question_answer1) Which one of the following represents the correct dimensions of the coefficient of viscosity?
A) \[[M{{L}^{-1}}{{T}^{-2}}]\] done clear
B) \[[ML{{T}^{-1}}]\] done clear
C) \[[M{{L}^{-1}}{{T}^{-1}}]\] done clear
D) \[[M{{L}^{-2}}{{T}^{-2}}]\] done clear
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) \[{{x}^{2}}\] done clear
B) \[{{e}^{x}}\] done clear
C) \[x\] done clear
D) \[lo{{g}_{e}}x\] done clear
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 done clear
B) \[7h/9\]m from the ground done clear
C) \[8h/9\]m from the ground done clear
D) \[17h/9\]m from the ground done clear
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) \[\frac{1}{{{R}_{2}}}\] done clear
B) \[\frac{1}{R}\] done clear
C) \[R\] done clear
D) \[{{R}^{2}}\] done clear
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 done clear
B) 40m done clear
C) 60 m done clear
D) 80 m done clear
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 done clear
B) Four done clear
C) Two done clear
D) Three done clear
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) \[0.2\text{ }m/{{s}^{2}}\] done clear
B) \[9.8\text{ }m/{{s}^{2}}\] done clear
C) \[5\text{ }m/{{s}^{2}}\] done clear
D) \[4.8\text{ }m/{{s}^{2}}\] done clear
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 done clear
B) 4.0 done clear
C) 1.6 done clear
D) 2.5 done clear
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) \[-7\] done clear
B) \[+7\] done clear
C) \[+10\] done clear
D) \[+13\] done clear
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 done clear
B) its acceleration is constant done clear
C) its kinetic energy is constant done clear
D) it moves in a straight line done clear
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,\[60{}^\circ \] done clear
B) Yes,\[30{}^\circ \] done clear
C) No done clear
D) Yes,\[45{}^\circ \] done clear
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) \[{{I}_{A}}={{I}_{B}}\] done clear
B) \[{{I}_{A}}>{{I}_{B}}\] done clear
C) \[{{I}_{A}}<{{I}_{B}}\] done clear
D) \[\frac{{{I}_{A}}}{{{I}_{B}}}=\frac{{{d}_{A}}}{{{d}_{B}}}\] done clear
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) \[gx\] done clear
B) \[\frac{gR}{R-x}\] done clear
C) \[\frac{g{{R}^{2}}}{R+x}\] done clear
D) \[{{\left( \frac{g{{R}^{2}}}{R+x} \right)}^{1/2}}\] done clear
View Answer play_arrowquestion_answer14) The time period of an earth satellite in circular orbit is independent of
A) the mass of the satellite done clear
B) radius of its orbit done clear
C) both the mass and radius of the orbit done clear
D) neither the mass of the satellite nor the radius of its orbit done clear
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) \[2mgR\] done clear
B) \[\frac{1}{2}mgR\] done clear
C) \[\frac{1}{4}mgR\] done clear
D) \[mgR\] done clear
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) \[{{R}^{\left( \frac{n+1}{2} \right)}}\] done clear
B) \[{{R}^{\left( \frac{n-1}{2} \right)}}\] done clear
C) \[{{R}^{n}}\] done clear
D) \[{{R}^{\left( \frac{n-2}{2} \right)}}\] done clear
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) \[\frac{F}{2l}\] done clear
B) \[Fl\] done clear
C) \[2Fl\] done clear
D) \[\frac{Fl}{2}\] done clear
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 done clear
B) air flows from bigger bubble to the smaller bubble till the sizes are interchanged done clear
C) air flows from the smaller bubble to the bigger done clear
D) there is no flow of air done clear
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) \[t={{t}_{0}}\] done clear
B) \[t={{t}_{0}}/2\] done clear
C) \[t=2{{t}_{0}}\] done clear
D) \[t=4{{t}_{0}}\] done clear
View Answer play_arrowquestion_answer20) The total energy of a particle, executing simple harmonic motion is
A) \[\propto x\] done clear
B) \[\propto {{x}^{2}}\] done clear
C) independent of\[x\] done clear
D) \[\propto {{x}^{1/2}}\] done clear
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 done clear
B) 5 m/s done clear
C) 20 m/s done clear
D) 57cm/s done clear
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) \[\frac{m}{\omega _{0}^{2}-{{\omega }^{2}}}\] done clear
B) \[\frac{1}{m(\omega _{0}^{2}-{{\omega }^{2}})}\] done clear
C) \[\frac{1}{m(\omega _{0}^{2}+{{\omega }^{2}})}\] done clear
D) \[\frac{m}{\omega _{0}^{2}+{{\omega }^{2}}}\] done clear
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 done clear
B) 23/15 done clear
C) 35/23 done clear
D) 4/3 done clear
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 done clear
B) 16 done clear
C) 32 done clear
D) 64 done clear
View Answer play_arrowquestion_answer25) Which of the following statements is correct for any thermodynamic system?
A) The internal energy changes in all processes done clear
B) Internal energy and entropy are state functions done clear
C) The change in entropy can never be zero done clear
D) The work done in an adiabatic process, is always zero done clear
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) \[E/c\] done clear
B) \[2E/c\] done clear
C) \[Ec\] done clear
D) \[E/{{c}^{2}}\] done clear
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 done clear
B) 1/2 done clear
C) 2/3 done clear
D) 1/3 done clear
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 done clear
B) 30 cm done clear
C) 60 cm done clear
D) 80 cm done clear
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) \[{{\sin }^{-1}}(n)\] done clear
B) \[{{\sin }^{-1}}(1/n)\] done clear
C) \[{{\tan }^{-1}}(1/n)\] done clear
D) \[{{\tan }^{-1}}(n)\] done clear
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 done clear
B) wavelength is doubled and frequency becomes half done clear
C) wavelength is halved, and frequency remains unchanged done clear
D) wavelength and frequency both remain unchanged done clear
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) \[\frac{F}{4}\] done clear
B) \[\frac{3F}{4}\] done clear
C) \[\frac{F}{8}\] done clear
D) \[\frac{3F}{8}\] done clear
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) \[r\] done clear
B) \[2r\] done clear
C) \[r/2\] done clear
D) \[r/4\] done clear
View Answer play_arrowquestion_answer33) Alternating current cannot be measured by DC ammeter because
A) AC cannot pass through DC ammeter done clear
B) AC changes direction done clear
C) average value of current for complete cycle is zero done clear
D) DC ammeter will get damaged done clear
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 done clear
B) 3 done clear
C) 2 done clear
D) 1 done clear
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 done clear
B) 1/3 done clear
C) 8/9 done clear
D) 2 done clear
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 done clear
B) 80 cm done clear
C) 40cm done clear
D) 70cm done clear
View Answer play_arrowquestion_answer37) The thermistors are usually made of
A) metals with low temperature coefficient of resistivity done clear
B) metals with high temperature coefficient of resistivity done clear
C) metal oxides with high temperature coefficient of resistivity done clear
D) semiconducting materials having low temperature coefficient of resistivity done clear
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 done clear
B) 100s done clear
C) 150s done clear
D) 200s done clear
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) \[700{}^\circ C\] done clear
B) \[350{}^\circ C\] done clear
C) \[1400{}^\circ C\] done clear
D) no neutral temperature is possible for this thermocouple done clear
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) \[19.8\times {{10}^{-7}}kg\] done clear
B) \[9.9\times {{10}^{-7}}kg\] done clear
C) \[6.6\times {{10}^{-7}}kg\] done clear
D) \[1.1\times {{10}^{-7}}kg\] done clear
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) \[nB\] done clear
B) \[{{n}^{2}}B\] done clear
C) \[2nB\] done clear
D) \[2{{n}^{2}}B\] done clear
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) \[250\mu T\] done clear
B) \[150\mu T\] done clear
C) \[125\mu T\] done clear
D) \[75\mu T\] done clear
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) \[-2F\] done clear
B) \[F/3\] done clear
C) \[-2F/3\] done clear
D) \[-F/3\] done clear
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) \[2s\] done clear
B) \[2/3\text{ }s\] done clear
C) \[2\sqrt{3}s\] done clear
D) \[2/\sqrt{3}\text{ }s\] done clear
View Answer play_arrowquestion_answer45) The materials suitable for making electromagnets should have
A) high retentivity and high coercivity done clear
B) low retentivity and low coercivity done clear
C) high retentivity and low coercivity done clear
D) low retentivity and high coercivity done clear
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 done clear
B) \[50\sqrt{2}V\] done clear
C) 100 V done clear
D) 0 (zero) done clear
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 done clear
B) 2L done clear
C) L/2 done clear
D) L/4 done clear
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) \[5\mu V\] done clear
B) \[5\mu V\] done clear
C) \[5mV\] done clear
D) \[50\,mV\] done clear
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 done clear
B) 400 nm done clear
C) 310 nm done clear
D) 220 nm done clear
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) \[3.3\times {{10}^{-18}}C\] done clear
B) \[3.2\times {{10}^{-18}}C\] done clear
C) \[1.6\times {{10}^{-18}}C\] done clear
D) \[4.8\times {{10}^{-18}}C\] done clear
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) \[{{2}^{1/3}}:1\] done clear
B) \[1:{{3}^{1/2}}\] done clear
C) \[{{3}^{1/2}}:1\] done clear
D) \[1:{{2}^{1/3}}\] done clear
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 done clear
B) 26.9 MeV done clear
C) 23.6 MeV done clear
D) 19.2 MeV done clear
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) \[1\overset{o}{\mathop{\text{A}}}\,\] done clear
B) \[{{10}^{-10}}cm\] done clear
C) \[{{10}^{-12}}cm\] done clear
D) \[{{10}^{-15}}cm\] done clear
View Answer play_arrowquestion_answer54) When\[npn\]transistor is used as an amplifier
A) electrons move from base to collector done clear
B) holes move from emitter to base done clear
C) electrons move from collector to base done clear
D) holes move from base to emitter done clear
View Answer play_arrowquestion_answer55) The manifestation of band structure in solids is due to
A) Heisenbergs uncertainty principle done clear
B) Faults exclusion principle done clear
C) Bohrs correspondence, principle done clear
D) Boltzmanns law done clear
View Answer play_arrowquestion_answer56) Which of the following sets of quantum numbers is correct for an electron in 4f orbital?
A) \[n=4,l=3,m=+4,s=+1/2\] done clear
B) \[n=4,l=4,m=-4,s=-1/2\] done clear
C) \[n=4,\text{ l}=3,m=+1,s=+1/2\] done clear
D) \[n=3,l=2,\text{ }m=-2,\text{ s}=+1/2\] done clear
View Answer play_arrowquestion_answer57) Which one of the following ions has the highest value of ionic radius?
A) \[L{{i}^{+}}\] done clear
B) \[{{B}^{3+}}\] done clear
C) \[{{O}^{2-}}\] done clear
D) \[{{F}^{-}}\] done clear
View Answer play_arrowquestion_answer58) Which one of the following sets of ions represents the collection of isoelectronic species?
A) \[{{K}^{+}},C{{a}^{2+}},S{{c}^{3+}},C{{l}^{-}}\] done clear
B) \[N{{a}^{+}},C{{a}^{2+}},S{{c}^{3+}},{{F}^{-}}\] done clear
C) \[{{K}^{+}},C{{l}^{-}},M{{g}^{2+}},S{{c}^{3+}}\] done clear
D) \[N{{a}^{+}},M{{g}^{2+}},A{{l}^{3+}},C{{l}^{-}}\] done clear
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\[NO\] done clear
B) Bond length in\[NO\]is greater than in\[N{{O}^{+}}\] done clear
C) Bond length in\[N{{O}^{+}}\]is equal to that in\[NO\] done clear
D) Bond length is unpredictable done clear
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 done clear
B) \[\sqrt{313/293}\] done clear
C) 313/293 done clear
D) 2 done clear
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 done clear
B) \[s{{p}^{3}}d\]hybridization done clear
C) \[ds{{p}^{2}}\]hybridization done clear
D) \[s{{p}^{2}}{{d}^{2}}\]hybridization done clear
View Answer play_arrowquestion_answer62) Which among the following factors is the most important in making fluorine the strongest oxidizing agent?
A) Electron affinity done clear
B) lonization enthalpy done clear
C) Hydration enthalpy done clear
D) Bond dissociation energy done clear
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 done clear
B) intermolecular attraction done clear
C) volume occupied by the molecules done clear
D) intermolecular collisions per unit volume done clear
View Answer play_arrowquestion_answer64) The conjugate base of\[{{H}_{2}}PO_{4}^{-}\]is
A) \[PO_{4}^{3-}\] done clear
B) PRs done clear
C) \[{{H}_{3}}P{{O}_{4}}\] done clear
D) \[HPO_{4}^{2-}\] done clear
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 done clear
B) 20 mL done clear
C) 40 mL done clear
D) 60 mL done clear
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 done clear
B) Vapour pressure at the same temperature done clear
C) Boiling points done clear
D) Gaseous densities at the same temperature and pressure done clear
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 done clear
B) The osmotic pressure\[(\pi )\]of a solution is given by the equation\[\pi =MRT,\]where M is the molarity of the solution done clear
C) The correct order of osmotic pressure for 0.01 M aqueous solution of each compound is \[BaC{{l}_{2}}>KC1>C{{H}_{3}}COOH>sucrose\] done clear
D) Two sucrose solutions of same molality prepared in different solvents will have the same freezing point depression done clear
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) \[-900J\] done clear
B) \[-900\text{ }kJ\] done clear
C) \[270kJ\] done clear
D) \[900kJ\] done clear
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 done clear
B) 15 min done clear
C) 7.5 min done clear
D) 60 min done clear
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) \[{{K}_{c}}=\frac{[{{P}_{4}}{{O}_{10}}]}{[{{P}_{4}}]{{[{{O}_{2}}]}^{5}}}\] done clear
B) \[{{K}_{c}}=\frac{[{{P}_{4}}{{O}_{10}}]}{5[{{P}_{4}}][{{O}_{2}}]}\] done clear
C) \[{{K}_{c}}={{[{{O}_{2}}]}^{5}}\] done clear
D) \[{{K}_{c}}=\frac{1}{{{[{{O}_{2}}]}^{5}}}\] done clear
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 \[{{s}^{-1}}\] done clear
B) \[{{t}_{1/2}}\]is a constant done clear
C) rate of formation of C is twice the rate of, disappearance of A done clear
D) value of k is independent of the initial concentrations of A and B done clear
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 done clear
B) 1.40V done clear
C) 0.91V done clear
D) 0.63V done clear
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) \[s={{({{K}_{sp}}/128)}^{1/4}}\] done clear
B) \[s={{(128{{K}_{sp}})}^{1/4}}\] done clear
C) \[s={{(256{{K}_{sp}})}^{1/5}}\] done clear
D) \[s={{({{K}_{sp}}/256)}^{1/5}}\] done clear
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) \[1.0\times {{10}^{1}}\] done clear
B) \[1.0\times {{10}^{5}}\] done clear
C) \[1.0\times {{10}^{10}}\] done clear
D) \[1.0\times {{10}^{30}}\] done clear
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 done clear
B) 676.5 kJ done clear
C) \[-676.5\text{ }kJ\] done clear
D) \[-110.5kJ\] done clear
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) \[128\text{ }S\text{ }c{{m}^{2}}mo{{l}^{-1}}\] done clear
B) \[176\text{ }S\text{ }c{{m}^{2}}mo{{l}^{-1}}\] done clear
C) \[278\text{ }S\text{ }c{{m}^{2}}mo{{l}^{-1}}\] done clear
D) \[302\text{ }S\text{ }c{{m}^{2}}mo{{l}^{-1}}\] done clear
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 done clear
B) It is used as a cryogenic agent for carrying out experiments at low temperatures done clear
C) It is used to produce and sustain powerful superconducting magnets done clear
D) It is used in gas-cooled nuclear reactors done clear
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\[(T\sim 1000\text{ }K)\] done clear
B) Enzymes are normally heterogeneous catalysts that are very specific in their action done clear
C) Enzymes are specific biological catalysts that cannot be poisoned done clear
D) Enzymes are specific biological catalysts that possess well defined active sites. done clear
View Answer play_arrowquestion_answer79) One mole of magnesium nitride on the reaction with an excess of water gives
A) one mole of ammonia done clear
B) one mole of nitric acid done clear
C) two moles of ammonia done clear
D) two moles of nitric acid done clear
View Answer play_arrowquestion_answer80) Which one of the following ores is best concentrated by froth-floatation method?
A) Magnetite done clear
B) Cassiterite done clear
C) Galena done clear
D) Malachite done clear
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 done clear
B) forming polymeric hydrides done clear
C) forming covalent halides done clear
D) exhibiting amphoteric nature in their oxides done clear
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) \[A{{l}^{3+}}+3C{{l}^{-}}\] done clear
B) \[{{[Al{{({{H}_{2}}O)}_{6}}]}^{3+}}+3C{{l}^{-}}\] done clear
C) \[{{[Al{{(OH)}_{6}}]}^{3-}}+3HCl\] done clear
D) \[A{{l}_{2}}{{O}_{3}}+6HCl\] done clear
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 done clear
B) an interaction with nitrogen of the air at very low temperatures done clear
C) a change in the partial pressure of oxygen in the air done clear
D) an interaction with water vapour contained in the humid air done clear
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 done clear
B) \[Cu{{I}_{2}}\]is formed done clear
C) \[N{{a}_{2}}{{S}_{2}}{{O}_{3}}\]is oxidized done clear
D) Evolved\[{{I}_{2}}\]is reduced done clear
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 done clear
B) the number of ligands around a metal ion bonded by pi-bonds done clear
C) the number of ligands around a metal ion bonded by sigma and pi-bonds both done clear
D) the number of only anionic ligands bonded to the metal ion done clear
View Answer play_arrowquestion_answer86) Which one of the following complexes is an outer orbital complex?
A) \[{{[Fe{{(CN)}_{6}}]}^{4-}}\] done clear
B) \[{{[Mn{{(CN)}_{6}}]}^{4-}}\] done clear
C) \[{{[Co{{(N{{H}_{3}})}_{6}}]}^{3+}}\] done clear
D) \[{{[Ni{{(N{{H}_{3}})}_{6}}]}^{2+}}\] (Atomic numbers\[Mn=25,\text{ }Fe=26,\text{ }Co=27,\] \[Ni=28\]) done clear
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 done clear
B) Haemoglobin is the red pigment of blood and contains iron done clear
C) Cyanocobalamin is vitamin\[{{B}_{12}}\]and contains cobalt done clear
D) Carboxypeptidase-A is an enzyme and contains zinc done clear
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 done clear
B) The +3 oxidation state of cerium is more stable than the +4 oxidation state done clear
C) The +4 oxidation state of cerium is not known in solutions done clear
D) Cerium (IV) acts as an oxidising agent done clear
View Answer play_arrowquestion_answer89) The correct order of magnetic moments (spin only values in BM) among the following is
A) \[{{[MnC{{l}_{4}}]}^{2-}}>{{[CoC{{l}_{4}}]}^{2-}}>{{[Fe{{(CN)}_{6}}]}^{4-}}\] done clear
B) \[{{[MnC{{l}_{4}}]}^{2-}}>{{[Fe{{(CN)}_{6}}]}^{4-}}>{{[CoC{{l}_{4}}]}^{2-}}\] done clear
C) \[{{[Fe{{(CN)}_{6}}]}^{4-}}>{{[MnC{{l}_{4}}]}^{2-}}>{{[CoC{{l}_{4}}]}^{2-}}\] done clear
D) \[{{[Fe{{(CN)}_{6}}]}^{4-}}>{{[CoC{{l}_{4}}]}^{2-}}>{{[MnC{{l}_{4}}]}^{2-}}\] done clear
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 done clear
B) 144 done clear
C) 140 done clear
D) 146 done clear
View Answer play_arrowquestion_answer91) The compound formed in the positive test for nitrogen with the Lassaigne solution of an organic compound is
A) \[F{{e}_{4}}{{[Fe{{(CN)}_{6}}]}_{3}}\] done clear
B) \[N{{a}_{3}}[Fe{{(CN)}_{6}}]\] done clear
C) \[Fe{{(CN)}_{3}}\] done clear
D) \[N{{a}_{4}}[Fe{{(CN)}_{5}}NOS]\] done clear
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 done clear
B) benzAmide done clear
C) urea done clear
D) thiourea done clear
View Answer play_arrowquestion_answer93) Which one of the following has the minimum boiling point?
A) n-butane done clear
B) 1-butyne done clear
C) 1-butene done clear
D) Isobutene done clear
View Answer play_arrowquestion_answer94) The IUPAC name of the compound is
A) 3,3-dimethyl-1-hydroxy cyclohexane done clear
B) 1,1-dimethyl-3-hydroxy cyclohexane done clear
C) 3,3-dimethyl-1-cyclohexanol done clear
D) 1,1-dimethyl-3-cyclohexanol done clear
View Answer play_arrowquestion_answer95) Which one of the following does not have\[s{{p}^{2}}\]hybridised carbon?
A) Acetone done clear
B) Acetic acid done clear
C) Acetonitrile done clear
D) Acetamide done clear
View Answer play_arrowquestion_answer96) Which of the following will have a meso-isomer also?
A) 2-chlorobutane done clear
B) 2,3-dichlorobufane done clear
C) 2,3-dichloropentane done clear
D) 2-hydroxypropanoic acid done clear
View Answer play_arrowquestion_answer97) Rate of the reaction is fastest when Z is
A) \[Cl\] done clear
B) \[N{{H}_{2}}\] done clear
C) \[O{{C}_{2}}{{H}_{5}}\] done clear
D) \[OCOC{{H}_{3}}\] done clear
View Answer play_arrowquestion_answer98) Amongst the following compounds, the optically active alkane having lowest molecular mass is
A) \[C{{H}_{3}}-C{{H}_{2}}-C{{H}_{2}}-C{{H}_{3}}\] done clear
B) \[C{{H}_{3}}C{{H}_{2}}\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{CH}}\,C{{H}_{3}}\] done clear
C) done clear
D) \[C{{H}_{3}}C{{H}_{2}}-C\equiv CH\] done clear
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) \[I>II>III>IV\] done clear
B) \[II>IV>III>I\] done clear
C) \[II>IV>I>III\] done clear
D) \[II>III>IV>I\] done clear
View Answer play_arrowquestion_answer100) Which of the following is the strongest base?
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer101) Which base is present in RNA but not in DNA?
A) Uracil done clear
B) Cytosine done clear
C) Guanine done clear
D) Thymine done clear
View Answer play_arrowquestion_answer102) The compound formed on heating chlorobenzene with chloral in the presence of concentrated sulphuric acid is
A) gammexane done clear
B) DDT done clear
C) freon done clear
D) hexachloroethane done clear
View Answer play_arrowquestion_answer103) On mixing ethyl acetate with aqueous sodium chloride, the composition of the resultant solution is
A) \[C{{H}_{3}}COO{{C}_{2}}{{H}_{5}}+NaCl\] done clear
B) \[C{{H}_{3}}COONa+{{C}_{2}}{{H}_{5}}OH\] done clear
C) \[C{{H}_{3}}COCl+{{C}_{2}}{{H}_{5}}OH+NaOH\] done clear
D) \[C{{H}_{3}}Cl+{{C}_{2}}{{H}_{5}}COONa\] done clear
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 done clear
B) acetamide done clear
C) 2-methyl-2-propanol done clear
D) acetyl iodide done clear
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 done clear
B) Acetic acid done clear
C) Acetamide done clear
D) Butan-2-one done clear
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 done clear
B) Benzaldehyde done clear
C) Butanal done clear
D) Benzoic acid done clear
View Answer play_arrowquestion_answer107) Among the following compounds which can be dehydrated very easily?
A) \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}C{{H}_{2}}C{{H}_{2}}OH\] done clear
B) \[C{{H}_{3}}C{{H}_{2}}\overset{\begin{smallmatrix} OH \\ | \end{smallmatrix}}{\mathop{C{{H}_{2}}}}\,CHC{{H}_{3}}\] done clear
C) \[C{{H}_{3}}C{{H}_{2}}\overset{\begin{smallmatrix} OH \\ | \end{smallmatrix}}{\mathop{\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,}}\,C{{H}_{2}}C{{H}_{3}}\] done clear
D) \[C{{H}_{3}}C{{H}_{2}}\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{CH}}\,C{{H}_{2}}C{{H}_{2}}OH\] done clear
View Answer play_arrowquestion_answer108) Which of the following compounds is not chiral?
A) 1-chloropentane done clear
B) 2-chloropentane done clear
C) 1-chloro-2-methyl pentane done clear
D) 3-chloro-2-methyl pentane done clear
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 done clear
B) A hormone done clear
C) An enzyme done clear
D) An antibiotic done clear
View Answer play_arrowquestion_answer110) The smog is essentially caused by the presence of
A) \[{{O}_{2}}\]and \[{{O}_{3}}\] done clear
B) \[{{O}_{2}}\]and \[{{N}_{2}}\] done clear
C) oxides of sulphur and nitrogen done clear
D) \[{{O}_{3}}\]and\[{{N}_{2}}\] done clear
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 done clear
B) transitive done clear
C) not symmetric done clear
D) reflexive done clear
View Answer play_arrowquestion_answer112) The range of the function\[f(x){{=}^{7-x}}{{P}_{x-3}}\]is
A) \[\{1,\text{ }2,\text{ }3\}\] done clear
B) \[\{1,\text{ }2,\text{ }3,\text{ }4,\text{ }5,\text{ }6\}\] done clear
C) \[\{1,2,3,4\}\] done clear
D) \[\{1,\,\,2,\,\,3,\,\,4,\,\,5\}\] done clear
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) \[\frac{\pi }{4}\] done clear
B) \[\frac{\pi }{2}\] done clear
C) \[\frac{3\pi }{4}\] done clear
D) \[\frac{5\pi }{4}\] done clear
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 done clear
B) \[-1\] done clear
C) 2 done clear
D) \[-2\] done clear
View Answer play_arrowquestion_answer115) If\[|{{z}^{2}}-1|=|z{{|}^{2}}+1,\]then z lies on
A) the real axis done clear
B) the imaginary axis done clear
C) a circle done clear
D) an ellipse done clear
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 done clear
B) \[A=(-1),I\]where I is a unit matrix done clear
C) \[{{A}^{-1}}\]does not exist done clear
D) \[{{A}^{2}}=I\] done clear
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) \[-2\] done clear
B) 1 done clear
C) 2 done clear
D) 5 done clear
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 done clear
B) 1 done clear
C) 2 done clear
D) \[-2\] done clear
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) \[{{x}^{2}}+18x+16=0\] done clear
B) \[{{x}^{2}}-18x+16=0\] done clear
C) \[{{x}^{2}}+18x-16=0\] done clear
D) \[{{x}^{2}}-18x-16=0\] done clear
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 done clear
B) \[-1,1\] done clear
C) 0,-1 done clear
D) \[-1,2\] done clear
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 done clear
B) 240 done clear
C) 360 done clear
D) 480 done clear
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 done clear
B) \[-21\] done clear
C) \[{{3}^{8}}\] done clear
D) \[^{8}{{C}_{3}}\] done clear
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) \[\frac{49}{4}\] done clear
B) 12 done clear
C) 3 done clear
D) 4 done clear
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) \[-\frac{5}{3}\] done clear
B) \[\frac{10}{3}\] done clear
C) \[-\frac{3}{10}\] done clear
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, \[^{4}{{C}_{2}}{{\alpha }^{2}}{{=}^{6}}{{C}_{3}}{{(-\alpha )}^{3}}\] \[\Rightarrow \] \[\frac{4!}{2!2!}{{\alpha }^{2}}=-\frac{6!}{3!3!}{{\alpha }^{3}}\] \[\Rightarrow \] \[6{{\alpha }^{2}}=-20{{\alpha }^{3}}\] \[\Rightarrow \] \[\alpha =-\frac{6}{20}\] \[\Rightarrow \] \[\alpha =-\frac{3}{10}\] done clear
View Answer play_arrowquestion_answer125) The coefficient of\[{{x}^{n}}\]in expansion of \[(1+x){{(1-x)}^{n}}\]is
A) \[(n-1)\] done clear
B) \[{{(-1)}^{n}}(1-n)\] done clear
C) \[{{(-1)}^{n-1}}{{(n-1)}^{2}}\] done clear
D) \[{{(-1)}^{n-1}}n\] done clear
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) \[\frac{n}{2}\] done clear
B) \[\frac{n}{2}-1\] done clear
C) \[n-1\] done clear
D) \[\frac{2n-1}{2}\] done clear
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) \[0\] done clear
B) \[1\] done clear
C) \[\frac{1}{mn}\] done clear
D) \[\frac{1}{m}+\frac{1}{n}\] done clear
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) \[\frac{3n(n+1)}{2}\] done clear
B) \[\frac{{{n}^{2}}(n+1)}{2}\] done clear
C) \[\frac{n{{(n+1)}^{2}}}{4}\] done clear
D) \[{{\left[ \frac{n(n+1)}{2} \right]}^{2}}\] done clear
View Answer play_arrowquestion_answer129) The sum of series\[\frac{1}{2!}+\frac{1}{4!}+\frac{1}{6!}+...\]is
A) \[\frac{({{e}^{2}}-1)}{2}\] done clear
B) \[\frac{{{(e-1)}^{2}}}{2e}\] done clear
C) \[\frac{({{e}^{2}}-1)}{2e}\] done clear
D) \[\frac{({{e}^{2}}-2)}{e}\] done clear
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) \[-\frac{3}{\sqrt{130}}\] done clear
B) \[\frac{3}{\sqrt{130}}\] done clear
C) \[\frac{6}{65}\] done clear
D) \[-\frac{6}{65}\] done clear
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) \[2({{a}^{2}}+{{b}^{2}})\] done clear
B) \[2\sqrt{{{a}^{2}}+{{b}^{2}}}\] done clear
C) \[{{(a+b)}^{2}}\] done clear
D) \[{{(a-b)}^{2}}\] done clear
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) \[60{}^\circ \] done clear
B) \[90{}^\circ \] done clear
C) \[120{}^\circ \] done clear
D) \[150{}^\circ \] done clear
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] done clear
B) \[[-1,\text{ }1]\] done clear
C) [0, 1] done clear
D) \[[-1,\text{ }3]\] done clear
View Answer play_arrowquestion_answer134) The domain of the function \[f(x)=\frac{{{\sin }^{-1}}(x-3)}{\sqrt{9-{{x}^{2}}}}\]
A) [2, 3] done clear
B) [2, 3) done clear
C) [1, 2] done clear
D) [1, 2) done clear
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) \[a\in R,b\in R\] done clear
B) \[a=1,b\in R\] done clear
C) \[a\in R,b=2\] done clear
D) \[a=1,b=2\] done clear
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 done clear
B) \[1/2\] done clear
C) \[-1/2\] done clear
D) \[-1\] done clear
View Answer play_arrowquestion_answer137) If\[x={{e}^{y+{{e}^{y+......to\,\infty }}}},x>0,\]the\[\frac{dy}{dx}\]is
A) \[\frac{x}{1+x}\] done clear
B) \[\frac{1}{x}\] done clear
C) \[\frac{1-x}{x}\] done clear
D) \[\frac{1+x}{x}\] done clear
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) \[(2,\,4)\] done clear
B) \[(2,\,-4)\] done clear
C) \[\left( -\frac{9}{8},\frac{9}{2} \right)\] done clear
D) \[\left( \frac{9}{8},\frac{9}{2} \right)\] done clear
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) \[{{(x-1)}^{2}}\] done clear
B) \[{{(x-1)}^{3}}\] done clear
C) \[{{(x+1)}^{3}}\] done clear
D) \[{{(x+1)}^{2}}\] done clear
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) \[(a,\text{ }0)\] done clear
B) \[(0,\text{ }a)\] done clear
C) (0, 0) done clear
D) \[(a,\text{ }a)\] done clear
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) done clear
B) (1, 2) done clear
C) (2, 3) done clear
D) (1, 3) done clear
View Answer play_arrowquestion_answer142) \[\underset{n\to \infty }{\mathop{\lim }}\,\sum\limits_{r=1}^{n}{\frac{1}{n}{{e}^{r/n}}}\]is
A) \[e\] done clear
B) \[e-1\] done clear
C) \[1-e\] done clear
D) \[e+1\] done clear
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) \[(\sin \alpha ,\cos \alpha )\] done clear
B) \[(\cos \alpha ,\sin \alpha )\] done clear
C) \[(-\sin \alpha ,\cos \alpha )\] done clear
D) \[(-\cos \alpha ,\sin \alpha )\] done clear
View Answer play_arrowquestion_answer144) \[\int{\frac{dx}{\cos x-\sin x}}\]is equal to
A) \[\frac{1}{\sqrt{2}}\log \left| \tan \left( \frac{x}{2}-\frac{\pi }{8} \right) \right|+c\] done clear
B) \[\frac{1}{\sqrt{2}}\log \left| cot\left( \frac{x}{2} \right) \right|+c\] done clear
C) \[\frac{1}{\sqrt{2}}\log \left| \tan \left( \frac{x}{2}-\frac{3\pi }{8} \right) \right|+c\] done clear
D) \[\frac{1}{\sqrt{2}}\log \left| \tan \left( \frac{x}{2}+\frac{3\pi }{8} \right) \right|+c\] done clear
View Answer play_arrowquestion_answer145) The value of\[\int_{-2}^{3}{|1-{{x}^{2}}|dx}\]is
A) \[\frac{28}{3}\] done clear
B) \[\frac{14}{3}\] done clear
C) \[\frac{7}{3}\] done clear
D) \[\frac{1}{3}\] done clear
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 done clear
B) 1 done clear
C) 2 done clear
D) 3 done clear
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 done clear
B) \[\pi \] done clear
C) \[\frac{\pi }{4}\] done clear
D) \[2\pi \] done clear
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 done clear
B) 2 done clear
C) 3 done clear
D) 4 done clear
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) \[2({{x}^{2}}-{{y}^{2}})y=xy\] done clear
B) \[2({{x}^{2}}+{{y}^{2}})y=xy\] done clear
C) \[({{x}^{2}}-{{y}^{2}})y=2xy\] done clear
D) \[({{x}^{2}}+{{y}^{2}})y=2xy\] done clear
View Answer play_arrowquestion_answer150) The solution of the differential equation\[y\,dx+(x+{{x}^{2}}y)dy=0\]is
A) \[-\frac{1}{xy}=c\] done clear
B) \[-\frac{1}{xy}+\log y=c\] done clear
C) \[\frac{1}{xy}+\log y=c\] done clear
D) \[\log y=cx\] done clear
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) \[2x+3y=9\] done clear
B) \[2x-3y=7\] done clear
C) \[3x+2y=5\] done clear
D) \[3x-2y=3\] done clear
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\[\frac{x}{-2}+\frac{y}{1}=-1\] done clear
B) \[\frac{x}{2}-\frac{y}{3}=-1\]and\[\frac{x}{-2}+\frac{y}{1}=-1\] done clear
C) \[\frac{x}{2}+\frac{y}{3}=1\]and\[\frac{x}{-2}+\frac{y}{1}=1\] done clear
D) \[\frac{x}{2}-\frac{y}{3}=1\]and\[\frac{x}{-2}+\frac{y}{1}=1\] done clear
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 done clear
B) \[-1\] done clear
C) 2 done clear
D) \[-2\] done clear
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 done clear
B) \[-1\] done clear
C) 3 done clear
D) \[-3\] done clear
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) \[2ax+2by+({{a}^{2}}+{{b}^{2}}+4)=0\] done clear
B) \[2ax+2by-({{a}^{2}}+{{b}^{2}}+4)=0\] done clear
C) \[2ax-2by+({{a}^{2}}+{{b}^{2}}+4)=0\] done clear
D) \[2ax-2by-({{a}^{2}}+{{b}^{2}}+4)=0\] done clear
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) \[{{x}^{2}}+{{y}^{2}}-2x+2y-23=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-2x-2y-23=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}+2x+2y-23=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}+2x-2y-23=0\] done clear
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) \[{{x}^{2}}+{{y}^{2}}-x-y=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-x+y=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}+x+y=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}+x-y=0\] done clear
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) \[{{d}^{2}}+{{(2b+3c)}^{2}}=0\] done clear
B) \[{{d}^{2}}+{{(3b+2c)}^{2}}=0\] done clear
C) \[{{d}^{2}}+{{(2b-3c)}^{2}}=0\] done clear
D) \[{{d}^{2}}+{{(3b-2c)}^{2}}=0\] done clear
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) \[3{{x}^{2}}+4{{y}^{2}}=1\] done clear
B) \[3{{x}^{2}}+4{{y}^{2}}=12\] done clear
C) \[4{{x}^{2}}+3{{y}^{2}}=12\] done clear
D) \[4{{x}^{2}}+3{{y}^{2}}=1\] done clear
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) \[\frac{2}{3}\] done clear
B) \[\frac{1}{5}\] done clear
C) \[\frac{3}{5}\] done clear
D) \[\frac{2}{5}\] done clear
View Answer play_arrowquestion_answer161) Distance between two parallel planes \[2x+y+2z=8\]and\[4x+2y+4z+5=0\]is
A) \[\frac{3}{2}\] done clear
B) \[\frac{5}{2}\] done clear
C) \[\frac{7}{2}\] done clear
D) \[\frac{9}{2}\] done clear
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) \[(3a,3a,3a)(a,a,a)\] done clear
B) \[(3a,2a,3a)(a,a,a)\] done clear
C) \[(3a,2a,3a)(a,a,2a)\] done clear
D) \[(2a,3a,3a)(2a,a,a)\] done clear
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) \[-2\] done clear
B) \[-1\] done clear
C) \[-\frac{1}{2}\] done clear
D) \[0\] done clear
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) \[\lambda \overrightarrow{a}\] done clear
B) \[\lambda \overrightarrow{b}\] done clear
C) \[\lambda \overrightarrow{c}\] done clear
D) 0 done clear
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 done clear
B) 30 done clear
C) 25 done clear
D) 15 done clear
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 done clear
B) all except one value of k done clear
C) all except two values of X done clear
D) no value of k done clear
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 done clear
B) \[\sqrt{7}\] done clear
C) \[\sqrt{14}\] done clear
D) 14 done clear
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) \[\frac{37}{256}\] done clear
B) \[\frac{219}{256}\] done clear
C) \[\frac{128}{256}\] done clear
D) \[\frac{28}{256}\] done clear
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\[(2-\sqrt{2})N\] done clear
B) \[(2+\sqrt{3})N\]and\[(2-\sqrt{3})N\] done clear
C) \[\left( 2+\frac{1}{2}\sqrt{2} \right)N\]and\[\left( 2-\frac{1}{2}\sqrt{2} \right)N\] done clear
D) \[\left( 2+\frac{1}{2}\sqrt{3} \right)N\]and\[\left( 2-\frac{1}{2}\sqrt{3} \right)N\] done clear
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 done clear
B) 4 done clear
C) 5 done clear
D) 9 done clear
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