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Mathematics QUESTION #7475

Let $\vec{u}$ be a vector coplanar with the vectors $\vec{a} = 2\hat{i} + 3\hat{j} - \hat{k}$ and $\vec{b} = \hat{j} + \hat{k}$. If $\vec{u}$ is perpendicular to $\vec{a}$ and $\vec{u} \cdot \vec{b} = 24$, then $|\vec{u}|^2$ is equal to:

256
84
336✔️
315

Correct Answer Logic:

Since $\vec{u}$ is coplanar with $\vec{a}$ and $\vec{b}$, we can write $\vec{u} = x\vec{a} + y\vec{b} = x(2\hat{i}+3\hat{j}-\hat{k}) + y(\hat{j}+\hat{k}) = 2x\hat{i} + (3x+y)\hat{j} + (-x+y)\hat{k}$. Condition $\vec{u} \perp \vec{a}$: $\vec{u} \cdot \vec{a} = 2x(2) + (3x+y)(3) + (-x+y)(-1) = 0$, giving $4x + 9x + 3y + x - y = 0$, so $14x + 2y = 0$, thus $y = -7x$. Condition $\vec{u} \cdot \vec{b} = 24$: $(3x+y)(1) + (-x+y)(1) = 24$, giving $3x+y-x+y = 24$, so $2x+2y = 24$, thus $x+y = 12$. From $y=-7x$: $x-7x = 12$, so $-6x=12$ and $x=-2$, giving $y=14$. Thus $\vec{u} = -4\hat{i} + 8\hat{j} + 16\hat{k}$, and $|\vec{u}|^2 = 16 + 64 + 256 = 336$.

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General Knowledge QUESTION #2593

Question 3162

In the decimal (base-10) number system, how many unique digit symbols are available for use?

8 digits (0 to 7)
9 digits (1 to 9)
10 digits (0 to 9)✔️
16 digits (0 to 9 and A to F)

Correct Answer Logic:

In the decimal system, there are 10 possible numbers you can use ranging from zero to nine (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). This is why it is called 'base-10' — it has a base of ten distinct symbols.

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Math Physics Chemistry Biology QUESTION #739

Question 3163

The range of visible wavelength spectrum is:

400-750 nm✔️
100-400 nm
400-1000 nm
300-600 nm

Correct Answer Logic:

The visible light spectrum ranges from approximately 400 nm (violet) to 750 nm (red).

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Urdu QUESTION #5249

Question 3164

'اس آباد خرابے میں' کس کی خود نوشت ہے؟

کلیم عاجز
اختر الایمان
عبدالمجید سالک✔️
اظہر وقار اظیم

Correct Answer Logic:

اس آباد خرابے میں عبدالمجید سالک کی خود نوشت سوانح عمری ہے۔

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3211

Question 3165

'Negative Feedback' mechanism is used by the body to:

Increase a stimulus continuously
Oppose a change and restore balance✔️
Store fat
Produce sound

Correct Answer Logic:

Most hormones are regulated by negative feedback to maintain homeostasis.

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Boilers Mechanical Engineering QUESTION #2444

Question 3166

The transmissibility (TR) in vibration isolation represents:

Output force at support divided by static force
The ratio of force transmitted to the foundation to the applied excitation force: $TR = \sqrt{\frac{1+(2\zeta r)^2}{(1-r^2)^2+(2\zeta r)^2}}$ where $r=p/\omega_n$✔️
The ratio of damped to undamped amplitude
The ratio of kinetic to potential energy

Correct Answer Logic:

Transmissibility: $TR=F_{transmitted}/F_0=\sqrt{\frac{1+(2\zeta r)^2}{(1-r^2)^2+(2\zeta r)^2}}$. For effective isolation, TR < 1 requires $r > \sqrt{2}$.

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Geography QUESTION #6345

Question 3167

The concept of 'time-space convergence' in economic geography refers to:

Increasing speed reducing effective distance between places✔️
Synchronization of time zones for global business
Historical convergence of development levels
Urban areas expanding into rural zones

Correct Answer Logic:

Time-space convergence describes how transport/communication improvements reduce travel time between places, making them functionally closer despite unchanged physical distance. A trip taking weeks in the 1800s now takes hours, facilitating globalization.

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Mathematics QUESTION #7477

Question 3168

Let $\vec{a} = \hat{i} - \hat{j}$, $\vec{b} = \hat{i} + \hat{j} + \hat{k}$ and $\vec{c}$ be a vector such that $\vec{a} \times \vec{c} + \vec{b} = \vec{0}$ and $\vec{a} \cdot \vec{c} = 4$, then $|\vec{c}|^2$ is equal to:

$\frac{19}{2}$✔️
9
8
$\frac{17}{2}$

Correct Answer Logic:

From $\vec{a} \times \vec{c} + \vec{b} = \vec{0}$, we get $\vec{a} \times \vec{c} = -\vec{b}$. Taking dot product with $\vec{a}$: $\vec{a} \cdot (\vec{a} \times \vec{c}) = -\vec{a} \cdot \vec{b}$. Since $\vec{a} \cdot (\vec{a} \times \vec{c}) = 0$, we have $\vec{a} \cdot \vec{b} = 0$, which checks: $(1)(-1)+(-1)(1)+(0)(1) = 0$. Nope: $\vec{a} = \hat{i}-\hat{j}$ (only 2D) and $\vec{b} = \hat{i}+\hat{j}+\hat{k}$, so $\vec{a} \cdot \vec{b} = 1-1 = 0$. Good. Taking magnitude: $|\vec{a} \times \vec{c}| = |\vec{b}| = \sqrt{3}$. Also $|\vec{a} \times \vec{c}|^2 = |\vec{a}|^2|\vec{c}|^2 - (\vec{a} \cdot \vec{c})^2$, so $3 = 2|\vec{c}|^2 - 16$, giving $|\vec{c}|^2 = \frac{19}{2}$.

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Boilers Mechanical Engineering QUESTION #3981

Question 3169

The 'Economizer' in a boiler system is used to heat:

The fuel before combustion
Feed water using flue gases✔️
The steam to make it superheated
The air entering the furnace

Correct Answer Logic:

Economizers improve efficiency by recovering waste heat from exhaust gases to pre-heat feed water.

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Reading and Writing (Module-1) QUESTION #5340

Question 3170

In 1953, James Watson and Francis Crick discovered the double-helix structure of DNA. This ______ changed the field of genetics forever. Which choice completes the text with the most logical and precise word?

breakthrough✔️
incident
mishap
rumor

Correct Answer Logic:

A major scientific discovery is best described as a 'breakthrough.'

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Pharmacology and Toxicology QUESTION #3853

Question 3171

Through which mechanism does allopurinol lower serum uric acid levels?

To increase renal excretion of uric acid
To inhibit formation of uric acid✔️
To inhibit absorption of dietary purines
To inhibit prostaglandin synthesis

Correct Answer Logic:

Allopurinol inhibits xanthine oxidase, thereby reducing the enzymatic conversion of hypoxanthine and xanthine to uric acid.

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Ability / HR / Governance / Special Education QUESTION #1903

Question 3172

Under Rule 3(d) retention in service of a government servant engaged in subversive activities must be what for action to be taken?

Contrary to departmental policy
Prejudicial to national security✔️
Against the wishes of the Prime Minister
Contrary to NAB guidelines

Correct Answer Logic:

Rule 3(d) specifically requires that the government servant's retention in service must be prejudicial to national security as the additional condition for action on grounds of subversive activities or disclosure of official secrets.

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Math Physics Chemistry Biology QUESTION #4199

Question 3173

Which of the following best describes the relationship between endoplasmic reticulum (ER) and Golgi apparatus?

Both ER and Golgi apparatus are completely separate organelles with no interaction
ER is precursor organelle to Golgi apparatus because material is transported from ER to Golgi✔️
Golgi apparatus is precursor organelle to ER because material is transported from Golgi to ER
ER and Golgi apparatus have similar roles

Correct Answer Logic:

ER synthesizes proteins/lipids that are transported to Golgi apparatus for processing and packaging.

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The Elections Act 2017 QUESTION #9469

Question 3174

Section 48A(2), inserted by the Elections (Second Amendment) Act 2017, deals with the status of Ahmadis on electoral rolls. If an objection is filed that a voter is not a Muslim, the Revising Authority issues a notice requiring the voter to appear within how many days and sign a specified declaration of belief in the finality of Prophethood?

Seven days
Thirty days
Fifteen days✔️
Twenty-one days

Correct Answer Logic:

Section 48A(2) states: 'the Revising Authority shall issue a notice to him to appear before it within fifteen days and require him to sign a declaration... regarding his belief about the absolute and unqualified finality of the Prophethood of Muhammad (peace be upon him).'

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Physics QUESTION #402

Question 3175

A wire has resistance 100 Ohm at 0?C and 200 Ohm at 100?C. What is its temperature coefficient in K???

?0.01
?1/273
0.01
1/273✔️

Correct Answer Logic:

? = (R??R?)/(R??T) = 100/(100?100) = 0.01 K??, but answer key shows D

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Mathematics QUESTION #4165

Question 3176

Using Green's theorem, $\oint_C \vec{F} \cdot d\vec{r} = \iint_R \left(\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y}\right) dA$ where $\vec{F} = [\frac{1}{2}xy^4, \frac{1}{2}x^4y]$. For the rectangle $[0,3] \times [0,2]$, what is the value?

$6$
$12$
$18$✔️
$36$

Correct Answer Logic:

$\frac{\partial Q}{\partial x} = 2x^3y$, $\frac{\partial P}{\partial y} = 2xy^3$. So $\iint_R (2x^3y - 2xy^3) dA = \int_0^3\int_0^2 (2x^3y - 2xy^3) dy dx = 18$.

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Paper-II (Pharmacognosy and Pharmaceutics-I) QUESTION #2976

Question 3177

The 'Ebers Papyrus' is an ancient document related to the pharmacy of which civilization?

Greek
Roman
Egyptian✔️
Chinese

Correct Answer Logic:

The Ebers Papyrus (1550 BC) is one of the most important pharmaceutical records of Ancient Egypt.

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General Knowledge QUESTION #8828

Question 3178

The constellation 'Southern Cross' (Crux) consists of how many main stars?

Seven Stars
Four Stars✔️
Five Stars
None of these

Correct Answer Logic:

The Southern Cross has four main stars.

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Reading and Writing (Module-1) QUESTION #5418

Question 3179

Samuel Coleridge-Taylor was a prominent classical music composer from England who toured the US three times in the early 1900s. The child of a West African father and an English mother, Coleridge-Taylor emphasized his mixed-race ancestry. For example, he referred to himself as Anglo-African. _______ he incorporated the sounds of traditional African music into his classical music compositions. Which choice completes the text with the most logical transition?

In addition,✔️
Actually,
However,
Regardless,

Correct Answer Logic:

'In addition' signals that incorporating African music is a second example of how Coleridge-Taylor emphasized his mixed-race ancestry.

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Physics QUESTION #7321

Question 3180

The velocity of a particle is given by $v = At + Bt^2$, where $A$ and $B$ are constants. The distance travelled between $t = 1\text{ s}$ and $t = 2\text{ s}$ is:

$\dfrac{3}{2}A + 4B$
$3A + 7B$
$\dfrac{3}{2}A + \dfrac{7}{3}B$✔️
$\dfrac{A}{2} + \dfrac{B}{3}$

Correct Answer Logic:

$x = \displaystyle\int_1^2 v\,dt = \int_1^2 (At + Bt^2)\,dt = \left[\dfrac{At^2}{2} + \dfrac{Bt^3}{3}\right]_1^2$

$= \left(\dfrac{4A}{2} + \dfrac{8B}{3}\right) - \left(\dfrac{A}{2} + \dfrac{B}{3}\right) = \mathbf{\dfrac{3A}{2} + \dfrac{7B}{3}}$

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