Please be patient as the PDF generation may take up to a minute.

Let \(\omega_{1},\omega_{2}\) and \(\omega_{3}\) be the angular speeds of the second hand, minute hand, and hour hand of a smoothly running analog clock, respectively. If \(x_{1},x_{2}\) and \(x_{3}\) are their respective angular distance in \(1~\text{minute},\) then the factor that remains constant \((k)\) is:

1.	\(\dfrac{\omega_1}{x_1}=\dfrac{\omega_2}{x_2}=\dfrac{\omega_3}{x_3}={k}\)
2.	\(\omega_{1}x_{1}=\omega_{2}x_{2}=\omega_{3}x_{3}={k}\)
3.	\(\omega_{1}x_{1}^{2}=\omega_{2}x_{2}^{2}=\omega_{3}x_{3}^{2}={k}\)
4.	\(\omega_{1}^{2}x_{1}=\omega_{2}^{2}x_{2}=\omega_{3}^{2}x_{3}={k}\)

A man standing on a still boat jumps out horizontally with a speed of \(20~\text{m/s}\) with respect to the boat. If the mass of the man is \(70~\text{kg}\) and that of the boat is \(210~\text{kg},\) then the speed of the boat after the man jumps will be:
1. \(20~\text{m/s}\)
2. \(6.67~\text{m/s}\)
3. \(5~\text{m/s}\)
4. \(15~\text{m/s}\)

Two identical uniform semi-circular pieces are joined smoothly at their ends so as to form a planar \(S\)-shape. The mass of each piece is \(m\) and radius \(R.\) The moment of inertia of this \(S,\) about the common tangent at its joint (at \(P\)) is given by:
   

1.	\(mR^2\)	2.	\({\dfrac32}mR^2\)
3.	\(2mR^2\)	4.	\(3mR^2\)

The angular momentum of a planet of mass \(m,\) moving around the sun (mass: \(M\gg m\)) in an orbit of radius \(r\) is proportional to:

1.	\(mr\)	2.	\(\dfrac{m}{r}\)
3.	\(m\sqrt r\)	4.	\(\dfrac{m}{\sqrt r}\)

A large cylindrical piece of a dense solid elastic metal stands on its end as shown in the figure. The metal is uniform and isotropic. The stress in the material as a function of height is shown correctly by:
 

1.		2.
3.		4.

Considering the disproportionation reaction of copper(I) ions in an aqueous solution at 298 K:

\(2\text{Cu}^+(\text{aq}) \rightleftharpoons \text{Cu}(\text{s}) + \text{Cu}^{2+}(\text{aq})\)

Which of the following added ions will cause the equilibrium to shift to the right, thereby favoring the formation of the products \([\text{Cu}(\text{s}) ~\text {and} ~\text{Cu}^{2+}(\text{aq})]\)?

I.	\({NO}_3^{-}\)
II.	\({SCN}^{-}\)
III.	\({Cl}^{-}\)
IV.	\({CN}^{-}\)

1. I and II
2. I, II and III
3. II, III and IV
4. I, II, III and IV

Which of the following pair of halide ions can be oxidized by dioxygen in an acidic medium?
1. \(Cl^- , Br^-\)
2. \(Br^-, I^-\)
3. \(Cl^-, F^{-}\)
4. \(I^-, F^{-}\)

Determine the final concentration of the weak acid \(\text {HX}\) (given \(\mathrm{K}_{\mathrm{a}}=4 \times 10^{-10}\)) after a \(0.01~ \mathrm{M}\) solution has been diluted to achieve a \(\mathrm{pH}=6\). Express this final concentration in the form \(\mathrm{x \times 10^{-4} M}\), and then state the numerical value of x:
1. 14
2. 25
3. 31
4. 12

Calculate the bond energy for the triple bond between two X atoms (\(X \equiv X\)) in the molecule \(X_2H_2\) (structure\( H - X \equiv X - H\)). Use the following thermochemical data and the given \( X-H\) bond energy of \(350 \text{ Kcal mol}^{-1}\)}:

\( 2X(s)+H_2 (g)\rightarrow X_2 H_2;\quad \Delta H=225 ~\text Kcal \text mol^{-1}\)

\(2X(s) \longrightarrow 2X(g);\quad \Delta H=1410 ~\text Kcal \text mol^{-1}\)

\(H_2 (g )\rightarrow 2 H (g); \quad \Delta H=330~ \text Kcal \text mol^{-1}\)

1. \(965\)
2. \(737\)
3. \(815\)
4. \(865\)

The equilibrium constant \(K_C\) at \(298~K\) for the reaction \(A+B \rightleftharpoons C+D\) is \(100.\)
Starting with an equimolar solution with concentrations of A, B, C and D all equal to \(1~M,\) if the equilibrium concentration of D comes out to be \(x \times10^{-2}M\), then find the value of \(x\):
1. 181
2. 190
3. 188
4. 192

Consider the given two statements:

Statement I	A closed circulatory system is found only in the most active molluscs, such as squids and octopuses, because they require an efficient oxygen supply for sustained muscular activity.
Statement II	All flying animals possess a closed circulatory system because flight requires high metabolic activity.

Which of the following statements is correct?

1.	Both Statement I and II are correct
2.	Statement I is correct, but Statement II is incorrect
3.	Statement I is incorrect, but Statement II is correct
4.	Both Statement I and II are incorrect

Consider the following two statements:

Statement I	In a trained athlete, the resting heart rate is lower than that of an untrained adult, yet the cardiac output remains nearly the same.
Statement II	The stroke volume in a trained athlete is higher than that of an untrained adult, compensating for the lower heart rate to maintain the same cardiac output.

Which of the following statements is correct?

1.	Both Statement I and II are correct
2.	Statement I is correct, but Statement II is incorrect
3.	Statement I is incorrect, but Statement II is correct
4.	Both Statement I and II are incorrect

How many of the given statements are correct?

I	A single bone makes up the entire structure of human larynx.
II	All initial bronchioles are supported by complete cartilaginous rings.
III	Trachea divides at the level of fifth thoracic vertebra into right and left primary bronchi.

1. 0
2. 1
3. 2
4. 3

Consider the following two statements:

Statement I:	The exchange of substances between the blood and the interstitial fluid occurs only in capillaries, because they have thin walls, and in veins, because they have low pressure.
Statement II:	The walls of arteries and the veins are similar in organisation.

Which of the following statements is correct?

1.	Both Statement I and II are correct
2.	Statement I is correct, but Statement II is incorrect
3.	Statement I is incorrect, but Statement II is correct
4.	Both Statement I and II are incorrect

Which part of the nephron is mainly responsible for increasing the medullary interstitial osmolarity when the human kidney is eliminating concentrated urine?

1.	Proximal convoluted tubule (PCT)
2.	Descending limb of loop of Henle
3.	Ascending limb of loop of Henle
4.	Distal convoluted tubule (DCT)

Consider the two statements regarding the comparison of root and shoot in flowering plants:

I	In contrast to roots, the shoot has nodes and internodes, with one or more leaves attached at each node.
II	The shoot apex produces leaves and axillary buds, which develop into lateral shoots. The root apex produces no lateral organs.

 

1.	Only I is correct
2.	Only II is correct
3.	Both I and II are correct
4.	Both I and II are incorrect

Consider the given two statements:

Statement I	Mature mammalian erythrocytes lack nuclei.
Statement II	Mature mammalian erythrocytes lack mitochondria.

Which of the following is correct?

1.	Both Statement I and II are correct and while the first adaptation increases the efficiency of oxygen transport, the second adaptation decreases the efficiency of oxygen transport.
2.	Both Statement I and II are correct and both adaptations increase the efficiency of oxygen transport by the same mechanism only - providing more space to accommodate haemoglobin.
3.	Both Statement I and II are correct and the first adaptation primarily provides more space to accommodate haemoglobin, the second adaptation prevents erythrocytes from consuming oxygen for their own metabolism, ensuring more oxygen is delivered to tissues.
4.	Statement I is correct, but Statement II is incorrect

Identify the correct statements:

I	Vital capacity + Residual volume = Total lung capacity; therefore, Total lung capacity - Vital capacity = Residual volume.
II	The partial pressure of nitrogen in atmospheric air will approximately be given by 0.78 X 760 = about 593 mm Hg.
III	If tidal volume is 500 ml and respiratory rate is 12 to 16 per minute in a healthy man, he can inspire or expire 6000 to 8000 ml of air per minute.

1. Only I and II
2. Only I and III
3. Only II and III
4. I, II and III

Regarding the regulation of respiration in humans:

I	Central chemoreceptors primarily respond to carbon dioxide and hydrogen ion levels; peripheral chemoreceptors primarily respond to oxygen levels in the blood.
II	The rhythm centre in medulla does not have any control over diaphragm since diaphragm is responsible for almost all breathing at rest.
III	Pneumotaxic center, located in medulla oblongata, increases the duration of inspiration and decreases respiratory rate.

1. I, II and III are correct
2. Only I and II are correct
3. Only II and III are correct
4. I, II and III are incorrect 

How many of the given statements are correct?

I	Carbon dioxide is an excretory product in humans.
II	ANF is a vasodilator.
III	Aldosterone increases sodium reabsorption in PCT.
IV	On an average, 1 to 1.5 litres of urea is eliminated per day in humans.
V	The most common nephrons in the human kidney have a well-developed vasa recta associated with them.

1. 2
2. 3
3. 4
4. 5