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Mechanical Engineering QUESTION #2475

The Grübler–Dobrovolski formula for the mobility (DOF) $M$ of a general spatial mechanism of family $f$ with $n$ movable links and kinematic pairs of class $j$ is:

$M = 3n - 2c_5 - c_4$
$M = 6n - \sum_{j=f+1}^{5}(j-f)c_j$
$M = (6-f)n - \sum_{j=f+1}^{5}(j-f)c_j$✔️
$M = 6n - 5c_5 - 4c_4$

Correct Answer Logic:

The Dobrovolski formula is $M=(6-f)n-\sum_{j=f+1}^{5}(j-f)c_j$, where $f$ is the family number, $n$ is the number of movable links, and $c_j$ is the number of kinematic pairs of class $j$. For planar mechanisms $f=3$, this reduces to $M=3n-2c_5-c_4$.

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Biology QUESTION #4178

Question 2

Polysaccharides such as starch and glycogen are mainly used for:

Structural framework only
Short-term and long-term energy storage✔️
Enzyme catalysis
Ready source of energy

Correct Answer Logic:

Starch and glycogen serve as energy storage molecules (polysaccharides).

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Reading and Writing (Module-1) QUESTION #5396

Question 3

The following text is adapted from Susan Glaspell's 1912 short story "'Out There.'" An elderly shop owner is looking at a picture that he recently acquired and hopes to sell. It did seem that the picture failed to fit in with the rest of the shop. A persuasive young fellow who claimed he was closing out his stock let the old man have it for what he called a song. It was only a little out-of-the-way store which subsisted chiefly on the framing of pictures. The old man looked around at his views of the city, his pictures of cats and dogs, his flaming bits of landscape. "Don't belong in here," he fumed. And yet the old man was secretly proud of his acquisition. There was a hidden dignity in his scowling as he shuffled about pondering the least ridiculous place for the picture. Which choice best states the main purpose of the text?

To reveal the shop owner's conflicted feelings about the new picture✔️
To convey the shop owner's resentment of the person he got the new picture from
To describe the items that the shop owner most highly prizes
To explain differences between the new picture and other pictures in the shop

Correct Answer Logic:

The text shows the shop owner both frustrated ("Don't belong in here") and proud of the new picture, revealing his conflicted feelings.

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Physics QUESTION #1029

Question 4

In an oscillating spring-mass system, sand leaks slowly out of the box vertically as it oscillates. Which schematic correctly shows changes in average frequency $\omega(t)$ and average amplitude $A(t)$ with time?

Frequency increases (curve up), amplitude increases (curve up)✔️
Frequency decreases (curve down), amplitude decreases (curve down)
Frequency increases (curve up), amplitude stays constant (flat)
Frequency increases (curve up), amplitude decreases (curve down)

Correct Answer Logic:

As sand leaks out, mass decreases. $\omega = \sqrt{k/m}$: as $m$ decreases, $\omega$ increases. Amplitude: since sand leaks vertically (no horizontal impulse), energy is not added but mass decreases — the amplitude increases as $A = v_{max}/\omega$ and the system conserves momentum. Frequency increases and amplitude increases gradually.

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General Science and Ability QUESTION #200

Question 5

Which of the following is the common language for Artificial Intelligence?

Java
Python
Lisp✔️
None of these

Correct Answer Logic:

Lisp is one of the oldest and most influential languages for AI development.

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Chemistry QUESTION #1011

Question 6

Match List-I (Partial Derivatives) with List-II (Thermodynamic Quantities): (A) $\left(\dfrac{\partial G}{\partial T}\right)_P$ (B) $\left(\dfrac{\partial H}{\partial T}\right)_P$ (C) $\left(\dfrac{\partial G}{\partial P}\right)_T$ (D) $\left(\dfrac{\partial U}{\partial T}\right)_V$ with (I) $C_P$ (II) $-S$ (III) $C_V$ (IV) $V$

(A)-(II), (B)-(I), (C)-(III), (D)-(IV)
(A)-(I), (B)-(II), (C)-(IV), (D)-(III)
(A)-(II), (B)-(I), (C)-(IV), (D)-(III)✔️
(A)-(II), (B)-(III), (C)-(I), (D)-(IV)

Correct Answer Logic:

Using thermodynamic relations: $\left(\frac{\partial G}{\partial T}\right)_P = -S$ (II). $\left(\frac{\partial H}{\partial T}\right)_P = C_P$ (I). $\left(\frac{\partial G}{\partial P}\right)_T = V$ (IV). $\left(\frac{\partial U}{\partial T}\right)_V = C_V$ (III). Matching: A-II, B-I, C-IV, D-III.

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Mathematics QUESTION #4118

Question 7

Which IS a valid basis for the subspace of symmetric $2 \times 2$ matrices?

$\left\{\begin{pmatrix} 1 & 0 \ 0 & 0 \end{pmatrix}, \begin{pmatrix} 0 & 0 \ 0 & 1 \end{pmatrix}\right\}$
$\left\{\begin{pmatrix} 1 & 1 \ 1 & 0 \end{pmatrix}, \begin{pmatrix} 0 & 1 \ 1 & 1 \end{pmatrix}, \begin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix}\right\}$
$\left\{\begin{pmatrix} 1 & 0 \ 0 & 0 \end{pmatrix}, \begin{pmatrix} 0 & 1 \ 1 & 0 \end{pmatrix}, \begin{pmatrix} 0 & 0 \ 0 & 1 \end{pmatrix}\right\}$✔️
$\left\{\begin{pmatrix} 1 & 1 \ 0 & 0 \end{pmatrix}, \begin{pmatrix} 0 & 0 \ 1 & 1 \end{pmatrix}, \begin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix}\right\}$

Correct Answer Logic:

Option C gives standard basis for symmetric matrices. Option A has only 2 matrices (dimension 3 needed). Option B matrices are linearly dependent. Option D contains non-symmetric matrices.

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GATE General Aptitude QUESTION #3766

Question 8

Four landmarks H1, H2, H3, and H4 are located in a park. 1) H2 and H3 are not the easternmost. 2) H2 and H3 are not the westernmost. 3) The easternmost and westernmost are not the southernmost. 4) Two landmarks are west of H2. 5) The southernmost has at least two landmarks to its east. Which landmark is the southernmost?

H1✔️
H2
H3
H4

Correct Answer Logic:

Based on logical deduction of positions, H1 is the only landmark satisfying the condition of being the southernmost with at least two hills to its east.

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Commerce QUESTION #1198

Question 9

Which financial statement in a sole proprietorship reflects the owner's withdrawals for personal use?

Income Statement
Statement of Financial Position
Statement of Cash Flows
Statement of Owner's Equity✔️

Correct Answer Logic:

The Statement of Owner's Equity (also called the Capital Statement) shows changes in the owner's capital account during the period. It reflects the opening capital, plus net income, minus owner's drawings (personal withdrawals). Drawings reduce the owner's equity and are not shown in the Income Statement.

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Economics QUESTION #1704

Question 10

Pakistan's chronically low tax-to-GDP ratio — among the lowest in South Asia — is attributable to which combination of structural and institutional factors?

Disproportionate reliance on regressive indirect taxes
Agricultural sector exemptions and exclusion of large informal income from the tax net
Weak documentation of the tax base and inadequate enforcement capacity
All of these✔️

Correct Answer Logic:

Pakistan's tax-to-GDP ratio (historically around 9–11%) is explained by a confluence of factors: (1) heavy reliance on indirect taxes (sales tax, customs duties) rather than broad-based direct taxes; (2) constitutional and political exemptions for agriculture, despite its large economic size; (3) a large undocumented informal economy estimated at 35–40% of GDP; and (4) weak FBR enforcement, narrow withholding tax net, and rampant tax evasion by powerful sectors.

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Physics QUESTION #1027

Question 11

The current passing through the battery in the given circuit (5V source with complex resistor network including $1.5\Omega, 5\Omega, 2.5\Omega, 5.5\Omega, 6\Omega, 3\Omega, 1.5\Omega, \frac{1}{3}\Omega$):

2.5 A
1.5 A
2.0 A✔️
0.5 A

Correct Answer Logic:

Analysing the circuit by combining resistors: the network simplifies to a total resistance of $2.5\ \Omega$ across the 5V battery. Current $= \frac{5}{2.5} = 2.0\ \text{A}$.

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Reading and Writing (Module-1) QUESTION #5341

Question 12

Many people enjoy drinking tea for its caffeine content. ______, others prefer it for the calming ritual of its preparation. Which choice completes the text with a transition that most logically connects the ideas?

Similarly,
However,✔️
Therefore,
In fact,

Correct Answer Logic:

'However' connects the two different reasons people enjoy tea.

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Paper-II (Pharmacognosy and Pharmaceutics-I) QUESTION #3653

Question 13

Which of the following is a 'Purgative' drug?

Ginger
Senna✔️
Cinnamon
Clove

Correct Answer Logic:

Senna contains anthraquinones that stimulate bowel movement.

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General Science and Ability QUESTION #254

Question 14

The pH of soil is raised using:

Lime stone✔️
Gypsum
Urea
None of these

Correct Answer Logic:

Limestone (calcium carbonate) is alkaline and is used to neutralize acidic soil.

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Pakistan Affairs QUESTION #608

Question 15

Whose behaviour disheartened M.A. Jinnah, leading him to decide to stay away from India?

M.K Gandhi
Jawahar Lal Nehru
Sardar Patel
None of these✔️

Correct Answer Logic:

Jinnah was disillusioned by the overall political atmosphere, specifically after the 1928 Nehru Report and the Lucknow Pact's failure .

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Others section QUESTION #4783

Question 16

Which Nobel Prize category was the last to be established, added in 1968?

Medicine
Literature
Economics✔️
Peace

Correct Answer Logic:

The Nobel Memorial Prize in Economic Sciences was established in 1968 by Sveriges Riksbank (Sweden's central bank) in memory of Alfred Nobel, making it the most recently added Nobel Prize category.

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Chemistry QUESTION #4354

Question 17

Consider the balanced chemical equation: $2H_2 + O_2 \rightarrow 2H_2O$. If $4\ g$ of $H_2$ reacts with $32\ g$ of $O_2$ to produce $28\ g$ of $H_2O$, what is the percentage yield of the reaction? (Molar mass of $H_2 = 2\ g/mol$, $O_2 = 32\ g/mol$, $H_2O = 18\ g/mol$)

63.6%
77.8%✔️
87.5%
92.5%

Correct Answer Logic:

Moles of $H_2 = \frac{4}{2} = 2\ mol$. Theoretical yield of $H_2O = 2 \times 18 = 36\ g$. $\% yield = \frac{28}{36} \times 100 = 77.8\%$.

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Pakistan Affairs QUESTION #296

Question 18

What marked Benazir Bhutto's tenure as Prime Minister from 1988 to 1990?

Economic growth
The first time a woman led a Muslim-majority country✔️
Political harmony
Constitutional development

Correct Answer Logic:

She made history as the first female Prime Minister in the Muslim world.+1

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Mechanical Engineering QUESTION #2418

Question 19

Newton's Law of Cooling for convection heat transfer gives the heat flux $q''_{conv}$ as:

$q''_{conv} = k(T_w - T_\infty)/L$
$q''_{conv} = h(T_w - T_\infty)$ where $h$ is the convection coefficient (W/m²·K)✔️
$q''_{conv} = \sigma\varepsilon T_w^4$
$q''_{conv} = \rho c_p (T_w - T_\infty)$

Correct Answer Logic:

Newton's Law of Cooling: $q''_{conv}=h(T_w-T_\infty)$, where $h$ (W/m²·K) is the convection heat transfer coefficient.

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Math (Module-1) QUESTION #5473

Question 20

Square $P$ has side length $x$ inches. Square $Q$ has a perimeter that is $176$ inches greater than the perimeter of square $P$. The function $f$ gives the area of square $Q$. Which defines $f$?

$f(x) = (x + 44)^2$✔️
$f(x) = (x + 176)^2$
$f(x) = (176x + 44)^2$
$f(x) = (176x + 176)^2$

Correct Answer Logic:

$Perimeter_P = 4x$. $Perimeter_Q = 4x + 176 = 4(x + 44)$. So $Side_Q = x + 44$. Area $f(x) = (x + 44)^2$.

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