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Mathematics QUESTION #6982

Two cards are drawn one after another with replacement from a well-shuffled standard deck of 52 cards. Let $X$ be the number of aces obtained. Find $P(X=1)+P(X=2)$.

$\dfrac{49}{169}$
$\dfrac{52}{169}$
$\dfrac{24}{169}$
$\dfrac{25}{169}$✔️

Correct Answer Logic:

$p=P(\text{ace})=\dfrac{4}{52}=\dfrac{1}{13}$, $q=\dfrac{12}{13}$. Binomial with $n=2$.

$P(X=1)=\binom{2}{1}\cdot\dfrac{1}{13}\cdot\dfrac{12}{13}=\dfrac{24}{169}$

$P(X=2)=\binom{2}{2}\cdot\left(\dfrac{1}{13}\right)^2=\dfrac{1}{169}$

$P(X=1)+P(X=2)=\dfrac{24}{169}+\dfrac{1}{169}=\dfrac{25}{169}$

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English QUESTION #8454

Question 2922

Nida is a(n) _______ student. She reads every page of her textbooks and studies for hours.

meticulous✔️
lethargic
apathetic
relaxed

Correct Answer Logic:

Meticulous means very careful and thorough.

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Pakistan Affairs QUESTION #590

Question 2923

In 1905 Bengal was partitioned during the Viceroyalty of:

Lord Mayo
Lord William Bentick
Lord Curzon✔️
None of These

Correct Answer Logic:

Lord Curzon announced the partition of Bengal in 1905.

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Administration QUESTION #2914

Question 2924

What do "Proactive Strategies" in administration generally imply?

Actions based on current conditions
Anticipation of future events✔️
Response to past failures
Static operational procedures

Correct Answer Logic:

Proactive management involves planning ahead and taking action to anticipate future challenges or opportunities before they occur.

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Law QUESTION #9507

Question 2925

A written statement is not filed by the defendant within the prescribed time. The trial Court strikes off the defence and proceeds ex parte. The defendant argues the Court cannot impose this sanction. Is the Court's action valid?

No; the Court can only adjourn and cannot strike off defence
No; striking off the defence requires the consent of the plaintiff
Yes; under Order VIII Rule 10, if a defendant fails to file a written statement within the time fixed, the Court may proceed to pronounce judgment or may, at its discretion, allow further time after striking off the right to file a written statement✔️
No; the Court must give unlimited opportunities to file a written statement

Correct Answer Logic:

Order VIII Rule 10 CPC empowers the Court to pronounce judgment or take any other order it deems fit if a defendant omits or refuses to file a written statement within the time allowed. Striking off the defence and proceeding ex parte is within the Court's discretion as a consequence of non-compliance.

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Physics QUESTION #7076

Question 2926

A simple pendulum has a time period $T$ when measured in a stationary elevator. If the elevator begins to accelerate upwards at a rate of $g/2$, what is the new time period of the pendulum?

$\sqrt{\frac{2}{3}}T$✔️
$\sqrt{3}T$
$\sqrt{\frac{3}{2}}T$
$\frac{T}{\sqrt{3}}$

Correct Answer Logic:

The effective gravity $g_{eff}$ in an upward accelerating lift is $g + a = g + g/2 = 3g/2$. Since the time period $T \propto \frac{1}{\sqrt{g}}$, the new period $T' = T \sqrt{\frac{g}{3g/2}} = T \sqrt{\frac{2}{3}}$.

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Boilers Mechanical Engineering QUESTION #2386

Question 2927

The steady-state error for a unit step input applied to a type-zero closed-loop system (with unity feedback) is:

$E_s = 0$
$E_s = \frac{1}{1+K_p}$ where $K_p = \lim_{s\to 0} Y_1(s)$✔️
$E_s = 1$
$E_s = \infty$

Correct Answer Logic:

For a type-zero system with unit step input: $E_s=\frac{1}{1+Y_1(0)}=\frac{1}{1+K_p}$ where $K_p$ is the position error constant. For a type-one system (pole at origin), $E_s=0$ for a step input.

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General Knowledge QUESTION #8825

Question 2928

Which country has been declared a 'major non-NATO ally' of the United States?

Turkey
Pakistan✔️
India
Italy

Correct Answer Logic:

Pakistan is a major non-NATO ally.

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Physics QUESTION #1037

Question 2929

A uniform rod of mass 20 kg and length 5 m leans against a smooth wall at $60°$. Friction force from the floor is (Take $g=10\ \text{m/s}^2$):

200 N
$200\sqrt{3}\ \text{N}$
100 N✔️
$100\sqrt{3}\ \text{N}$

Correct Answer Logic:

Taking torques about the contact point on the floor. The angle with the wall is $60°$, so angle with floor is $30°$. Normal from wall (horizontal) $\times L\sin30° = mg\times\frac{L}{2}\cos30°$. Wait — using torque about foot: $N_w\cdot L\sin30° = mg\cdot\frac{L}{2}\cos30°\Rightarrow N_w = \frac{mg\cos30°}{2\sin30°} = \frac{20\times10\times\frac{\sqrt{3}}{2}}{2\times\frac{1}{2}}=100\sqrt{3}$. Friction $= N_w = 100\sqrt{3}\approx173\ \text{N}$. Answer: $100\sqrt{3}\ \text{N}$.

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Paper-II (Pharmacognosy and Pharmaceutics-I) QUESTION #3062

Question 2930

What is the 'HLB Value' system used for?

Measuring drug potency
Classifying surfactants for emulsions✔️
Calculating doses for the elderly
Determining glass type

Correct Answer Logic:

The Hydrophilic-Lipophilic Balance (HLB) value helps select the right emulsifying agent.

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Paper-II (Pharmacognosy and Pharmaceutics-I) QUESTION #3618

Question 2931

'Ash Value' is a physical parameter used to detect:

The amount of active ingredient
The presence of inorganic earthy matter/impurities✔️
The moisture content
The volatile oil content

Correct Answer Logic:

Ash content indicates the mineral or earthy residue left after burning.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3296

Question 2932

An 'Antigen' is best defined as a substance that:

Kills bacteria
Is produced by white blood cells
Can trigger an immune response✔️
Is found only in viruses

Correct Answer Logic:

Antigens are usually proteins or polysaccharides that the body recognizes as 'foreign'.

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Pakistan Affairs QUESTION #142

Question 2933

Who is the author of 'Diplomatic Footprints'?

G.W. Chaudhry
Aizaz Ahmad Chaudhry
Abdul Sattar✔️
Khurshid Kasuri

Correct Answer Logic:

Abdul Sattar, a former Foreign Minister, is the author of 'Pakistan's Foreign Policy 1947–2012: A Concise History' often associated with 'Diplomatic Footprints' contexts, but the specific book 'Diplomatic Footprints' is by Abdul Sattar.

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Chemistry QUESTION #432

Question 2934

In many of its properties __________ is quite different from the other alkali metals.

Li✔️
Be
Na
K

Correct Answer Logic:

Lithium shows anomalous behavior among alkali metals

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Education QUESTION #6720

Question 2935

When a lesson plan includes multiple short activities addressing auditory, visual, and kinesthetic modalities, the teacher is PRIMARILY demonstrating understanding of:

Classroom management
Learning style diversity and multi-methodology✔️
Time management
Behavioral psychology

Correct Answer Logic:

Incorporating varied modalities (auditory: discussion; visual: diagrams; kinesthetic: hands-on) addresses diverse learning styles. Multi-methodology recognizes that students process information differently and benefit from varied instructional approaches within single lessons.

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Verbal Reasoning QUESTION #8073

Question 2936

Given that $|-\overline{3}| = -m$, compare:

Column A: $m$

Column B: 3

Column A is greater
Column B is greater
The two quantities are equal✔️
The relationship cannot be determined

Correct Answer Logic:

First, evaluate the left side: $|-\overline{3}| = |-3| = 3$

So we have: $3 = -m$

Solving for $m$: $m = -3$

Now compare:

Column A: $m = -3$
Column B: $3$

Since $-3 < 3$, Column B is greater.

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Islamic Studies QUESTION #8223

Question 2937

The tragic incident of Karbala took place during the month of Muharram in the Hijri:

55 AH
61 AH✔️
70 AH
72 AH

Correct Answer Logic:

This is a repeat of questions 97 and 162. The tragedy of Karbala occurred in 61 AH (680 CE) on the 10th of Muharram (Day of Ashura). Imam Hussain (RA), grandson of the Prophet (PBUH), along with his family and companions, was martyred by Yazid's forces. This event profoundly impacted Islamic history and is commemorated annually, particularly by Shia Muslims through mourning rituals during the first ten days of Muharram.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3230

Question 2938

A 'Stroke' (Cerebrovascular Accident) is caused by:

Interrupted blood flow to the heart
Interrupted blood flow to the brain✔️
A broken bone
A stomach ulcer

Correct Answer Logic:

Ischemia or hemorrhage in the brain results in neurological deficits.

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Psychology QUESTION #9898

Question 2939

The non-directive approach is most characteristic of:

Psychoanalysis
Behaviour modification
Client-centered therapy✔️
Hypnosis

Correct Answer Logic:

Client-centered therapy (Rogers) is the quintessential non-directive approach — the therapist creates facilitative conditions allowing clients to lead their own process, without directing, advising, interpreting, or prescribing solutions.

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Home Economics QUESTION #6269

Question 2940

What is the biological value of a protein a measure of?

The amount of nitrogen retained for growth and maintenance✔️
The number of calories per gram of protein
The speed of digestion in the stomach
The total weight of the protein in grams

Correct Answer Logic:

Biological value (BV) measures how efficiently the body utilizes protein from the diet.

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