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For $n=3$: $\text{adj}(\text{adj}(M)) = |M|^{n-2} M$. So $\text{adj}(\text{adj}(2A)) = |2A|^1 \cdot 2A = 8|A| \cdot 2A = 8A$. Thus $|B| = |8A| = 8^3|A| = 512 \cdot \frac{1}{2} = 256$ and $\text{trace}(B) = \text{trace}(8A) = 8\cdot3 = 24$. So $|B| + \text{trace}(B) = 256 + 24 = 280$.

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Reading and Writing (Module-1) QUESTION #10384

Question 5

Although the twins looked nearly identical, their personalities were utterly -------: one was gregarious, the other withdrawn.

complementary
disparate✔️
similar
harmonious

Correct Answer Logic:

One being gregarious and the other withdrawn shows the personalities are 'disparate,' or very different.

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Geography QUESTION #6309

Question 6

In diffusion of innovation theory, which adopter category represents the critical mass for widespread acceptance?

Innovators (2.5%)
Early Adopters (13.5%)
Early Majority (34%)✔️
Late Majority (34%)

Correct Answer Logic:

The Early Majority (34%) represents the critical mass or 'tipping point' in Rogers' diffusion model. Once this pragmatic group adopts an innovation, widespread acceptance becomes inevitable. They adopt just before the average member of society.

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Math Physics Chemistry Biology QUESTION #4275

Question 7

The first consequence of lymphatic blockage in tissues is:

Deficiency of oxygen
Loss of nerve signals
Drop in blood pressure
Excess fluid accumulation in tissue✔️

Correct Answer Logic:

When lymphatic vessels are blocked, lymph cannot drain from tissues, leading to accumulation of interstitial fluid, causing edema (swelling).

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Maths QUESTION #2904

Question 8

A man walks $6$ km in $2$ hours. How much distance in $5$ hours?

12 km
15 km✔️
18 km
20 km

Correct Answer Logic:

Speed $= 6/2 = 3$ km/h. Distance in $5$ hours $= 3 \times 5 = 15$ km.

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Physics QUESTION #7015

Question 9

A block of mass $m$ is positioned on a surface defined by the vertical cross-section $y = \frac{x^3}{6}$. If the coefficient of static friction is $0.5$, determine the maximum height above the ground at which the block can remain at rest without slipping.

$\frac{1}{3} m$
$\frac{1}{2} m$
$\frac{1}{6} m$✔️
$m$

Correct Answer Logic:

To find the maximum height, we use the condition for slipping: $\tan \theta = \mu$. Since $\tan \theta$ is the slope $\frac{dy}{dx}$, we differentiate $y = \frac{x^3}{6}$ to get $\frac{dy}{dx} = \frac{x^2}{2}$. Setting $\frac{x^2}{2} = 0.5$ gives $x = 1$. Substituting $x=1$ back into the original equation $y = \frac{1^3}{6}$ gives $y = \frac{1}{6}$.

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General Knowledge QUESTION #4750

Question 10

India's Kishanganga Dam (also known as Kishan Ganga) is being constructed in which area?

Jammu
Srinagar
Baramula✔️
Kargil

Correct Answer Logic:

The Kishanganga Hydroelectric Plant is located near Bandipore in the Baramulla district of Indian-administered Jammu and Kashmir.

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Maths QUESTION #2811

Question 11

A student scored 540 marks out of 750. What percentage did the student score?

68%
70%
72%✔️
75%

Correct Answer Logic:

Percentage $= \dfrac{540}{750} \times 100 = \dfrac{54000}{750} = 72\%$.

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Agronomy QUESTION #2047

Question 12

The Economic Threshold Level (ETL) in crop pest management is defined as:

The pest density at which the crop begins to show visible damage symptoms
The pest population density at which control measures must be initiated to prevent the pest from reaching the Economic Injury Level (EIL) — accounting for the time needed for control measures to take effect✔️
The maximum pest density a crop can tolerate without any yield loss
The point at which 50% of the crop stand is destroyed by the pest

Correct Answer Logic:

ETL (action threshold) is always set BELOW the Economic Injury Level (EIL) — the pest density at which economic damage equals cost of control. The ETL triggers action while the pest population is still rising, allowing time for control measures to prevent the EIL from being reached. ETL < EIL is a fundamental IPM concept.

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General Knowledge QUESTION #7708

Question 13

Which two nations restored diplomatic ties in 2023 through Chinese mediation?

Israel and Iran
Saudi Arabia and Iran✔️
Turkiye and Armenia
None of these

Correct Answer Logic:

Saudi Arabia and Iran restored diplomatic relations in March 2023 through mediation by China. This historic agreement ended a seven-year diplomatic rift between the two regional powers and marked a significant shift in Middle Eastern geopolitics.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3141

Question 14

Which hormone is responsible for the 'Milk Ejection' reflex and uterine contractions?

Prolactin
Oxytocin✔️
Estrogen
Progesterone

Correct Answer Logic:

Oxytocin is the 'bonding' and 'contraction' hormone.

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Math Physics Chemistry Biology QUESTION #11422

Question 15

Which one can be considered as living characteristics of a virus?

Can replicate itself✔️
No cellular respiration
Enzyme-less biochemistry
Lack of cytoplasm

Correct Answer Logic:

The primary living characteristic of viruses is their ability to replicate (reproduce) — albeit only inside a living host cell. Viruses contain genetic material (DNA or RNA) and direct the host's cellular machinery to produce new virus particles. All other listed options (no respiration, no enzymes, no cytoplasm) are non-living characteristics.

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Mathematics QUESTION #4154

Question 16

For a uniform lamina in the shape of a triangle with vertices $(0,0)$, $(a,0)$, $(0,b)$, what is the $y$-coordinate of the center of mass?

$\frac{b}{2}$
$\frac{b}{3}$✔️
$\frac{2b}{3}$
$\frac{b}{4}$

Correct Answer Logic:

For a triangular lamina, center of mass is at the centroid: $(\frac{a}{3}, \frac{b}{3})$. So $\bar{y} = \frac{b}{3}$.

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General Knowledge QUESTION #8778

Question 17

Which category of Nobel Prizes was NOT originally created by Alfred Nobel?

Peace
Literature
Economics✔️
Medicine

Correct Answer Logic:

The Economics Prize was established later by Sweden's central bank.

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Chemistry QUESTION #1451

Question 18

Which type of substitution occurs predominantly in benzene?

Nucleophilic substitution
Electrophilic substitution✔️
Free radical substitution
None of these

Correct Answer Logic:

Benzene undergoes electrophilic aromatic substitution (EAS) predominantly. The high electron density of the aromatic $\pi$ system makes benzene an electron donor that attracts electrophiles. The reaction proceeds via a carbocation intermediate (arenium ion/Wheland intermediate), followed by deprotonation to restore aromaticity. Nucleophilic substitution on benzene requires special conditions (e.g., very strong electron-withdrawing groups).

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General Ability and Fire Fighting QUESTION #5624

Question 19

Removing one side of the Fire Tetrahedron will:

Increase the intensity of the fire
Have no effect on combustion
Extinguish or suppress the fire✔️
Only slow the fire temporarily

Correct Answer Logic:

If any one of the four elements (Fuel

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Civil / Architecture QUESTION #2365

Question 20

In the design of steel plate girders, the proportioning of the web panel to prevent shear buckling without tension field action requires the shear buckling coefficient $k_v$. For an unstiffened web with $a/h \to \infty$ (no transverse stiffeners), the value of $k_v$ used in calculating the critical shear stress is:

4.0
5.34✔️
6.34
2.0

Correct Answer Logic:

For a web plate with no transverse stiffeners (pure shear panel, $a/h \to \infty$), the shear buckling coefficient is $k_v = 5.34$. When transverse stiffeners are present with aspect ratio $a/h \leq 1$: $k_v = 4.0 + \dfrac{5.34}{(a/h)^2}$. The critical shear stress is $F_{cr} = \dfrac{k_v \pi^2 E}{12(1-\nu^2)(h/t_w)^2}$. AISC uses $k_v = 5.34$ as the baseline for unstiffened webs.

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