JEE Advanced Practice Test- 7 National Level Test Series MCQs & solutions

A tank of uniform cross-section is completely filled with ice. The height of ice is H and its mass is m. When the entire ice melts, the work done by gravity is  

(ρ_ice = 0.9 gm/cc, ρ_water = 1 g/cc and g represents acceleration due to gravity) 

A hydrogen like species having atomic number Z = 2, in ground state, is excited by means of electromagnetic radiation of frequency 1.315 × 10¹⁶ Hz. How many spectral lines will be observed in the emission spectrum? 

(Planck’s constant h = 4.14 × 10^-15 eVs) 

Velocity of a point on the equator of a rotating spherical planet is v. The angular velocity of the planet is such that the apparent value of acceleration due to gravity ‘g’ at the equator is half of that at the poles. The escape velocity of a particle from the surface of the planet is  

A positive charge q is projected from origin with a velocity along positive x-axis in a region having uniform magnetic field directed towards negative y-axis. If T is the time period of circular motion then the velocity vector of charge q at some instant t where 

Four charges q₁, q₂, q₃ and q₄ are placed at the positions as shown in the figure, given q₁ +q₂+ q₃ + q₄ = 0 . The electric field on z-axis  

For the circuit as shown in the figure q₁ and q₂ be the charges on 3μF and 6μF capacitors respectively, then 

A ball is released from position A and drops 10 m before striking a smooth incline. The coefficient of .  If the time taken by the ball to strike the incline again is t then find the value of t² [in (second)²]. (g = 10 m/s²) 

Two identical beads P and Q of mass 1 kg each are connected by an inextensible massless string and they can slide along the two arms AB and BC of a rigid smooth wire frame in vertical plane. If the system is released from rest and vQ is the speed of bead Q when they have both moved by a distance of 0.1 m then find the value of (in m/s). (g = 10 m/s²) 

A solid uniform sphere rotating about its axis with kinetic energy E_o is gently placed on a rough horizontal plane. The coefficient of friction on the plane varies from point to point. After some time, the sphere begins pure rolling with total kinetic energy equal to E. Then find the value of 

A variable voltage V = 2t is applied across an inductor of inductance L = 2H as shown in figure. Then find the rate at which magnetic potential energy stored in the inductor is increasing at t = 1 s (in J/s). Take the current through the inductor at t = 0 as zero. 

A calorimeter of mass m contains an equal mass of water in it. The temperature of water and calorimeter is t₂. A block of ice of mass m and temperature t₃ < 0^oC is gently dropped into the calorimeter. Let C₁, C₂ and C₃ be the specific heats of calorimeter, water and ice respectively and L be the latent heat of fusion of ice.  

Q. 

The whole mixture in the calorimeter becomes ice if  

A calorimeter of mass m contains an equal mass of water in it. The temperature of water and calorimeter is t₂. A block of ice of mass m and temperature t₃ < 0^oC is gently dropped into the calorimeter. Let C₁, C₂ and C₃ be the specific heats of calorimeter, water and ice respectively and L be the latent heat of fusion of ice.  

Q. 

The whole mixture in the calorimeter becomes water if  

A calorimeter of mass m contains an equal mass of water in it. The temperature of water and calorimeter is t₂. A block of ice of mass m and temperature t₃ < 0^oC is gently dropped into the calorimeter. Let C₁, C₂ and C₃ be the specific heats of calorimeter, water and ice respectively and L be the latent heat of fusion of ice.

Q. 

Water equivalent of calorimeter is  

A parallel plate capacitor has its plate horizontal with air occupying the space between the plates. The upper plate is fixed with a rigid support and the lower one is connected to a spring as shown. The distance between the plates is d₁. Now the capacitor is connected with an electric source having voltage V. The separation between the plates changes to d₂ at equilibrium. The mass of lower plate is ‘m’ and cross-sectional area of each plate is A.

Q. 

The spring constant k is  

A parallel plate capacitor has its plate horizontal with air occupying the space between the plates. The upper plate is fixed with a rigid support and the lower one is connected to a spring as shown. The distance between the plates is d₁. Now the capacitor is connected with an electric source having voltage V. The separation between the plates changes to d₂ at equilibrium. The mass of lower plate is ‘m’ and cross-sectional area of each plate is A.

Q. 

The maximum voltage V_m for a given k for which an equilibrium exists is  

A parallel plate capacitor has its plate horizontal with air occupying the space between the plates. The upper plate is fixed with a rigid support and the lower one is connected to a spring as shown. The distance between the plates is d₁. Now the capacitor is connected with an electric source having voltage V. The separation between the plates changes to d₂ at equilibrium. The mass of lower plate is ‘m’ and cross-sectional area of each plate is A.

Q. 

When lower plate is slightly displaced about equilibrium position, time period T of small oscillations is  

A certain weak acid has a dissociation constant 1.0 x 10^-4. The equilibrium constant for its reaction with strong base is  

The major product formed in the following reaction is 

Identify the major product of the following reaction: 

The oxidation state of molybdenum in [(η⁷-tropylium)Mo(CO)₃]⁺ is 

In metal-olefin interaction, the extent of increase in metal ⎯→ olefin π-back-donation would 

The highest oxidation state of an element in the following compound that behaves as an acid in H₂SO₄ is  

AcOH, HNO₂,  HNO₃, H₂O, HClO, HClO₄

How many unpaired electrons are present in O₂ molecule? 

One mole of Pb₃O₄ is separately reacted with excess of HCl and HNO₃. The difference in moles of HCl and HNO₃ is 

How many moles of phenyl hydrazine are used in the formation of osazone from glucose? 

How many S – S bonds are present in (SO₃)₃. 

If a concentrated solution of copper sulphate is placed at the bottom of a beaker of water or that of a dilute solution of copper sulphate is carefully poured over it there will be a two distinct layer visible. However, after some time the boundaries will disappear. This property is called diffusion. If we now consider a solution which is separated from the pure solvent by a semipermeable membrane then the solvent particles move from the pure solvent region through the SPM to the solution region. This phenomenon is called osmosis.

Q. 

for an indefinitely dilute boundary then dμ₁ is 

If a concentrated solution of copper sulphate is placed at the bottom of a beaker of water or that of a dilute solution of copper sulphate is carefully poured over it there will be a two distinct layer visible. However, after some time the boundaries will disappear. This property is called diffusion. If we now consider a solution which is separated from the pure solvent by a semipermeable membrane then the solvent particles move from the pure solvent region through the SPM to the solution region. This phenomenon is called osmosis.

Q. 

Which of the following solution has highest osmotic pressure? 

If a concentrated solution of copper sulphate is placed at the bottom of a beaker of water or that of a dilute solution of copper sulphate is carefully poured over it there will be a two distinct layer visible. However, after some time the boundaries will disappear. This property is called diffusion. If we now consider a solution which is separated from the pure solvent by a semipermeable membrane then the solvent particles move from the pure solvent region through the SPM to the solution region. This phenomenon is called osmosis.

Q. 

Which of the following is correct?

Thionyl chloride can be synthesized by chlorinating SO₂ using PCl₅. Thionyl chloride is used to prepare anhydrous ferric chloride starting from its hexahydrated salt. Alternatively, the anhydrous ferric chloride can also be prepared from hexahydrated salt by treating with 2,2-dimethoxypropane.

Q. 

Consider the following reaction 

The compound X is