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Statistics QUESTION #1962

The paired t-test is most appropriately applied when observations in two samples satisfy which condition?

They are equal in number only
They are paired (matched)
They exhibit high correlation
All of the above✔️

Correct Answer Logic:

Paired t-test requires observations to be paired (matched), equal in number, and typically correlated. All three conditions together define the paired t-test setting.

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English QUESTION #4453

Question 2

Which of the following sentences is correct?

Despite of her sheer hard work, she failed.
Though I am sick but I will go to office.
Me and my friend often visit Islamabad.
None of these✔️

Correct Answer Logic:

All are incorrect: A should be 'Despite' (no 'of'), B has redundant 'but', and C should be 'My friend and I'.

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Ability / HR / Governance / Special Education QUESTION #1846

Question 3

Which authority constitutes the Selection Board for promotion/transfer to posts in BPS 19 to 21?

Establishment Division
Federal Public Service Commission
Federal Government✔️
Prime Minister

Correct Answer Logic:

Rule 2(b) defines Selection Board as a Board constituted by the Federal Government for selection for promotion or transfer to posts in BPS 19 to 21 and equivalent.

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Mathematics QUESTION #7462

Question 4

The expression $\frac{\tan A}{1-\cot A} + \frac{\cot A}{1-\tan A}$ can be written as:

sinA cosA + 1
secA cosecA + 1✔️
tanA + cotA
secA + cosecA

Correct Answer Logic:

Rewriting in terms of sine and cosine: $\frac{\frac{\sin A}{\cos A}}{1-\frac{\cos A}{\sin A}} + \frac{\frac{\cos A}{\sin A}}{1-\frac{\sin A}{\cos A}} = \frac{\frac{\sin A}{\cos A}}{\frac{\sin A - \cos A}{\sin A}} + \frac{\frac{\cos A}{\sin A}}{\frac{\cos A - \sin A}{\cos A}} = \frac{\sin^2 A}{\cos A(\sin A - \cos A)} + \frac{\cos^2 A}{\sin A(\cos A - \sin A)}$. Taking common denominator: $= \frac{\sin^2 A}{\cos A(\sin A - \cos A)} - \frac{\cos^2 A}{\sin A(\sin A - \cos A)} = \frac{\sin^3 A - \cos^3 A}{\sin A \cos A (\sin A - \cos A)}$. Using $a^3-b^3 = (a-b)(a^2+ab+b^2)$: $= \frac{(\sin A - \cos A)(\sin^2 A + \sin A \cos A + \cos^2 A)}{\sin A \cos A (\sin A - \cos A)} = \frac{1 + \sin A \cos A}{\sin A \cos A} = \frac{1}{\sin A \cos A} + 1 = \sec A \csc A + 1$.

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Biology QUESTION #535

Question 5

The dew drops on tips of grass leaves is an example of

Infestation
Bleeding
Exudation✔️
Imbibition

Correct Answer Logic:

Guttation/exudation produces dew drops

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Mathematics QUESTION #4159

Question 6

The D'Alembert solution of the wave equation $u_{tt} = c^2 u_{xx}$ with $u(x,0) = f(x)$ and $u_t(x,0) = g(x)$ is:

$u(x,t) = \frac{f(x+ct) + f(x-ct)}{2} + \frac{1}{2c}\int_{x-ct}^{x+ct} g(s)ds$✔️
$u(x,t) = f(x+ct) + f(x-ct)$
$u(x,t) = \frac{1}{2}[f(x+ct) - f(x-ct)]$
$u(x,t) = \frac{1}{c}\int_{x-ct}^{x+ct} g(s)ds$

Correct Answer Logic:

D'Alembert's formula: $u(x,t) = \frac{f(x+ct) + f(x-ct)}{2} + \frac{1}{2c}\int_{x-ct}^{x+ct} g(s)ds$. First term from initial displacement, second from initial velocity.

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Home Economics QUESTION #6266

Question 7

Which enzyme is responsible for the initial digestion of starch in the buccal cavity?

Trypsin
Salivary Amylase✔️
Lipase
Pepsin

Correct Answer Logic:

Salivary amylase (ptyalin) begins the chemical breakdown of complex carbohydrates into maltose.

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Mathematics QUESTION #6958

Question 8

Evaluate: $\displaystyle\lim_{x\to0}\dfrac{\sin^2 x}{\sqrt{2}-\sqrt{1+\cos x}}$

4✔️
$4\sqrt{2}$
$8\sqrt{2}$
8

Correct Answer Logic:

Rationalise the denominator by multiplying by $\dfrac{\sqrt{2}+\sqrt{1+\cos x}}{\sqrt{2}+\sqrt{1+\cos x}}$:

Denominator becomes $2-(1+\cos x)=1-\cos x$.

$\lim_{x\to0}\dfrac{\sin^2x(\sqrt{2}+\sqrt{1+\cos x})}{1-\cos x}$

Use $\dfrac{\sin^2x}{1-\cos x}=\dfrac{1-\cos^2x}{1-\cos x}=1+\cos x$:

$=\lim_{x\to0}(1+\cos x)(\sqrt{2}+\sqrt{1+\cos x})=(1+1)(\sqrt{2}+\sqrt{2})=2\cdot2\sqrt{2}=\mathbf{4\sqrt{2}}$

Wait: $2\times2\sqrt{2}=4\sqrt{2}$... but option A is 4. Let me recheck: $(2)(\sqrt{2}+\sqrt{2})=2\cdot2\sqrt{2}=4\sqrt{2}$. Answer: $4\sqrt{2}$ is not listed as option A (which is 4). The correct answer is $\mathbf{4\sqrt{2}}$ (index 1).

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Boilers Mechanical Engineering QUESTION #2473

Question 9

The tensile strength $S_{ut}$ of spring wire of diameter $d$ is estimated by the power law $S_{ut} = A/d^m$. For music wire, the exponent $m \approx 0.163$. This means:

Strength is independent of wire diameter
Strength INCREASES as wire diameter DECREASES (smaller wire is stronger)✔️
Strength increases as wire diameter increases
Strength is linearly proportional to wire diameter

Correct Answer Logic:

Since $S_{ut}=A/d^m$ with $m>0$, smaller diameter wire has higher tensile strength due to more cold-drawing and work-hardening effect.

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Chemistry QUESTION #5525

Question 10

Match the drugs with their correct pharmacological classification: (A) Norethindrone → ?, (B) Ofloxacin → ?, (C) Equanil → ?; Options: (P) Antibiotic, (Q) Anti-fertility, (R) Hypertension, (S) Analgesic

$(A)\to(Q);\ (B)\to(R);\ (C)\to(S)$
$(A)\to(Q);\ (B)\to(P);\ (C)\to(R)$✔️
$(A)\to(R);\ (B)\to(P);\ (C)\to(S)$
$(A)\to(R);\ (B)\to(P);\ (C)\to(R)$

Correct Answer Logic:

Norethindrone is a synthetic progesterone used as an anti-fertility (contraceptive) drug → (Q). Ofloxacin is a fluoroquinolone antibiotic → (P). Equanil (meprobamate) is a tranquilizer used to control anxiety and hypertension → (R). Correct match: $A \to Q,\ B \to P,\ C \to R$.

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Biology QUESTION #4237

Question 11

The part of male reproductive system that maintains the temperature for sperm production is:

Testes
Scrotum✔️
Vas deferens
Epididymis

Correct Answer Logic:

Scrotum maintains temperature for sperm production.

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Agronomy QUESTION #8061

Question 12

ds fsadf adsfa sd

Sub-Questions:

Question 1

s sfda fsdf

s sadfs
d fasd
sdfa
✔️
sdfasdfsd
✔️

Question 2

sdf sadfasd

s dfsad
sd asdf
✔️
s fasd
✔️
safsa

Correct Answer Logic:

s safsa sfa sfsa saf

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Biology Zoology Botany QUESTION #1350

Question 13

Which of the following statements is TRUE about animal behavior?

Animals will derive their current behavior from past experiences✔️
Two animals of the same species will have exactly identical behavior
Animals will behave in the same manner with all human beings
None of these

Correct Answer Logic:

Animal behavior is shaped by both genetics (innate) and experience (learned). Animals can learn from past experiences through conditioning, habituation, imprinting, and trial-and-error, which modifies their current behavior. Two animals of the same species do NOT have identical behavior due to individual variation and different experiences. Behavior also varies with context.

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Biology QUESTION #4236

Question 14

Osmoreceptors that detect the osmotic pressure of blood are primarily located in the:

Cerebellum
Medulla oblongata
Hypothalamus✔️
Cerebral cortex

Correct Answer Logic:

Osmoreceptors are in hypothalamus.

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Physics QUESTION #7850

Question 15

Black body radiates at all wavelengths:

Inconsistently
Distinctly
Equally✔️
Unequally

Correct Answer Logic:

Black body emits a continuous spectrum; the power distribution follows Planck's law (unequal intensity across wavelengths). But the word equally" is wrong. The correct statement: it radiates at all wavelengths with varying intensity. MDCAT answer often "equally" is wrong. But question says "radiates at all wavelengths ___" They want "equally"? No

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Electrical Engineering QUESTION #2169

Question 16

The characteristic equation $s^4 + 2s^3 + 3s^2 + 4s + 5 = 0$ describes a control system. Using the Routh-Hurwitz criterion, how many roots lie in the right-half s-plane?

$2$✔️
$0$
$4$
$1$

Correct Answer Logic:

Routh first-column elements are: $1, 2, 1, -6, 5$. There are 2 sign changes (at $-6$ and back to $5$), confirming 2 roots in the RHP and an unstable system.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3362

Question 17

'Exotoxins' are usually released by:

Dead bacteria only
Living, growing bacteria✔️
Viruses
The host's own cells

Correct Answer Logic:

Exotoxins are secreted proteins that can cause damage even at low concentrations.

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General Knowledge QUESTION #4812

Question 18

The lowest percentage of internet users globally is found in which region?

North America
Africa✔️
Australia
Latin America

Correct Answer Logic:

Africa has historically had the lowest internet penetration rate among all global regions, though the rate has been growing rapidly in recent years with mobile internet expansion.

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Paper-II (Pharmacology and Social Behaviour, Law & Ethics and Computer Sciences) QUESTION #5807

Question 19

The 'Late Adopters' (Laggards) represent approximately what percentage of the population?

16%✔️
34%
2.5%
13.5%

Correct Answer Logic:

Laggards or late adopters make up 16%[cite: 7].

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Mathematics QUESTION #7456

Question 20

The distance of the point $(1, 3, -7)$ from the plane passing through the point $(1, -1, -1)$, having normal perpendicular to both the lines $\frac{x-1}{1} = \frac{y+2}{-2} = \frac{z-4}{3}$ and $\frac{x-2}{2} = \frac{y+1}{-1} = \frac{z+7}{-1}$, is:

$\frac{20}{\sqrt{74}}$
$\frac{10}{\sqrt{83}}$
$\frac{5}{\sqrt{83}}$
$\frac{10}{\sqrt{74}}$✔️

Correct Answer Logic:

The direction ratios of the two lines are $(1,-2,3)$ and $(2,-1,-1)$. The normal to the plane is perpendicular to both, so it's their cross product: $\vec{n} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 1 & -2 & 3 \\ 2 & -1 & -1 \end{vmatrix} = \hat{i}(2-(-3)) - \hat{j}(-1-6) + \hat{k}(-1-(-4)) = 5\hat{i} + 7\hat{j} + 3\hat{k}$. The plane equation through $(1,-1,-1)$ with normal $(5,7,3)$ is $5(x-1) + 7(y+1) + 3(z+1) = 0$, which gives $5x+7y+3z+5 = 0$. Distance from $(1,3,-7)$ is $\frac{|5(1)+7(3)+3(-7)+5|}{\sqrt{25+49+9}} = \frac{|5+21-21+5|}{\sqrt{83}} = \frac{10}{\sqrt{83}}$.

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