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Mathematics QUESTION #966

If $A$ and $B$ are two events such that $P(A \cap B) = 0.1$, and $P(A|B)$ and $P(B|A)$ are the roots of the equation $12x^2 - 7x + 1 = 0$, then the value of $\dfrac{P(\overline{A} \cup \overline{B})}{P(\overline{A} \cap \overline{B})}$ is:

$\dfrac{4}{3}$
$\dfrac{7}{4}$
$\dfrac{5}{3}$
$\dfrac{9}{4}$✔️

Correct Answer Logic:

Roots of $12x^2-7x+1=0$ are $\frac{1}{3}$ and $\frac{1}{4}$. Since $P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{1}{3}$ gives $P(B)=0.3$, and $P(B|A)=\frac{1}{4}$ gives $P(A)=0.4$. Then $P(A\cup B)=0.6$, $P(\overline{A}\cup\overline{B})=1-0.1=0.9$, $P(\overline{A}\cap\overline{B})=0.4$. Ratio $=\frac{0.9}{0.4}=\frac{9}{4}$.

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Boilers Mechanical Engineering QUESTION #4054

Question 2

'Fluidized Bed Combustion' (FBC) allows for:

Burning water
Burning low-grade fuels and reducing $SO_x/NO_x$ emissions✔️
Very high noise
Slow combustion

Correct Answer Logic:

Fuel is suspended in a hot bed of ash and sand, ensuring excellent mixing.

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General Abilities QUESTION #4553

Question 3

What is $\frac{5}{8}$ in decimal form?

$0.58$
$0.625$✔️
$0.85$
$1.6$

Correct Answer Logic:

$\frac{5}{8} = 5 \div 8 = 0.625$

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Electrical Engineering QUESTION #2135

Question 4

In a purely inductive circuit, if the frequency of the AC supply is doubled, what happens to the current $I$ flowing through the circuit?

It is doubled
It is halved✔️
It remains the same
It becomes four times

Correct Answer Logic:

Inductive reactance $X_L = 2\pi fL$ is directly proportional to frequency $f$. Doubling $f$ doubles $X_L$, which halves the current $I = V/X_L$.

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Biology QUESTION #551

Question 5

_____ did not have the adaptations to remove the flooding of their cells in fresh water.

Both B, D
Hydrophytes✔️
None of B, D
Xerophytes

Correct Answer Logic:

Hydrophytes are adapted to prevent flooding

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Chemistry QUESTION #4368

Question 6

Poly vinyl chloride (PVC) is the type of:

Homopolymer
Thermosetting polymer
Thermoplastic polymer✔️
Copolymer

Correct Answer Logic:

PVC is formed by addition polymerization of vinyl chloride ($CH_2=CHCl$) monomers. It is a thermoplastic polymer — it softens on heating and re-hardens on cooling, and can be reshaped.

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Physics QUESTION #4386

Question 7

A fluid is flowing through a tube. To undergo transition from laminar to turbulent flow, its velocity must be:

Slightly less than critical velocity
Equal to critical velocity
Greater than critical velocity✔️
Increasing gradually but less than critical velocity

Correct Answer Logic:

Flow transitions from laminar to turbulent when the Reynolds number $Re = \dfrac{\rho v d}{\eta}$ exceeds a critical value. This occurs when fluid velocity exceeds the critical velocity.

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Accounting & Finance QUESTION #6156

Question 8

Sales $250,000; Variable production costs $150,000; Fixed production costs $30,000; Gross profit $70,000; Fixed admin costs $50,000; Profit $20,000. What is the break-even point in sales revenue?

$100,000
$170,000
$200,000✔️
$230,000

Correct Answer Logic:

Option C ($200,000) is correct.

Contribution = $250,000 − $150,000 = $100,000; CS ratio = 40%

Total fixed costs = $30,000 + $50,000 = $80,000

Break-even sales = $80,000 ÷ 0.40 = $200,000

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General Knowledge QUESTION #4471

Question 9

_____ is the author of “Essay on Population (1798)”.

Thomas Malthus✔️
Ester Boserup
Garret Hardin
None of these

Correct Answer Logic:

Thomas Malthus authored 'An Essay on the Principle of Population' in 1798.

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Boilers Mechanical Engineering QUESTION #2400

Question 10

In the general Bernoulli energy equation, the term $H_A$ represents:

Head loss due to friction
Energy added to the fluid by a pump (pump head)✔️
Energy extracted from the fluid by a turbine
Velocity head at section A

Correct Answer Logic:

In the extended Bernoulli equation: $H_A$ is the head added by a pump, $H_L$ is the head loss due to friction, and $H_E$ is the head extracted by a turbine.

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Chemistry QUESTION #7820

Question 11

Mass of 1 mole of calcium carbonate (CaCO₃) is:

50 g
75 g
100 g✔️
125 g

Correct Answer Logic:

Ca=40, C=12, O=16×3=48 → total 100 g/mol.

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Statistics QUESTION #1980

Question 12

The Poisson distribution is derived as the limiting form of the Binomial distribution when:

n is small and p is large
n is large, p is small, and $np = \lambda$ remains constant✔️
n and p both approach zero
n is fixed and p approaches 0.5

Correct Answer Logic:

The Poisson distribution arises as $n \to \infty$ and $p \to 0$ such that $\lambda = np$ remains a finite constant. Under these conditions, $\binom{n}{x}p^x(1-p)^{n-x} \to \dfrac{e^{-\lambda}\lambda^x}{x!}$.

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General Abilities QUESTION #2855

Question 13

If $x + \dfrac{1}{x} = 5$, find $x^2 + \dfrac{1}{x^2}$.

23✔️
25
27
29

Correct Answer Logic:

$\left(x + \dfrac{1}{x}\right)^2 = x^2 + 2 + \dfrac{1}{x^2}$. So $25 = x^2 + 2 + \dfrac{1}{x^2} \Rightarrow x^2 + \dfrac{1}{x^2} = 23$.

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General Knowledge QUESTION #4746

Question 14

India constructed the Baglihar Dam in which district of occupied Kashmir?

Udhampur
Doda✔️
Jammu
Kupwara

Correct Answer Logic:

India constructed the controversial Baglihar Dam (also called Baglihar Hydroelectric Power Project) on the Chenab River in the Doda district of Indian-administered Jammu and Kashmir.

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CISA QUESTION #6845

Question 15

In evaluating cryptographic controls, an auditor finds that SSL 3.0 is still enabled on web servers despite known vulnerabilities and availability of TLS 1.2 and 1.3. Management states they need SSL 3.0 for backward compatibility. What should the auditor recommend?

Accept management's reasoning
Disable SSL 3.0 and conduct impact analysis to identify legitimate compatibility requirements✔️
Enable all protocol versions
Document as acceptable risk

Correct Answer Logic:

Known vulnerabilities in deprecated protocols like SSL 3.0 create unacceptable risk. Keeping vulnerable protocols enabled 'just in case' without identifying specific requirements is poor security practice. The auditor should recommend disabling the vulnerable protocol and conducting proper analysis to identify any legitimate compatibility needs that can be addressed through secure means.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3254

Question 16

'Total Peripheral Resistance' ($TPR$) increases when:

Blood vessels dilate
Blood viscosity increases✔️
Blood pressure drops
Exercise starts

Correct Answer Logic:

Thicker blood (higher viscosity) or constricted vessels increase resistance.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3571

Question 17

'Tannins' give a bluish-black or greenish-black color with:

Ferric Chloride✔️
Iodine
Water
Alcohol

Correct Answer Logic:

This is a standard chemical test for tannins.

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General Knowledge QUESTION #7715

Question 18

In 2024, which country's presidential election saw mass protests over alleged rigging?

Russia
India
Bangladesh✔️
None of these

Correct Answer Logic:

Bangladesh witnessed mass protests in 2024 over the January parliamentary elections, which the opposition boycotted citing concerns about fairness. The protests eventually led to significant political changes in the country during mid-2024.

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Tourism & Hospitality Management QUESTION #1653

Question 19

The Destination Branding course covers the 'branding process' for tourism destinations. Which of the following correctly sequences the key stages of destination brand development as identified in the curriculum?

Logo design → Slogan creation → Social media launch → Press conference
Destination audit → Segmentation analysis → Consumer perception research → Competitor analysis → Brand building → Applying brand guidelines → Managing and tracking the brand✔️
Market research → Price setting → Distribution → Promotion
Visitor survey → Government approval → Budget allocation → Staff training

Correct Answer Logic:

The Destination Branding course (Module 2) identifies the destination branding process as: Destination audit, Segmentation analysis, Consumer perception research, Competitor analysis, Brand building process and models (understanding visitor vs non-visitor), Brand architecture, and addressing Challenges — followed by Module 3 (bringing the brand to life: guidelines, logo, slogans) and Module 4 (managing and tracking the brand).

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Mathematics QUESTION #7484

Question 20

Let N be the set of natural numbers and two functions f and g be defined as $f,g: \mathbb{N} \to \mathbb{N}$ such that $f(n) = \begin{cases} \frac{n+1}{2} & \text{if } n \text{ is odd} \\ \frac{n}{2} & \text{if } n \text{ is even} \end{cases}$ and $g(n) = n - (-1)^n$. Then fog is:

onto but not one-one
one-one but not onto
both one-one and onto✔️
neither one-one nor onto

Correct Answer Logic:

First, $g(n) = n - (-1)^n = \begin{cases} n-1 & \text{if } n \text{ is odd} \\ n+1 & \text{if } n \text{ is even} \end{cases}$. For odd n, $g(n) = n-1$ is even, and for even n, $g(n) = n+1$ is odd. Now $(f \circ g)(n) = f(g(n))$. If n is odd: $g(n) = n-1$ (even), so $f(g(n)) = \frac{n-1}{2}$. If n is even: $g(n) = n+1$ (odd), so $f(g(n)) = \frac{(n+1)+1}{2} = \frac{n+2}{2}$. For injectivity: if $(f \circ g)(n_1) = (f \circ g)(n_2)$, we need to show $n_1 = n_2$. If both are odd: $\frac{n_1-1}{2} = \frac{n_2-1}{2}$, so $n_1 = n_2$. If both even: $\frac{n_1+2}{2} = \frac{n_2+2}{2}$, so $n_1 = n_2$. If one odd and one even: $\frac{n_1-1}{2} = \frac{n_2+2}{2}$, giving $n_1 = n_2+3$, which contradicts parity. So fog is injective. For surjectivity: any $m \in \mathbb{N}$ can be written as $m = \frac{2m-1}{2}$ (from odd $n=2m-1$) or $m = \frac{2m+2}{2}$ (from even $n=2m-2$). So fog is surjective. Thus fog is bijective.

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