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A wall is moving with constant velocity u towards a fixed source of sound of frequency 'f'. The velocity of sound is 'v'. The wavelength of the sound reflected by the wall is
Frequency of sound reflected by wall f' =
∴ Wave length of sound reflected by wall =
In the figure shown, a small block of mass m moves in fixed semicircular smooth track of radius R in vertical plane. It is released from the top. The maximum centrifugal force on the block at the lowest point of track is.
A uniform thin rod of mass m and length R is placed normally on surface of earth as shown. The mass of earth is M and its radius is R. Then the magnitude of gravitational force exerted by earth on the rod is
At the middle of the mercury barometer tube there is a little column of air with the length and there is vacuum at the top as shown. Under the normal atmospheric pressure and the temperature of 300 kelvin,
= 10 cm. Neglect expansion of the tube. The length of the air column if the temperature rises to 330 kelvin will be -
Pressure in the air inside the column of merucry is equal to the weight of mercury ove the air divided by the internal cross sectional area of the tube. when the temprature increase, the weight of the upper part of the mercury column does not change. That is why the pressure in the air is also constant. For the isobaric process, the change in volume is proportional to the change in temperature. The same is true for the lengths of the air column.
A transverse periodic wave on a string with a linear mass density of 0.200 kg/m is described by the following equation y = 0.05 sin(420t – 21.0 x) where x and y are in metres and t is in seconds. The tension in the string is equal to :
(μ = mass per unit length)
A uniform thin rod of mass ‘m’ and length L is held horizontally by two vertical strings attached to the two ends. One of the string is cut. Find the angular acceleration soon after it is cut :
Immediately after string connected to end B is cut, the rod has tendency to rotate about point A.
Torque on rod AB about axis passing through A and normal to plane of paper is -
Alternative
Applying Newton's law on center of mass
mg-T = ma ..(I)
Writing τ = Iα about center of mass
..(II)
..(III)
From (i) , (ii) and (iii)
Calculate moment of inertia of the system about axis AB shown in figure. Each segment of the system is made of a uniform wire of mass per unit length , where r is radius of each segment. The axis of full ring is along Y–axis. The axis of the semicircular rings are along x and z–axis. The centres of all rings coincide at the origin.
An aircraft moving with a speed of 972 km/h is at a height of 6000 m, just overhead of an anti-aircraft gun. If the muzzle velocity of the gun is 540 ms, the firing angle θ for the bullet to hit the aircraft should be
Displacement of airctaft in time t = horizontal displacement of projectile
A train is running at a speed of 108 km/hr. An inspection cart is also moving with a speed 10m/s in the same direction as train. The train hits the cart . The velocity of the cart after the collision is (in m/s) nearly.
(Assuming mass of train is much larger compared to mass of cart)
From momentum conservation
M * 30 + m * 10 = Mv1 + mv2 ..(i)
e * velocity of approch = velocity of separation
on solving,
An ice block at 0°C is dropped from height ‘h’ above the ground. What should be the value of ‘h’ so that it just melts completely by the time it reaches the bottom assuming the loss of whole gravitational potential energy is used as heat by the ice ? [Given : Lf = 80 cal/gm]
Applying energy conservation :
mgh = mLf
Find maximum amplitude for safe SHM(block does not topple during SHM) of a uniform cubical block of side 'a' on a smooth horizontal floor as shown in figure (sptring is massless) :
In the figure shown, the pulleys and strings are massless. The acceleration of the block of mass 4m just after the system is released from rest is
The FBD of blocks is as shown
From Newton's second law
4mg - 2T cos θ = 4mA ....(1)
and T - mg = ma .....(2)
and from constraint we get a = A cos θ ... (3)
solving equation (1) , (2) and (3)
we get acceleration of block of mass 4 m, a = 5g/11 downwards.
In the figure shown, a light container is kept on a horizontal rough surface of coefficient of friction . A very small hole of area S is made at depth 'h'. Water of volume 'V' is filled in the container. The friction is not sufficient to keep the container at rest. The acceleration of the container initially is
Let the density of water be ρ, then the force by escaping liquid on container =
∴ acceleration of container a =
A solid sphere of iron at 2°C is lying at the bottom of a bucket full of water at 2°C. If the temperature of the water is increased to 3°C, the buoyant force on the sphere due to water will.
As the temperature of water is increased from 2°C to 3°C the density of water increases (remember anamolous behaviour of water), also the volume of sphere increases. Therefore bouyant force on sphere due to water shall increase.
Two sources S1 and S2 of same frequency f emits sound. The sources are moving as shown with speed u each. A stationary observer hears that sound. The beat frequency is (v = velocity of sound)
Apparent frequency of S1 and S2 heard by observer is
∴
A body performs SHM along the straight line segment ABCDE with C as the mid point of segment AE (A and E are the extreme position for the SHM). Its kinetic energies at B and D are each one fourth of its maximum value. If length of segment AE is 2R, then the distance between B and D is
When the particle crosses D, its speed is half the maximum speed.
A wall is made of two layers A and B of the same thickness but different materials as shown. The thermal conductivity of A is thrice that of B. In steady state, the temperature difference across the wall is 360C. The temperature difference across the layer A is :
The two are in series.
KA = 3KB
i.e thermal resistance of A(say RA) is one third that of B(say RB)
i.e RB = 3RA
∴ Temperature difference across 'A' =
Man A is sitting in a car moving with a speed of 54 km/hr observes a man B in front of the car crossing perpendicularly a road of width 15 m in three seconds. Then the velocity of man B (in m/s) will be:
Velocity of A and Velocity of B relative to A are as shown.
and direction of is away from
In the figure shown, the minimum force F to be applied perpendicular to the incline so that the block does not slide is : (The block is always in contact with the incline)
A large open tank has two small holes in its vertical wall as shown in figure. One is a square hole of side 'L' at a depth '4y' from the top and the other is a circular hole of radius 'R' at a depth ‘y’ from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both holes are the same. Then, 'R' is equal to :
Let v1 and v2 be the velocity of efflux from square and circular hole respectively. S1 and S2 be cross - section areas of square and circular holes.
The volume of water coming our of square and circular hole per second is
Given that
where a = constant. Using dimensional analysis, the value of n is
A train passes an electric post in 8 seconds and a bridge of length 1km in 108 seconds. The speed of the engine is
The negineer of a train moving at a speed v1 sights a freight train a distance d ahead of him on the same track moving in the same direction with a slow speed v2. He puts on the brakes and gives his train a constant deceleration α. Then there will be no collision if
Sixty four spherical rain drops of equal size are falling vertically through air with a terminal velocity 1.5 ms–1. If these drops coalesce to form a big spherical drop, then terminal velocity of big drop is
The average force necessary to stop a bullet of 20 kg at a speed of 250 m/s as it penetrates wood to a distance of 12 cm is
If a body is placed on another body which is accelerating by an external force then work done by frictional force on the upper body relative to ground is
A pump can hoist 9000 kg of coal per hour from a mine of 120 m deep. Then the power in watts, assuming that its efficiency is 75% is
Let ar and at represent radial and tangential acceleration. The motion of a particle may be circular if
A rod is of length 3 m and its mass per unit length is directly proportional to the distance x from its one end. The cetnre of gravity of the rod from that end will be at
Given that,
Length = 3 m
Let us consider an elementary length dx.
Its mass acting per unit length is directly proportional to distance x from one of its end.
Its mass is
Where,
We need to calculate the center of gravity of the rod
Using formula of center of gravity
Put the value into the formula
Hence, The center of gravity from the end of the rod is 2 cm.
The speed of a homogeneous solid sphere after rolling downs an inclined plane of verticle height h, from rest
without sliding is
The angular velocity of the wheel increases from 1200 to 4500 rev per min in 10 seconds. Then the number of revolutions made during this time is
The period of the satellite of the earth orbiting very near to the surface of the earth is T0. What is the period of the geostationary satellite in term of T0 ?
A particle undergoing SHM has the equation : x = A sin (ωt + φ), where x represents the displacement of the particle. The kinetic energy (K.E.) oscillates with the time period
A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If entire arrangement is put in a freely falling elevator, the length of water column in the capillary tube will be
Two mole of argon are mixed with one mole of hydrogen, the Cp/ Cv for the mixture is nearly
The rms speed of a certain gas is v at 400 K. The temperature at which the rms speed become two times, will be
For isothermal expansion of a perfect gas, the value of is equal to
The maximum wavelength of radiation emitted at 900K is 4 μm. The maximum wavelength of radiation emitted at 1200 K, will be
On producing the waves of frequency 1000 Hz in a Kundt’s tube, the total distance between 6 successive nodes is 85 cm. Speed of sound in the gas filled in the tube is
The phase difference between two points separated by 0.8 m in a wave of frequency 120 Hz is 0.5 π. The velocity of wave will be
Wave number of a spectral line for a given transition is x cm–1 for Be+3, then its value for He+ for same transition is
Equilibrium constant of the reaction of NH4OH with strong acid is 109. Initially a solution of 0.05 M (NH4)2SO4 and 0.1 M NH4NO3 is prepared. If 0.1 M NaOH is added in equal volume, then pH change of solution nearly will be(log 2 = 0.3):
pKb = 5, c = Concentration of NH4+ (undergoes hydrolysis)
= 0.05 x 2 + 0.1 = 0.2 M
So change in pH = 9-4.85 = 4.15
At what temperature root mean square speed of N2 gas is equal to that of propane gas at S.T.P. conditions
Let Temp (T) where Vms of N2 = Vms of C3H8 at STP
T1 = 173.72 K
Which one of the following statements is correct in relation to ionization enthalpy ?
As value of ‘n’ i.e. principal quantum number increases, the size of atom increases and the distance between valence electrons and nucleus increases. As a result, the attraction between the valence electrons and nucleus decreases. This fascilitates the easier removal of valence electrons.
What is the molecular geometry of 1 : 1 adduct of pyridine (Lewis base) and SF4 (Lewis acid) about sulphur atom ?
(A) It is optically active due to presence of only one chiral carbon.
(B) It has two chiral carbon atoms but due to plane of symmetry it is optically inactive.
(C) It has two chiral carbons atoms (*) without plane of symmetry
hence it is chiral compund
(D) There is no chiral carbon in allene, but the molecule is dissymmetric so it is chiral.
The parent chain is So basic name is Ethyl prpanoate then, consider two substitutes at position 2 and name them.
In the reaction CuS + KMnO4 + H+ → Cu2+ + SO2 + Mn+2 + H2O, moles of CuS reacting completely with 2 moles of KMnO4 are :
(A) According to VSEPR theory in trigonal bi pyramidal structure, more electronegative atom should occupy axial positions.
(B) Among the H2O and H2S, H2S has lesser bond angle because of Drago rule.
(C) O2F2 has smaller O-O bond length than in H2O2, due to lesser repulsion between two O-atoms in O2F2
(D) Based of facts
Of the five isomeric hexanes,the isomer which can give five monochlorinated structural products :
2-Methylpentane has five chemically different types of hydrogen atoms so it can give five monochlorinated structural compounds.
A solution is a mixture of 0.05 M KCI and 0.05 M NaI. The concentration of I— in the solution when AgCI just starts to precipitate is equal to: (KSPAgCI = 10–10 M2; KSPAgI = 4 × 10–16 M2)
For AgCl precipitation
For Agl precipitation
Thus agl will precipitation first. AgCl will precipitate only when,
[Ag+] = 2 x 10-9; thus
H2O2 acts as both oxidising as well as reducing agent. As oxidising agent, its product is H2O but as reducing
agent, its product is O2. Volume strength has great significance for chemical reactions. The strength of ‘10V’ means 1 volume (or litre) of H2O2 on decomposition (H2O2 → H2O + ½ O2) gives 10 volumes (or litre) of oxygen at NTP. 15 g Ba(MnO4)2 sample containing inert impurity is completely reacting with 100 mL of ‘11.2 V’ H2O2, then what will be the % purity of Ba (MnO4)2 in the sample : (Atomic mass : Ba = 137, Mn = 55)
Milli equivalents of Ba(MnO4)2 reacted = milli equivalents of H2O2 reacted
∴ m = 7.5g
∴ wt. of Ba(MnO4)2 in sample = 7.5g
% purity of Ba(MnO4)2 in sample =
consider the following reactions :
The heat of formation of CO (g) is :
ΔH2 = -y kJ/mole
so,
Bicarbonate (HCO3–) exists in KHCO3 and NaHCO3 respectively as :
HCO3- in crystalline KHCO3 exists as dimer and HCO3- in crystalline NaHCO3 exists as polymeric chain form.
The number of six membered carbon rings in the structure of Buckminsterfullerene (i.e. C60) is :
It contains twenty six–membered rings and twelve five–membered rings.
D-Fructose (C6H12O6) has IUPAC name 1, 3, 4, 5, 6-Pentahydroxyhexan-2-one. Its last asymmetric carbon atom (C*5) has D-configuration. The correct stereochemical formula of L-Fructose is :
Mirror image of D-fructose
The hyperconjugative stability of tert-butyl cation is due to :
in tert-butyl cation, carbon bearing ⊕ charges has one vacant p orbital hence it is σ - p (empty) conjuction or Hyperconjugation.
Mirror image non Superimposable isomers.
Na2O2 is powerful oxidant and bleaching agent and bleaches red litmus paper to white in aqueous solution.
Caluclate ΔfG0 for (NH4Cl, s) at 310K
Given :
ΔfH0 (NH4Cl, s)= -314.5 kJ/mol; Δr Cp = 0
All given data are at 300 K
B2H6 + 2P(CH3)3 → 2H3 B P(CH3)3
Small amines such as NH3 , CH3NH2 and (CH3)2 NH given unsymmetrical cleavage of diborane
For a neutral unexcited atom, consider four electrons identified by the quantum number n and l :
(i) n = 4, l = 1
(ii) n = 4, l = 0
(iii) n = 3, l = 2
(iv) n = 3, l = 1
They can be placed in order of increasing energy as
Which of the following pairs will combine through a coordinate bond?
A real gas obeying van der Waals equation will resemble an ideal gas if
If the enthalpy of vaporization of water is 186.5 J mol–1, the entropy of its vaporization will be
If at 298 K the bond energies of C – H, C – C, C = C and H – H bonds are 414 kJ mol–1, 347 kJ mol–1, 615 kJ mol-1 and 435 kJ mol–1 respectively, the value of enthalpy change for the reaction
H2C = CH2 (g) + H2 (g) → H3C – CH3 (g)
at 298 K will be
When 1 mole of ethanol is mixed with 1 mole of acetic acid, 0.67 mole of ethyl acetate is produced at equilibrium. Calculate Kc for the reaction.
When AgNo3 is heated in a closed vessel, O2 gas is liberated and AgNO2 is left behind .
At equilibrium
When equal volumes of the following solutions are mixed, the precipitation of AgCl will occur only with (given
Ksp of AgCl = 1.8 × 10–10)
For a weak monoprotic acid, the pH of a given concentration is calculated by the equation
A commercial sample of H2O2 can be slowed down by the addition of small amount of phosphoric acid which acts as
The total number of isomers having the molecular formula C4H8 is
Homolytic fission of carbon-carbon bond of ethane produces an intermediate in which the carbon atom is in
In CH3CH2OH, the bond that undergoes heterolytic cleavage most readily is
Which of the following regents will not convert ethyl alcohol into ethyl chloride?
Consider the following –
integument of pinus seed, endosperm of cycas, gemmae cup, prothallus, protonema, foot of sporophyte, leaf of pteris, coralloid roots, rhizoids of marchantia
How many are diploid
sporophytic generation is haploid and gametophytic generation is diploid
marchantia is bryophyte and have notile male gamete
b) both archegonium and anther have same ploidy
Anther culture offers excellent opportunities for large-scale production of haploids, although problems include the occurrence of albinos and induction of genetic variation.
Ploidy level of antheridium and archegonium is haploidic (1n). Antheridium is a male reproductive structure producing male gametes i.e, sperm in plants such as mosses, fungi and ferns etc.
Consider the following-
(1) all tracheophyte are cryptogemae
(2) all archegoniateae are diplontic
how many are correct
bryophyte are haplodiplontic archegoniateae and bryophyte are cryptogemae
gametophyte of diplontic plant is always dioceious
Adiantum is homosporus pteridophyte can have monoceious gametophyte
Metabolic reactions are features of living organism as which is most correct –
metabolic reactions are feature of living as it occur inside body
D
nitobactor is eubacteria
Consider the following feature-
Chla, PSII, chloroplast, flagellated, aquatic, equal flagella
Given features are present in-
fucus have equal size flagella
Consider the following statement-
(A) Dikaryon not occurs in agaricus
(B) zygospore is diplod spore
(C) deuteromycets have thallus similar to ascomycetes and basidiomycetes
(D) name virus was given by Ivanwosky
Mark the correct statement-
A
Which of the following example have endogenously produced asexual spores-
C
C
Albugo is not dikaryon as it belong to ascomycetes
Which of the following organism not belong to exclusively marine group-
aplysia belong to mollusca
myxine is Agnatha
A
C
D
D
Organism with proboscis, collar and trunk have all features except-
features are of hemichordata
C
Which of the following example of flower have ovary as monocarpellary superior-
soyabean and groundnut are monocarpellary and superior
Consider the following statement-
(A)In asparagus cladode is present
(B) In Australian acacia petiole of leaves are photosynthetic
Mark the correct statement-
Australian acacia petiole is photosynthetic and lamina is reduced
B
B
How many are correctly matched –
(A) Sorosis- pineapple
(B) capitulum- fig
(C) dioceious flower- castor
(D) dioceious plant- vallisneria
capitulum present in asteraceae
How many are correctly matched –
(A) dioceious flower- maize
(B) Composite fruit- Jackfruit
(C) Pome- pomegranate
(D) zygomorphic- pea
pomegranate is not pome
How many are correctly matched–
(A) Groundnut – simple fruit
(B) balausta – pomegranate
(C) cassia- fabaceae
(D) Gulmohur- fabaceae
cassia and gulmohur belong to fabaceae
gloriosa belong to liliaceae which not show vexillary aestivation
Few features are given –how many can be present in dicot stem
Trichome, collenchyma, phloem fibre, phloem parenchyma, radial
bundle, open bundle , conjoint bundle , cork cambium, lenticels, root hair, cuticle
root hair and radial bundle are absent in dicot root
How many are correctly matched –
(A) cuticle - dicot root and dicot stem
(B) lateral meristem - cork cambium and intrafasicular cambium
(C) collenchyma - dicot stem and dicot root
(D) bulliform cell - gloriosa leaf
gloriosa have bulliform cells as it is monocpt
pericycle form both lateral branches and cambium
Consider the following statements-
(1) bulliform cells are present in monocot leaf and are non-photosynthetic
(2) In dicot leaf vascular bundle are near same size
How many statement are correct-
bulliform cells are colourless
Consider the following statements-
(1) cortex of stem and root is made up of simple permanent tissue
(2) large pith and unequal size V.B present in monocot stem
how many statements is/ are correct-
pith absent in monocot stem
protoxylem and metaxylem differ in time of maturity
As protein synthesis occur in all phase
centriole get double in s-phase
In plants which is a haplontic algae then which of the following statement are correct-
(1) 2C amount is present both before and after mitosis
(2) 4C amount present in zygote undergoing meiosis
(3) cell show only 1C and 2C amout in entire cell cycle during asexual reproduction
(4) 4C amount is result of fertilization of gamets
mark the correct answer-
haplontic algae amount vary between 2c and c
In fungi imperfecti which is correct
(1) amount of DNA is varies between 1C and 2C
(2) 4C amount never present in this fungi
How many statement are correct-
in fungi imperfecti sexual reproduction absent so amount vary between 2c and c
In prophase ER , Golgi and Nucleolus get absent
consider the following -
(a) submeta-centric chromosome have unequal chromatid
(b) kinetochore located on centromere
how many correct-
chromatid length s not variable
Which of the following group of compounds obtained in acid insoluble pool when chemicals extracted in tricholoroacetic acid.
ptotein ,polysaccharide and fat appear in acid insoluble pool
Consider the following statements-
(A) all proteins are heteropolymer
(B) some polysaccharides are heteropolymer
Mark the correct statement-
all protein are made of different amino acids and hence are heteropolymer
Consider the following statements-
(A) starch and glycogen is homopolymer
(B)Both DNA and RNA have polynucleotide chain
Mark the correct statement-
both DNA and RNA is made up of polynucleotide chain
Consider the following-
(a) Dark reaction mainly determine rate of reaction
(b) Fixation by RUBISCO determine rate of photosynthesis
Mark the correct statement-
dark reaction is slower than light reaction
CO2 is not product of light rection
RUBP is sugar of 5c
high solute concentration develop high root pressure in xylem