Lakhmir Singh

Which of the following statements is correct? (i) Elements of group 15 form electron deficient hydrides. (ii) All elements of group 14 form electron precise hydrides. (iii) Electron precise hydrides have tetrahedral geometries. (iv) Electron rich hydrides can act as Lewis acids.

Solution: Option (ii) and (iii) are the answers. Inorganic electron-specific hydrides are those hydrides in which the exact quantity of electrons required to form a typical covalent bond is present....

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The hardness of water may be temporary or permanent. Permanent hardness is due to the presence of (i) Chlorides of Ca and Mg in water (ii) Sulphates of Ca and Mg in water (iii) Hydrogen carbonates of Ca and Mg in water (iv) Carbonates of alkali metals in water

Solution: Option (i) and (ii) are the answers. Permanent hardness is caused by the presence of soluble magnesium and calcium salts in the form of chorides and sulphates in the water, which causes...

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Some of the properties of water are described below. Which of them is/are not correct? (i) Water is known to be a universal solvent. (ii) Hydrogen bonding is present to a large extent in liquid water. (iii) There is no hydrogen bonding in the frozen state of water. (iv) Frozen water is heavier than liquid water.

Solution: Option (iii) and (iv) are the answers. In ice, there is a great deal of hydrogen bonding. Because of the empty spaces found in tetrahedrons generated by hydrogen bonding, ice is...

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Which of the following statement(s) is/are correct in the case of heavy water? (i) Heavy water is used as a moderator in a nuclear reactor. (ii) Heavy water is more effective as a solvent than ordinary water. (iii) Heavy water is more associated than ordinary water. (iv) Heavy water has a lower boiling point than ordinary water.

Solution: Option (i) and (iii) are the answers. Heavy water is a moderator in nuclear reactors. It has a greater boiling point than regular water. It is thus more associated than plain water....

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Dihydrogen can be prepared on a commercial scale by different methods. In its preparation by the action of steam on hydrocarbons, a mixture of CO and H2 gas is formed. It is known as ____________. (i) Water-gas (ii) Syngas (iii) Producer gas (d) Industrial gas

Solution: Option (i) and (ii) are the answers. It is used to produce hydrogen, carbon monoxide, and other products from hydrocarbons like natural gas. This is done in a reformer, which uses...

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Which of the following statements are not true for hydrogen? (i) It exists as a diatomic molecule. (ii) It has one electron in the outermost shell. (iii) It can lose an electron to form a cation which can freely exist (iv) It forms a large number of ionic compounds by losing an electron

Solution: Option (iii) and (iv) are the answers. Because hydrogen has only one electron in its outermost shell, it can form diatomic molecules by covalent bonding. Its high ionisation enthalpy...

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Which of the following reactions is an example of use of water gas in the synthesis of other compounds? (i) CH4 (g) + H2O (g) → (1270KNi) CO (g) + H2 (g) (ii) CO (g) + H2O (g) → (Catalyst673K) CO2 (g) + H2 (g) (iii) CnH2n+2 + nH2O (g) → (1270KNi) nCO + (2n+1) H2 (iv) CO (g) + 2H2 (g) Cobalt → (Catalyst) CH3OH (l)

Solution: Option (iv) is the answer. The mixture of carbon monoxide and hydrogen is referred to as water gas. The term "synthesis gas" or "syngas" refers to the mixture of carbon monoxide and...

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Rohan heard that instructions were given to the laboratory attendant to store a particular chemical i.e., keep it in the darkroom, add some urea in it, and keep it away from dust. This chemical acts as an oxidising as well as a reducing agent in both acidic and alkaline media. This chemical is important for use in the pollution control treatment of domestic and industrial effluents (i) Write the name of this compound. (ii) Explain why such precautions are taken for storing this chemical.

Answer: The compound hydrogen peroxide, which functions as both an oxidising and reducing agent in both acidic and alkaline conditions, is referred to as hydrogen peroxide. After coming into touch...

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When the first element of the periodic table is treated with dioxygen, it gives a compound whose solid-state floats on its liquid state. This compound can act as an acid as well as a base. What products will be formed when this compound undergoes authorisation?

Answer: The first element, hydrogen, interacts with dioxygen to make water. Water is amphoteric, meaning it is both acid and basic. Water's solid state is ice. Due to its decreased density, it...

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Consider the reactions (A) H2O2 + 2HI → I2 + 2H2O (B) HOCl + H2O2 → H3O++ Cl–+ O2 Which of the following statements is correct about H2O2 with reference to these reactions? Hydrogen peroxide is ________. (i) an oxidising agent in both (A) and (B) (ii) an oxidising agent in (A) and reducing agent in (B) (iii) a reducing agent in (A) and oxidising agent in (B) (iv) a reducing agent in both (A) and (B)

Solution: Option (ii) is the answer. (A) $H_2O_2 + 2HI → I_2 + 2H_2O$ Iodine undergoes oxidation, transitioning from the -1 oxidation state to the 0 oxidation state. As a result, H2O2 works as an...

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Why does H+ ion always get associated with other atoms or molecules? (i) Ionisation enthalpy of hydrogen resembles that of alkali metals. (ii) Its reactivity is similar to halogens. (iii) It resembles both alkali metals and halogens. (iv) Loss of an electron from hydrogen atom results in a nucleus of very small size as compared to other atoms or ions. Due to the small size, it cannot exist free.

Solution: Option (iv) is the answer. Hydrogen has one electron in its s orbital and like alkali metals, it can lose one electron from its outer shell. So hydrogen is like alkalis. Onions reacting...

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Hydrogen resembles halogens in many respects for which several factors are responsible. Of the following factors which one is most important in this respect? (i) Its tendency to lose an electron to form a cation. (ii) Its tendency to gain a single electron in its valence shell to attain stable electronic configuration. (iii) Its low negative electron gain enthalpy value. (iv) Its small size.

Solution: Option (ii) is the answer. Hydrogen, like halogens, prefers to gain an electron to achieve a stable noble gas structure. Hydrogen's electrical configuration is 1s. The electrical...

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Two strips of metal are riveted together at their ends by four rivets, each of diameter 6.0 \mathrm{~mm} . What is the maximum tension that can be exerted by the riveted strip if the shearing stress on the rivet is not to exceed 6.9 \times 10^{7} Pa? Assume that each rivet is to carry one-quarter of the load.

Diameter of the metal strips is given as $6 \mathrm{~mm}=6 \times 10^{-3} \mathrm{~m}$ Radius will be then, $r=3 \times 10^{-3} \mathrm{~m}$ Shearing stress on the rivet is given as $6.9 \times...

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A rod of length 1.05 \mathrm{~m} having negligible mass is supported at its ends by two wires of steel (wire A) and aluminium (wire B) of equal lengths as shown in the figure. The cross-sectional areas of wires A and B are 1.0 \mathrm{~mm}^{2} and 2.0 \mathrm{~mm}^{2}, respectively. At what point along the rod should a mass m be suspended in order to produce (a) equal stresses and (b) equal strains in both steel and aluminium wires.

Solution: Cross-sectional area of wire A is given as $a_{1}=1.0 \mathrm{~mm}^{2}=1.0 \times 10^{-6} \mathrm{~m}^{2}$ Cross-sectional area of wire B is given as $a_{2}=2 m m^{2}=2 \times 10^{-6}...

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Anvils made of single crystals of diamond, with the shape as shown in the figure, are used to investigate the behaviour of materials under very high pressures. Flat faces at the narrow end of the anvil have a diameter of 0.50 mm, and the wide ends are subjected to a compressional force of 50,000 N. What is the pressure at the tip of the anvil?

The diameter of the flat faces at the narrow end of the anvil is given as, $d=0.50mm=0.5\times 10^{-3} m$ Radius will be, $r=d/2=0.25\times 10^{-3} m$ Compressional force is given as $F=50000N$...

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Four identical hollow cylindrical columns of mild steel support a big structure of a mass \mathbf{5 0 , 0 0 0} \mathrm{kg}. The inner and outer radii of each column are \mathbf{3 0} and \mathbf{6 0} \mathrm{cm} respectively. Assuming the load distribution to be uniform, calculate the compressional strain of each column.

Mass of the big structure is given as $M=50,000 \mathrm{~kg}$ Total force exerted on the four columns will be equal to the total weight of the structure, that is, $50000 \times 9.8 \mathrm{~N}$ The...

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The edge of an aluminium cube is 10 \mathrm{~cm} long. One face of the cube is firmly fixed to a vertical wall. A mass of 100 \mathrm{~kg} is then attached to the opposite face of the cube. The shear modulus of aluminium is 25 \mathbf{G P a}. What is the vertical deflection of this face?

Edge of the aluminium cube is given as $L=10 \mathrm{~cm}=10 / 100=0.1 \mathrm{~m}$ Area of each face wil be, $A=(0.1)^{2}=0.01 \mathrm{~m}^{2}$ Mass attached to the opposite face of the cube is...

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Two wires of diameter 0.25 \mathrm{~cm}, one made of steel and the other made of brass are loaded as shown in Fig. The unloaded length of steel wire is 1.5 \mathrm{~m} and that of brass wire is \mathbf{1 . 0} \mathrm{m}. Compute the elongations of the steel and the brass wires. [Young’s modulus of steel is 2.0 \mathrm{x} \left.10^{11} \mathrm{~Pa} .\left(1 \mathrm{~Pa}=1 \mathrm{~N} \mathrm{~m}^{2}\right)\right]

Diameter of the two wires is given as $d=0.25 \mathrm{~m}$ Radius of the wires is given as $r=d / 2=0.125 \mathrm{~cm}$ Unloaded length of the steel wire is given as $l_{1}=1.5 \mathrm{~m}$ Unloaded...

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On a frictionless track, a trolley moves with a speed of 36 \mathrm{~km} / \mathrm{h} with a mass of \mathbf{2 0 0} \mathrm{Kg}. A child whose mass is 20 kg runs on the trolley with a speed of 4 \mathbf{m} \mathbf{s}^{1} from one end to other which is 20 \mathrm{~m}. The speed is relative to the trolley in the direction opposite to its motion. Find the final speed of the trolley and the distance the trolley moved from the time the child began to run.

Mass is given as $m=200 \mathrm{Kg}$ Speed is given as $v=36 \mathrm{~km} / \mathrm{h}=10 \mathrm{~m} / \mathrm{s}$ Mass of boy is given as $=20 \mathrm{Kg}$ Initial momentum will be, $(M+m) v$...

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A bolt of mass 0.3 \mathrm{~kg} falls from the ceiling of an elevator moving down with a uniform speed of 7 \mathrm{~ms}^{-1}. It hits the floor of the elevator (length of elevator =\mathbf{3} \mathbf{m} ) and does not rebound. What is the heat produced by the impact? Would your answer be different if the elevator were stationary?

Mass of the bolt is given as $m=0.3 \mathrm{~kg}$ Potential energy of the bolt is given as $m g h=0.3 \times 9.8 \times 3=8.82\rfloor$ The bolt does not return to its original position. As a result,...

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A 1 \mathrm{~kg} block situated on a rough incline is connected to a spring of spring constant 100 \mathrm{N} \mathrm{m}^{-1} as shown in Fig. The block is released from rest with the spring in the unstretched position. The block moves 10 \mathrm{~cm} down the incline before coming to rest. Find the coefficient of friction between the block and the incline. Assume that the spring has a negligible mass and the pulley is frictionless.

Solution: Spring constant is given as $\mathrm{k}=100 \mathrm{~N} \mathrm{~m}^{m}$ Displacement in the block is given as $\mathrm{x}=10 \mathrm{~cm}=0.1 \mathrm{~m}$ At equilibrium: Normal reaction...

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A bullet of mass 0.012 \mathrm{~kg} and horizontal speed 70 \mathrm{~m} \mathrm{~s}^{-1} strikes a block of wood of mass 0.4 \mathrm{~kg} and instantly comes to rest with respect to the block. The block is suspended from the ceiling by means of thin wires. Calculate the height to which the block rises. Also, estimate the amount of heat produced in the block.

Mass of the bullet is given as $m_{1}=0.012 \mathrm{~kg}$ Initial speed of the bullet is given as $u_{1}=70 \mathrm{~m} / \mathrm{s}$ Mass of the wooden block is given as $m_{2}=0.4 \mathrm{~kg}$...

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A person trying to lose weight (dieter) lifts a 10 kg mass, one thousand times, to a height of 0.5 \mathrm{~m} each time. Assume that the potential energy lost each time she lowers the mass is dissipated. (a) How much work does she do against the gravitational force? (b) Fat supplies 3.8 \times 10^{7} \mathrm{~J} of energy per kilogram which is converted to mechanical energy with a 20 \% efficiency rate. How much fat will the dieter use up?

Mass is given as $\mathrm{m}=10 \mathrm{~kg}$ Height to which the mass is lifted is given as $h=0.5 \mathrm{~m}$ Number of times is hiven as $n=1000$ (a) Work done against gravitational force can be...

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The bob of a pendulum is released from a horizontal position. If the length of the pendulum is 1.5 \mathrm{~m}, what is the speed with which the bob arrives at the lowermost point, given that it dissipated 5 \% of its initial energy against air resistance?

Length of the pendulum is given as $\mid=1.5 \mathrm{~m}$ Potential of the bob at the horizontal position is given as $=m g h=m g \mid$ When the bob goes from the horizontal position to the lowest...

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Two identical ball bearings in contact with each other and resting on a frictionless table is hit head-on by another ball bearing of the same mass moving initially with a speed V. If the collision is elastic, which of the following figure is a possible result after collision?

Solution: The mass of the ball bearing is given as $\mathrm{m}$ Before the collision, Total Kinetic Energy of the system will be $=1 / 2 m v^{2}+0=1 / 2 m v^{2}$ After the collision, Total Kinetic...

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Answer carefully, with reasons :
(a) In an inelastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision of the balls (i.e. when they are in contact)?
Is the total linear momentum conserved during the short time of an inelastic collision of two balls?
(b) If the potential energy of two billiard balls depends only on the separation distance between their centres, is the collision elastic or inelastic? (Note, we are talking here of potential energy corresponding to the force during a collision, not gravitational potential energy).

(a) In an inelastic collision, there will be a loss of kinetic energy. After a collision, the K.E is always lower than the K.E before the impact. In an inelastic collision, the system's total linear...

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Underline the correct alternative:
(a) The rate of change of total momentum of a many-particle system is proportional to the external force/sum of the internal forces on the system
(b) In an inelastic collision of two bodies, the quantities which do not change after the collision is the total kinetic energy/total linear momentum/total energy of the system of two bodies.

(a) External force Internal forces, regardless of their direction, cannot cause a change in momentum. As a result, the change in total momentum is proportional to the system's external force. (b)...

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Underline the correct alternative:
(a) When a conservative force does positive work on a body, the potential energy of the body increases/decreases/remains unaltered.
(b) Work done by a body against friction always results in a loss of its kinetic/potential energy.

(a) Decreases When a body is displaced in the direction of the force, the conservative force does positive work on it, causing the body to migrate to the center of force. As a result, the distance...

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Answer the following:
(a) An artificial satellite orbiting the earth in a very thin atmosphere loses its energy gradually due to dissipation against atmospheric resistance, however small. Why then does its speed increase progressively as it comes closer and closer to the earth?(b) In the Figure, the man walks 2 \mathbf{m} carrying a mass of 15 \mathrm{~kg} on his hands. In Fig., he walks the same distance pulling the rope behind him. The rope goes over a pulley, and a mass of 15 \mathrm{~kg} hangs at its other end. In which case is the work done greater?

Solution: (a) As the satellite approaches the Earth, its potential energy drops, and since the system's total energy should remain constant, the kinetic energy increases. As a result, the...

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The potential energy function for a particle executing linear simple harmonic motion is given by V(x)=k x^{2} / 2, where k is the force constant of the oscillator. For k=0.5 \mathrm{~N} m^{-1}, the graph of \mathrm{V}(\mathbf{x}) versus \mathrm{x} is shown in Figure. Show that a particle of total energy 1 \mathrm{~J} moving under this potential must ‘turn back’ when it reaches x=\pm 2 \mathbf{m}.

Solution: Energy of the particle will be, $\mathrm{E}=1 \mathrm{~J}$ $\mathrm{K}=0.5 \mathrm{~N} \mathrm{~m}^{-1}$ $\mathrm{K} . \mathrm{E}=\frac{1}{2} \mathrm{mv}^{2}$ Based on law of conservation...

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Given in Figure, are examples of some potential energy functions in one dimension. The total energy of the particle is indicated by a cross on the ordinate axis. In each case, specify the regions, if any, in which the particle cannot be found for the given energy. Also, indicate the minimum total energy the particle must have in each case. Think of simple physical contexts for which these potential energy shapes are relevant.

(a)   (b) The total energy is given by the relation, $E=K . E .+P . E$. So, $K_{. E}=E-P . E .$ There can never be a negative amount of kinetic energy. In the region where K.E. becomes negative, the...

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A body of mass 2 \mathrm{~kg} initially at rest moves under the action of an applied horizontal force of 7 \mathrm{~N} on a table with the coefficient of kinetic friction =0.1 . Compute the
(a) work done by the net force on the body in 10 \mathrm{~s},
(b) change in kinetic energy of the body in 10 \mathrm{~s}.

Mass of the body is given as $2 \mathrm{~kg}$ Horizontal force applied is given as $7 \mathrm{~N}$ Coefficient of kinetic friction is given as $0.1$ Acceleration produced by the applied force can be...

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The sign of work done by a force on a body is important to understand. State carefully if the following quantities are positive or negative:
(a) work done by friction on a body sliding down an inclined plane,
(b) work done by an applied force on a body moving on a rough horizontal plane with uniform velocity

(a) The direction of motion of the object is opposite the direction of the frictional force, as can be seen. As a result, the work completed is negative. (b) The frictional force acting on an object...

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Assertion (A): The black body is an ideal body that emits and absorbs radiations of all frequencies. Reason (R): The frequency of radiation emitted by a body goes from a lower frequency to higher frequency with an increase in temperature.

(i) Both A and R are true and R is the correct explanation of A. (ii) Both A and R are true but R is not the explanation of A. (iii) A is true and R is false. (iv) Both A and R are false.  ...

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The hydrogen atom has only one electron, so mutual repulsion between electrons is absent. However, in multielectron atoms mutual repulsion between the electrons is significant. How does this affect the energy of an electron in the orbitals of the same principal quantum number in multielectron atoms?

Hydrogen atom has only one electron, so the mutual repulsion between the electrons is non-existent. However, in multielectron atoms the interaction between electrons is important. This is because,...

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According to de Broglie, the matter should exhibit dual behavior that is both particle and wave-like properties. However, a cricket ball of mass 100 g does not move like a wave when it is thrown by a bowler at a speed of 100 km/h. Calculate the wavelength of the ball and explain why it does not show wave nature.

Calculation: Given, Mass, m = 100g / 0.1kg Velocity = 100km/h Velocity =100×1000 / 60×60 Velocity = 1000/36m/s λ =h/mν λ = 2.387 × 10-34 m

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The Balmer series in the hydrogen spectrum corresponds to the transition from n1 = 2 to n2 = 3,4,………. This series lies in the visible region. Calculate the wavenumber of the line associated with the transition in Balmer series when the electron moves to n = 4 orbit. (RH= 109677 cm-1)

Calculation: According to Bohr’s model for the hydrogen atom; ν = RH(1/n12-1/ n22)cm-1 Given, n1 = 2 n2 = 4 H (Rydberg’s constant) = 109677 Wave number = 109677 ( ¼-1/16) Hence, Wave number =...

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Which of the following is responsible to rule out the existence of definite paths or trajectories of electrons? (i) Pauli’s exclusion principle. (ii) Heisenberg’s uncertainty principle. (iii) Hund’s rule of maximum multiplicity. (iv) Aufbau principle.

Correct Answer: (ii) Heisenberg’s uncertainty principle. Explanation: The Heisenberg's uncertainty principle states that it is impossible to know the exact position and speed of an object...

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A box contains some identical red coloured balls, labelled as A, each weighing 2 grams. Another box contains identical blue coloured balls, labelled as B, each weighing 5 grams. Consider the combinations AB, AB2, A2B and A2B3 and show that the law of multiple proportions is applicable.

AB ab2 A,B A2B3 Mass of A (in g) 2 2 4 415 Mass of B (in g) 5 10 5   According to the law of multiple proportions, Masses of B combines with a constant mass of A are 10g, 20g, 5g, 15g Simple...

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A vessel contains 1.6 g of dioxygen at STP (273.15K, 1 atm pressure). The gas is now transferred to another vessel at a constant temperature, where the pressure becomes half of the original pressure. Calculate: (i) the volume of the new vessel. (ii) a number of molecules of dioxygen.

(i) Calculation: Moles of oxygen = 1.6/32 Moles of oxygen = 0.05mol 1 mol of oxygen= 22.4L (at STP) Volume of Oxygen (V1) = 22.4 × 0.05 Volume of Oxygen (V1) = 1.12L V2 =? P1 = 1atm P2 = ½ P2 =...

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Assertion (A): Significant figures for 0.200 is 3 whereas for 200 it is 1. Reason (R): Zero at the end or right of a number are significantly provided they are not on the right side of the decimal point. (i) Both A and R are true and R is the correct explanation of A. (ii) Both A and R are true but R is not a correct explanation of A. (iii) A is true but R is false. (iv) Both A and R are false.

Correct Answer: (iii) A is true but R is false Explanation: Zero at the end of a number without the decimal point is not significantly based on the rate of accuracy.

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Assertion (A): One atomic mass unit is defined as one-twelfth of the mass of one carbon-12 atom. Reason (R): Carbon-12 isotope is the most abundant isotope of carbon and has been chosen as the standard. (i) Both A and R are true and R is the correct explanation of A. (ii) Both A and R are true but R is not the correct explanation of A. (iii) A is true but R is false. (iv) Both A and R are false.

Correct Answer: (ii) Both A and R are true but R is not the correct explanation of A Explanation: The carbon 12 isotope defines the mass of atoms and molecules.

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Assertion (A): The empirical mass of ethene is half of its molecular mass. Reason (R): The empirical formula represents the simplest whole-number the ratio of various atoms present in a compound. (i) Both A and R are true and R is the correct explanation of A. (ii) A is true but R is false. (iii) A is false but R is true. (iv) Both A and R are false.

Correct Answer: (i) Both A and R are true and R is the correct explanation of A Explanation: The empirical formula represents the simplest whole-number the ratio of various atoms present in a...

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The reactant which is entirely consumed in the reaction is known as limiting reagent. In the reaction 2A + 4B → 3C + 4D, when 5 moles of A react with 6 moles of B, then (i) which is the limiting reagent? (ii) calculate the amount of C formed?

(i) The reactant B is the the limiting reagent. (ii) Calculation: Let us consider that the reactant B got completely consumed as it is the limiting reagent. 4 mol of B gives 3 mol of C 6 mol of B...

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If two elements can combine to form more than one compound, the masses of one element that combine with a fixed mass of the other element, are in whole-number ratio. (a) Is this statement true? (b) If yes, according to which law? (c) Give one example related to this law.

(a) If two elements can combine to form more than one compound, the masses of one element that combine with a fixed mass of the other element, are in whole-number ratio and this statement is true....

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One of the statements of Dalton’s atomic theory is given below: “Compounds are formed when atoms of different elements combine in a fixed ratio” Which of the following laws is not related to this statement? (i) Law of conservation of mass (ii) Law of definite proportions (iii) Law of multiple proportions (iv) Avogadro’s law

Correct Answers: (i) Law of conservation of mass; (iv) Avogadro's law Explanation: According to the Dalton's atomic theory, The Chemical compounds are formed when atoms of various elements join in a...

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Which of the following statements is correct about the reaction given below: 4Fe(s) + 3O2(g) → 2Fe2O3(g) (i) The total mass of iron and oxygen in reactants = total mass of iron and oxygen in product therefore it follows the law of conservation of mass. (ii) The total mass of reactants = total mass of product; therefore, the law of multiple proportions is followed. (iii) Amount of Fe2O3 can be increased by taking any one of the reactants (iron or oxygen) in excess. (iv) Amount of Fe2O3 produced will decrease if the amount of any one of the reactants (iron or oxygen) is taken in excess.

Correct Answer: (i) The total mass of iron and oxygen in reactants = total mass of iron and oxygen in product therefore it follows the law of conservation of mass. Explanation: From the reaction,...

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Which of the following statements about a compound is incorrect? (i) A molecule of a compound has atoms of different elements. (ii) A compound cannot be separated into its constituent elements by physical methods of separation. (iii) A compound retains the physical properties of its constituent elements. (iv) The ratio of atoms of different elements in a compound is fixed.

Correct Answer: (iii) A compound retains the physical properties of its constituent elements Explanation: Molecule of a compound is made up of atoms of various elements which cannot be separated...

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Q36. The electrical resistivities of five substances A, B, C, S, and E are given below: A = 5.20×10-8 Ωm B = 110×10-8 Ωm C = 2.60×10-8 Ωm D = 10.0×10-8 Ωm E = 1.70×10-8 Ωmc) Which substance would you advice to be used for making heating elements of electric irons? Why? d) Which two substances should be used for making electric wires? Why?

c) B can be used in the making of the heating elements of an electric iron because the resistivity of B is the highest . d) C and E are the two substances that should be used for making electric...

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Q36. The electrical resistivities of five substances A, B, C, S, and E are given below: A = 5.20×10-8 Ωm B = 110×10-8 Ωm C = 2.60×10-8 Ωm D = 10.0×10-8 Ωm E = 1.70×10-8 Ωm a) Which substance is the best conductor of electricity? Why? b) Which one is a better conductor: A or C? Why?

Answer: a) E is the best conductor of electricity because it has the least resistivity . b) C is a better conductor between A and C because the resistivity of C is lesser than that of A .

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Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass:
(i) Show p=p_{i}^{\prime}+m_{i} V Where p_{i} is the momentum of the i^{\text {th }} particle (of mass \left.m_{i}\right) and p_{i}=m_{i} v_{i}^{t} . Note v_{i}^{\prime} is the velocity of the \mathrm{i}^{\mathrm{ith}} particle with respect to the centre of mass.Also, verify using the definition of the centre of mass that \Sigma p_{i}=0
(ii) Prove that \mathrm{K}=\mathrm{K}^{\prime}+1 / 2 \mathrm{MV}^{2} Where K is the total kinetic energy of the system of particles, K^{\prime} is the total kinetic energy of the system when the particle velocities are taken relative to the center of mass and \mathrm{MV}^{2} / 2 is the kinetic energy of the translation of the system as a whole.

i)Here $\vec{r}_{i}=\vec{r}_{i}+\vec{R}+R \ldots$ also, $\vec{V}_{i}=\vec{V}_{i}+\vec{V} \ldots \ldots .$ Where $\vec{r}_{i}^{\overrightarrow{3}}$ and $\vec{v}_{i}^{\overrightarrow{3}}$ denote the...

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