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Math (Module-1) QUESTION #5457

A group of students voted on five after-school activities. The bar graph (not shown) displays the number of students who chose each activity. Based on the graph, how many students chose activity 3?

25
39
48✔️
50

Correct Answer Logic:

The bar for activity 3 reaches 48 on the vertical axis.

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Mathematics QUESTION #7467

Question 2

If sum of all the solutions of the equation $8\cos x \cdot (\cos(\frac{\pi}{6}+x) \cdot \cos(\frac{\pi}{6}-x) - \frac{1}{2}) = 1$ in [0, π] is kπ, then k is equal to:

$\frac{8}{9}$
$\frac{20}{9}$
$\frac{2}{3}$
$\frac{13}{9}$✔️

Correct Answer Logic:

Simplifying the product: $\cos(\frac{\pi}{6}+x)\cos(\frac{\pi}{6}-x) = \frac{1}{2}[\cos(\frac{\pi}{3}) + \cos(2x)] = \frac{1}{2}[\frac{1}{2} + \cos 2x] = \frac{1}{4} + \frac{\cos 2x}{2}$. The equation becomes: $8\cos x(\frac{1}{4} + \frac{\cos 2x}{2} - \frac{1}{2}) = 1$, which gives $8\cos x(\frac{\cos 2x}{2} - \frac{1}{4}) = 1$, or $4\cos x(\cos 2x - \frac{1}{2}) = 1$. Since $\cos 2x = 2\cos^2 x - 1$: $4\cos x(2\cos^2 x - 1 - \frac{1}{2}) = 1$, giving $4\cos x(2\cos^2 x - \frac{3}{2}) = 1$, or $8\cos^3 x - 6\cos x - 1 = 0$. Solving this cubic and finding solutions in [0,π], then summing them gives $k = \frac{2}{3}$.

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Dairy Food Science and Technology QUESTION #5915

Question 3

The detection of alkali (neutralizer) addition to milk uses which test?

Alizarin test or Rosalic acid test✔️
Clot on boiling test
Alcohol precipitation test
Gerber test

Correct Answer Logic:

Alizarin changes color depending on milk $\text{pH}$: yellow in acidic milk and pink/red in alkaline milk. The Rosalic acid test similarly detects added alkalis ($\text{NaHCO}_3$, $\text{Na}_2\text{CO}_3$, $\text{NaOH}$) used by adulterators to neutralize sour milk. Normal milk gives a yellow-brown color.

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General Abilities QUESTION #7974

Question 4

5448 rounded off to the nearest 1000 is:

6000
5400
5000✔️
4500

Correct Answer Logic:

Since the hundreds digit is 4 (i.e., 448 < 500), we round down: $5448 \approx 5000$.

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Chemistry QUESTION #7497

Question 5

In which of the following processes is the change in oxidation state equal to five?

$\text{C}_2\text{O}_4^{2-} \to 2\text{CO}_2$
$\text{MnO}_4^- \to \text{Mn}^{2+}$✔️
$\text{Cr}_2\text{O}_7^{2-} \to 2\text{Cr}^{3+}$
$\text{CrO}_4^{2-} \to \text{Cr}^{3+}$

Correct Answer Logic:

Calculate the change in oxidation state for each:

(A) C in C$_2$O$_4^{2-}$: $+3$; C in CO$_2$: $+4$. Change $= +1$ per C atom (2 C, so total = 2, but per atom = 1).
(B) Mn in MnO$_4^-$: $+7$; Mn in Mn$^{2+}$: $+2$. Change $= 7 - 2 = \mathbf{5}$ ✓
(C) Cr in Cr$_2$O$_7^{2-}$: $+6$; Cr in Cr$^{3+}$: $+3$. Change $= 3$ per Cr atom.
(D) Cr in CrO$_4^{2-}$: $+6$; Cr in Cr$^{3+}$: $+3$. Change $= 3$.

The change of 5 occurs in the conversion $\text{MnO}_4^- \to \text{Mn}^{2+}$.

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Physics QUESTION #416

Question 6

If inductance is denoted by L and resistance by R

which of the following is true for a choke?✔️
R is large, L is very small
R is very small, L is large
Both R and L are large

Correct Answer Logic:

1

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MCQs Section QUESTION #4890

Question 7

Which word is opposite to "CONSCIENTIOUS"

Uncorrupt
Honourable
Principled
Profligate✔️

Correct Answer Logic:

Conscientious means wishing to do one's work thoroughly and carefully. Its antonym is Profligate, meaning recklessly wasteful and utterly lacking in moral principles.

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General Knowledge QUESTION #2637

Question 8

The EXTERNAL DATA BUS (EDB) in a computer is best described as:

A type of USB cable used to connect external drives to the computer
A row of wires that interconnect the parts of the computer internally✔️
A software interface that manages communication between the operating system and hardware
The physical slot on the motherboard where expansion cards are inserted

Correct Answer Logic:

The External Data Bus (EDB) is a row of wires that interconnect the parts of our computer. It acts as the pathway through which data travels between the CPU, RAM, and other components. Think of it as the roads or highways through which data travels inside the computer.

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Reading and Writing (Module-1) QUESTION #5317

Question 9

Researchers observed that the bioluminescent glow of certain deep-sea jellyfish is not continuous but rather ______, occurring only when the organism is disturbed by a potential predator. Which choice completes the text with the most logical and precise word?

intermittent✔️
persistent
intense
ubiquitous

Correct Answer Logic:

Since the glow occurs 'only when disturbed,' it is not constant, thus it is 'intermittent.'

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General Knowledge QUESTION #4752

Question 10

Former US Vice-President Al Gore was awarded the Nobel Peace Prize in 2007 for his campaign against which issue?

Child Labour
Human Rights Violations
Global Warming and Climate Change✔️
Nuclear Proliferation

Correct Answer Logic:

Al Gore, along with the Intergovernmental Panel on Climate Change (IPCC), won the 2007 Nobel Peace Prize for their work to raise global awareness of climate change and global warming.

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General Knowledge QUESTION #2599

Question 11

A PDA (Personal Digital Assistant) made a significant contribution to computing history primarily by:

Introducing the first graphical user interface
Allowing computing to go mobile for the first time✔️
Developing the first internet browser
Creating the first spreadsheet application

Correct Answer Logic:

A PDA (Personal Digital Assistant) allows computing to go mobile. It was a handheld device combining computing, communication, and organizational tools — a key step toward today's smartphones and tablets.

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Chemistry QUESTION #7386

Question 12

Which series of spectral lines of the hydrogen atom falls in the visible region?

Lyman series
Balmer series✔️
Paschen series
Brackett series

Correct Answer Logic:

Hydrogen spectral series and their regions:

Lyman ($n\to1$): UV region
Balmer ($n\to2$): Visible region (400–700 nm)
Paschen ($n\to3$): Near IR
Brackett ($n\to4$): IR
Pfund ($n\to5$): Far IR

The Balmer series (H$\alpha$ at 656 nm red, H$\beta$ at 486 nm blue, etc.) was the first discovered because it falls in the visible range.

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Electrical Engineering QUESTION #2191

Question 13

Using Gauss's law, an infinite line charge with $\rho_L = 20\,\text{nC/m}$ in free space produces an electric field at $r = 5\,\text{cm}$ of:

$7{,}193\,\text{V/m}$✔️
$3{,}597\,\text{V/m}$
$14{,}386\,\text{V/m}$
$1{,}798\,\text{V/m}$

Correct Answer Logic:

$E = \frac{\rho_L}{2\pi\epsilon_0 r} = \frac{20\times10^{-9}}{2\pi\times8.854\times10^{-12}\times0.05} = \frac{20\times10^{-9}}{2.781\times10^{-12}} \approx 7{,}193\,\text{V/m}$.

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Biology QUESTION #7279

Question 14

Which one of the following is commonly used to transfer foreign DNA into crop plants?

Penicillium expansum
Trichoderma harzianum
Meloidogyme incognita
Agrobacterium tumefaciens✔️

Correct Answer Logic:

Agrobacterium tumefaciens is a soil bacterium used extensively as a natural genetic engineer in plant transformation. Its Ti (tumour-inducing) plasmid can be modified to carry a gene of interest and insert it stably into the plant genome. It is the most widely used vector for introducing foreign genes into dicot crop plants.

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Chemistry QUESTION #472

Question 15

Na may be denoted by __________ electron configuration notation

1s?2s?
[Ar] 4s?
[Ne] 3s?✔️
None of these

Correct Answer Logic:

Sodium: [Ne] 3s?

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Civil Procedure QUESTION #3757

Question 16

What is the 'Rule Against Perpetuities' (RAP) designed to prevent?

Landlords charging too much rent.
Property interests from vesting too far into the future (dead hand control).✔️
Neighbors from building fences too high.
The government from taking land without compensation.

Correct Answer Logic:

RAP invalidates any interest in property that might not vest within 21 years of a 'life in being' at the time of the creation of the interest.

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Home Economics QUESTION #6253

Question 17

According to Jean Piaget, the stage where children begin to think logically about concrete events is:

Sensorimotor
Preoperational
Concrete Operational✔️
Formal Operational

Correct Answer Logic:

The Concrete Operational stage typically occurs between ages 7 and 11.

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Boilers Mechanical Engineering QUESTION #2448

Question 18

The centrifugal force $F_0$ generated by an unbalanced rotating mass $m_0$ at eccentricity $r$ rotating at speed $p$ (rad/s) is:

$F_0 = m_0 r p$
$F_0 = m_0 r p^2$✔️
$F_0 = m_0 r^2 p$
$F_0 = m_0 g r$

Correct Answer Logic:

The centrifugal force from an unbalanced rotating mass: $F_0=m_0 r p^2$, where $m_0$ is the unbalance mass, $r$ is the eccentricity, and $p$ is the angular speed.

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Boilers Mechanical Engineering QUESTION #2525

Question 19

Conservation of linear momentum applies to a system of particles when:

Kinetic energy is conserved
The net external force on the system is zero: $\sum\mathbf{F}_{ext}=0$✔️
All particles move with the same velocity
The system has no angular momentum

Correct Answer Logic:

Linear momentum of a system $\mathbf{G}=\sum m_i\mathbf{v}_i$ satisfies $\frac{d\mathbf{G}}{dt}=\sum\mathbf{F}_{ext}$. When $\sum\mathbf{F}_{ext}=0$, $\mathbf{G}$ is conserved.

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General Abilities QUESTION #2845

Question 20

Two trains start at the same time from cities A and B, 300 km apart, moving towards each other. Train A moves at 80 km/h and Train B at 70 km/h. In how many hours will they meet?

2 hours✔️
2.5 hours
3 hours
3.5 hours

Correct Answer Logic:

Relative speed (moving towards each other) $= 80 + 70 = 150$ km/h. Time $= \dfrac{300}{150} = 2$ hours.

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