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On smooth: $a_s = g\sin45°$. On rough: $a_r = g(\sin45°-\mu_k\cos45°)$. Time ratio: $t_r/t_s=2$. Since $L = \frac{1}{2}at^2$: $t\propto 1/\sqrt{a}$. So $\frac{t_r}{t_s}=\sqrt{\frac{a_s}{a_r}}=2\Rightarrow \frac{a_s}{a_r}=4\Rightarrow a_r=\frac{a_s}{4}$. $g(\sin45°-\mu_k\cos45°)=\frac{g\sin45°}{4}\Rightarrow 1-\mu_k=\frac{1}{4}\Rightarrow \mu_k=0.75$.

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Paper-II (Pharmacognosy and Pharmaceutics-I) QUESTION #3681

Question 4

'Beeswax' is used in pharmacy for:

Making candles only
Preparing ointments and plasters✔️
Eating
Injecting

Correct Answer Logic:

It provides consistency to semi-solid preparations.

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Physics QUESTION #369

Question 5

If the mass of the bob of a pendulum is doubled its time period is:

Halved
Doubled
Unchanged✔️
Increases four times

Correct Answer Logic:

Time period of a pendulum is independent of mass

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Geography QUESTION #1235

Question 6

Which one of the following is a depositional landform of a river?

Alluvial Fans✔️
Waterfall
Potholes
None of these

Correct Answer Logic:

Alluvial fans are depositional landforms formed where a river emerges from a mountain or valley onto a plain, losing velocity and depositing its load in a fan-shaped spread. Waterfalls and potholes are erosional landforms formed by the cutting action of rivers. Alluvial fans, floodplains, and deltas are all depositional landforms.

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Statistics QUESTION #1997

Question 7

Using moments $\mu_1' = -0.35$, $\mu_2' = 2.09$ about $a = 16$, the variance $\mu_2$ (second central moment) of the distribution equals:

2.09
1.9675✔️
2.2125
1.7

Correct Answer Logic:

Variance $\mu_2 = \mu_2' - (\mu_1')^2 = 2.09 - (-0.35)^2 = 2.09 - 0.1225 = 1.9675$. The central moment is obtained by subtracting the squared first raw moment from the second raw moment.

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Tourism & Hospitality Management QUESTION #1627

Question 8

The Heritage Management course's Module on 'Conservation Projects Management' specifically addresses which type of professional activity?

Organizing tourism marketing campaigns for heritage sites
Commissioning, planning, and managing conservation projects including structural survey, assessment and diagnosis of failure, repair techniques, maintenance programmes, and environmental monitoring✔️
Training tourist guides for heritage site interpretation
Designing visitor parking and transportation systems for heritage sites

Correct Answer Logic:

Module 8 of the Heritage Management course — Conservation Projects Management — specifically covers: collections management, condition surveys, commissioning and planning conservation projects, history of structures, survey techniques, report writing, diagnosis of structural failure, repair philosophy and technology, maintenance programmes, and environmental control and monitoring.

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Physics QUESTION #1161

Question 9

For the successful operation of a heat engine, which condition should be met?

Cyclic process
Operated at a certain temperature difference
Both (A) & (B)✔️
None of these

Correct Answer Logic:

A heat engine must: (1) operate in a cyclic process so that it can continuously perform work, and (2) operate between two temperature reservoirs (a hot source at $T_H$ and a cold sink at $T_C$) with $T_H > T_C$. Both conditions are essential as stated by the second law of thermodynamics.

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Electrical Engineering QUESTION #2177

Question 10

A three-phase induction motor runs at $1440\,\text{rpm}$ on a $50\,\text{Hz}$ supply. The number of poles and percent slip are respectively:

4 poles, $4\%$✔️
6 poles, $4\%$
4 poles, $6\%$
8 poles, $4\%$

Correct Answer Logic:

Synchronous speed for $P = 4$: $N_s = \frac{120\times50}{4} = 1500\,\text{rpm}$. Slip $s = \frac{1500-1440}{1500}\times100 = 4\%$. For $P=6$: $N_s=1000\,\text{rpm}$, which would give negative slip — physically impossible.

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Boilers Mechanical Engineering QUESTION #4025

Question 11

'Differential Pressure' across an air filter indicates:

The speed of the boiler
How clogged or dirty the filter is✔️
The temperature of the room
The price of the air

Correct Answer Logic:

High 'DP' means the filter needs cleaning or replacement.

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General Knowledge QUESTION #271

Question 12

The capital of Costa Rica is:

San Jose✔️
Tegucigalpa
Managua
None of these

Correct Answer Logic:

San Jose is the largest city and capital of Costa Rica.

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Federal Rules of Evidence (US) QUESTION #3776

Question 13

In a criminal trial for armed robbery, the prosecution seeks to introduce a witness's testimony that the defendant's brother offered the witness $\$5,000$ to 'forget' what he saw. The defendant was not present during this conversation and there is no evidence he authorized it. Is this testimony admissible?

No, because it is hearsay not subject to any exception.
Yes, as a statement by a co-conspirator under Rule 801(d)(2)(E).
Yes, to show the defendant's 'consciousness of guilt' via his agent.
No, because the statement cannot be attributed to the defendant under Rule 801(d)(2).✔️

Correct Answer Logic:

Under Rule 801(d)(2), a statement is not hearsay if it is offered against an opposing party and was made by the party's agent. However, without proof of agency or authorization, the brother's statement is inadmissible hearsay against the defendant. It fails the 'opposing party's statement' test.

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Security Measures to Maintain Law and Order QUESTION #848

Question 14

"Profiling" in security measures to maintain order refers to:

Taking photos
Assessing behavioral patterns✔️
Checking bank balance
Social media monitoring

Correct Answer Logic:

Behavioral profiling helps identify individuals who may pose a threat to law and order based on suspicious patterns.

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Paper-II (Pharmacognosy and Pharmaceutics-I) QUESTION #3676

Question 15

'Tannins' give a bluish-black or greenish-black color with:

Ferric Chloride✔️
Iodine
Water
Alcohol

Correct Answer Logic:

This is a standard chemical test for tannins.

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Islamic Studies QUESTION #210

Question 16

Which financial institution was established by Caliph Umar (رضي الله عنه)?

Bayt al-Mal✔️
Islamic Bank
Zakat Fund
All of these

Correct Answer Logic:

The Bayt al-Mal was the state treasury for collecting and distributing revenues.

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Biology Zoology Botany QUESTION #1352

Question 17

The portion of the digestive tract of a pigeon that produces 'pigeon's milk' used in feeding young is the:

Proventriculus
Gizzard
Crop✔️
None of these

Correct Answer Logic:

The crop is the enlarged pouch in the oesophagus of pigeons and doves. During the breeding season, the crop lining of both parents proliferates under the influence of prolactin to produce 'pigeon milk' — a protein- and fat-rich secretion regurgitated to feed nestlings. The proventriculus is the glandular stomach and the gizzard is the muscular grinding stomach.

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Statistics QUESTION #1978

Question 18

Given $n_1 = 2$ samples with replacement from population $\{4, 6, 8\}$ and $n_2 = 2$ from $\{1, 2, 3\}$, the variance of the sampling distribution of $\bar{X}_1 - \bar{X}_2$ equals:

$\dfrac{\sigma_1^2}{n_1} - \dfrac{\sigma_2^2}{n_2}$
$\dfrac{\sigma_1^2}{n_1} + \dfrac{\sigma_2^2}{n_2}$✔️
$\sigma_1^2 + \sigma_2^2$
$\dfrac{\sigma_1^2 + \sigma_2^2}{n_1 + n_2}$

Correct Answer Logic:

For independent samples, $\sigma^2_{\bar{X}_1 - \bar{X}_2} = \dfrac{\sigma_1^2}{n_1} + \dfrac{\sigma_2^2}{n_2}$. For population $\{4,6,8\}$: $\mu_1=6$, $\sigma_1^2 = \frac{8}{3}$. For $\{1,2,3\}$: $\mu_2=2$, $\sigma_2^2=\frac{2}{3}$. So variance $= \frac{8/3}{2}+\frac{2/3}{2} = \frac{4}{3}+\frac{1}{3}=\frac{5}{3}$.

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