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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:
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.
Uploaded by: Fani Warraich
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:
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:
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؟
Correct Answer Logic:
اردو شاعری پر ایک نظر کلیم الدین احمد کی مشہور تنقیدی تصنیف ہے۔
Uploaded by: Fani Warraich
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:
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.
Uploaded by: Fani Warraich
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:
Correct Answer Logic:
Podophyllum resin is used for warts and some cancers.
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General Abilities
QUESTION #2859
Question 28
Solve: \(x^2 - 7x + 12 = 0\)
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:
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?
Chemistry
QUESTION #5573
Question 32
Arrange the following cyclic amines in decreasing order of basicity: (I) Pyridine, (II) Pyrrole, (III) Piperidine
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: \(1, 4, 9, 16, 25, \_\_\_\)
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.'
Correct Answer Logic:
Standard indirect: 'said that he did not eat mangoes'.
Uploaded by: Fani Warraich
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?
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.
Uploaded by: Fani Warraich
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.
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.
Uploaded by: Fani Warraich
Boilers Mechanical Engineering
QUESTION #4032
Question 37
'Steam Tables' are used by engineers to determine:
Correct Answer Logic:
Essential for calculating heat balance and efficiency.
Uploaded by: Fani Warraich
Paper-I (Anatomy/Physiology and Biochemistry/Microbiology)
QUESTION #3141
Question 38
Which hormone is responsible for the 'Milk Ejection' reflex and uterine contractions?
Correct Answer Logic:
Oxytocin is the 'bonding' and 'contraction' hormone.
Uploaded by: Fani Warraich
General Knowledge
QUESTION #4654
Question 39
Inflation rose but stock prices remained steady. What explains the National stock Index reaction?
General Abilities
QUESTION #4545
Question 40
Convert $0.75$ to a fraction in lowest terms:
Correct Answer Logic:
$0.75 = \frac{75}{100} = \frac{3}{4}$ (dividing numerator and denominator by $25$)
Uploaded by: Fani Warraich
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