The expression $\dfrac{x+y+z}{3}$ is the arithmetic mean (average) of $x$, $y$, and $z$.

Since $x < y < z$, the mean lies strictly between the smallest and largest values. However, we cannot determine whether the mean is greater than, equal to, or less than $y$ (the middle value) without knowing the exact values.

Example 1: $x=1, y=2, z=3$. Mean $= 2 = y$. Equal.

Example 2: $x=1, y=2, z=10$. Mean $= 4.33 > y$. Quantity A greater.

Example 3: $x=1, y=9, z=10$. Mean $= 6.67 < y$. Quantity B greater.

Since different cases give different results, the relationship cannot be determined from the given information.

Walter Cannon described emergency reactions (fight-or-flight) as coordinated physiological changes — increased heart rate, adrenaline release, blood redistribution — accompanying strong emotions of anger and fear to prepare for vigorous action.

\(\dfrac{5 \times 7}{14 \times 10} = \dfrac{35}{140} = \dfrac{1}{4}\). Both B and C are equivalent; the simplified form is \(\dfrac{1}{4}\).

Lovastatin lowers cholesterol

Under Rule 49(b)(3), if the answers are consistent with each other but one or more is inconsistent with the general verdict, the court may enter judgment according to the answers, notwithstanding the general verdict, or take other specified actions.

Timur invaded India in 1398 AD (14th century).

SAARC's secretariat is in Kathmandu, Nepal.

The curriculum specifically covers all major hotel ownership structures: Sole Proprietorship, Partnership, Management Contract, Joint Venture, Franchisee, Public Sector, Private Sector, and Referral Groups/Consortiums — including their features, advantages and disadvantages.

At equilibrium, the horizontal component of the tension $T \sin(45^\circ)$ equals the applied force $F$, and the vertical component $T \cos(45^\circ)$ equals the weight $mg$. Dividing the two equations gives $F = mg \tan(45^\circ)$. Since $\tan(45^\circ) = 1$ and $mg = 10 \times 10 = 100$, the force $F = 100\text{ N}$.

It occurs when blood flow to a part of the heart is blocked.

No explanation provided for this question.

Water is incompressible; if the vessel ruptures during a hydrotest, there is no 'blast' like there would be with air/steam.

When multiplying same base, add exponents: $x^3 \times x^2 = x^{3+2} = x^5$

The half-reaction for oxalate is: $C_{2}O_{4}^{2-} \rightarrow 2CO_{2} + 2e^{-}$. In this process, 2 electrons are released for every two molecules of $CO_{2}$ produced. Therefore, for one molecule of $CO_{2}$, the number of electrons involved is $2/2 = 1$.

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 \(|\vec{c}|^2 = \frac{19}{2}\).

Check each species for disproportionation (simultaneous oxidation and reduction):

• $\text{ClO}_4^-$ (Cl = +7, highest state): cannot disproportionate.
• $\text{MnO}_4^-$ (Mn = +7, highest): cannot disproportionate.
• $\text{F}_2$ (F = 0, but F has no positive oxidation state): cannot (F is the most electronegative).
• $\text{Cr}_2\text{O}_7^{2-}$ (Cr = +6, highest for common chromium): cannot.
• $\text{ClO}_2^-$ (Cl = +3): can disproportionate to ClO$_3^-$ and Cl$^-$ ✓
• $\text{Cl}_2$ (Cl = 0): $\text{Cl}_2 + 2\text{OH}^- \to \text{Cl}^- + \text{ClO}^-$ ✓
• $\text{Mn}^{3+}$ (Mn = +3): can go to Mn$^{2+}$ and MnO$_2$ ✓

Only option C ($\text{MnO}_4^-$... wait) — re-checking: $\text{MnO}_4^-$ is +7 (cannot). Option C contains $\text{MnO}_4^-$ which cannot. Official answer is C per JEE key.

The Freundlich equation is $x/m = kP^{1/n}$. Taking the log on both sides gives:
$\log(x/m) = \log k + (1/n)\log P$.
Comparing this to the straight-line equation $y = mx + c$:

• $y = \log(x/m)$
• $x = \log P$
• Slope ($m$) = $1/n$
• Intercept ($c$) = $\log k$

The sentence shows a cause-and-effect relationship: the rain caused the flooding. 'As a result' is the correct transitional phrase to express this consequence. 'Similarly' shows comparison, 'instead' shows alternative, and 'in contrast' shows opposition.

Jinnah parted ways with Congress following the rejection of his proposed amendments to the Nehru Report in 1928 .

The development of broadcast regulation in the U.S. followed a logical progression:

• Early radio (post-1920): Anyone could build and operate a radio station, leading to hundreds of unlicensed stations fighting for limited frequencies and even engaging in “power wars” to drown out competitors
• Radio Act of 1927: Created the Federal Radio Commission (FRC) to organise the licensing of transmitters and assign radio station frequencies
• Communications Act of 1934: Reorganised the FRC into the Federal Communications Commission (FCC), which expanded regulatory authority to include telephone and telegraph as well as broadcasting

The driving force behind regulation was the entry of commercial advertising money and corporate interests — once radio became profitable, the government had strong incentives to impose order. The FCC's regulatory powers later expanded to include television.