question_answer2) If L, C and R denote the inductance, capacitance and resistance respectively, the dimensional formula for \[a{{\cos }^{3}}\alpha +3a{{\cos }^{2}}\alpha \sin \alpha =n,\]is
question_answer3) Number of particles is given by \[2{{a}^{3}}\]crossing a unit area perpendicular to X-axis is unit time, where \[\sqrt{5}-\sqrt{6}\] and \[\sqrt{5}+\sqrt{6}\]are number of particles per unit volume for the value of x meant to \[\sqrt{5}\pm \sqrt{6}\]and \[5\pm \sqrt{6}\]. Find dimensions of D called as diffusion constant.
question_answer4) A body starts from the origin and moves along the x-axis such that velocity at any instant is given by \[\sqrt{13}\]where ( is in second and velocity is in m/s. What is the acceleration of the particle, when it is 2m from the origin?
question_answer6) Two seconds after projection, a projectile is travelling in a direction inclined at 30° to the horizontal. After one more sec, it is travelling horizontally, the magnitude and direction of its velocity are
question_answer7) The kinetic energy & of a particle moving along a circle of radius R depends on the distance covered. It is given as \[8\sqrt{3}\]where a is a constant. The force acting on the particle is
question_answer8) Three blocks of masses 2 kg, 3 kg and 5 kg are connected to each other with light string and are then placed on a frictionless surface as shown in the figure. The system is pulled by a force F = 10 N, then tension \[y-\sqrt{3}x+3=0\]
question_answer10) A body A of mass 1 kg rests on a smooth surface. Another body B of mass 0.2 kg is placed over A as shown. The coefficient of static friction between A and B is 0.15. B will begin to slide on A, if A is pulled with a force greater than
question_answer11) A particle which is constrained to move along the x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin is \[\frac{4\sqrt{3}}{3}\]. Here, k and a are positive constants. For \[\frac{2(\sqrt{3}+2)}{3}\] the functional from of the potential energy\[{{y}^{2}}=4ax\]of the particle is
A)
doneclear
B)
doneclear
C)
doneclear
D)
We know \[[{{M}^{0}}{{L}^{2}}{{T}^{-1}}]\] \[(4{{t}^{3}}-2t),\]\[2\sqrt{20}m/s,60{}^\circ \] \[20\sqrt{3}m/s,60{}^\circ \]\[6\sqrt{40}m/s,30{}^\circ \] \[40\sqrt{6}m/s,30{}^\circ \]We get U = 0 at x = 0 and \[KE=a{{s}^{2}},\] Also we get U = negative for \[2a\frac{{{s}^{2}}}{R}\] From the given function we can see that F = 0 at x = O./.e., slope of U-x graph is zero at x = 0.
question_answer12) Four thin rods of same mass M and same length I, form a square as shown in figure. Moment of inertia of this system about an axis through centre O and perpendicular to its plane is
question_answer13) A wheel is rotating with an angular speed of 20 rad/s. It is stopped to rest by applying a constant torque in 4s. If the moment of inertia of the wheel about its axis is 0.20 kg/m2, then the work done by the torque in two seconds will be
question_answer14) The strain stress curves of three wires of different materials are shown in the figure. P, Q and R are the elastic limits of the wires. The figure shows that
question_answer15) Several spherical drops of a liquid of radius r coalesce to form a single drop to radius R. If T is surface tension and V is volume under consideration, then the release of energy is
question_answer16) Two substances of densities \[{{x}^{2}}-{{y}^{2}}={{a}^{2}}\]and \[{{y}^{2}}=4ax.\]are mixed in equal volume and the relative density of mixture is 4. When they are mixed in equal masses, the relative density of the mixture is 3. The values of \[{{y}^{2}}=(x-a){{x}^{3}}\] and \[{{y}^{2}}(x-a)={{x}^{3}}\]are
question_answer17) The pressure p, volume V and temperature T of a gas in the jar A and the other gas in the jar B at pressure 2p, volume V/4 and temperature 2T, then the ratio of the number of molecules in the jar A and B will be
question_answer18) Two identical containers each of volume \[f(x)=\sqrt{\sin x},g(x)={{x}^{2}}\] are joined by a small pipe. The containers contain identical gases at temperature \[f(x)=|x|,g(x)=\sin x\] and pressure \[f(x)=\sqrt{x},g(x)={{\sin }^{2}}x\]. One container is heated to temperature \[f(x)=\sin \sqrt{x},g(x)={{x}^{2}}\]while maintaining the other at the same temperature. The common pressure of the gas is P and n is the number of moles of gas in container at temperature \[f:R\to R\]
question_answer19) An experiment is carried on a fixed amount of gas at different temperature and at high pressure such that it deviates from the ideal gas behaviour. The variation of\[f(x+y)+f(x-y)\] with p is shown in the diagram. The correct variation will correspond to
question_answer21) Two rods (one semi-circular and other straight) of same material and of same cross-sectional area are joined as shown in the figure. The points A and B are maintained at different temperature. The ratio of the heat transferred through a cross-section of a semi-circular rod to the heat transferred through a cross-section of the straight rod in a given time is
question_answer22) Two particles executes SHM of same amplitude and frequency along the same straight line. They pass one another when going in opposite directions. Each time their displacement is half of their amplitude. The phase difference between them is
question_answer24) The amount of work done in increasing the voltage across the plates of a capacitor from 5V to 10V is W. The work done in increasing it from 10 V to 5 V will be
question_answer26) The minimum intensity of light to be detected by human eye is \[\frac{3\pi }{4}\]The number of photons of wavelength \[\sum\limits_{m=1}^{n}{{{\tan }^{-1}}}\left( \frac{2m}{{{m}^{4}}+{{m}^{2}}+2} \right)\]entering the eye, with pupil area \[{{\tan }^{-1}}\left( \frac{{{n}^{2}}+n}{{{n}^{2}}+n+2} \right)\]per second for vision will be nearly
question_answer27) In a photo emissive cell with exciting wavelength \[{{\tan }^{-1}}\left( \frac{{{n}^{2}}-n}{{{n}^{2}}-n+2} \right)\]the fastest electron has speed \[{{\tan }^{-1}}\left( \frac{{{n}^{2}}+n+2}{{{n}^{2}}+n} \right)\]. If the exciting wavelength is changed by \[\underset{x\to \frac{\pi }{2}}{\mathop{\lim }}\,\frac{\left( 1-\tan \frac{x}{2} \right)(1-\sin x)}{\left( 1+\tan \frac{x}{2} \right){{(\pi -2x)}^{3}}}\], the speed of the fastest emitted electron will be
question_answer29) The fraction of atoms of radioactive element that decays in 6 days is 7/8. The fraction that decays in 10 days will be
A)
77/80
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B)
71/80
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C)
31/32
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D)
15/16 By using \[\Delta l.\] \[\Delta T\]\[\Delta l\] \[\Delta T\]\[\rho \] \[100\Omega \]\[{{f}_{1}}\] Hence,\[{{f}_{2}}\] \[n=3,{{f}_{2}}=\frac{3}{4}{{f}_{1}}\]\[n=5,{{f}_{2}}=\frac{3}{4}{{f}_{1}}\]\[n=3,{{f}_{2}}=\frac{5}{4}{{f}_{1}}\]\[n=5,{{f}_{2}}=\frac{5}{4}{{f}_{1}}\] So, fraction that decays \[{{T}_{1}}\]
question_answer31) When \[y=|\sin x{{|}^{|x|}},\] transforms to \[\frac{dy}{dx}\]then the number to the emitted \[x=\frac{-\pi }{6}\] and \[{{\frac{2}{6}}^{\frac{-\pi }{6}}}[6\log 2-\sqrt{3}\pi ]\]particles is, respectively
question_answer33) A short bar magnet is placed with its south pole towards geographical north. The neutral points are situated at a distance of 20 cm from the centre of the magnet. If \[f(x)=3\sin x-4{{\sin }^{3}}x\]then the magnetic moment of the magnet is
question_answer34) A magnet makes 40 oscillations per minute at a place having magnetic field intensity By \[\frac{\pi }{3}\] At another place, it takes 2.5 s to complete one vibration. The value of the earth's horizontal field at the place
question_answer35) The coereivity of a small bar magnet is \[{{\left( \frac{x}{a} \right)}^{n}}+{{\left( \frac{y}{b} \right)}^{n}}=2\] A/m. It is inserted inside a solenoid of 500 turns and length 1 m to demagnetize it. The amount of current to be passed through the solenoid will be
question_answer36) A wire in the form of a square of side a carries a current i. Then, the magnetic induction at the centre of the square wire is (magnetic permeability of free space \[\frac{x}{a}+\frac{y}{b}=2\]).
question_answer37) Given, \[{{a}_{n}}=\frac{{{n}^{2}}}{{{n}^{3}}+200}\] \[\frac{529}{49}\] \[\frac{8}{89}\] \[\frac{49}{543}\] The time constant (in [is) for the circuits I, II, III are respectively
question_answer38) Two blocks A and B of masses 2m and m, respectively, are connected by a mass less and inextensible string. The whole system is suspended by a mass less spring as shown in the figure. The magnitudes of acceleration of A and B, immediately after the string is cut, are respectively
question_answer39) A point object is placed at a distance of 20 cm from a thin plano-convex lens of focal length 15 cm, if the plane surface is silvered. The image will form at
question_answer40) A biconvex lens of focal length / forms a circular image of sun of radius r in focal plane. Then,
A)
\[\pi {{r}^{2}}=f\]
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B)
\[\pi {{r}^{2}}-f\]
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C)
if bower hall part is covered by black sheet, then area of the image is equal to \[f(x)=\left\{ \begin{align} & |{{x}^{3}}+{{x}^{2}}+3x+\sin x|.\left( 3+\sin \frac{1}{x} \right),\,x\ne 0 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x=3 \\ \end{align} \right.\]
question_answer43) A mass less rod is suspended by two identical strings AB and CD of equal length. A block of mass m is suspended from point 0 such that BO is equal to 'y'. Further, it is observed that the frequency of 1st harmonic (fundamental frequency) in AB is equal to 2nd harmonic frequency in CD. Then, length of BO is
question_answer44) A system of binary stars of masses \[\log \left[ {{\tan }^{-1}}\left( x+\frac{1}{x} \right) \right]+C\]and mg are moving in circular orbits of radii \[\int_{{}}^{{}}{\frac{\cos x}{{{\sin }^{2}}x.(\sin x+\cos x)}dx}\]and \[\log \left| \frac{1+\tan x}{\tan x} \right|-\cot x+C\]respectively. If \[\log \left| \frac{\tan x}{1+\tan x} \right|+C\] and \[\log \left| \frac{\tan x}{1+\tan x} \right|-\tan x+C\] are the time periods of masses \[\log \left| \frac{\tan x}{1+\tan x} \right|+\cot x+C\] and \[\int_{{}}^{{}}{\frac{dx}{\sin x-\cos x+\sqrt{2}}}\] respectively, then
question_answer45) A solid sphere of mass M, radius R and having moment of inertia about an axis passing through the centre of mass as I, is recast into a disc of thickness t, whose moment of inertia about an axis passing through its edge and perpendicular to its plane remains I. Then, radius of the disc will be
question_answer46) A student performs an experiment for determination of \[\frac{\pi }{2}(\sin 1+\sin 2)\]and he commits an error of \[\frac{\pi }{2}(\sin 1-\cos 1)\] For The takes the time of n oscillations with the stop watch of least count \[\frac{\pi }{2}(\sin \pi -\sin 2)\] and he commits a human error 0.1 of s. For which of the following data, the measurement of g will be most accurate?
A)
\[\int_{1/n}^{(an-1yn)}{\frac{\sqrt{x}}{\sqrt{a-x+\sqrt{x}}}}dx\] \[\frac{a}{2}\] n Amplitude of oscillation 5 mm 0.2 s 10 5 mm
question_answer48) Consider the cylindrical element as shown in the figure. Current flowing the through element is I and resistivity of material of the cylinder is \[\frac{n.a+2}{2n}\]. Choose the correct option out the following.
A)
Power loss in first half is four times the power loss 5 in second half
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B)
Voltage drop in first half is twice of voltage drop in second half
question_answer49) Ideal gas is contained in a thermally insulated and rigid container and it is heated through a resistance \[\frac{n.a-2}{2n}\]by passing a current of 1 A for five minutes, then change in internal energy of the gas is
question_answer50) Two litre of water at initial temperature of 27°C is heated by a heater of power 1 kW. If the lid of kettle is opened, then heat is lost at the constant rate of 160 J/s. Find, the time required to raise the temperature of water to 77°C with the lid open (specific heat of water 4.2 kJ/kg)
question_answer51) An open organ pipe resonated with frequency \[\frac{n.a}{2}\] and 2nd harmonic. Now, one end is closed and the frequency is slowly increased, then it resonates with frequency \[y=x|\sin x|\] and nth harmonic then,
question_answer53) \[|y+x|\le 1,\]is the time period of simple pendulum. The point of suspension moves vertically upwards according to \[|y-x|\le 1\]where \[2{{x}^{2}}+2{{y}^{2}}=1\]New time period is \[\left( 2+\frac{\pi }{2} \right)\] then \[\left( 2-\frac{\pi }{2} \right)\]
question_answer54) In the figure shown, a cubical block is held stationary against a rough wall by applying force 'F, then incorrect statement among the following is
question_answer55) Three infinitely charged sheets are kept parallel to x-y plane having charge densities as shown. Then, the value of electric field at 'P is
question_answer56) A circular disc of radius \[m=\frac{3}{2}\]is cut from a circular disc of radius R and mass 9M as shown. Then, moment of inertia of remaining disc about 'O perpendicular to the plane of the disc is
question_answer57) A cylindrical conducting rod is kept with its axis along positive z-axis, where a uniform magnetic field exists parallel to z-axis. The current induced in the cylinder is
question_answer58) Ratio of area of hole to beaker is 0.1. Height of liquid in beaker is 3m, and hole is at the height of 52.5 cm from the bottom of beaker, find the square of the velocity of liquid coming out from the hole
question_answer59) Temperature of a gas is \[\frac{5\pi }{6}\]and pressure is changed from \[\frac{\pi }{3}\]to \[\frac{2\pi }{3}\] If volume is decreased isothermally by 10%, Bulk modulus of gas is
question_answer60) The atomic number (Z) of an element whose \[(q-r)\hat{i}+(r-p)\hat{j}+(p-q)\hat{k}\]wavelength is \[r.(\hat{i}-\hat{j}+\hat{k})=5\] is 11. The atomic number of an element whose \[r=\hat{i}+\hat{j}+\hat{k}\]wavelength is \[3\sqrt{5}\]is equal to
question_answer61) Which of the following compounds will not react with Mg metal in the presence of ether to give a Grignard reagent?
A)
\[10\sqrt{3}\]
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B)
\[5\sqrt{3}\]
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C)
\[3\sqrt{10}\]
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D)
\[\hat{i}+3\hat{k}\] Compounds containing acidic hydrogen cannot be used in Grignard's synthesis and the compound \[\text{m}{{\text{s}}^{\text{-1}}}\] contains acidic hydrogen.
question_answer64) An aqueous solution of phosphoric acid, \[\hat{i}+2\hat{j}-\hat{k}\]being titrated has molarity equal to 0.25 M. Which of the following could be normality of this solution?
question_answer65) For the reaction represented by the equation, \[\frac{496}{729}\]9.0 g of \[\frac{400}{729}\] completely reacts with 1.74 g of oxygen. The approximate molar mass of X will be
question_answer72) Find the pressure of a sample of \[\frac{1}{7}\]if mole occupies 35L at 77°C. Assume \[\frac{1}{8}\]obeys the van der Waals equation of state. \[\frac{1}{49}\]
question_answer73) KBr crystallises in NaCI type of crystal lattice and its density is \[{{\sin }^{-1}}a+{{\sin }^{-1}}b+{{\sin }^{-1}}c=\pi ,\] Number of unit 3 cells of KBr present in a 1.00 mm3 grain of KBr are
question_answer74) A body centre cubic lattice is made up of two different types of atoms A and B. Atom A occupies the body centre and B occupying the corner positions. One of the corners is left unoccupied per unit cell. Empirical formula of Option nahi hey There is one A per unit cell Number of B per unit cell \[E_{cell}^{0}=+0.84V\] Empirical formula \[E_{cell}^{0}=+1.28V\] \[\alpha \] A substance is carried out through the following transformations The equation \[\mu \]
A)
is true only if the steps are carried out reversibly
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B)
is always true because entropy is a state function
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C)
may be true but need more in formations on the processes
question_answer75) At 298 K the entropy of rhombic sulphur is 32.04 J/mol K and that of monoclinic sulphur is 32.68 J/mol K. The heat of their combustion are respectively-298246 and -297948\[x+y+z=6,x+2y+3z=10\].\[x+2y+\lambda z=\mu \] for the reaction; rhombic \[\lambda =3,\mu \ne 10\] will be
question_answer77) Which of the following sets of quantum numbers could represent the last electron added to complete the electron configuration for a ground state atom of Br(Z = 35) according to the Aufbau principle, \[\lambda \ne 3,\mu =10\]
question_answer79) When the substances \[f(x)=({{x}^{2}}-1)|{{x}^{2}}-3x+2|\] and \[+\cos |x|\]are arranged is order of increasing boiling point, what is the correct order?
question_answer80) The nitrite ion in represented by (I)\[\frac{{{\sin }^{2}}(a+y)}{\sin a}\] (II)\[\frac{{{\cos }^{2}}(a+y)}{\cos a}\] Which of the structures represents possible resonance forms of this ion?
question_answer81) Equal moles of \[\frac{{{\sin }^{2}}(a+y)}{\cos a}\] and N.O(g) are to be placed in a container to produce \[\frac{{{\cos }^{2}}(a+y)}{\sin a}\] according to the reaction, \[f(x)={{x}^{3}}-7{{x}^{2}}+15,\] How many moles of \[f(x)={{x}^{3}}-3{{x}^{2}}+2x\] and NO be placed in the 5.0 L container to have an equilibrium concentration of \[c=\pm 1\]to be 0.05 M?
question_answer83) Consider the following reaction in aqueous solution. \[c=1\pm \frac{1}{\sqrt{3}}\]\[c=\pm 2\] If the rate of appearance of \[3x-y+2z-4=0\] at a particular moment during the reaction is 0.025 \[x+y+z-2=0\], what is the rate of disappearance (in \[7x+5y+4z+8=0\]) of \[7x+5y+4z-8=0\] at that moment?
question_answer94) Which reagents would you use to carry out the reaction Ethyl benzene \[\sqrt{3}x+y-\sqrt{3}=0,\sqrt{3}x-y-\sqrt{3}=0\] and 4- chloro 1- ethyl benzene?
A)
\[\sqrt{3}x+y+\sqrt{3}=0,\sqrt{3}x-y+\sqrt{3}=0\] light and heat
question_answer99) Potassium stearate is obtained by the saponification of an oil or fat. It has formula \[\frac{x+5}{1}=\frac{y+3}{4}=\frac{z-6}{-9}.\] The molecule has a lyophobic terminal \[\frac{x-2}{6}=\frac{y-4}{3}=\frac{z+1}{2}\]and a lyophilic terminal ? COOK. Potassium stearate is an example of
question_answer100) Suppose that gold is being plated on to another metal in an electrolytic cell. The half-cell reaction producing the Au(s) is\[\frac{x+2}{6}=\frac{y-4}{3}=\frac{z+1}{2}\] lf a 0.30 A current runs for 15.00 min, what mass of Au(s) will be plated, assuming all the electrons are used in the reduction of \[\frac{x+2}{-6}=\frac{y-4}{3}=\frac{z+1}{2}\] ? The Faraday constant is 96485 C/mol and molar mass of Au is 197.
question_answer101) What is the cell potential (standard emf, E°) for the reaction below? \[\frac{x+2}{6}=\frac{y+4}{3}=\frac{z+1}{2}\]and\[{{\cos }^{2}}A+{{\cos }^{2}}C={{\sin }^{2}}B,\] \[\Delta ABC\] \[\left| \begin{matrix} x+y+2z & x & y \\ z & y=z+2x & y \\ z & x & z=x+2y \\ \end{matrix} \right|\]
question_answer102) If in a solvent, n simple molecules of solute combine to form an associated molecule, \[{{e}^{3}}\] is the degree of association, the van't Hoffs factor is equal to
question_answer103) If the osmotic pressure of a 0.010 M aqueous solution of sucrose at 27°C is 0.25 atm, then the osmotic pressure of a 0.010 M aqueous solution. of NaCl at 27°C is
question_answer104) A certain radioactive isotope \[\Rightarrow \] (half-life = 10 days) decays to give \[[a]=[p][{{V}^{2}}]=[M{{L}^{-1}}{{T}^{-2}}][{{L}^{6}}]=[M{{L}^{5}}{{T}^{-2}}]\]If 1.0 g of X is kept in a sealed vessel find the volume of He accumulated at STP in 20 days. Molar mass of \[a=gm\times c{{m}^{5}}\times {{s}^{-2}}\]
question_answer105) Raw milk sours in about 4 h at 27°C, but in about 48 h in a refrigerator at 17°C. What is the activation energy for souring of milk?
question_answer106) If 200 mL of a 0.031 molar solution of \[\left[ \frac{L}{R} \right]\]are added to 84 mL of a 0.150 M KOH solution, what is the pH of the resulting solution?
question_answer113) Out of the following redox reactions I.\[x=\int_{{}}^{{}}{vdt,x={{t}^{4}}-{{t}^{2}}+C,}\] II.\[t=0,x=0\] III.\[\Rightarrow \] disproportionation is not shown in
question_answer114) The complex \[2={{t}^{4}}-{{t}^{2}}\Rightarrow {{t}^{4}}-{{t}^{2}}-2=0\] is formed in the ring test for nitrate ion when freshly prepared \[\Rightarrow \]solution is added to aqueous solution of \[({{t}^{2}}-2)({{t}^{2}}+1)=0\]followed by addition of Cone. \[\Rightarrow \] This complex is formed by charge transfer in which
A)
\[t=\sqrt{2}s\]changes to \[a=\frac{dv}{dt}=\frac{d}{dt}(4{{t}^{3}}-2t)\]and \[a=12{{t}^{2}}-2\]changes to NO
doneclear
B)
\[t=\sqrt{2}\sec \]changes to \[a=12\times {{(\sqrt{2})}^{2}}-2=22m/{{s}^{2}}\] and NO changes to\[\therefore \frac{da}{dt}=k\]
doneclear
C)
\[\Rightarrow a=kt\] changes to \[\Rightarrow \] and NO changes to \[\frac{dv}{dt}=kt\Rightarrow dv=ktdt\]
question_answer119) Which of the following best define the term hyper conjugation?
A)
Transfer of H from a\[u\sin \theta =10\times 3\]bond to the \[u\sin \theta =30\]system
doneclear
B)
Participation of an H-atom on terminal carbon in the electron sharing
doneclear
C)
Delocalisation of electron density from a properly oriented \[u\cos \theta =v\cos {{30}^{o}}\]bond into \[v\sin {{30}^{o}}=u\sin \theta -g\times 2\]system
doneclear
D)
Interaction between a properly aligned lone electron pair with the empty \[v\sin {{30}^{o}}=30-20\]system