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Let $e_E=e$ and $e_H=3e$. Focal distances: $2ae=2\sqrt{3}\Rightarrow ae=\sqrt{3}$ and $2Ae_H=2\sqrt{3}\Rightarrow 3Ae=\sqrt{3}\Rightarrow Ae=\frac{1}{\sqrt{3}}$. Then $\frac{a}{A}=3$ and $a-A=2\Rightarrow A=1, a=3$. So $e=\frac{\sqrt{3}}{3}=\frac{1}{\sqrt{3}}$, $b^2=a^2(1-e^2)=9\cdot\frac{2}{3}=6$. For $H$: $e_H=\sqrt{3}$, $B^2=A^2(e_H^2-1)=2$. Sum of latus rectums $=\frac{2b^2}{a}+\frac{2B^2}{A}=\frac{12}{3}+\frac{4}{1}=4+4=8$.

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Dairy Food Science and Technology QUESTION #5955

Question 6

Which of the following is NOT a function of water in ice cream?

Acts as solvent for sugar, minerals, and other water-soluble components
Participates in the freezing process forming ice crystals that contribute to texture ($40\text{–}70\%$ of water frozen at $-14^{\circ}\text{C}$)
Acts as an emulsifying agent for fat globules✔️
Determines the final ice crystal size distribution and texture of ice cream

Correct Answer Logic:

Water in ice cream dissolves sugars, proteins, and minerals, and freezes to form ice crystals ($40\text{–}70\%$ of water frozen at serving temperature $-14^{\circ}\text{C}$). Water does NOT act as an emulsifier — that function is performed by emulsifiers (lecithin, mono/diglycerides) and proteins.

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Quantitative Reasoning QUESTION #8038

Question 7

CONTIGUOUS : ABUT :: (Find the pair that best matches the relationship between the given words)

possible : occur
simultaneous : coincide✔️
comprehensive : except
constant : stabilize

Correct Answer Logic:

CONTIGUOUS means sharing a border — things that are contiguous ABUT (touch/border) each other. The adjective describes the state created by the verb. Similarly, simultaneous means happening at the same time — things that are simultaneous coincide. Both pairs = [adjective describing a relationship] : [verb enacting that relationship]. The other pairs don't share this precise structural logic.

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Accounting & Finance QUESTION #1224

Question 8

Which of the following is the main tool of Fiscal Policy?

Deficit Financing
Subsidies
Transfer Payments
Taxes✔️

Correct Answer Logic:

Taxes are the primary tool of fiscal policy. Fiscal policy involves the use of government revenue (taxation) and government expenditure (spending) to influence the economy. Taxes are the government's main instrument to raise revenue and regulate economic activity. While subsidies and transfer payments are also fiscal tools, taxation is considered the main one.

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Pakistan Affairs QUESTION #306

Question 9

Pakistan was re-elected for the seventh time to the UN committee on Non-Governmental Organizations on:

11 Feb 2022
19 March 2022
17 April 2021
13 April 2022✔️

Correct Answer Logic:

Pakistan secured re-election to this 19-member committee in April 2022 for the 2023-2026 term.+1

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3564

Question 10

The 'Umbel' inflorescence is characteristic of which family?

Solanaceae
Umbelliferae✔️
Lamiaceae
Rosaceae

Correct Answer Logic:

Fennel and Coriander have umbel-shaped flowers.

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Quantitative Reasoning QUESTION #8020

Question 11

Choose the word that is most nearly opposite in meaning to LOQUACIOUS

tranquil
skeptical
morose
taciturn✔️

Correct Answer Logic:

LOQUACIOUS means very talkative or chatty. The opposite would be quiet or not talkative. Taciturn is correct: taciturn means reserved, uncommunicative, or saying little, which is the direct opposite of loquacious (very talkative).

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General Ability and Fire Fighting QUESTION #5616

Question 12

What is the primary mechanism by which water extinguishes a fire?

It removes the fuel
It absorbs heat and cools the fuel below ignition temperature✔️
It smothers the fire
It breaks the chemical chain reaction

Correct Answer Logic:

Water's primary action is cooling — it absorbs large amounts of heat and brings the fuel temperature below its ignition point

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Verbal Reasoning QUESTION #8086

Question 13

In 1950, if the printing cost per newspaper was $0.05, what would have been the total cost of printing the average daily circulation?

[Note: From the graph, average daily circulation in 1950 was 520,000 newspapers]

$32,500
$26,000✔️
$23,500
$22,000

Correct Answer Logic:

Total cost = (number of newspapers) × (cost per newspaper)

Total cost $= 520{,}000 \times 0.05$

$= 520{,}000 \times \frac{5}{100} = 520{,}000 \times \frac{1}{20} = \frac{520{,}000}{20} = 26{,}000$

Therefore, the total cost would be $26,000.

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Paper-I (Pharmaceutics II (Industrial and Quality Control) and Pharmaceutics III (Hospital and Community Pharmacy)) QUESTION #5691

Question 14

During the sterilization of parenteral preparations, the $F_{0}$ value represents the equivalent time at what temperature?

$100^{\circ}C$
$121^{\circ}C$✔️
$115^{\circ}C$
$134^{\circ}C$

Correct Answer Logic:

$F_{0}$ is the equivalent time (in minutes) at $121^{\circ}C$ to provide the same lethality as the actual thermal process.

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Islamic Studies QUESTION #330

Question 15

What was the original name of the host of the Prophet (ﷺ), Abu Ayub Ansari (RA)?

Zaid bin Thabit
Khalid bin Zaid✔️
Qais bin Saad
Hanzla bin Aamir

Correct Answer Logic:

His original name was Khalid bin Zaid bin Kulayb.

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Mathematics QUESTION #7442

Question 16

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:

Using sum-to-product formulas: $(\cos x + \cos 4x) + (\cos 2x + \cos 3x) = 0$. This gives $2\cos\frac{5x}{2}\cos\frac{3x}{2} + 2\cos\frac{5x}{2}\cos\frac{x}{2} = 0$, which factors as $2\cos\frac{5x}{2}(\cos\frac{3x}{2} + \cos\frac{x}{2}) = 0$. Either $\cos\frac{5x}{2} = 0$ or $\cos\frac{3x}{2} + \cos\frac{x}{2} = 0$. For the first: $\frac{5x}{2} = \frac{\pi}{2}, \frac{3\pi}{2}, \frac{5\pi}{2}, \frac{7\pi}{2}, \frac{9\pi}{2}$, giving $x = \frac{\pi}{5}, \frac{3\pi}{5}, \pi, \frac{7\pi}{5}, \frac{9\pi}{5}$ (5 solutions). For the second: $2\cos x \cos\frac{x}{2} = 0$, giving $\cos x = 0$ or $\cos\frac{x}{2} = 0$. From $\cos x = 0$: $x = \frac{\pi}{2}, \frac{3\pi}{2}$ (2 more solutions not in first set). From $\cos\frac{x}{2} = 0$: $x = \pi$ (already counted). Total = 5 + 2 = 7 solutions.

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Boilers Mechanical Engineering QUESTION #3997

Question 17

Operating a boiler without a 'Valid Certificate' is considered:

A minor oversight
An illegal act subject to penalties and fines✔️
Allowed if the boiler is new
Allowed if no accident happens

Correct Answer Logic:

The law strictly prohibits the use of uncertified boilers to prevent loss of life and property.

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Chemistry QUESTION #5562

Question 18

Which of the following is an anionic detergent?

Sodium lauryl sulphate✔️
Cetyltrimethyl ammonium bromide
Glyceryl oleate
Sodium stearate

Correct Answer Logic:

Anionic detergents have a negatively charged hydrophilic head. Sodium lauryl sulphate ($CH_3(CH_2)_{11}OSO_3^- Na^+$) has an anionic sulphate group → anionic detergent. Cetyltrimethylammonium bromide has a cationic nitrogen → cationic detergent. Glyceryl oleate is a nonionic detergent. Sodium stearate ($C_{17}H_{35}COO^-Na^+$) is a soap, not a synthetic detergent.

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Boilers Mechanical Engineering QUESTION #2467

Question 19

The base circle diameter $d_b$ of a gear with pitch diameter $d$ and pressure angle $\phi$ is:

$d_b = d / \cos\phi$
$d_b = d \cdot \tan\phi$
$d_b = d \cdot \cos\phi$✔️
$d_b = d \cdot \sin\phi$

Correct Answer Logic:

The base circle radius is related to the pitch circle radius by $r_b = r\cos\phi$, hence $d_b = d\cos\phi$.

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General Abilities QUESTION #7650

Question 20

Which of the following is a surd?

$\sqrt{16}$
$\sqrt{16} + \sqrt{25}$
$\sqrt{21}$✔️
None of these

Correct Answer Logic:

A surd is an irrational root that cannot be simplified to a rational number. $\sqrt{16} = 4$ and $\sqrt{25} = 5$ are rational numbers. However, $\sqrt{21}$ cannot be simplified to a whole number or fraction, making it a surd (irrational number).

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