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Mathematics QUESTION #7479

Let $\vec{a} = 2\hat{i} + \lambda_1\hat{j} + 3\hat{k}$, $\vec{b} = 4\hat{i} + (3-\lambda_2)\hat{j} + 6\hat{k}$ and $\vec{c} = 3\hat{i} + 6\hat{j} + (\lambda_3-1)\hat{k}$ be three vectors such that $\vec{b} = 2\vec{a}$ and $\vec{a}$ is perpendicular to $\vec{c}$. Then a possible value of $(\lambda_1, \lambda_2, \lambda_3)$ is:

(1, 3, 1)
$(-\frac{1}{2}, 4, 0)$✔️
$(\frac{1}{2}, 4, -2)$
(1, 5, 1)

Correct Answer Logic:

From $\vec{b} = 2\vec{a}$: $4\hat{i}+(3-\lambda_2)\hat{j}+6\hat{k} = 4\hat{i}+2\lambda_1\hat{j}+6\hat{k}$. Comparing: $3-\lambda_2 = 2\lambda_1$, so $\lambda_2 = 3-2\lambda_1$. From $\vec{a} \perp \vec{c}$: $2(3) + \lambda_1(6) + 3(\lambda_3-1) = 0$, giving $6+6\lambda_1+3\lambda_3-3 = 0$, so $6\lambda_1+3\lambda_3 = -3$, thus $2\lambda_1+\lambda_3 = -1$. Testing option B: $\lambda_1 = -\frac{1}{2}$, $\lambda_2 = 4$, $\lambda_3 = 0$. Check: $\lambda_2 = 3-2(-\frac{1}{2}) = 3+1 = 4$ ✓. And $2(-\frac{1}{2})+0 = -1$ ✓.

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Civil Procedure QUESTION #3736

Question 4722

In a criminal trial for assault, the prosecution wants to introduce evidence that the defendant has a reputation in the community for being a 'violent bully.' The defendant has not yet testified or introduced any evidence of his own character. Is this evidence admissible?

Yes, to show that the defendant likely committed the assault.
No, because the prosecution cannot introduce negative character evidence to show propensity until the defendant 'opens the door.'✔️
Yes, but only as 'habit' evidence.
No, unless it is a bench trial.

Correct Answer Logic:

Under Federal Rule of Evidence 404(a), character evidence is generally inadmissible to prove that on a particular occasion the person acted in accordance with the character (propensity), unless the defendant first introduces evidence of their own good character.

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Math Physics Chemistry Biology QUESTION #7742

Question 4723

What happens to calcium ions when a skeletal muscle recovers (relaxes) after contraction?

Released from SR
Released from myosin head
Pumped into SR✔️
Exchanged for sodium

Correct Answer Logic:

During relaxation, Ca²⁺ is actively pumped back into the sarcoplasmic reticulum (SR) via Ca²⁺-ATPase (SERCA), lowering cytosolic Ca²⁺ and allowing tropomyosin to block myosin-binding sites.

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Professional QUESTION #1832

Question 4724

Section 10 of the Civil Servants Act 1973 governs posting and transfer. Where a civil servant is required to serve in a post OUTSIDE his service or cadre, what protection is guaranteed regarding his pay?

His pay shall be enhanced by a special allowance
His pay shall be fixed at the scale of the new post
His terms and conditions as to pay shall not be less favourable than those he would have been entitled to had he not been required to serve outside his cadre✔️
His pay shall be determined by the authority ordering the transfer

Correct Answer Logic:

The second proviso to Section 10 protects the financial interests of a civil servant posted outside his service or cadre by ensuring his terms and conditions as to pay shall not be less favourable than those to which he would have been entitled had he not been required to serve outside his cadre.

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Civil Engineering QUESTION #6644

Question 4725

What does a 'Plastic Hinge' in a reinforced concrete frame represent?

A point of zero moment
A zone where the reinforcement has yielded and large rotations occur at nearly constant moment✔️
A structural defect that must be avoided at all costs
A joint where concrete has completely crushed

Correct Answer Logic:

Plastic hinges allow for moment redistribution in indeterminate structures by allowing sections to rotate significantly after reaching their yield capacity.

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Chemistry QUESTION #4353

Question 4726

Which one of the following is a coinage metal?

Pd
Cu✔️
Cd
Hg

Correct Answer Logic:

Coinage metals are $Cu$ (copper), $Ag$ (silver), and $Au$ (gold) — Group 11 elements. They are called coinage metals because they have historically been used to make coins.

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Education QUESTION #7600

Question 4727

What is used to enhance cognitive functioning among learners?

Motivation✔️
Feedback
Reinforcement
None of these

Correct Answer Logic:

Motivation energizes, directs, and sustains learning behavior, playing a crucial role in activating cognitive processes such as attention, memory, and problem-solving.

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General Knowledge QUESTION #8903

Question 4728

A computer mainly consists of electronic:

Connections
Devices
Circuits✔️
Chips

Correct Answer Logic:

Computers are made of electronic circuits.

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English QUESTION #8560

Question 4729

What does the idiom 'had a cow' mean in: 'When I told my mom I would come home at 1 am, she had a cow'

My mom bought a baby cow
My mom was not happy
My mom was really upset✔️
none of these

Correct Answer Logic:

'Have a cow' means to become very angry or upset.

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Planning QUESTION #4980

Question 4730

In Le Corbusier's Radiant City concept, what was the recommended minimum distance between high-rise buildings?

Equal to building height
Twice the building height
Three times the building height✔️
Five times the building height

Correct Answer Logic:

Le Corbusier's 'towers in the park' concept recommended spacing high-rises at three times their height to ensure adequate sunlight, air circulation, and open space between buildings while achieving high densities through vertical development.

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General Knowledge QUESTION #8818

Question 4731

Nelson Mandela, the anti-apartheid revolutionary, belonged to which country?

Kenya
Somalia
South Africa✔️
Uganda

Correct Answer Logic:

Mandela was South African.

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CISA QUESTION #1738

Question 4732

What is the primary justification for securing and protecting audit documentation and working papers throughout and after an engagement?

Audit evidence must be made publicly available to satisfy regulatory disclosure obligations.
A documented paper trail is required to substantiate that the auditor's conclusions are correct and the auditee was wrong.
The auditor may need to prove illegal activity in a judicial proceeding.
Audit working papers often contain highly confidential information that must be protected from unauthorised disclosure or loss, and must be safeguarded through appropriate security and backup controls.✔️

Correct Answer Logic:

Audit documentation inevitably contains sensitive and confidential information about the client's systems, processes, vulnerabilities, and personnel. Disclosure of this material could cause serious harm — including enabling further attacks or exploitation. The auditor is professionally and ethically obligated to implement appropriate controls to protect the confidentiality, integrity, and availability of all audit documentation, including maintaining secure backups.

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Civil Engineering QUESTION #6630

Question 4733

The 'effective flange width' of a T-beam is limited primarily to account for:

Shear lag effects✔️
Concrete shrinkage
Torsional stiffness
The weight of the slab

Correct Answer Logic:

The flange of a T-beam does not experience uniform stress across its entire width due to shear lag; hence, an 'effective' width is used for design calculations.

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General Knowledge QUESTION #8969

Question 4734

The Earth is closest to the Sun (perihelion) in which month?

January✔️
June
July
September

Correct Answer Logic:

Perihelion occurs in early January.

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Boilers Mechanical Engineering QUESTION #4068

Question 4735

'Telltale Holes' are sometimes drilled into stay-bolts to:

Look inside the boiler
Leak steam/water if the bolt cracks inside, alerting the operator✔️
Let air out
Light the fire

Correct Answer Logic:

It is a simple visual warning system for structural failure.

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Math Physics Chemistry Biology QUESTION #7782

Question 4736

Which function is NOT controlled by the autonomic nervous system?

Cardiac muscle contraction
Salivation
Smooth muscle contraction
Thoughts and emotions✔️

Correct Answer Logic:

Autonomic (sympathetic/parasympathetic) controls involuntary functions: heart rate, digestion, salivation, smooth muscle. Thoughts and emotions are controlled by the central nervous system (cerebrum/limbic system).

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Contracts QUESTION #5859

Question 4737

A Seller breaches a contract for the sale of common office chairs. The Buyer buys substitute chairs elsewhere for $200 more. What is this remedy called?

Specific Performance.
Cover.✔️
Incidental Damages.
Liquidated Damages.

Correct Answer Logic:

Under UCC §2-712, 'Cover' allows the buyer to purchase substitute goods and recover the difference between the cover price and the contract price.

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Chemistry QUESTION #7526

Question 4738

For the reaction $2\text{C}_{57}\text{H}_{110}\text{O}_6(s) + 163\ \text{O}_2(g) \to 114\ \text{CO}_2(g) + 110\ \text{H}_2\text{O}(l)$, find the mass of water produced from 445 g of C$_{57}$H$_{110}$O$_6$.

490 g
445 g
495 g✔️
890 g

Correct Answer Logic:

Molar mass of C$_{57}$H$_{110}$O$_6$: $57(12)+110(1)+6(16)=684+110+96=890\ \text{g mol}^{-1}$

Moles of C$_{57}$H$_{110}$O$_6 = \dfrac{445}{890} = 0.5\ \text{mol}$

From stoichiometry: 2 mol fat → 110 mol H$_2$O

So 0.5 mol fat → $\dfrac{110 \times 0.5}{2} = 27.5\ \text{mol H}_2\text{O}$

Mass of H$_2$O $= 27.5 \times 18 = \mathbf{495\ \text{g}}$

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General Knowledge QUESTION #8645

Question 4739

Which component of blood is responsible for the safety mechanism (clotting)?

White Blood Cells
Red Blood Cells
Lymphatic system
Blood platelets✔️

Correct Answer Logic:

Platelets are responsible for blood clotting.

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Physics QUESTION #1039

Question 4740

Two cities X and Y connected by buses every T min. A girl on scooter at 60 km/h sees buses every 30 min in her direction and every 10 min opposite. Period T and bus speed:

10 min, 90 km/h
15 min, 120 km/h✔️
9 min, 40 km/h
25 min, 100 km/h

Correct Answer Logic:

Let bus speed $=v$, period $=T$. Relative speed with girl (same direction): $v-60$. Buses come every 30 min: $\frac{vT}{v-60}=30$. Opposite direction: $\frac{vT}{v+60}=10$. Dividing: $\frac{v+60}{v-60}=3\Rightarrow v+60=3v-180\Rightarrow v=120\ \text{km/h}$. Then $T=\frac{10(120+60)}{120}=15\ \text{min}$.

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