The sympathetic nervous system (SNS) is a division of the autonomic nervous system that activates the 'fight or flight' response during perceived threats or stress. It increases heart rate, dilates pupils, inhibits digestion, and releases adrenaline. The parasympathetic nervous system ('rest and digest') is responsible for rest, relaxation, and digestion. Voluntary muscle movement is controlled by the somatic nervous system.

Enzymes are biological catalysts that speed up reactions by lowering the activation energy (\(E_a\)) of the reaction — they provide an alternative reaction pathway with a lower energy barrier. Importantly, enzymes do NOT change the equilibrium constant or the thermodynamic spontaneity of the reaction; they only affect the rate at which equilibrium is reached.

An integrating element: \(\dot{x}_o(t)=K_I x_i(t)\), so \(sX_o(s)=K_I X_i(s)\), giving \(Y(s)=K_I/s\). Integration in time corresponds to division by \(s\) in the Laplace domain.

The line through \((1,-5,9)\) with direction ratios \((1,1,1)\) is \(\frac{x-1}{1} = \frac{y+5}{1} = \frac{z-9}{1} = t\). Points on this line are \((1+t, -5+t, 9+t)\). For intersection with plane \(x-y+z=5\): \((1+t)-(-5+t)+(9+t) = 5\), giving \(15+t = 5\), so \(t = -10\). The intersection point is \((-9, -15, -1)\). Distance = \(\sqrt{(1-(-9))^2 + (-5-(-15))^2 + (9-(-1))^2} = \sqrt{100+100+100} = \sqrt{300} = 10\sqrt{3}\). But this gives option A. Let me recalculate: \(|t| = 10\), and since direction ratios are \((1,1,1)\), distance = \(|t|\sqrt{1^2+1^2+1^2} = 10\sqrt{3}\). Wait, that's option A. But the given answer is D. Let me check if distance formula should be different. Actually, the distance along the line is simply \(|t|\sqrt{3} = 10\sqrt{3}\). There's a discrepancy here. Based on typical JEE answers, let me verify once more. If the answer is \(\frac{20}{3}\), then perhaps there's a different calculation method.

Both A and R are true. R–I reacts faster in S\(_N\)2 than R–Cl because I\(^-\) is a much better leaving group — it is larger, more polarizable, and the C–I bond is weaker. The large size of iodine means the C–I bond is longer and weaker, making it easier to break. R correctly explains A.

Area of the second playground: $64 \times 48 = 3072$ square meters.

The first playground has width 24 m and the same area:

$24 \times \text{length} = 3072$

$\text{length} = \dfrac{3072}{24} = 128$ meters.

Perimeter $= 2(24 + 128) = 2 \times 152 = \mathbf{304}$ meters.

Speed $= 6/2 = 3$ km/h. Distance in $5$ hours $= 3 \times 5 = 15$ km.

We need two numbers that multiply to 6 and add to \(-5\): those are \(-2\) and \(-3\). So \(x^2 - 5x + 6 = (x-2)(x-3)\).

Cooperative (Co-op) Advertising is a system in which two parties with a shared interest in selling a product jointly fund advertising campaigns. The textbook example is: a soft-drink manufacturer and a local grocery store split the cost of advertising the manufacturer's soft drinks. Both parties benefit: the manufacturer gains brand exposure and sales, while the store gains foot traffic and sales revenue. This model is especially beneficial for small business owners who could not afford to advertise on their own — they leverage the manufacturer's resources to reach a wider audience. Cooperative advertising is a formal industry practice: manufacturers often provide co-op funds (typically a percentage of a retailer's purchases) that can be used for agreed advertising activities. It must be carefully distinguished from comparative advertising (comparing one brand to competitors) and institutional advertising (promoting corporate image rather than specific products).

Using the Relativistic Doppler Effect formula for an approaching source:

$f' = f \sqrt{\frac{1 + v/c}{1 - v/c}}$

Given $v = 0.5c$:

$f' = 10 \sqrt{\frac{1 + 0.5}{1 - 0.5}} = 10 \sqrt{\frac{1.5}{0.5}} = 10 \sqrt{3} \approx 10 \times 1.732 = 17.32 \text{ GHz}$.

'In the direction of' is correct.

Dr. Fazal ur Rehman was a prominent Pakistani Islamic scholar and academic .

Traditional desi ghee production: milk \(\rightarrow\) dahi (yoghurt) \(\rightarrow\) churning dahi \(\rightarrow\) desi butter (makkhan) \(\rightarrow\) heating at \(110\text{–}120^{\circ}\text{C}\) to remove moisture and MSNF \(\rightarrow\) filtering \(\rightarrow\) desi ghee. Maillard reaction during heating gives desi ghee its characteristic flavor.

'Advised' is appropriate for giving moral instruction.

The oxygen atom is electronegative, creating a dipole.

Five years ago: P + Q = 30, so today P + Q = 40.
Today: P + Q + R = 60 (since average = 20).
Therefore R = 60 − 40 = 20 years today.
After 10 years: R = 20 + 10 = 30 years.

1

For the potential to become zero after connection, the total charge must be zero (charges cancel). Taking signs into account:

$Q_1 - Q_2 = 0 \Rightarrow C_1 \times 120 = C_2 \times 200$

$\frac{C_1}{C_2} = \frac{200}{120} = \frac{5}{3}$

$\Rightarrow 3C_1 = 5C_2$

The capacitors must have been charged with opposite polarities so that when connected, charges cancel. Conservation of charge gives $120C_1 = 200C_2$, yielding $3C_1 = 5C_2$.

'Quantum sufficiat' (q.s.) means as much as is sufficient.

The Creditors Control Account credit side records: opening balance and credit purchases (amounts owed to suppliers). The debit side records: purchase returns, payments made to suppliers, discounts received, and the closing balance (carried forward). Purchase returns reduce what is owed to creditors, hence they appear on the debit side.