question_answer1) Which one of the following represents the correct dimensions of the coefficient of viscosity?
A) \[[M{{L}^{-1}}{{T}^{-2}}]\]
B) \[[ML{{T}^{-1}}]\]
C) \[[M{{L}^{-1}}{{T}^{-1}}]\]
D) \[[M{{L}^{-2}}{{T}^{-2}}]\]
View Answer play_arrowquestion_answer2) A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement \[x\]is proportional to:
A) \[{{x}^{2}}\]
B) \[{{e}^{x}}\]
C) \[x\]
D) \[lo{{g}_{e}}x\]
View Answer play_arrowquestion_answer3) A ball is released from the top of a tower of height h m. It takes T s to reach the ground. What is the position of the ball in 773 s?
A) \[h/9\]m from the ground
B) \[7h/9\]m from the ground
C) \[8h/9\]m from the ground
D) \[17h/9\]m from the ground
View Answer play_arrowquestion_answer4) A projectile can have the same range R for two angles of projection. If\[{{T}_{1}}\]and\[{{T}_{2}}\]be the times of flights in the two cases, then the product of the two times of flights is directly proportional to
A) \[\frac{1}{{{R}_{2}}}\]
B) \[\frac{1}{R}\]
C) \[R\]
D) \[{{R}^{2}}\]
View Answer play_arrowquestion_answer5) An automobile travelling with a speed of 60 km/h, can brake to stop within a distance of 20 m. If the car is going twice as fast, ie., 120 km/h, the stopping distance will be:
A) 20m
B) 40m
C) 60 m
D) 80 m
View Answer play_arrowquestion_answer6) A machine gun fires a bullet of mass 40 g with velocity\[1200\text{ }m{{s}^{-1}}\]. The man holding it, can exert a maximum force of 144 N on the gun. How many bullets can he fire per second at the most?
A) One
B) Four
C) Two
D) Three
View Answer play_arrowquestion_answer7) Two masses\[{{m}_{1}}=5\,kg\]and\[{{m}_{2}}=4.8\text{ }kg\] tied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when lift is free to move? \[(g=9.8m/{{s}^{2}})\]
A) \[0.2\text{ }m/{{s}^{2}}\]
B) \[9.8\text{ }m/{{s}^{2}}\]
C) \[5\text{ }m/{{s}^{2}}\]
D) \[4.8\text{ }m/{{s}^{2}}\]
View Answer play_arrowquestion_answer8) A block rests on a rough inclined plane making an angle of\[30{}^\circ \]with the horizontal. The coefficient of static friction between the block and the plane is 0.8. If the frictional force on the block is 10 N, the mass of the block Jin kg) is (take\[g=10\text{ }m/{{s}^{2}})\]
A) 2.0
B) 4.0
C) 1.6
D) 2.5
View Answer play_arrowquestion_answer9) A force\[\overrightarrow{F}=(5\hat{i}+3\text{ }\hat{j}+2\hat{k})N\]is applied over a particle which displaces it from its origin to the point\[\overrightarrow{r}=(2\hat{i}-\hat{j})m\]. The work done on the particle in joules is
A) \[-7\]
B) \[+7\]
C) \[+10\]
D) \[+13\]
View Answer play_arrowquestion_answer10) A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane, it follows that
A) its velocity is constant
B) its acceleration is constant
C) its kinetic energy is constant
D) it moves in a straight line
View Answer play_arrowquestion_answer11) A ball is thrown from a point with a speed\[{{v}_{0}}\]at an angle of projection\[\theta \]. From the same point and at the same instant, a person starts running with a constant speed\[\frac{{{v}_{0}}}{2}\]to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection?
A) Yes,\[60{}^\circ \]
B) Yes,\[30{}^\circ \]
C) No
D) Yes,\[45{}^\circ \]
View Answer play_arrowquestion_answer12) One solid sphere A and another hollow sphere B are of same mass and same outer radii. Their moment of inertia about their diameters are respectively\[{{I}_{A}}\]and\[{{I}_{B}}\]such that
A) \[{{I}_{A}}={{I}_{B}}\]
B) \[{{I}_{A}}>{{I}_{B}}\]
C) \[{{I}_{A}}<{{I}_{B}}\]
D) \[\frac{{{I}_{A}}}{{{I}_{B}}}=\frac{{{d}_{A}}}{{{d}_{B}}}\]
View Answer play_arrowquestion_answer13) A satellite of mass m revolves around the earth of radius R at a height\[x\]from its surface. If g is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is
A) \[gx\]
B) \[\frac{gR}{R-x}\]
C) \[\frac{g{{R}^{2}}}{R+x}\]
D) \[{{\left( \frac{g{{R}^{2}}}{R+x} \right)}^{1/2}}\]
View Answer play_arrowquestion_answer14) The time period of an earth satellite in circular orbit is independent of
A) the mass of the satellite
B) radius of its orbit
C) both the mass and radius of the orbit
D) neither the mass of the satellite nor the radius of its orbit
View Answer play_arrowquestion_answer15) If g is the acceleration due to gravity on the earths surface, the gain in the potential energy of an object of mass m raised from the surface of the earth to a height equal to the radius R of the earth, is
A) \[2mgR\]
B) \[\frac{1}{2}mgR\]
C) \[\frac{1}{4}mgR\]
D) \[mgR\]
View Answer play_arrowquestion_answer16) Suppose the gravitational force varies inversely as the nth power of distance. Then the time period of a planet in circular orbit of radius R around the sun will be proportional to
A) \[{{R}^{\left( \frac{n+1}{2} \right)}}\]
B) \[{{R}^{\left( \frac{n-1}{2} \right)}}\]
C) \[{{R}^{n}}\]
D) \[{{R}^{\left( \frac{n-2}{2} \right)}}\]
View Answer play_arrowquestion_answer17) A wire fixed at the upper end 3tretches by length\[l\]by applying a force F. The work done, in stretching is
A) \[\frac{F}{2l}\]
B) \[Fl\]
C) \[2Fl\]
D) \[\frac{Fl}{2}\]
View Answer play_arrowquestion_answer18) If two soap bubbles of different radii are connected by a tube
A) air flows from the bigger bubble to the smaller bubble till the sizes become equal
B) air flows from bigger bubble to the smaller bubble till the sizes are interchanged
C) air flows from the smaller bubble to the bigger
D) there is no flow of air
View Answer play_arrowquestion_answer19) The bob of a simple pendulum executes simple harmonic motion in water with a period t, while the period of oscillation of the bob is\[{{t}_{0}}\]in air. Neglecting frictional force of water and given that the density of the bob is \[(4/3)\times 1000kg/{{m}^{3}}\]. What relationship between\[t\]and\[{{t}_{0}}\]is true?
A) \[t={{t}_{0}}\]
B) \[t={{t}_{0}}/2\]
C) \[t=2{{t}_{0}}\]
D) \[t=4{{t}_{0}}\]
View Answer play_arrowquestion_answer20) The total energy of a particle, executing simple harmonic motion is
A) \[\propto x\]
B) \[\propto {{x}^{2}}\]
C) independent of\[x\]
D) \[\propto {{x}^{1/2}}\]
View Answer play_arrowquestion_answer21) The displacement y of a particle in a medium can be expressed as \[y={{10}^{-6}}\sin \left( 100t+20x+\frac{\pi }{4} \right)m,\]where t is in second and x in metre. The speed of the wave is
A) 2000 m/s
B) 5 m/s
C) 20 m/s
D) 57cm/s
View Answer play_arrowquestion_answer22) A particle of mass m is attached to a spring (of spring constant k) and has a natural angular frequency\[{{\omega }_{0}}\]. An external force F(t) proportional to\[\cos \omega t(\omega \ne {{\omega }_{0}})\]is applied to the oscillator. The time displacement of the oscillator will be proportional to
A) \[\frac{m}{\omega _{0}^{2}-{{\omega }^{2}}}\]
B) \[\frac{1}{m(\omega _{0}^{2}-{{\omega }^{2}})}\]
C) \[\frac{1}{m(\omega _{0}^{2}+{{\omega }^{2}})}\]
D) \[\frac{m}{\omega _{0}^{2}+{{\omega }^{2}}}\]
View Answer play_arrowquestion_answer23) One mole of ideal monoatomic gas\[(\gamma =5/3)\].is mixed with one mole of diatomic gas\[(\gamma =7/5)\]. What is\[\gamma \]for the mixture? \[\gamma \] denotes the ratio of specific heat at constant pressure, to that at constant volume:
A) 3/2
B) 23/15
C) 35/23
D) 4/3
View Answer play_arrowquestion_answer24) If the temperature of the sun were to increase from T to 2T and its radius from R to 2R, then the ratio of the radiant energy received on earth to what it was previously, will be
A) 4
B) 16
C) 32
D) 64
View Answer play_arrowquestion_answer25) Which of the following statements is correct for any thermodynamic system?
A) The internal energy changes in all processes
B) Internal energy and entropy are state functions
C) The change in entropy can never be zero
D) The work done in an adiabatic process, is always zero
View Answer play_arrowquestion_answer26) A radiation of energy E falls normally on a perfectly reflecting surface. The momentum transferred to the surface is:
A) \[E/c\]
B) \[2E/c\]
C) \[Ec\]
D) \[E/{{c}^{2}}\]
View Answer play_arrowquestion_answer27) The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity K and 2K and thickness\[x\]and\[4x,\]respectively are\[{{T}_{2}}\]and\[{{T}_{1}}({{T}_{2}}>{{T}_{1}})\]. The rate of heat transfer through the slab, in a steady state is \[\left( \frac{A({{T}_{2}}-{{T}_{1}})K}{x} \right)f,\]with\[f\]equals to
A) 1
B) 1/2
C) 2/3
D) 1/3
View Answer play_arrowquestion_answer28) A plano-convex lens of refractive index 1.5 and radius of curvature 30 cm is silvered at the curved surface. Now, this lens has been .used to form the image of an object. At what distance from this lens, an object be placed in order to have a real image of the size of the object?
A) 20 cm
B) 30 cm
C) 60 cm
D) 80 cm
View Answer play_arrowquestion_answer29) The angle of incidence at which reflected light is totally polarized for reflection from air to glass (refractive index n), is
A) \[{{\sin }^{-1}}(n)\]
B) \[{{\sin }^{-1}}(1/n)\]
C) \[{{\tan }^{-1}}(1/n)\]
D) \[{{\tan }^{-1}}(n)\]
View Answer play_arrowquestion_answer30) An electromagnetic wave of frequency \[v=3.0\text{ }MHz\]passes from vacuum into a dielectric medium with permittivity\[\varepsilon =4.0\]. Then
A) wavelength is doubled and the frequency remains unchanged
B) wavelength is doubled and frequency becomes half
C) wavelength is halved, and frequency remains unchanged
D) wavelength and frequency both remain unchanged
View Answer play_arrowquestion_answer31) Two spherical conductors B and C having equal radii and carrying equal charges in them repel each other with a force F when kept apart at some distance. A third spherical conductor having same radius as that of B but uncharged, is brought in contact with B, then brought in contact with C and finally removed away from both. The new force of repulsion between B and C is
A) \[\frac{F}{4}\]
B) \[\frac{3F}{4}\]
C) \[\frac{F}{8}\]
D) \[\frac{3F}{8}\]
View Answer play_arrowquestion_answer32) A charged particle q is shot towards another charged particle Q which is fixed, with a speed v. It approaches Q upto a closest distance r and then returns. If q was given a speed 2v, the closest distance of approach would be
A) \[r\]
B) \[2r\]
C) \[r/2\]
D) \[r/4\]
View Answer play_arrowquestion_answer33) Alternating current cannot be measured by DC ammeter because
A) AC cannot pass through DC ammeter
B) AC changes direction
C) average value of current for complete cycle is zero
D) DC ammeter will get damaged
View Answer play_arrowquestion_answer34) The resistance of the series combination of two resistances is S. When they are joined in parallel, the total resistance is P. If\[S=nP,\]then the minimum possible value of n is
A) 4
B) 3
C) 2
D) 1
View Answer play_arrowquestion_answer35) An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the lengths and radii of the wires are in the ratio of 4/3 and 2/3, then the ratio of the currents passing through the wire will be
A) 3
B) 1/3
C) 8/9
D) 2
View Answer play_arrowquestion_answer36) In a metre bridge experiment, null point is obtained at 20 cm from one end of the wire when resistance\[X\]is balanced against another resistance Y. If\[X<Y,\]then where will be the new position of the null point from the same end, if one decides to balance a resistance of\[4X\]against\[Y\]?
A) 50 cm
B) 80 cm
C) 40cm
D) 70cm
View Answer play_arrowquestion_answer37) The thermistors are usually made of
A) metals with low temperature coefficient of resistivity
B) metals with high temperature coefficient of resistivity
C) metal oxides with high temperature coefficient of resistivity
D) semiconducting materials having low temperature coefficient of resistivity
View Answer play_arrowquestion_answer38) Time taken by a 836 W heater to heat one litre of water from\[10{}^\circ C\]to\[40{}^\circ C\]is
A) 50s
B) 100s
C) 150s
D) 200s
View Answer play_arrowquestion_answer39) The thermo-emf of a thermocouple varies with the temperature\[\theta \]of the hot junction as\[E=a\theta +b{{\theta }^{2}}\]in volts where the ratio a/b is\[700{}^\circ C\]. If the cold junction is kept at\[0{}^\circ C,\] then the neutral temperature is
A) \[700{}^\circ C\]
B) \[350{}^\circ C\]
C) \[1400{}^\circ C\]
D) no neutral temperature is possible for this thermocouple
View Answer play_arrowquestion_answer40) The electrochemical equivalent of metal is \[3.3\times {{10}^{-7}}\]kg per coulomb. The mass of the metal liberated at the cathode when a 3 A current is passed for 2 s, will be
A) \[19.8\times {{10}^{-7}}kg\]
B) \[9.9\times {{10}^{-7}}kg\]
C) \[6.6\times {{10}^{-7}}kg\]
D) \[1.1\times {{10}^{-7}}kg\]
View Answer play_arrowquestion_answer41) A long wire carries a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the coil is B. It is then bent into a circular loop of n turns. The magnetic field at the centre of the coil will be
A) \[nB\]
B) \[{{n}^{2}}B\]
C) \[2nB\]
D) \[2{{n}^{2}}B\]
View Answer play_arrowquestion_answer42) The magnetic field due to a current carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm from the centre is\[5\mu T\]. What will be its value at the centre of the loop?
A) \[250\mu T\]
B) \[150\mu T\]
C) \[125\mu T\]
D) \[75\mu T\]
View Answer play_arrowquestion_answer43) Two long conductors, separated by a distance d carry currents\[{{I}_{1}}\]and\[{{I}_{2}}\]in the same direction. They exert a force F on each other. Now the current in one of them is increased to two times and its direction is reversed. The distance is also increased to 3 d. The new value of the force between them is
A) \[-2F\]
B) \[F/3\]
C) \[-2F/3\]
D) \[-F/3\]
View Answer play_arrowquestion_answer44) The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is 2 s. The magnet is cut along its length into three equal parts and three parts are then placed on each other with their like poles together. The time period of this combination will be:
A) \[2s\]
B) \[2/3\text{ }s\]
C) \[2\sqrt{3}s\]
D) \[2/\sqrt{3}\text{ }s\]
View Answer play_arrowquestion_answer45) The materials suitable for making electromagnets should have
A) high retentivity and high coercivity
B) low retentivity and low coercivity
C) high retentivity and low coercivity
D) low retentivity and high coercivity
View Answer play_arrowquestion_answer46) In an LCR series ac circuit, the voltage across each of the components. L, C and R is 50 V. The voltage across the LC combination will be
A) 50V
B) \[50\sqrt{2}V\]
C) 100 V
D) 0 (zero)
View Answer play_arrowquestion_answer47) In an LCR circuit, capacitance is changed from C to 2C. For the resonant frequency to remain unchanged, the inductance should be changed from L to
A) 4L
B) 2L
C) L/2
D) L/4
View Answer play_arrowquestion_answer48) A metal conductor of length 1m rotates vertically about one of its ends at angular velocity 5 radians per second. If the horizontal component of earths magnetic field is\[0.2\times {{10}^{-4}}T,\]then the emf developed between the two ends of the conductor is
A) \[5\mu V\]
B) \[5\mu V\]
C) \[5mV\]
D) \[50\,mV\]
View Answer play_arrowquestion_answer49) The work function of a substance is 4.0 eV. The longest wavelength of light that can cause photoelectron emission from this substance is approximately
A) 540 nm
B) 400 nm
C) 310 nm
D) 220 nm
View Answer play_arrowquestion_answer50) A charged oil drop is suspended in uniform field of \[3\times {{10}^{4}}V/m\]so that it neither falls nor rises. The charge on the drop will be (Take the mass of the charge\[=9.9\times {{10}^{-15}}kg\]and\[=10m/{{s}^{2}}\])
A) \[3.3\times {{10}^{-18}}C\]
B) \[3.2\times {{10}^{-18}}C\]
C) \[1.6\times {{10}^{-18}}C\]
D) \[4.8\times {{10}^{-18}}C\]
View Answer play_arrowquestion_answer51) A nucleus disintegrates into two nuclear parts which have their velocities in the ratio\[2:1\]. The ratio of their nuclear sizes will be
A) \[{{2}^{1/3}}:1\]
B) \[1:{{3}^{1/2}}\]
C) \[{{3}^{1/2}}:1\]
D) \[1:{{2}^{1/3}}\]
View Answer play_arrowquestion_answer52) The binding energy per nucleon of deuteron \[(_{1}^{2}H)\]and helium nucleus\[(_{2}^{4}He)\]is 1.1 MeV and 7 MeV respectively. If two deuteron nuclei react to form a single helium nucleus, then the energy released is
A) 13.9 MeV
B) 26.9 MeV
C) 23.6 MeV
D) 19.2 MeV
View Answer play_arrowquestion_answer53) An\[\alpha -\]particle of energy 5 MeV is scattered through\[180{}^\circ \]by a fixed uranium nucleus. The distance of the closest approach is of the order of
A) \[1\overset{o}{\mathop{\text{A}}}\,\]
B) \[{{10}^{-10}}cm\]
C) \[{{10}^{-12}}cm\]
D) \[{{10}^{-15}}cm\]
View Answer play_arrowquestion_answer54) When\[npn\]transistor is used as an amplifier
A) electrons move from base to collector
B) holes move from emitter to base
C) electrons move from collector to base
D) holes move from base to emitter
View Answer play_arrowquestion_answer55) The manifestation of band structure in solids is due to
A) Heisenbergs uncertainty principle
B) Faults exclusion principle
C) Bohrs correspondence, principle
D) Boltzmanns law
View Answer play_arrowquestion_answer56) Which of the following sets of quantum numbers is correct for an electron in 4f orbital?
A) \[n=4,l=3,m=+4,s=+1/2\]
B) \[n=4,l=4,m=-4,s=-1/2\]
C) \[n=4,\text{ l}=3,m=+1,s=+1/2\]
D) \[n=3,l=2,\text{ }m=-2,\text{ s}=+1/2\]
View Answer play_arrowquestion_answer57) Which one of the following ions has the highest value of ionic radius?
A) \[L{{i}^{+}}\]
B) \[{{B}^{3+}}\]
C) \[{{O}^{2-}}\]
D) \[{{F}^{-}}\]
View Answer play_arrowquestion_answer58) Which one of the following sets of ions represents the collection of isoelectronic species?
A) \[{{K}^{+}},C{{a}^{2+}},S{{c}^{3+}},C{{l}^{-}}\]
B) \[N{{a}^{+}},C{{a}^{2+}},S{{c}^{3+}},{{F}^{-}}\]
C) \[{{K}^{+}},C{{l}^{-}},M{{g}^{2+}},S{{c}^{3+}}\]
D) \[N{{a}^{+}},M{{g}^{2+}},A{{l}^{3+}},C{{l}^{-}}\]
View Answer play_arrowquestion_answer59) The bond order in NO is 2.5 while that in\[N{{O}^{+}}\] is 3. Which of the following statements is true for these two species?
A) Bond length in\[N{{O}^{+}}\]is greater than in\[NO\]
B) Bond length in\[NO\]is greater than in\[N{{O}^{+}}\]
C) Bond length in\[N{{O}^{+}}\]is equal to that in\[NO\]
D) Bond length is unpredictable
View Answer play_arrowquestion_answer60) As the temperature is raised from\[20{}^\circ C\]to\[40{}^\circ C\],the average kinetic energy of neon atoms changes by a factor of which of the following?
A) 1/2
B) \[\sqrt{313/293}\]
C) 313/293
D) 2
View Answer play_arrowquestion_answer61) The maximum number of\[90{}^\circ \]angles between bond pair-bond pair of electrons is observed in
A) \[ds{{p}^{3}}\]hybridization
B) \[s{{p}^{3}}d\]hybridization
C) \[ds{{p}^{2}}\]hybridization
D) \[s{{p}^{2}}{{d}^{2}}\]hybridization
View Answer play_arrowquestion_answer62) Which among the following factors is the most important in making fluorine the strongest oxidizing agent?
A) Electron affinity
B) lonization enthalpy
C) Hydration enthalpy
D) Bond dissociation energy
View Answer play_arrowquestion_answer63) In van der Waals equation of state of the gas law, the constant V is a measure of
A) intermolecular repulsions
B) intermolecular attraction
C) volume occupied by the molecules
D) intermolecular collisions per unit volume
View Answer play_arrowquestion_answer64) The conjugate base of\[{{H}_{2}}PO_{4}^{-}\]is
A) \[PO_{4}^{3-}\]
B) PRs
C) \[{{H}_{3}}P{{O}_{4}}\]
D) \[HPO_{4}^{2-}\]
View Answer play_arrowquestion_answer65) To neutralise completely 20 mL of 0.1M aqueous solution of phosphorous acid \[({{H}_{3}}P{{O}_{3}}),\]the volume of 0.1M aqueous KOH solution required is
A) 10 mL
B) 20 mL
C) 40 mL
D) 60 mL
View Answer play_arrowquestion_answer66) For which of the following parameters the structural isomers\[{{C}_{2}}{{H}_{5}}OH\]and\[C{{H}_{3}}OC{{H}_{3}}\] would be expected to have the same values? (Assume ideal behaviour)
A) Heat of vaporization
B) Vapour pressure at the same temperature
C) Boiling points
D) Gaseous densities at the same temperature and pressure
View Answer play_arrowquestion_answer67) Which one of the following statements is false?
A) Raoulfs law states that the vapour pressure of a component over a solution is proportional to its mole fraction
B) The osmotic pressure\[(\pi )\]of a solution is given by the equation\[\pi =MRT,\]where M is the molarity of the solution
C) The correct order of osmotic pressure for 0.01 M aqueous solution of each compound is \[BaC{{l}_{2}}>KC1>C{{H}_{3}}COOH>sucrose\]
D) Two sucrose solutions of same molality prepared in different solvents will have the same freezing point depression
View Answer play_arrowquestion_answer68) An ideal gas expands in volume from \[1\times {{10}^{-3}}{{m}^{3}}\]to\[1\times {{10}^{-2}}{{m}^{3}}\]at 300K against a constant pressure of\[1\times {{10}^{5}}N{{m}^{-2}}\]. The work done is
A) \[-900J\]
B) \[-900\text{ }kJ\]
C) \[270kJ\]
D) \[900kJ\]
View Answer play_arrowquestion_answer69) In a first order reaction, the concentration of the reactant, decreases from 0.8 M to 0.4 M in 15 min. The time taken for the concentration to change from 0.1 M to 0.025 M is
A) 30 min
B) 15 min
C) 7.5 min
D) 60 min
View Answer play_arrowquestion_answer70) What is the equilibrium expression for the reaction \[{{P}_{4}}(s)+5{{O}_{2}}(g){{P}_{4}}{{O}_{10}}(s)?\]
A) \[{{K}_{c}}=\frac{[{{P}_{4}}{{O}_{10}}]}{[{{P}_{4}}]{{[{{O}_{2}}]}^{5}}}\]
B) \[{{K}_{c}}=\frac{[{{P}_{4}}{{O}_{10}}]}{5[{{P}_{4}}][{{O}_{2}}]}\]
C) \[{{K}_{c}}={{[{{O}_{2}}]}^{5}}\]
D) \[{{K}_{c}}=\frac{1}{{{[{{O}_{2}}]}^{5}}}\]
View Answer play_arrowquestion_answer71) The rate equation for the reaction\[2A+B\to C\] is found to be rate\[=k[A]\,[B]\] The correct statement in relation to this reaction is that the
A) unit of k must be \[{{s}^{-1}}\]
B) \[{{t}_{1/2}}\]is a constant
C) rate of formation of C is twice the rate of, disappearance of A
D) value of k is independent of the initial concentrations of A and B
View Answer play_arrowquestion_answer72) Consider the following\[E{}^\circ \]values \[E_{F{{e}^{3+}}/F{{e}^{2+}}}^{o}=+0.77\,V\] \[E_{S{{n}^{2+}}/Sn}^{o}=-0.14\,V\] Under standard conditions the potential for the reaction \[Sn(s)+2F{{e}^{3+}}(aq)\to 2F{{e}^{2+}}(aq)+S{{n}^{2+}}(aq)\]is
A) 1.68V
B) 1.40V
C) 0.91V
D) 0.63V
View Answer play_arrowquestion_answer73) The molar solubility (in\[mol\text{ }{{L}^{-1}}\]) of a sparingly soluble salt\[M\,{{X}_{4}}\]is s. The corresponding solubility product is\[{{K}_{sp}}\]. s is given in terms of. \[{{K}_{sp}}\]by the relation
A) \[s={{({{K}_{sp}}/128)}^{1/4}}\]
B) \[s={{(128{{K}_{sp}})}^{1/4}}\]
C) \[s={{(256{{K}_{sp}})}^{1/5}}\]
D) \[s={{({{K}_{sp}}/256)}^{1/5}}\]
View Answer play_arrowquestion_answer74) The standard emf of a cell, involving one electron change is found to be 0.591 V at\[25{}^\circ C\]. The equilibrium constant of the reaction is \[(F=96,500\text{ }C\text{ }mo{{l}^{-1}})\]
A) \[1.0\times {{10}^{1}}\]
B) \[1.0\times {{10}^{5}}\]
C) \[1.0\times {{10}^{10}}\]
D) \[1.0\times {{10}^{30}}\]
View Answer play_arrowquestion_answer75) The enthalpies of combustion of carbon and carbon monoxide are\[-393.5\]and\[-283k\text{ }J\] \[mo{{l}^{-1}}\]respectively. The enthalpy of formation of carbon monoxide per mole is
A) 110.5kJ
B) 676.5 kJ
C) \[-676.5\text{ }kJ\]
D) \[-110.5kJ\]
View Answer play_arrowquestion_answer76) The limiting molar conductivities\[a{}^\circ \]for \[NaCl,KBr\]and\[KCl\]are 126, 152 and 150 S \[c{{m}^{2}}mo{{l}^{-1}}\] respectively. The\[a{}^\circ \]for\[NaBr\]is
A) \[128\text{ }S\text{ }c{{m}^{2}}mo{{l}^{-1}}\]
B) \[176\text{ }S\text{ }c{{m}^{2}}mo{{l}^{-1}}\]
C) \[278\text{ }S\text{ }c{{m}^{2}}mo{{l}^{-1}}\]
D) \[302\text{ }S\text{ }c{{m}^{2}}mo{{l}^{-1}}\]
View Answer play_arrowquestion_answer77) Which one of the following statements regarding helium is incorrect?
A) It is used to fill gas balloons instead of hydrogen because it is lighter and non-inflammable
B) It is used as a cryogenic agent for carrying out experiments at low temperatures
C) It is used to produce and sustain powerful superconducting magnets
D) It is used in gas-cooled nuclear reactors
View Answer play_arrowquestion_answer78) Identify the correct statement regarding enzymes
A) Enzymes are specific biological catalysts that can normally function at very high temperatures\[(T\sim 1000\text{ }K)\]
B) Enzymes are normally heterogeneous catalysts that are very specific in their action
C) Enzymes are specific biological catalysts that cannot be poisoned
D) Enzymes are specific biological catalysts that possess well defined active sites.
View Answer play_arrowquestion_answer79) One mole of magnesium nitride on the reaction with an excess of water gives
A) one mole of ammonia
B) one mole of nitric acid
C) two moles of ammonia
D) two moles of nitric acid
View Answer play_arrowquestion_answer80) Which one of the following ores is best concentrated by froth-floatation method?
A) Magnetite
B) Cassiterite
C) Galena
D) Malachite
View Answer play_arrowquestion_answer81) Beryllium and aluminium exhibit many properties which are similar. But, the two elements differ in
A) exhibiting maximum covalency in compounds
B) forming polymeric hydrides
C) forming covalent halides
D) exhibiting amphoteric nature in their oxides
View Answer play_arrowquestion_answer82) Aluminium chloride exists as dimer,\[A{{l}_{2}}C{{l}_{6}}\]in solid state as well as in solution of non-polar solvents such as benzene. When dissolved in water, it gives
A) \[A{{l}^{3+}}+3C{{l}^{-}}\]
B) \[{{[Al{{({{H}_{2}}O)}_{6}}]}^{3+}}+3C{{l}^{-}}\]
C) \[{{[Al{{(OH)}_{6}}]}^{3-}}+3HCl\]
D) \[A{{l}_{2}}{{O}_{3}}+6HCl\]
View Answer play_arrowquestion_answer83) The soldiers of Napolean army while at Alps during freezing winter suffered a serious problem as regards to the tin buttons of their uniforms. White metallic tin buttons got converted to grey powder. This transformation is related to
A) a change in the crystalline structure of tin
B) an interaction with nitrogen of the air at very low temperatures
C) a change in the partial pressure of oxygen in the air
D) an interaction with water vapour contained in the humid air
View Answer play_arrowquestion_answer84) Excess of\[KI\]reacts with\[CuS{{O}_{4}}\]solution and then\[N{{a}_{2}}{{S}_{2}}{{O}_{3}}\]solution is added to it. Which of the statements is incorrect for this reaction?
A) \[C{{u}_{2}}{{I}_{2}}\]is formed
B) \[Cu{{I}_{2}}\]is formed
C) \[N{{a}_{2}}{{S}_{2}}{{O}_{3}}\]is oxidized
D) Evolved\[{{I}_{2}}\]is reduced
View Answer play_arrowquestion_answer85) The co-ordination number of a central metal atom in a complex is determined by
A) the number of ligands around a metal ion bonded by sigma bonds
B) the number of ligands around a metal ion bonded by pi-bonds
C) the number of ligands around a metal ion bonded by sigma and pi-bonds both
D) the number of only anionic ligands bonded to the metal ion
View Answer play_arrowquestion_answer86) Which one of the following complexes is an outer orbital complex?
A) \[{{[Fe{{(CN)}_{6}}]}^{4-}}\]
B) \[{{[Mn{{(CN)}_{6}}]}^{4-}}\]
C) \[{{[Co{{(N{{H}_{3}})}_{6}}]}^{3+}}\]
D) \[{{[Ni{{(N{{H}_{3}})}_{6}}]}^{2+}}\] (Atomic numbers\[Mn=25,\text{ }Fe=26,\text{ }Co=27,\] \[Ni=28\])
View Answer play_arrowquestion_answer87) Co-ordination compounds have great importance in biological systems. In this context which of the following statements is incorrect?
A) Chlorophylls are green pigments in plants and contain calcium
B) Haemoglobin is the red pigment of blood and contains iron
C) Cyanocobalamin is vitamin\[{{B}_{12}}\]and contains cobalt
D) Carboxypeptidase-A is an enzyme and contains zinc
View Answer play_arrowquestion_answer88) Cerium\[(Z=58)\]is an important member of the lanthanides. Which of the following statements about cerium is incorrect?
A) The common oxidation states of cerium are +3 and +4
B) The +3 oxidation state of cerium is more stable than the +4 oxidation state
C) The +4 oxidation state of cerium is not known in solutions
D) Cerium (IV) acts as an oxidising agent
View Answer play_arrowquestion_answer89) The correct order of magnetic moments (spin only values in BM) among the following is
A) \[{{[MnC{{l}_{4}}]}^{2-}}>{{[CoC{{l}_{4}}]}^{2-}}>{{[Fe{{(CN)}_{6}}]}^{4-}}\]
B) \[{{[MnC{{l}_{4}}]}^{2-}}>{{[Fe{{(CN)}_{6}}]}^{4-}}>{{[CoC{{l}_{4}}]}^{2-}}\]
C) \[{{[Fe{{(CN)}_{6}}]}^{4-}}>{{[MnC{{l}_{4}}]}^{2-}}>{{[CoC{{l}_{4}}]}^{2-}}\]
D) \[{{[Fe{{(CN)}_{6}}]}^{4-}}>{{[CoC{{l}_{4}}]}^{2-}}>{{[MnC{{l}_{4}}]}^{2-}}\]
View Answer play_arrowquestion_answer90) Consider the following nuclear reactions: \[_{92}^{238}M\to _{y}^{x}N+2_{2}^{4}He;_{y}^{x}N\to _{B}^{A}L+2{{\beta }^{+}}\] The number of neutrons in the element L is
A) 142
B) 144
C) 140
D) 146
View Answer play_arrowquestion_answer91) The compound formed in the positive test for nitrogen with the Lassaigne solution of an organic compound is
A) \[F{{e}_{4}}{{[Fe{{(CN)}_{6}}]}_{3}}\]
B) \[N{{a}_{3}}[Fe{{(CN)}_{6}}]\]
C) \[Fe{{(CN)}_{3}}\]
D) \[N{{a}_{4}}[Fe{{(CN)}_{5}}NOS]\]
View Answer play_arrowquestion_answer92) The ammonia evolved from the treatment of 0.30g of an organic compound for the estimation of nitrogen was passed in 10s) ml, of M sulphuric acid. The excess of acid required 20 mL of 0.5 M sodium hydroxide solution for complete neutralization. The organic compound is
A) acetamide
B) benzAmide
C) urea
D) thiourea
View Answer play_arrowquestion_answer93) Which one of the following has the minimum boiling point?
A) n-butane
B) 1-butyne
C) 1-butene
D) Isobutene
View Answer play_arrowquestion_answer94) The IUPAC name of the compound is
A) 3,3-dimethyl-1-hydroxy cyclohexane
B) 1,1-dimethyl-3-hydroxy cyclohexane
C) 3,3-dimethyl-1-cyclohexanol
D) 1,1-dimethyl-3-cyclohexanol
View Answer play_arrowquestion_answer95) Which one of the following does not have\[s{{p}^{2}}\]hybridised carbon?
A) Acetone
B) Acetic acid
C) Acetonitrile
D) Acetamide
View Answer play_arrowquestion_answer96) Which of the following will have a meso-isomer also?
A) 2-chlorobutane
B) 2,3-dichlorobufane
C) 2,3-dichloropentane
D) 2-hydroxypropanoic acid
View Answer play_arrowquestion_answer97) Rate of the reaction is fastest when Z is
A) \[Cl\]
B) \[N{{H}_{2}}\]
C) \[O{{C}_{2}}{{H}_{5}}\]
D) \[OCOC{{H}_{3}}\]
View Answer play_arrowquestion_answer98) Amongst the following compounds, the optically active alkane having lowest molecular mass is
A) \[C{{H}_{3}}-C{{H}_{2}}-C{{H}_{2}}-C{{H}_{3}}\]
B) \[C{{H}_{3}}C{{H}_{2}}\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{CH}}\,C{{H}_{3}}\]
C)
D) \[C{{H}_{3}}C{{H}_{2}}-C\equiv CH\]
View Answer play_arrowquestion_answer99) Consider the acidity of the carboxylic acids \[PhCOOH\] \[o-N{{O}_{2}}{{C}_{6}}{{H}_{4}}COOH\] \[p-N{{O}_{2}}{{C}_{6}}{{H}_{4}}COOH\] \[m-N{{O}_{2}}{{C}_{6}}{{H}_{4}}COOH\] Which of the following order is correct?
A) \[I>II>III>IV\]
B) \[II>IV>III>I\]
C) \[II>IV>I>III\]
D) \[II>III>IV>I\]
View Answer play_arrowquestion_answer100) Which of the following is the strongest base?
A)
B)
C)
D)
View Answer play_arrowquestion_answer101) Which base is present in RNA but not in DNA?
A) Uracil
B) Cytosine
C) Guanine
D) Thymine
View Answer play_arrowquestion_answer102) The compound formed on heating chlorobenzene with chloral in the presence of concentrated sulphuric acid is
A) gammexane
B) DDT
C) freon
D) hexachloroethane
View Answer play_arrowquestion_answer103) On mixing ethyl acetate with aqueous sodium chloride, the composition of the resultant solution is
A) \[C{{H}_{3}}COO{{C}_{2}}{{H}_{5}}+NaCl\]
B) \[C{{H}_{3}}COONa+{{C}_{2}}{{H}_{5}}OH\]
C) \[C{{H}_{3}}COCl+{{C}_{2}}{{H}_{5}}OH+NaOH\]
D) \[C{{H}_{3}}Cl+{{C}_{2}}{{H}_{5}}COONa\]
View Answer play_arrowquestion_answer104) Acetyl bromide reacts with excess of\[C{{H}_{3}}MgI\] followed by treatment with a saturated solution of\[N{{H}_{4}}Cl\]gives
A) acetone
B) acetamide
C) 2-methyl-2-propanol
D) acetyl iodide
View Answer play_arrowquestion_answer105) Which one of the following is reduced with zinc and hydrochloric acid to give the corresponding hydrocarbon?
A) Ethyl acetate
B) Acetic acid
C) Acetamide
D) Butan-2-one
View Answer play_arrowquestion_answer106) Which one of the following undergoes reaction with 50% sodium hydroxide solution to give the corresponding alcohol and acid?
A) Phenol
B) Benzaldehyde
C) Butanal
D) Benzoic acid
View Answer play_arrowquestion_answer107) Among the following compounds which can be dehydrated very easily?
A) \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}C{{H}_{2}}C{{H}_{2}}OH\]
B) \[C{{H}_{3}}C{{H}_{2}}\overset{\begin{smallmatrix} OH \\ | \end{smallmatrix}}{\mathop{C{{H}_{2}}}}\,CHC{{H}_{3}}\]
C) \[C{{H}_{3}}C{{H}_{2}}\overset{\begin{smallmatrix} OH \\ | \end{smallmatrix}}{\mathop{\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,}}\,C{{H}_{2}}C{{H}_{3}}\]
D) \[C{{H}_{3}}C{{H}_{2}}\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{CH}}\,C{{H}_{2}}C{{H}_{2}}OH\]
View Answer play_arrowquestion_answer108) Which of the following compounds is not chiral?
A) 1-chloropentane
B) 2-chloropentane
C) 1-chloro-2-methyl pentane
D) 3-chloro-2-methyl pentane
View Answer play_arrowquestion_answer109) Insulin production and its action in human body are responsible for the level of diabetes. This compound belongs to which of the following categories?
A) A co-enzyme
B) A hormone
C) An enzyme
D) An antibiotic
View Answer play_arrowquestion_answer110) The smog is essentially caused by the presence of
A) \[{{O}_{2}}\]and \[{{O}_{3}}\]
B) \[{{O}_{2}}\]and \[{{N}_{2}}\]
C) oxides of sulphur and nitrogen
D) \[{{O}_{3}}\]and\[{{N}_{2}}\]
View Answer play_arrowquestion_answer111) Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set\[A=\{1,2,3,4\}\]. The relation R is
A) a function
B) transitive
C) not symmetric
D) reflexive
View Answer play_arrowquestion_answer112) The range of the function\[f(x){{=}^{7-x}}{{P}_{x-3}}\]is
A) \[\{1,\text{ }2,\text{ }3\}\]
B) \[\{1,\text{ }2,\text{ }3,\text{ }4,\text{ }5,\text{ }6\}\]
C) \[\{1,2,3,4\}\]
D) \[\{1,\,\,2,\,\,3,\,\,4,\,\,5\}\]
View Answer play_arrowquestion_answer113) Let\[z,w\]be complex numbers such that \[\overline{z}+i\overline{w}=0\]and arg\[zw=\pi \]Then arg z equals:
A) \[\frac{\pi }{4}\]
B) \[\frac{\pi }{2}\]
C) \[\frac{3\pi }{4}\]
D) \[\frac{5\pi }{4}\]
View Answer play_arrowquestion_answer114) If\[z=x-iy\]and\[{{z}^{1/3}}=p-iq,\]then\[{\left( \frac{x}{p}+\frac{y}{p} \right)}/{({{p}^{2}}+{{q}^{2}})}\;\]is equal to
A) 1
B) \[-1\]
C) 2
D) \[-2\]
View Answer play_arrowquestion_answer115) If\[|{{z}^{2}}-1|=|z{{|}^{2}}+1,\]then z lies on
A) the real axis
B) the imaginary axis
C) a circle
D) an ellipse
View Answer play_arrowquestion_answer116) Let\[A=\left[ \begin{matrix} 0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0 \\ \end{matrix} \right]\].The only correct statement about the matrix A is
A) A is a zero matrix
B) \[A=(-1),I\]where I is a unit matrix
C) \[{{A}^{-1}}\]does not exist
D) \[{{A}^{2}}=I\]
View Answer play_arrowquestion_answer117) Let\[A=\left[ \begin{matrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \\ \end{matrix} \right]\]and\[(10)B=\left[ \begin{matrix} 4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3 \\ \end{matrix} \right]\].If B is the inverse of matrix A, then a is
A) \[-2\]
B) 1
C) 2
D) 5
View Answer play_arrowquestion_answer118) If\[a,{{a}_{2}},{{a}_{3}},........{{a}_{n}},....\]are in GP, then the value of the determinant\[\left| \begin{matrix} \log {{a}_{n}} & \log {{a}_{n+1}} & \log {{a}_{n+2}} \\ \log {{a}_{n+3}} & \log {{a}_{n+4}} & \log {{a}_{n+5}} \\ \log {{a}_{n+6}} & \log {{a}_{n+7}} & \log {{a}_{n+8}} \\ \end{matrix} \right|,\]is
A) 0
B) 1
C) 2
D) \[-2\]
View Answer play_arrowquestion_answer119) Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation
A) \[{{x}^{2}}+18x+16=0\]
B) \[{{x}^{2}}-18x+16=0\]
C) \[{{x}^{2}}+18x-16=0\]
D) \[{{x}^{2}}-18x-16=0\]
View Answer play_arrowquestion_answer120) If\[(1-p)\]is a root of quadratic equation \[{{x}^{2}}+px+(1-p)=0,\]then its roots are
A) 0, 1
B) \[-1,1\]
C) 0,-1
D) \[-1,2\]
View Answer play_arrowquestion_answer121) How many ways are there to arrange the letters in the Word GARDEN with the vowels in alphabetical order?
A) 120
B) 240
C) 360
D) 480
View Answer play_arrowquestion_answer122) The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty, is
A) 5
B) \[-21\]
C) \[{{3}^{8}}\]
D) \[^{8}{{C}_{3}}\]
View Answer play_arrowquestion_answer123) If one root of the equation\[{{x}^{2}}+px+12=0\]is 4, while the equation\[{{x}^{2}}+px+q=0\]has equal roots, then the value of q is
A) \[\frac{49}{4}\]
B) 12
C) 3
D) 4
View Answer play_arrowquestion_answer124) The coefficient of the middle term in the binomial expansion in powers of\[x\]of\[{{(1+ax)}^{4}}\] and of\[{{(1-ax)}^{6}}\]is the same, if a equals:
A) \[-\frac{5}{3}\]
B) \[\frac{10}{3}\]
C) \[-\frac{3}{10}\]
D) \[\frac{3}{5}\] The coefficient of\[x\]in the middle term of expansion of\[{{(1+\alpha x)}^{4}}{{=}^{4}}{{C}_{2}}.{{\alpha }^{2}}\] The coefficient of x in the middle term of the expansion of\[{{(1-\alpha x)}^{6}}{{=}^{6}}{{C}_{3}}{{(-\alpha )}^{3}}\] According to question, \[^{4}{{C}_{2}}{{\alpha }^{2}}{{=}^{6}}{{C}_{3}}{{(-\alpha )}^{3}}\] \[\Rightarrow \] \[\frac{4!}{2!2!}{{\alpha }^{2}}=-\frac{6!}{3!3!}{{\alpha }^{3}}\] \[\Rightarrow \] \[6{{\alpha }^{2}}=-20{{\alpha }^{3}}\] \[\Rightarrow \] \[\alpha =-\frac{6}{20}\] \[\Rightarrow \] \[\alpha =-\frac{3}{10}\]
View Answer play_arrowquestion_answer125) The coefficient of\[{{x}^{n}}\]in expansion of \[(1+x){{(1-x)}^{n}}\]is
A) \[(n-1)\]
B) \[{{(-1)}^{n}}(1-n)\]
C) \[{{(-1)}^{n-1}}{{(n-1)}^{2}}\]
D) \[{{(-1)}^{n-1}}n\]
View Answer play_arrowquestion_answer126) If\[{{s}_{n}}=\sum\limits_{r=0}^{n}{\frac{1}{^{n}{{C}_{r}}}}\]and\[{{t}_{n}}=\sum\limits_{r=0}^{n}{\frac{r}{^{n}{{C}_{r}}}},\]then\[\frac{{{t}_{n}}}{{{s}_{n}}}\]is equal to
A) \[\frac{n}{2}\]
B) \[\frac{n}{2}-1\]
C) \[n-1\]
D) \[\frac{2n-1}{2}\]
View Answer play_arrowquestion_answer127) Let\[{{T}_{r}}\]be the rth term of an A P whose first term is a and common difference is d. If for some positive integers\[m,n,m\ne n,{{T}_{m}}=\frac{1}{n}\]and \[{{T}_{n}}=\frac{1}{m},\]then\[a-d\]equals
A) \[0\]
B) \[1\]
C) \[\frac{1}{mn}\]
D) \[\frac{1}{m}+\frac{1}{n}\]
View Answer play_arrowquestion_answer128) The sum of the first n terms of the series\[{{1}^{2}}+{{2.2}^{2}}+{{3}^{2}}+{{2.4}^{2}}+{{5}^{2}}+{{2.6}^{2}}+...\]is \[\frac{n{{(n+1)}^{2}}}{2}\]when n is even. When n is odd the sum is
A) \[\frac{3n(n+1)}{2}\]
B) \[\frac{{{n}^{2}}(n+1)}{2}\]
C) \[\frac{n{{(n+1)}^{2}}}{4}\]
D) \[{{\left[ \frac{n(n+1)}{2} \right]}^{2}}\]
View Answer play_arrowquestion_answer129) The sum of series\[\frac{1}{2!}+\frac{1}{4!}+\frac{1}{6!}+...\]is
A) \[\frac{({{e}^{2}}-1)}{2}\]
B) \[\frac{{{(e-1)}^{2}}}{2e}\]
C) \[\frac{({{e}^{2}}-1)}{2e}\]
D) \[\frac{({{e}^{2}}-2)}{e}\]
View Answer play_arrowquestion_answer130) Let\[\alpha ,\beta \]be such that\[\pi <\alpha -\beta <3\pi \]. If \[\sin \alpha +\sin \beta =-\frac{21}{65}\]and \[\cos \alpha +\cos \beta =-\frac{27}{65},\]then the value of\[\cos \frac{\alpha -\beta }{2}\]is
A) \[-\frac{3}{\sqrt{130}}\]
B) \[\frac{3}{\sqrt{130}}\]
C) \[\frac{6}{65}\]
D) \[-\frac{6}{65}\]
View Answer play_arrowquestion_answer131) If\[u=\sqrt{{{a}^{2}}{{\cos }^{2}}\theta +{{b}^{2}}{{\sin }^{2}}\theta }\]\[+\sqrt{{{a}^{2}}{{\sin }^{2}}\theta +{{b}^{2}}{{\cos }^{2}}\theta },\]then the difference between the maximum and minimum values of\[{{u}^{2}}\]is given by
A) \[2({{a}^{2}}+{{b}^{2}})\]
B) \[2\sqrt{{{a}^{2}}+{{b}^{2}}}\]
C) \[{{(a+b)}^{2}}\]
D) \[{{(a-b)}^{2}}\]
View Answer play_arrowquestion_answer132) The sides of a triangle are\[\sin \alpha ,\cos \alpha \]and\[\sqrt{1+\sin \alpha \cos \alpha }\]for some\[0<\alpha <\frac{\pi }{2}\]. Then the greatest angle of the triangle is
A) \[60{}^\circ \]
B) \[90{}^\circ \]
C) \[120{}^\circ \]
D) \[150{}^\circ \]
View Answer play_arrowquestion_answer133) If\[f:R\to S,\]defined by \[f(x)=\sin x-\sqrt{3}\cos x+1,\]is onto , then the interval of S is
A) [0, 3]
B) \[[-1,\text{ }1]\]
C) [0, 1]
D) \[[-1,\text{ }3]\]
View Answer play_arrowquestion_answer134) The domain of the function \[f(x)=\frac{{{\sin }^{-1}}(x-3)}{\sqrt{9-{{x}^{2}}}}\]
A) [2, 3]
B) [2, 3)
C) [1, 2]
D) [1, 2)
View Answer play_arrowquestion_answer135) if\[\underset{x\to \infty }{\mathop{\lim }}\,{{\left( 1+\frac{a}{x}+\frac{b}{{{x}^{2}}} \right)}^{2x}}={{e}^{2}},\]then the values of a and b are
A) \[a\in R,b\in R\]
B) \[a=1,b\in R\]
C) \[a\in R,b=2\]
D) \[a=1,b=2\]
View Answer play_arrowquestion_answer136) Let \[f(x)=\frac{1-\tan x}{4x-n},x\ne \frac{\pi }{4},x\in \left[ 0,\frac{\pi }{2} \right]\]. If \[f(x)\]is continuous in\[\left[ 0,\frac{\pi }{2} \right],\]then\[f\left( \frac{\pi }{4} \right)\]is
A) 1
B) \[1/2\]
C) \[-1/2\]
D) \[-1\]
View Answer play_arrowquestion_answer137) If\[x={{e}^{y+{{e}^{y+......to\,\infty }}}},x>0,\]the\[\frac{dy}{dx}\]is
A) \[\frac{x}{1+x}\]
B) \[\frac{1}{x}\]
C) \[\frac{1-x}{x}\]
D) \[\frac{1+x}{x}\]
View Answer play_arrowquestion_answer138) A point on the parabola\[{{y}^{2}}=18x\]at which the ordinate increases at twice the rate of the abscissa, is
A) \[(2,\,4)\]
B) \[(2,\,-4)\]
C) \[\left( -\frac{9}{8},\frac{9}{2} \right)\]
D) \[\left( \frac{9}{8},\frac{9}{2} \right)\]
View Answer play_arrowquestion_answer139) A function\[y=f(x)\]as a second order derivative\[f=6(x-1)\]. If its graph passes through the point (2, 1) and at that point the tangent to the graph is\[y=3x-5,\]then the function is
A) \[{{(x-1)}^{2}}\]
B) \[{{(x-1)}^{3}}\]
C) \[{{(x+1)}^{3}}\]
D) \[{{(x+1)}^{2}}\]
View Answer play_arrowquestion_answer140) The normal to the curve\[x=a(1+cos\theta \text{)},\] \[y=a\sin \theta \]at\[\theta \]always passes through the fixed point
A) \[(a,\text{ }0)\]
B) \[(0,\text{ }a)\]
C) (0, 0)
D) \[(a,\text{ }a)\]
View Answer play_arrowquestion_answer141) If\[2a+3b+6c=0,\] then at least one root of the equation\[a{{x}^{2}}+bx+c=0\]lies in the interval
A) (0, 1)
B) (1, 2)
C) (2, 3)
D) (1, 3)
View Answer play_arrowquestion_answer142) \[\underset{n\to \infty }{\mathop{\lim }}\,\sum\limits_{r=1}^{n}{\frac{1}{n}{{e}^{r/n}}}\]is
A) \[e\]
B) \[e-1\]
C) \[1-e\]
D) \[e+1\]
View Answer play_arrowquestion_answer143) If \[\int{\frac{\sin x}{\sin (x-\alpha )}}dx=Ax+B\log \sin (x-\alpha )+c,\] then value of (A, B) is
A) \[(\sin \alpha ,\cos \alpha )\]
B) \[(\cos \alpha ,\sin \alpha )\]
C) \[(-\sin \alpha ,\cos \alpha )\]
D) \[(-\cos \alpha ,\sin \alpha )\]
View Answer play_arrowquestion_answer144) \[\int{\frac{dx}{\cos x-\sin x}}\]is equal to
A) \[\frac{1}{\sqrt{2}}\log \left| \tan \left( \frac{x}{2}-\frac{\pi }{8} \right) \right|+c\]
B) \[\frac{1}{\sqrt{2}}\log \left| cot\left( \frac{x}{2} \right) \right|+c\]
C) \[\frac{1}{\sqrt{2}}\log \left| \tan \left( \frac{x}{2}-\frac{3\pi }{8} \right) \right|+c\]
D) \[\frac{1}{\sqrt{2}}\log \left| \tan \left( \frac{x}{2}+\frac{3\pi }{8} \right) \right|+c\]
View Answer play_arrowquestion_answer145) The value of\[\int_{-2}^{3}{|1-{{x}^{2}}|dx}\]is
A) \[\frac{28}{3}\]
B) \[\frac{14}{3}\]
C) \[\frac{7}{3}\]
D) \[\frac{1}{3}\]
View Answer play_arrowquestion_answer146) The value of\[\int_{0}^{\pi /2}{\frac{{{(\sin x+\cos x)}^{2}}}{\sqrt{1+\sin 2x}}}dx\]is
A) 0
B) 1
C) 2
D) 3
View Answer play_arrowquestion_answer147) If\[\int_{0}^{\pi }{xf(\sin x)}dx=A\int_{0}^{\pi /2}{f(\sin x)dx,}\]then A is equal to
A) 0
B) \[\pi \]
C) \[\frac{\pi }{4}\]
D) \[2\pi \]
View Answer play_arrowquestion_answer148) The area of the region bounded by the curves \[y=|x-2|,x=1,x=3\]the\[x-\]axis is
A) 1
B) 2
C) 3
D) 4
View Answer play_arrowquestion_answer149) The differential equation for the family of curves\[{{x}^{2}}+{{y}^{2}}-2ay=0,\]where a is an arbitrary constant, is
A) \[2({{x}^{2}}-{{y}^{2}})y=xy\]
B) \[2({{x}^{2}}+{{y}^{2}})y=xy\]
C) \[({{x}^{2}}-{{y}^{2}})y=2xy\]
D) \[({{x}^{2}}+{{y}^{2}})y=2xy\]
View Answer play_arrowquestion_answer150) The solution of the differential equation\[y\,dx+(x+{{x}^{2}}y)dy=0\]is
A) \[-\frac{1}{xy}=c\]
B) \[-\frac{1}{xy}+\log y=c\]
C) \[\frac{1}{xy}+\log y=c\]
D) \[\log y=cx\]
View Answer play_arrowquestion_answer151) Let\[A(2,-3)\]and\[B(-2,1)\]be vertices of a triangle ABC. If the centroid of this triangle moves on the line\[2x+3y=1,\]then the locus of the vertex C is the line:
A) \[2x+3y=9\]
B) \[2x-3y=7\]
C) \[3x+2y=5\]
D) \[3x-2y=3\]
View Answer play_arrowquestion_answer152) The equation of the straight line passing through the point (4, 3) and making intercepts on the co-ordinate axes whose sum is\[-1,\]is
A) \[\frac{x}{2}+\frac{y}{3}=-1\]and\[\frac{x}{-2}+\frac{y}{1}=-1\]
B) \[\frac{x}{2}-\frac{y}{3}=-1\]and\[\frac{x}{-2}+\frac{y}{1}=-1\]
C) \[\frac{x}{2}+\frac{y}{3}=1\]and\[\frac{x}{-2}+\frac{y}{1}=1\]
D) \[\frac{x}{2}-\frac{y}{3}=1\]and\[\frac{x}{-2}+\frac{y}{1}=1\]
View Answer play_arrowquestion_answer153) If the sum of the slopes of the lines given by \[{{x}^{2}}-2cxy-7{{y}^{2}}=0\]is four times their product, then c has the value
A) 1
B) \[-1\]
C) 2
D) \[-2\]
View Answer play_arrowquestion_answer154) If one of the lines given by\[6{{x}^{2}}-xy+4c{{y}^{2}}=0\] is\[3x+4y=0,\]then c equals:
A) 1
B) \[-1\]
C) 3
D) \[-3\]
View Answer play_arrowquestion_answer155) If a circle passes through the point (a, b) and cuts the circle\[{{x}^{2}}+{{y}^{2}}=4\]orthogonally, then, the locus of its centre is
A) \[2ax+2by+({{a}^{2}}+{{b}^{2}}+4)=0\]
B) \[2ax+2by-({{a}^{2}}+{{b}^{2}}+4)=0\]
C) \[2ax-2by+({{a}^{2}}+{{b}^{2}}+4)=0\]
D) \[2ax-2by-({{a}^{2}}+{{b}^{2}}+4)=0\]
View Answer play_arrowquestion_answer156) If the lines\[2x+3y+1=0\]and\[3x-y-4=0\] lie along diameters of a circle of circumference\[10\pi ,\]then the equation of the circle is
A) \[{{x}^{2}}+{{y}^{2}}-2x+2y-23=0\]
B) \[{{x}^{2}}+{{y}^{2}}-2x-2y-23=0\]
C) \[{{x}^{2}}+{{y}^{2}}+2x+2y-23=0\]
D) \[{{x}^{2}}+{{y}^{2}}+2x-2y-23=0\]
View Answer play_arrowquestion_answer157) The intercept on the line\[y=x\]by the circle \[{{x}^{2}}+{{y}^{2}}-2x=0\]is AB, Equation of the circle on AB as a diameter is
A) \[{{x}^{2}}+{{y}^{2}}-x-y=0\]
B) \[{{x}^{2}}+{{y}^{2}}-x+y=0\]
C) \[{{x}^{2}}+{{y}^{2}}+x+y=0\]
D) \[{{x}^{2}}+{{y}^{2}}+x-y=0\]
View Answer play_arrowquestion_answer158) If\[a\ne 0\]and the line\[2bx+3cy+4d=0\]passes through the points of intersection of the parabolas\[{{y}^{2}}=4ax\]and\[{{x}^{2}}=4ay,\]then
A) \[{{d}^{2}}+{{(2b+3c)}^{2}}=0\]
B) \[{{d}^{2}}+{{(3b+2c)}^{2}}=0\]
C) \[{{d}^{2}}+{{(2b-3c)}^{2}}=0\]
D) \[{{d}^{2}}+{{(3b-2c)}^{2}}=0\]
View Answer play_arrowquestion_answer159) The eccentricity of an ellipse with its centre at the origin, is\[\frac{1}{2}\]. If one of the directrices is \[x=4,\]then the equation of the elapse is:
A) \[3{{x}^{2}}+4{{y}^{2}}=1\]
B) \[3{{x}^{2}}+4{{y}^{2}}=12\]
C) \[4{{x}^{2}}+3{{y}^{2}}=12\]
D) \[4{{x}^{2}}+3{{y}^{2}}=1\]
View Answer play_arrowquestion_answer160) A line makes the same angle. 9 with each of the\[x\]and z axis. If the angle P, which it makes with y-axis, is such that\[si{{n}^{2}}\beta =3\text{ }si{{n}^{2}}\theta ,\]then\[{{\cos }^{2}}\theta \]equals
A) \[\frac{2}{3}\]
B) \[\frac{1}{5}\]
C) \[\frac{3}{5}\]
D) \[\frac{2}{5}\]
View Answer play_arrowquestion_answer161) Distance between two parallel planes \[2x+y+2z=8\]and\[4x+2y+4z+5=0\]is
A) \[\frac{3}{2}\]
B) \[\frac{5}{2}\]
C) \[\frac{7}{2}\]
D) \[\frac{9}{2}\]
View Answer play_arrowquestion_answer162) A line with direction cosines proportional to 2,1, 2 meets each of the lines\[x=y+a=z\]and \[x+a=2y=2z\]. The co-ordinates of each of the points of intersection are given by
A) \[(3a,3a,3a)(a,a,a)\]
B) \[(3a,2a,3a)(a,a,a)\]
C) \[(3a,2a,3a)(a,a,2a)\]
D) \[(2a,3a,3a)(2a,a,a)\]
View Answer play_arrowquestion_answer163) If the straight lines\[x=1+s,y=-3-\lambda s,\]\[z=1+\lambda s\]and\[x=\frac{t}{2},y=1+t,z=2-t,\]with parameters s and t respectively, are co-planar, then\[\lambda \]equals
A) \[-2\]
B) \[-1\]
C) \[-\frac{1}{2}\]
D) \[0\]
View Answer play_arrowquestion_answer164) Let\[\overrightarrow{a},\overrightarrow{d}\]and\[\overrightarrow{c}\]be three non-zero vectors such that no two of these are collinear. If the vector\[\overrightarrow{a}+2\overrightarrow{b}\]is collinear with\[\overrightarrow{c}\]and\[\overrightarrow{b}+3\overrightarrow{c}\]is collinear with\[\overrightarrow{a}\] (\[\lambda \]being some non-zero scalar), then\[\overrightarrow{a}+2\overrightarrow{b}+6\overrightarrow{c}\]equals
A) \[\lambda \overrightarrow{a}\]
B) \[\lambda \overrightarrow{b}\]
C) \[\lambda \overrightarrow{c}\]
D) 0
View Answer play_arrowquestion_answer165) A particle is acted upon by constant forces\[4\hat{i}+\hat{j}-3\hat{k}\] and\[3\hat{i}+\hat{j}-\hat{k}\] which displace it from a point\[\hat{i}+2\hat{j}+3\hat{k}\]to the point\[5\hat{i}+4\hat{j}+\hat{k}\]. The work done in standard units by the forces is given by
A) 40
B) 30
C) 25
D) 15
View Answer play_arrowquestion_answer166) If\[\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}\]are non-coplanar vectors and\[\lambda \]is a real number, then the vectors\[\overrightarrow{a}+2\overrightarrow{b}+3\overrightarrow{c},\]and\[\lambda \overrightarrow{b}+4\overrightarrow{c}\]and\[(2\lambda -1)\overrightarrow{c}\]are non-coplanar for
A) all values of k
B) all except one value of k
C) all except two values of X
D) no value of k
View Answer play_arrowquestion_answer167) Let\[\overrightarrow{u},\overrightarrow{v},\overrightarrow{w}\]be such that\[|\overrightarrow{u}|=1,|\overrightarrow{v}|=2,\]\[|\overrightarrow{w}|=3.\] If the projection\[\overrightarrow{v}\]long\[\overrightarrow{u}\]is equal to that of\[\overrightarrow{w}\] along\[\overrightarrow{u}\]and\[\overrightarrow{v},\overrightarrow{w}\]are perpendicular to each other, then\[|\overrightarrow{u}-\overrightarrow{v}+\overrightarrow{w}|\]equals:
A) 2
B) \[\sqrt{7}\]
C) \[\sqrt{14}\]
D) 14
View Answer play_arrowquestion_answer168) The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is
A) \[\frac{37}{256}\]
B) \[\frac{219}{256}\]
C) \[\frac{128}{256}\]
D) \[\frac{28}{256}\]
View Answer play_arrowquestion_answer169) With two forces acting at a point, the maximum effect is obtained when their resultant is 4N. If they act at right angles, then their resultant is 3N. Then the forces are
A) \[(2+\sqrt{2})N\]and\[(2-\sqrt{2})N\]
B) \[(2+\sqrt{3})N\]and\[(2-\sqrt{3})N\]
C) \[\left( 2+\frac{1}{2}\sqrt{2} \right)N\]and\[\left( 2-\frac{1}{2}\sqrt{2} \right)N\]
D) \[\left( 2+\frac{1}{2}\sqrt{3} \right)N\]and\[\left( 2-\frac{1}{2}\sqrt{3} \right)N\]
View Answer play_arrowquestion_answer170) In a right angle\[\Delta ABC,\text{ }\angle A=90{}^\circ \]and sides a, b, c are respectively, 5 cm, 4 cm and 3 cm. If a force F has moments 0, 9 and 16 in N cm unit respectively about vertices A, B and C, the magnitude of F is
A) 3
B) 4
C) 5
D) 9
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