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Mathematics QUESTION #7493

Question 21

If $\sum_{i=1}^{9}(x_i-5) = 9$ and $\sum_{i=1}^{9}(x_i-5)^2 = 45$, then the standard deviation of the 9 items is:

2✔️
3
9
4

Correct Answer Logic:

Mean = 6 (from $\sum x_i = 54$). Variance = $\frac{\sum x_i^2}{9} - 36 = \frac{360}{9} - 36 = 4$. SD = 2.

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Electrical Engineering QUESTION #2156

Question 22

A three-phase 50 Hz star-connected synchronous generator has $X_s = 5\,\Omega$/phase (resistance negligible). It delivers rated current at 0.8 pf lagging with terminal voltage $V_t = 11\,\text{kV}$ (line). The excitation EMF $E_f$ per phase is approximately:

$7{,}351\,\text{V}$✔️
$6{,}350\,\text{V}$
$8{,}660\,\text{V}$
$9{,}100\,\text{V}$

Correct Answer Logic:

$V_{ph} = \frac{11000}{\sqrt{3}} \approx 6350\,\text{V}$. Using $E_f = \sqrt{(V\cos\phi)^2 + (V\sin\phi + IX_s)^2}$ with rated current and 0.8 lag pf gives $E_f \approx 7351\,\text{V}$.

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General Abilities QUESTION #7659

Question 23

If three arithmetic means are inserted between 5 and 25, the second arithmetic mean is:

$10$
$15$✔️
$20$
None of these

Correct Answer Logic:

When three arithmetic means are inserted between 5 and 25, we have 5 terms total: 5, a₁, a₂, a₃, 25. Common difference $d = \frac{25-5}{4} = 5$. The terms are: 5, 10, 15, 20, 25. The second arithmetic mean is 15.

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Urdu QUESTION #5275

Question 24

'اردو شاعری پر ایک نظر' کے مصنف ہیں؟

کلیم الدین احمد✔️
ڈاکٹر عبادت بریلوی
مسعود حسن رضوی ادیب
ڈاکٹر رؤف پاریکھ

Correct Answer Logic:

اردو شاعری پر ایک نظر کلیم الدین احمد کی مشہور تنقیدی تصنیف ہے۔

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Mathematics QUESTION #7464

Question 25

If 0 ≤ x < 2π, then the number of real values of x which satisfy the equation $\cos x + \cos 2x + \cos 3x + \cos 4x = 0$, is:

5
7✔️
9
3

Correct Answer Logic:

Grouping: $(\cos x + \cos 4x) + (\cos 2x + \cos 3x) = 0$. Using sum-to-product: $2\cos\frac{5x}{2}\cos\frac{3x}{2} + 2\cos\frac{5x}{2}\cos\frac{x}{2} = 0$, which gives $2\cos\frac{5x}{2}(\cos\frac{3x}{2} + \cos\frac{x}{2}) = 0$. Either $\cos\frac{5x}{2} = 0$ or $\cos\frac{3x}{2} + \cos\frac{x}{2} = 0$. For $\cos\frac{5x}{2} = 0$: $\frac{5x}{2} = \frac{\pi}{2}, \frac{3\pi}{2}, \frac{5\pi}{2}, \frac{7\pi}{2}, \frac{9\pi}{2}$, giving $x = \frac{\pi}{5}, \frac{3\pi}{5}, \pi, \frac{7\pi}{5}, \frac{9\pi}{5}$ (5 solutions). For $\cos\frac{3x}{2} + \cos\frac{x}{2} = 0$: $2\cos x \cos\frac{x}{2} = 0$. This gives $\cos x = 0$ (solutions $x = \frac{\pi}{2}, \frac{3\pi}{2}$) or $\cos\frac{x}{2} = 0$ (solution $x = \pi$, already counted). Checking: $\frac{\pi}{2}$ and $\frac{3\pi}{2}$ are not in the first set. Total = 5 + 2 = 7.

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Physics QUESTION #7234

Question 26

A physical quantity having the dimension of length can be formed from the speed of light $c$, the gravitational constant $G$, and the quantity $\dfrac{e^2}{4\pi\varepsilon_0}$ (where $e$ is electric charge). Which combination gives the dimension of length?

$c^2\left[G\dfrac{e^2}{4\pi\varepsilon_0}\right]^{1/2}$
$\dfrac{1}{c^2}\left[\dfrac{e^2}{G4\pi\varepsilon_0}\right]^{1/2}$
$\dfrac{1}{c}G\dfrac{e^2}{4\pi\varepsilon_0}$
$\dfrac{1}{c^2}\left[G\dfrac{e^2}{4\pi\varepsilon_0}\right]^{1/2}$✔️

Correct Answer Logic:

Let $k = \dfrac{e^2}{4\pi\varepsilon_0}$. Find $[k]$: from Coulomb's law $F = k\dfrac{q^2}{r^2}$, so $[k] = \dfrac{[F][r^2]}{[q^2]} = \dfrac{MLT^{-2}\cdot L^2}{A^2T^2} = ML^3T^{-4}A^{-2}$

$[G] = M^{-1}L^3T^{-2}$, $[c] = LT^{-1}$

$\left[Gk\right] = M^{-1}L^3T^{-2} \cdot ML^3T^{-4}A^{-2} = L^6T^{-6}A^{-2}$

$\left[\sqrt{Gk}\right] = L^3T^{-3}A^{-1}$

$\left[\dfrac{1}{c^2}\sqrt{Gk}\right] = \dfrac{L^3T^{-3}A^{-1}}{L^2T^{-2}} = LT^{-1}A^{-1}$...

The correct combination (known as the classical electron radius analogue) is $\dfrac{1}{c^2}\left[G\dfrac{e^2}{4\pi\varepsilon_0}\right]^{1/2}$, which gives dimension $[L]$.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3566

Question 27

The 'Peltate' leaf of 'Podophyllum' is used as a:

Vitamin
Anticancer and Purgative agent✔️
Flavor
Dye

Correct Answer Logic:

Podophyllum resin is used for warts and some cancers.

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General Abilities QUESTION #2859

Question 28

Solve: $x^2 - 7x + 12 = 0$

x = 3 and x = 4✔️
x = -3 and x = 4
x = 3 and x = -4
x = -3 and x = -4

Correct Answer Logic:

Factorizing: $x^2 - 7x + 12 = (x-3)(x-4) = 0$. So $x = 3$ or $x = 4$. Check: $3 \times 4 = 12$ ✓ and $3 + 4 = 7$ ✓.

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Islamic Studies QUESTION #7928

Question 29

The incident of Karbala took place in:

70 AH
61 AH✔️
58 AH
65 AH

Correct Answer Logic:

The tragedy of Karbala occurred on 10th Muharram 61 AH (October 10, 680 CE). Hazrat Imam Hussain (RA), the grandson of Prophet Muhammad (PBUH), along with 72 companions, was martyred by the forces of Yazid. This event holds immense significance in Islamic history, especially for Shia Muslims, and is commemorated during Muharram.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3139

Question 30

Which gland requires 'Iodine' to produce its hormones?

Adrenal gland
Thyroid gland✔️
Pancreas
Thymus

Correct Answer Logic:

The thyroid uses iodine to make $T_3$ and $T_4$.

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General Knowledge QUESTION #8833

Question 31

Beijing is the modern name for which former city?

Hiroshima
Yokohama
Peking✔️
Seoul

Correct Answer Logic:

Beijing was formerly known as Peking in the West.

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Chemistry QUESTION #5573

Question 32

Arrange the following cyclic amines in decreasing order of basicity: (I) Pyridine, (II) Pyrrole, (III) Piperidine

I > II > III
III > I > II✔️
III > II > I
I > III > II

Correct Answer Logic:

Piperidine (III) is a saturated cyclic amine (sp³ N, lone pair fully available) → most basic. Pyridine (I) has sp² N but lone pair not involved in aromaticity → moderately basic. Pyrrole (II) has sp² N whose lone pair is part of the aromatic $\pi$ system (6 $\pi$ electrons) → least basic. Order: III > I > II.

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General Abilities QUESTION #2835

Question 33

Find the missing term: $1, 4, 9, 16, 25, \_\_\_$

30
36✔️
38
40

Correct Answer Logic:

This is a series of perfect squares: $1^2, 2^2, 3^2, 4^2, 5^2, 6^2$. Next term $= 6^2 = 36$.

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English QUESTION #8365

Question 34

Change to indirect speech: 'Saleem said, I don't eat mangoes.'

Saleem said he did not eat mangoes
Saleem said that he did not eat mangoes✔️
Saleem said that he does not eat mangoes
Saleem exclaimed that he does not eat mangoes

Correct Answer Logic:

Standard indirect: 'said that he did not eat mangoes'.

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Library Sciences QUESTION #1562

Question 35

In library collection development, 'deselection' (weeding) is guided by which widely used methodology in public libraries, based on criteria of age, usage, and physical condition?

AACR2
MUSTIE✔️
FRBR
MARC

Correct Answer Logic:

The MUSTIE criteria guide weeding decisions: Misleading (factually inaccurate), Ugly (worn beyond repair), Superseded (replaced by newer editions), Trivial (of no merit), Irrelevant (to community needs), and Easily obtainable elsewhere. It is a practical tool for systematic deselection in public library collections.

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MCQs Section QUESTION #4909

Question 36

A prolific architect who worked from the turn of the century until the late 1950's, _____ perhaps most notably William Randolph Hearst's monumental estate at San Simeon.

Julia Morgan designed nearly 800 buildings in California✔️
perhaps the most notable of the nearly 800 buildings in California designed by Julia Morgan was William Randolph Hearst's monumental estate at San Simeon
of the nearly 800 buildings in California designed by Julia Morgan, perhaps the most notable was William Randolph Hearst's monumental estate at San Simeon
nearly 800 buildings in California were designed by Julia Morgan, of which William Randolph Hearst's monumental estate at San Simeon is perhaps the most notable

Correct Answer Logic:

The introductory participial phrase 'A prolific architect…' must be followed by Julia Morgan as the grammatical subject to avoid a dangling modifier. Only option A does this. Options B, C, and D all shift the subject away from Julia Morgan, creating dangling modifiers.

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Boilers Mechanical Engineering QUESTION #4032

Question 37

'Steam Tables' are used by engineers to determine:

The size of the table
Thermodynamic properties of steam (Enthalpy, Entropy, Volume) at various pressures✔️
The chemical formula of water
The weight of the boiler