Part Test - 3 (JEE Advanced)
66 Questions MCQ Test | Part Test - 3 (JEE Advanced)
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A particle undergoes SHM with a time period of 2 seconds. In how much time will it travel from its mean position to a displacement equal to half of its amplitude :
A horizontal rod of mass m and length L is pivoted smoothly at one end. The rod ’s other end is supported by a spring of force constant k. The rod is rotated (in vertical plane) by a small angle q from its horizontal equilibrium position and released. The angular frequency of the
subsequent simple harmonic motion is :
subsequent simple harmonic motion is :
it is not taken in calculation)
A traveling wave y = A sin
passes from a heavier string to a lighter string. The reflected wave has amplitude 0.5 A. The junction of the strings is at x = 0. The equation of the reflected wave is:
passes from a heavier string to a lighter string. The reflected wave has amplitude 0.5 A. The junction of the strings is at x = 0. The equation of the reflected wave is:As wave has been reflected from a rarer medium, therefore there is no change in phase. Hence equation for the
opposite direction can be written as
A string of length 1.5 m with its two ends clamped is vibrating in fundamental mode. Amplitude at the centre of the string is 4 mm. Minimum distance between the two points having amplitude 2 mm is:
The average density of Earth’s crust 10 km beneath the surface is 2.7 gm/cm3. The speed of longitudnal seismic waves at that depth is 5.4 km/s. The bulk modulus of Earth’s crust considering its behavior as fluid at that depth, is :
The second overtone of an open pipe A and a closed pipe B have the same frequencies at a given temperature. Both pipes contain air. The ratio of fundamental frequency of A to the fundamental frequency of B is:
A thin uniform rod is suspended in vertical plane as a physical pendulum about point A. The time period of oscillation is To. Not counting the point A, the number 'n' of other points of suspension on rod such that the time period of oscillation (in vertical plane) is again To. Then the value of n is : (Since the rod is thin, consider one point for each transverse cross section of rod)
When the point of suspension is at a distance x from centre of length of rod, the time period of oscillation is
The time period of oscillation will be same (T0) if the point of suspension
is a distance x = λ/2 or x = λ/6 from centre of the rod. Thus there will be three additional points.
Two radio station that are 250m apart emit radio waves of wavelength 100m. Point A is 400m from both station. Point B is 450m from both station. Point C is 400m from one station and 450 m from the other. The radio station emit radio waves in phase. Which of the following statement is true ?
Which of the following wave(s) can produce standing wave when superposed with y = Asin (ωt + kx)?
For standing wave to be formed the interfering waves must have same amplitude, same frequency and opposite direction of traveling. These are satisfied by options A, B and C.
A spring block system is put into SHM in two experiments. In the first, the block is pulled from the equilibrium position through a displacement d1 and then released. In the second, it is pulled from the equilibrium position through a greater distance d2 and then released. In both the experiments:
In Resonance tube experiment, if 400 Hz tuning fork is used, the first resonance occurs when length of air column is 19 cm. If the 400 Hz tuning fork is replaced by 1600 Hz tuning fork then to get resonance, the water level in the tube should be further lowered by (take end correction = 1 cm) :
Reasoning Type
Statement-1 : A SHM may be assumed as composition of many SHM's.
Statement-2 : Superposition of many SHM's (along same line) of same frequency will be a SHM.
Statement-2 itself explains statement-1.
REASONING TYPE
Statement-1 : When a wave enters from one medium to another, its frequency is not changed.
Statement-2 : Speed of a wave in a medium is property of the source.
Speed of wave in a medium is property of the medium.
A sinusoidal wave is propagating in negative x–direction in a string stretched along x-axis. A particle of string at x = 2m is found at its mean position and it is moving in positive y direction at t = 1 sec. The amplitude of the wave, the wavelength and the angular frequency of the wave are 0.1meter, π/4 meter and 4π rad/sec respectively.
Q. The equation of the wave is :
The equation of wave moving in negative x-direction, assuming origin of position at x = 2 and origin of time (i.e. initial time) at t = 1 sec.
Shifting the origin of position to left by 2m, that is, to x = 0. Also shifting the origin of time backwards by 1 sec, that
is to t = 0 sec.
A sinusoidal wave is propagating in negative x–direction in a string stretched along x-axis. A particle of string at x = 2m is found at its mean position and it is moving in positive y direction at t = 1 sec. The amplitude of the wave, the wavelength and the angular frequency of the wave are 0.1meter, π/4 meter and 4π rad/sec respectively.
Q. The speed of particle at x = 2 m and t = 1sec is :
A sinusoidal wave is propagating in negative x–direction in a string stretched along x-axis. A particle of string at x = 2m is found at its mean position and it is moving in positive y direction at t = 1 sec. The amplitude of the wave, the wavelength and the angular frequency of the wave are 0.1meter, π/4 meter and 4π rad/sec respectively.
Q. The instantaneous power transfer through x=2 m and t= 1.125 sec is :
Hence at t = 1.125 sec, that is, at T/4
seconds after t = 1 second, the particle is at rest at extreme position. Hence
instantaneous power at x = 2 at t = 1.125 sec is zero.
Matrix - Match Type
For a particle executing SHM along a straight line, match the statements in column-I with statement in column-II. (Note that displacement given in column-I is to be measured from mean position).
which maybe a circle if ω = 1 and ellipse of ω 
1.Acceleration-displacement graph is straight and acceleration time graph is sinusoidal
Two particles P1 and P2 are performing SHM along the same line about the same mean position. Initially they are at their positive extreme position. If the time period of each particle is 12 sec and the difference of their amplitudes is 12 cm then find the minimum time in seconds after which the separation between the particles become 6 cm.
A weightless rigid rod with a small iron bob at the end is hinged at point A to the wall so that it can rotate in all directions. The rod is kept in the horizontal position by a vertical inextensible string of length 20 cm, fixed at its mid point. The bob is displaced slightly, perpendicular to the plane of the rod and string. Find period of small oscillations of the system in the form 
second. and fill value of X. (g = 10 m/s2)
The bob will execute SHM about a stationary axis passing through AB. If its effective length is l' then
A straight line source of sound of length L = 10m, emitts a pulse of sound that travels radially outward from the source. What sound energy (in mW) is intercepted by an acoustic cylindrical detector of surface area 2.4cm2, located at a perpendicular distance 7m from the source. The waves reach perpendicularly at the surface of the detector. The total power emitted by the source in the form of sound is 2.2 × 104 W.
(Use π = 22/7)
Imagine a cylinder of radius 7m and length 10m. Intensity of sound at the surface of cylinder is same everywhere.
In the figure shown strings AB and BC have masses m and 2m respectively. Both are of same length l. Mass of each string is uniformly distributed on its length. The string is suspended vertically from the ceiling of a room. A small jerk wave pulse is given at the end 'C'. It goes up to upper end 'A' in time 't'. If m = 2 kg, l = 
, Then find the value of 't' in seconds
For the given reaction the correct reactivity order of H-atoms is :
Reactivity depends upon stability of free radicals generated at y,zx and w respectively.
In the given sequence of reactions which of the following is the correct structure of compound A.
Which of the following is not correctly ordered for resonance stability
Follow the rules for stability of resonating structures (structure with more number of p-bonds is more stable).
Amongst the following compounds select the strongest acid.
In acid (C), the group at ortho position is a –M group.
Amongst the following compounds select the strongest acid.
Sulphonic acid will be strongest acid.
Amongst the following compounds select the correct acidic strength order
–M effect increases acidic strength more as compare to –I effect.
Arrange the following carbocations in increasing order of stability:
Give the stability order of the following carbocations.
In (IV) and (I) the carbocation is directly stabilised by + m effect of NH2 and OCH3
According to the rules.
Which of the following orders is/are correct with their mentioned property?
Ortho effect in first compound of (A) increases acidity.
In (C) N atom in first compound does not undergo resonance. Hence, more basic.
In (D) NH2–OH is less basic because of –I effect of OH group.
In (B) first compound is more basic as lone pair of nitrogen easily available for the donation because of compact
structure.
In (C) basic strength in water is determined also due to H-bonding and solvation effect.
REASONING TYPE
Statement-1 : Sulphanilic acid (p-Aminobenzene sulphonic acid) is stronger acid than sulphonic acid.
Statement-2 : Sulphanilic acid exists as zwitter ion and 
ion is lost from group 
.
Statement-1 : o-hydroxybenzaldehyde is a liquid at room temperature while p-hydroxybenzaldehyde is a high melting solid.
Statement-2 : Chelation make the former molecule thermodynamically more stable.
Intramolecular H bonding decreases its assocation with other molecules, hence it is a liquid.
The concept of resonance explains various properties of compounds. The molecules with conjugated system of π bonds, are stabilized by resonace and have low heat of hydrogenation. Hyperconjugative stabilization also decreases heat of hydrogenation. In aromatic rings a functional group with a lone pair of electron exerts + m effect. Some functional groups like –NO, –NC, –CH=CH2 can function both as electron releasing (+m, +R) or electron withdrawing (– m, – R) groups. More extended conjugation provides more stabilization.
Q. The correct heat of hydrogenation order is
(p) 1, 3-Pentadiene (q) 1, 3-Butadiene
(r) 2, 3-Dimethyl-1, 3-butadiene (s) Propadiene
The concept of resonance explains various properties of compounds. The molecules with conjugated system of π bonds, are stabilized by resonace and have low heat of hydrogenation. Hyperconjugative stabilization also decreases heat of hydrogenation. In aromatic rings a functional group with a lone pair of electron exerts + m effect. Some functional groups like –NO, –NC, –CH=CH2 can function both as electron releasing (+m, +R) or electron withdrawing (– m, – R) groups. More extended conjugation provides more stabilization.
Q. The most stable carbocation is
The concept of resonance explains various properties of compounds. The molecules with conjugated system of π bonds, are stabilized by resonace and have low heat of hydrogenation. Hyperconjugative stabilization also decreases heat of hydrogenation. In aromatic rings a functional group with a lone pair of electron exerts + m effect. Some functional groups like –NO, –NC, –CH=CH2 can function both as electron releasing (+m, +R) or electron withdrawing (– m, – R) groups. More extended conjugation provides more stabilization.
Q. The most stable resonating structure of following compound is
Matrix - Match Type
Match the electronic effects responsible for the stability of given intermediates in Column-I.
How many compounds give CO2 gas on reaction with NaHCO3 ?
Picric acid, benzoic acid and sulphonic acid give CO2 gas with NaHCO3
In how many compounds delocalisation of electrons is possible ?
4, 6, 9, 10 have delocalisation.
How many products (structural isomers) are formed by monochlorination of given compound ?
All 13 carbon atoms are chemically different and all have hydrogen atoms.
Find the sum of number of stereoisomers and stereocentres for the given compound.
It is a case of symmetrical compound with 3 stereocenters & number of steroisomers = 2n–1 = 4.
So total = 7
In triangle ABC, area of triangle D and angle A are fixed. The angles B and C and length of sides a, b, c, are variable quantities. If length of the side a is minimum, then
Triangles ABC and DEF have sides of lengths a, b, c and d, e, f respectively (symbols are as per usual notations). a, b, c and d, e, f satisfy the relation 
then
Let θ1, θ2, θ3, ..... be a sequence with θ1 = π/3 and 
is equal to
If a, b, c are the sides of a triangle such that b c = λ2, for some positive values of λ, then
If a, b, c are the sides of a triangle, then the minimum value of 
is
where n is a prime number greater than 2, then the value of 
In a triangle ABC, a, b, and A are given, b > a and c1, c2 are two possible values of the third side c. If Δ1 and Δ2 are areas of two triangles with sides a, b, c1 and a, b, c2 then
In a triangle ABC, points D and E are taken on side BC such that BD = DE = EC.
If 
ADE = AED = θ then
In a triangle ABC, which of the following is not possible ?
A triangle is inscribed in a circle, the vertex of triangle divides the circle into three arcs of length 3, 4 and 5
unit,then area of ΔABC is –
REASONING TYPE
Statement-1 : In a ΔABC if cos A cos B + sin A sin B sin C = 1, then ABC is right angle triangle.
Statement-2 : If k < p + qr < p + q < k, then k = p + qr = p + q = k and r = 1.
where n! = 1.2 ........... . n, then 
Let ABC be a triangle and D, E, F be the feet of perpendiculars from incentre to sides BC, CA, AB respectively. If R1, R2, R3 are radii of circles with centres C1, C2, C3 inscribed in quadrilaterals AFIE, BDIF, CEID respectively. Tangent M1N1 to circle with centre C1 is parallel to BC, where M1N1 = x as shown in the figure. I1, I2, I3 are ex-centres of ΔABC.
Q. AC1 , AI, AI1 are proportional to
Let ABC be a triangle and D, E, F be the feet of perpendiculars from incentre to sides BC, CA, AB respectively. If R1, R2, R3 are radii of circles with centres C1, C2, C3 inscribed in quadrilaterals AFIE, BDIF, CEID respectively. Tangent M1N1 to circle with centre C1 is parallel to BC, where M1N1 = x as shown in the figure. I1, I2, I3 are ex-centres of ΔABC.
Q. 
Let ABC be a triangle and D, E, F be the feet of perpendiculars from incentre to sides BC, CA, AB respectively. If R1, R2, R3 are radii of circles with centres C1, C2, C3 inscribed in quadrilaterals AFIE, BDIF, CEID respectively. Tangent M1N1 to circle with centre C1 is parallel to BC, where M1N1 = x as shown in the figure. I1, I2, I3 are ex-centres of ΔABC.
Q
A triangle ABC satisfies the relation 2sec4C + sin22A + 
= 0 and a point P is taken on the longest
side of the triangle such that it divides the side in the ratio 1 : 3. Let Q and R be the circumcenter and
orthocenter of ΔABC. If PQ : QR : RP = 1 : α : β, then find the value of α2 + β2.
Find the smallest positive integer 'p' for which the equation cos (p sinx) = sin (p cosx) has a solution
in [0, 2π].
Find the number of pairs (x, y) satisfying the equations sin x + sin y = sin (x + y) and |x| + |y| = 1.
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