AIPMT 2007 Chemistry Question Paper with Answer and Solution

(C) The net work done on the ball is the sum of the work done by the gravitational force and the work done by the spring force.
$1$. Work done by gravity $(W_g)$: The ball falls through a total vertical distance of $(h + d)$. Since the force acts in the direction of displacement,$W_g = mg(h + d)$.
$2$. Work done by the spring $(W_s)$: The spring is compressed by a distance $d$. The work done by the spring force is given by $W_s = -\frac{1}{2}Kd^2$ because the spring force acts opposite to the displacement.
$3$. Net work done $(W_{net})$: $W_{net} = W_g + W_s = mg(h + d) - \frac{1}{2}Kd^2$.

(B) The angular momentum $L$ of a particle of mass $m$ moving with velocity $V$ relative to an origin $O$ is given by the formula $L = m \times (r \times V)$,where $r$ is the position vector of the particle.
Alternatively,the magnitude of angular momentum is given by $L = m \cdot V \cdot d$,where $d$ is the perpendicular distance from the origin $O$ to the line of motion of the particle.
Since the particle is moving along a straight line $AB$,the perpendicular distance $d$ from the origin $O$ to this line remains constant at all points on the line.
As $m$,$V$,and $d$ are all constant for the motion of the particle along the line $AB$,the angular momentum $L$ remains constant at all points on the line.
Therefore,the angular momentum at point $A$ $(L_A)$ must be equal to the angular momentum at point $B$ $(L_B)$.
Thus,$L_A = L_B$.

(D) Let $\theta$ be the angle that the path of the particle makes with the $x$-axis.
From the given coordinates $(x, y) = (\sqrt{3}, 3)$,the slope of the line is given by:
$\tan \theta = \frac{y}{x} = \frac{3}{\sqrt{3}}$
Simplifying the expression:
$\tan \theta = \sqrt{3}$
Taking the inverse tangent on both sides:
$\theta = \tan^{-1}(\sqrt{3}) = 60^{\circ}$
Thus,the path of the particle makes an angle of $60^{\circ}$ with the $x$-axis.

(A) The solubility of ionic compounds depends on the balance between hydration energy and lattice energy.
For a compound to be soluble,the hydration energy must be greater than the lattice energy.
Hydration energy is inversely proportional to the size of the cation $(Hydration \ energy \propto \frac{1}{\text{size of cation}})$.
As we move down the group from $Mg^{2+}$ to $Ra^{2+}$,the size of the cation increases,which decreases the hydration energy.
$Mg^{2+}$ has the smallest size among the given alkaline earth metal ions,resulting in a very high hydration energy that exceeds its lattice energy,making $MgSO_4$ highly soluble in water.

(D) The displacement of a particle in simple harmonic motion starting from the equilibrium position is given by $x = a \sin(\omega t)$.
Given that the particle travels half of the amplitude,we set $x = a/2$.
Substituting this into the equation: $a/2 = a \sin(\omega t) \Rightarrow \sin(\omega t) = 1/2$.
Since $\sin(\pi/6) = 1/2$,we have $\omega t = \pi/6$.
Substituting $\omega = 2\pi/T$,we get $(2\pi/T) \cdot t = \pi/6$.
Solving for $t$,we find $t = T/12$.

(C) The induced electromotive force $(emf)$ in the primary coil is given by Faraday's law of induction: $E_P = \frac{d\phi}{dt}$.
Given $\phi = \phi_0 + 4t$,we have $E_P = \frac{d}{dt}(\phi_0 + 4t) = 4 \text{ volts}$.
For an ideal transformer,the ratio of the secondary voltage $(E_S)$ to the primary voltage $(E_P)$ is equal to the ratio of the number of turns in the secondary coil $(N_S)$ to the number of turns in the primary coil $(N_P)$: $\frac{E_S}{E_P} = \frac{N_S}{N_P}$.
Substituting the given values: $\frac{E_S}{4} = \frac{1500}{50}$.
$\frac{E_S}{4} = 30$.
Therefore,$E_S = 30 \times 4 = 120 \text{ volts}$.

(A) According to the work-energy theorem,the net work done on an object is equal to the change in its kinetic energy.
In this process,the ball starts from rest at height $h$ above the spring and ends at rest after compressing the spring by distance $d$. Thus,the initial kinetic energy $K_i = 0$ and the final kinetic energy $K_f = 0$.
Therefore,the net work done $W_{net} = K_f - K_i = 0 - 0 = 0$.
Alternatively,considering the forces acting on the ball: the gravitational force does work $mg(h + d)$ and the spring force does work $-\frac{1}{2}kd^2$. The total work done is $W_{net} = mg(h + d) - \frac{1}{2}kd^2 = 0$.

(D) When a beam of electrons passes undeflected through mutually perpendicular electric $(E)$ and magnetic $(B)$ fields, the net force on the electrons is zero. This implies that the electric force $(F_e = qE)$ is equal and opposite to the magnetic force $(F_m = qvB)$, so $qE = qvB$, or $v = E/B$.
When the electric field is switched off, only the magnetic field remains. The magnetic force acting on a moving charge in a uniform magnetic field is given by $F = q(v \times B)$.
Since the velocity vector $v$ is perpendicular to the magnetic field vector $B$, the magnetic force acts as a centripetal force, which is always perpendicular to the velocity of the electron.
$A$ constant force acting perpendicular to the velocity of a particle results in circular motion. Therefore, the electrons will move in a circular orbit.

(B) The centripetal force is provided by the magnetic force.
$i.e., \frac{mv^2}{R} = qvB ......... (1)$
where $m = \text{mass of the ion}$,$v = \text{velocity}$,$q = \text{charge of ion}$,$B = \text{magnetic field flux density}$.
From $(1)$,the velocity of the ion is $v = \frac{qBR}{m}$.
The kinetic energy gained by the ion when accelerated through a potential $V$ is given by $E = qV$.
Also,$E = \frac{1}{2}mv^2$.
Equating the two expressions for energy:
$qV = \frac{1}{2}m \left( \frac{qBR}{m} \right)^2$
$qV = \frac{1}{2}m \frac{q^2 B^2 R^2}{m^2}$
$qV = \frac{q^2 B^2 R^2}{2m}$
Rearranging for the ratio $\frac{q}{m}$:
$\frac{q}{m} = \frac{2V}{B^2 R^2}$
Since $V$ and $B$ are constant,we have $\frac{q}{m} \propto \frac{1}{R^2}$.

(A) $ICBN$ stands for International Code of Botanical Nomenclature.
It is a set of rules and recommendations dealing with the formal botanical names that are given to plants.
This code is independent of zoological and bacteriological nomenclature.
The foundations of $ICBN$ were laid in the book $Philosophia$ $Botanica$,written by $C. Linnaeus$.

(A) $ICBN$ stands for International Code of Botanical Nomenclature.
It is a set of rules and recommendations dealing with the formal botanical names that are given to plants.
This code is independent of zoological and bacteriological nomenclature.
The foundations of $ICBN$ were established in the book $Philosophia$ $Botanica$,written by $C. Linnaeus$.

(A) Parrots are birds $(Aves)$,while platypus and kangaroos are mammals $(Mammalia)$. All three of these organisms are homeothermic,meaning they are warm-blooded animals capable of maintaining a constant body temperature regardless of the environmental temperature.

(A) In roots,the endodermis is the innermost layer of the cortex.
Some of the endodermal cells present opposite to the xylem patches are thin-walled and are called passage cells or transfusion cells.
Passage cells facilitate the transfer of water and dissolved minerals from the cortex directly into the xylem and ultimately to the pericycle.

(A) Glycolysis,Krebs' cycle,and the electron transport system are metabolic pathways designed for the synthesis of $ATP$ through a series of controlled,stepwise reactions.
$ATP$ serves as the primary energy currency of the cell,providing the necessary energy for various biological processes.

(D) Opening of floral buds into flowers is a type of autonomic movement of growth,specifically known as epinasty or hyponasty (a type of nastic movement).
This is a non-directional movement where the response is determined by the internal physiology of the responsive organ rather than the direction of the external stimulus.
Differential growth rates on the inner and outer surfaces of the floral parts cause the bud to open.

(A) In humans,there are $12$ pairs of ribs that form the bony lateral walls of the thoracic cage.
The first $7$ pairs are true ribs,the next $3$ pairs are false ribs,and the last $2$ pairs ($4$ ribs in total) are called floating ribs.
Floating ribs are called so because their anterior ends are not attached to the sternum or the cartilage of any other rib.
Therefore,the total number of floating ribs in humans is $4$.

(A) The $Parathyroid$ gland secretes $Parathyroid$ $Hormone$ $(PTH)$,which is a peptide hormone that plays a crucial role in regulating calcium and phosphorus levels in the blood.
$PTH$ increases the level of calcium ions in the blood by stimulating bone resorption (demineralization),increasing calcium reabsorption by the renal tubules,and promoting calcium absorption from digested food in the intestine.
It also decreases the blood phosphorus level by increasing the excretion of phosphorus in the urine.
Therefore,any dysfunction in the $Parathyroid$ gland directly impacts calcium and phosphorus metabolism.

(B) When a person experiences a stressful situation like an earthquake,the body's 'fight-or-flight' response is activated.
This response is primarily mediated by the hormone $Adrenaline$ (also known as $Epinephrine$),which is secreted by the adrenal medulla.
$Adrenaline$ prepares the body for immediate physical action by increasing the heart rate,dilating the pupils,and mobilizing energy reserves,allowing the person to react quickly to the danger.

(D) The genes which individually have a small effect but collectively produce significant phenotypic expression are called polygenes.
The inheritance of these genes is called polygenic inheritance,$e.g.,$ skin colour in humans.

(D) In convergent evolution,organisms from different ancestral lineages evolve similar traits or morphological features due to adaptation to similar environmental pressures or ecological niches. This process leads to analogous structures,such as the wings of butterflies and birds.

(D) The concept of chemical evolution,often referred to as the Oparin-Haldane hypothesis,suggests that life originated from non-living organic molecules. It proposes that the primitive Earth's atmosphere,which was reducing in nature,allowed for the synthesis of simple organic compounds from inorganic precursors through the influence of energy sources like lightning and solar radiation. These molecules eventually aggregated to form more complex structures,leading to the origin of life under suitable environmental conditions.

(C) The population growth curve is $J$-shaped,which is characteristic of exponential growth. In this type of growth,the population density increases rapidly in an exponential fashion when resources are abundant. The population then stops abruptly or crashes when environmental resistance or limiting factors (such as the end of the rainy season) become effective suddenly.

(A) $Podophyllum$ is an endangered Indian medicinal plant. Its dried roots and rhizomes are used in the treatment of chronic constipation and tumorous growths.

(B) An exotic species is an organism that is not native to a particular locality and has been introduced there by human activities or other agents.
In the context of India, $Lantana$ $camara$ and water hyacinth $(Eichhornia$ $crassipes)$ are classic examples of invasive exotic species that have caused significant ecological damage.
$Ficus$ $religiosa$ (Peepal) and $Prosopis$ $cineraria$ (Khejri) are native species to India.
Therefore, the correct pair is $Lantana$ $camara$ and water hyacinth.

(C) Bioindicators are organisms used to monitor the health of an environment. Sludge worms,blood worms,and sewage fungus are commonly used as indicators of organic water pollution. Stoneflies (order-Plecoptera) are generally sensitive to pollution and are often used as indicators of clean,well-oxygenated water,but they are not considered bioindicators of water pollution in the context of indicating the presence of pollutants like sewage or organic waste; rather,their absence indicates pollution.