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We know that total number of symmetric relation on set having n elements is

\(2^{\cfrac{n(n+1)}2}\).

Given = {a₁, a₂, a₃, a₄, a₅ } and B = {b₁, b₂, b₃, b₄ }.

Therefore, A has 5 elements and B has 4 elements.

Therefore, total number of symmetric relation on set A is  ^{\(2^\cfrac{5(5+1)}2\)} = 2¹⁵ .

And total number of symmetric relation on set B is ^{\(2^\cfrac{4(4+1)}2\)} = 2¹⁰.

Difference between their results is 2¹⁵ − 2¹⁰ = 2¹⁰(2⁵ − 1) = 2¹⁰(32 − 1) 

= 31 × 1024 = 31774.

Given that quadratic equation 2x² + kx + 2 = 0 has equal roots.

By comparing given quadratic equation with standard quadratic equation ax² + bx + c, we get a = 2, b = k and c = 2.

We know that the quadratic equation ax² + bx + c has equal roots, if b² - 4ac = 0.

Therefore, k² − 4 × 2 × 2 = 0 ⇒ k² = 16 = 4² ⇒ k = ±4.

Hence, for k = ±4, the quadratic equation 2x² + kx + 2 = 0 have equal roots.

1. Circuit: A circuit is a closed conducting path through which an electric current either flows or intended to flow. A circuit consists of active and passive elements in it.

2. Linear Circuit: A circuit whose parameters are constant with time and they don’t change with voltage or current and they obeys Ohm’s law.

3. Non-linear Circuit: It is that circuit whose parameters change with voltage or current.

4. Bilateral Circuit: A bilateral circuit is one whose properties are the same in either direction. Example, a transmission line & parameter such as resistor, inductor & capacitor.

5. Unilateral Circuit: It is a circuit whose properties change with the direction of its operation. Example such as diode, triode , transistor & SCR.

6. Active Network: is a network which contains one or more than one source of emf along with passive element.

7. Passive Network: is one which contains no source of emf.

8. Node: is a point in a circuit where two or more circuit elements are connected together.

9. Branch: is the part of a network which lies between two nodes.

10.Loop: It is a close path in a circuit in which no element or node is encountered more than once.

11.Mesh: It is a loop that contains no other loop within it.

It should be noted that, unless stated otherwise, an electric network would be assumed passive.

There are two general approaches to network analysis:

i. Direct Method

ii. Network Reduction Method

Direct Method: Here the network is left in its original form while determining its voltages and currents.

e.g.: Loop Analysis, Nodal Analysis, Superposition Theorem, Compensation Theorem, and Reciprocity Theorem.

Network Reduction Method: Here, the original network is converted into a much simpler equivalent circuit for rapid and easy calculation.

e.g.: Delta/Star and Star/delta Conversions, Thevenin’s Theorem and Norton’s Theorem.

Fractional crystallization is a suitable method to separate sugar and salt from an aqueous solution containing them due to differences in their solubilities in water.

1. There is no intermolecular force of attraction within gaseous molecules (at high pressure and low temperature there is appreciable intermolecular force of attraction). 

2. The actual volume of the molecule is negligible as compared to total volume of the gas. (At high pressure the gaseous molecule occupy minimum volume, which is not negligible).

Because more close packing of molecules is possible in trans-isomer due to more symmetry.

(i) Principal quantum number specifies size of an orbital 

(ii) Azimuthal quantum number specifies shape of an orbital.

(b) 25% 

VSWR = \(\frac{1+|r|}{1-|r|}\)

3 = \(\frac{1+|r|}{1-|r|}\)

r = 0.5

\(\frac{p_r}{p_i}\) = r² = (0.5)²

= 0.25

25% of incident power is reflected.

A. False The tendency is directly proportional to vessel diameter. 

B. False The tendency is directly proportional to fluid density. 

C. False The tendency is directly proportional to velocity. 

D. True The tendency is inversely proportional to viscosity. 

E. True In anaemia, the increase in velocity and decrease in viscosity of blood in the hyperdynamic circulation promote turbulence; bruits may be heard over peripheral arteries.

Correct option is (D) \(NH_2^- > NH_3 \)

Nucleophilicity \(\propto\) electro density on donor atom

Nucleophilicity \(\propto\) size of donor atom (in gas)

Nucleophilicity \(\propto\) 1/EN of atom (for period) 

Correct option is (1) Warm and humid places

Correct answer is (c) In the human brain

A frequency polygon is a graph constructed by using lines to join the midpoints of each interval, or bin. The heights of the points represent the frequencies. A frequency polygon can be created from the histogram or by calculating the midpoints of the bins from the frequency distribution table.

A. True This increases the rate of impulse generation and hence heart rate. 

B. True The increase in myocardial metabolism generates vasodilator metabolites. 

C. True Rapid spread of excitation in the ventricles results in more forceful contractions as the ventricular fibres are activated nearly simultaneously. 

D. True This enhances the force of contraction at any given filling pressure. 

E. True Due to the increased force of contraction.

A. True As seen in the Frank–Starling left ventricular function curve. 

B. False High K⁺ levels decrease cardiac contractility. 

C. False Calcium channel blockers decrease cardiac contractility. 

D. True Due to increased sympathetic drive to the ventricles and increased venous return. 

E. True Initially by increased ventricular filling: later by ventricular hypertrophy.

An opportunity cost is the cost of an alternative that must be forgone in order to pursue a certain action. In other words, the cost of enjoying more of one good in terms of sacrificing the benefit of another good is termed as opportunity cost of the additional unit of the good.

Example: We have Rs 15,000 with two choices a) to invest in the shares of a company XYZ or b) to make a fixed deposit which gives interest 9%. If the company XYZ gives a return of 15%, we will benefit when we invest in the shares as the alternative would be less profitable. However if company’s return is only 3% when we could have made a return of 9% from FD, then our opportunity cost is (9% - 3% = 6%).

A. False It is low because the capillary bed has a large total cross-sectional area. 

B. True The venous bed has a smaller total cross-sectional area than the venular bed. 

C. True There is a brief period of retrograde flow as the aortic valve closes. 

D. True Axial flow occurs in large vessels; near the walls, flow velocity is zero. 

E. False It rises due to the compensatory increase in cardiac output.

A. True This increases capillary hydrostatic pressure. 

B. True In the standing position, capillary pressure increases by the hydrostatic equivalent of the column of blood below the heart. 

C. False Lymphatic obstruction allows tissue fluid to accumulate; the rise in interstitial pressure reduces the capillary transmural hydrostatic pressure gradient. 

D. True Capillary pressure rises during the exercise hyperaemia. 

E. True Hypoproteinaemia decreases the transmural colloid osmotic pressure gradient.

A. True Pulmonary blood flo = right ventricular output = cardiac output. 

B. False The O₂ content of arterial and mixed venous blood are measured. 

C. False To measure O₂ consumption, the subject breathes from a spirometer filled with oxygen with a CO₂ absorber in the circuit; an open circuit method may also be used. 

D. True The pulmonary artery is relatively easy to catheterize and the venous blood it contains is thoroughly mixed. 

E. False Pulmonary veins are difficult to catheterize. Blood from any artery may be used since the O₂ content of peripheral arterial blood is the same as that in the pulmonary vein.

A. False The cells increase in size (hypertrophy), not in number (hyperplasia). 

B. True Due to the left ventricular hypertrophy. 

C. True Due to increased left ventricular work. 

D. True Due to left ventricular failure. 

E. True Due to damage to retinal blood vessels.

A. True Hence no blood leaves the ventricles. 

B. False Pressure in the aorta falls as run-off of blood to the tissues continues. 

C. False It rises as ventricular pressure causes the AV valves to bulge into the atria. 

D. True The blood vessels are squeezed by the contracting myocardium. 

E. False The greater force of contraction in the left ventricle gives a greater rate of rise of pressure.

A. True The output from the left and right ventricle is the same. 

B. True It depends on what happens to stroke volume. 

C. True Lying down normally increases the filling pressure of the heart. 

D. True To meet the needs of increased metabolism and increased skin blood flow. 

E. False The output does increase due to changes in the filling pressure, level of circulating hormones, etc.

A. False This applies to both heart sounds. 

B. False It is about 20 per cent shorter. 

C. True About 50 Hz compared with 35 Hz for the first sound. 

D. False Both may be split due to asynchronous valve closure. 

E. True The first sound is due to ventricular systole; the second occurs during ventricular relaxation when the aortic valves snap shut as ventricular pressure falls below aortic.

A. True The pressure head needed to drive cardiac output through the pulmonary circuit (about 15 mmHg) is much less than that needed in the systemic circuit (about 90 mmHg). 

B. False The reverse is true; low alveolar P_O2 may cause pulmonary hypertension. 

C. False These are conductance units, the reciprocal of resistance units. 

D. True Thus there is little rise in pulmonary arterial pressure during exercise despite the increased flow rate. Release of nitric oxide from the pulmonary vascular endothelium may account for the vasodilatation. 

E. False Pulmonary vascular resistance is controlled by local rather than by nervous mechanisms.

A. True Around three-quarters; veins are referred to as ‘capacitance’ vessels. 

B. True These modulate venous capacity. 

C. False Their vasa arise from neighbouring arteries. 

D. True This ‘myogenic’ response helps to limit the degree of distension. 

E. True Another functional adaptation to resist distension.

A. False Their wall thickness is similar since the workload of the two atria is similar. 

B. False It begins at the sinuatrial node in the right atrium. 

C. False Excitation can only pass from atria to ventricles via specialized conducting tissue in the AV bundle. 

D. False Delay of excitation in the AV bundle makes atrial precede ventricular contraction. 

E. True Due to the spiral arrangement of some muscle fibres; circular fibres reduce ventricular circumference. 

A. False Pulse waves travel at about ten times the blood velocity. 

B. False It rises; arterial elasticity normally damps the pulse pressure. 

C. False Blood flows off rapidly via collaterals so that little pressure change occurs. 

D. True By the hydrostatic equivalent of the column of blood between it and the heart. 

E. False Brachial arterial pulse pressures are greater due to the superimposition of waves reflected from the end of the arterial tree.

A. True They conduct at around 4 metres/second. Small diameter nerve fibres conduct impulses at about 1 metre per second. 

B. True This facilitates rapid conduction. 

C. False Purkinje fibres travel to the apex before proceeding to the base of the heart. 

D. True They spread depolarization rapidly over the entire ventricular myocardium. 

E. True Damage to the cells (as in bundle-branch block) changes the pattern of spread of ventricular depolarization, and hence the shape of the QRS complex.