Procedure QUESTION #3709

Question 2494

A plaintiff (State A) sues a defendant (State B) in federal court in State A for $\text{\$50,000}$ for a car accident. The plaintiff also sues the same defendant for $\text{\$30,000}$ for an unrelated breach of contract. Does the court have subject matter jurisdiction?

No, because the claims are unrelated and neither meets the amount in controversy.
Yes, because a single plaintiff may aggregate all claims against a single defendant to meet the amount in controversy.✔️
No, aggregation is only allowed for claims arising from the same transaction.
Yes, because the total is over $\text{\$75,000}$ and there is diversity.

Correct Answer Logic:

Under the aggregation rules for 28 U.S.C. $\S 1332$, a single plaintiff may aggregate any and all claims they have against a single defendant, regardless of whether the claims are related.

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English QUESTION #8306

Question 2495

He is one of my best _______.

Friend
Friends✔️
Friendship
None of these

Correct Answer Logic:

After 'one of my best', use plural 'friends'.

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English QUESTION #8383

Question 2496

CULPABLE means:

Involved
Guilty✔️
Affected
None of these

Correct Answer Logic:

Culpable means deserving blame; guilty.

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Paper-II (Pharmacology and Social Behaviour, Law & Ethics and Computer Sciences) QUESTION #5788

Question 2497

Which of the following is NOT a form of non-verbal communication?

Gestures
Tone of voice
Body language
Emails✔️

Correct Answer Logic:

Emails are a form of written (verbal) communication[cite: 7].

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The Elections Act 2017 QUESTION #9456

Question 2498

Under Section 136(2), if the Commission fails to finalize scrutiny of a return of election expenses within ninety days, what is the legal consequence?

The candidate must resubmit the return
The Returning Officer must initiate proceedings for illegal practice
The return of election expenses shall be deemed to be scrutinized and accepted as correct✔️
The Commission may extend the scrutiny period for a further thirty days

Correct Answer Logic:

Section 136(2) states: 'If the Commission fails to finalize scrutiny of any return of election expenses within ninety days under sub-section (1), the return of election expenses shall be deemed to be scrutinized and accepted as correct.'

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English QUESTION #8332

Question 2499

He is interested _______ stamp collection.

at
in✔️
of
with

Correct Answer Logic:

'Interested in' is the correct preposition.

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Physics QUESTION #7072

Question 2500

Two radioactive isotopes, $A$ and $B$, have half-lives of $20$ minutes and $40$ minutes, respectively. If both samples start with an identical number of nuclei, determine the ratio of the number of decayed nuclei of $A$ to those of $B$ after a period of $80$ minutes.

$4:1$
$1:4$
$5:4$✔️
$1:16$

Correct Answer Logic:

After $80$ minutes, $A$ undergoes $4$ half-lives ($80/20$), leaving $N_A = N_0/2^4 = N_0/16$. The number of decayed nuclei for $A$ is $N_0 - N_0/16 = 15N_0/16$. $B$ undergoes $2$ half-lives ($80/40$), leaving $N_B = N_0/2^2 = N_0/4$. The number of decayed nuclei for $B$ is $N_0 - N_0/4 = 3N_0/4 = 12N_0/16$. The ratio of decayed nuclei is $15:12$, which simplifies to $5:4$.

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