question_answer1) If E = energy, G = gravitational constant, \[I=\]impulse and \[M=\]mass, then dimensions of \[\frac{GI{{M}^{2}}}{{{E}^{2}}}\]are same as that of
A) time done clear
B) mass done clear
C) length done clear
D) force done clear
View Answer play_arrowquestion_answer2) A point initially at rest moves along \[x-\]axis. Its acceleration varies with time as \[a=(6t+5)m/{{s}^{2}}.\]If it starts from origin, the distance covered in 2 s is
A) 20 m done clear
B) 18 m done clear
C) 16 m done clear
D) 25 m done clear
View Answer play_arrowquestion_answer3) Three blocks of masses 2 kg, 3 kg and 5 kg are connected to each other with light string and are then placed on a frictionless surface as shown in the figure. The system is pulled by a force \[F=10N,\]then tension \[{{T}_{1}}=\]
A) 1 N done clear
B) 5 N done clear
C) 8 N done clear
D) 10 N done clear
View Answer play_arrowquestion_answer4) A solid sphere rolls down two different inclined planes of same height, but of different inclinations. In both cases
A) speed and time of descent will be same done clear
B) speed will be same, but time of descent will be different done clear
C) speed will be different, but time of descent will be same done clear
D) speed and time of descent both are different done clear
View Answer play_arrowquestion_answer5) The angular amplitude of a simple pendulum is \[{{\theta }_{0}}.\]The maximum tension in its string will be
A) \[mg(1-{{\theta }_{0}})\] done clear
B) \[mg(1+{{\theta }_{0}})\] done clear
C) \[mg(1-\theta _{0}^{2})\] done clear
D) \[mg(1+\theta _{0}^{2})\] done clear
View Answer play_arrowquestion_answer6) An engine pumps up 100 kg of water through a height of 10 m in 5s. Given that the efficiency of engine is 60%. If \[g=10\,m{{s}^{-2}},\] the power of the engine is
A) 3.3 kW done clear
B) 0.33 kW done clear
C) 0.033 kW done clear
D) 33 kW done clear
View Answer play_arrowquestion_answer7) At what speed, the velocity head of water is equal to pressure head of 40 cm of Hg?
A) 10.3 m/s done clear
B) 2.8 m/s done clear
C) 5.6 m/s done clear
D) 8.4 m/s done clear
View Answer play_arrowquestion_answer8) If the electric flux entering and leaving an enclosed surface respectively are \[{{\phi }_{1}}\] and \[{{\phi }_{2}}\] the electric charge inside the surface will be
A) \[\frac{{{\phi }_{2}}-{{\phi }_{1}}}{{{\varepsilon }_{0}}}\] done clear
B) \[\frac{{{\phi }_{1}}+{{\phi }_{2}}}{{{\varepsilon }_{0}}}\] done clear
C) \[\frac{{{\phi }_{1}}-{{\phi }_{2}}}{{{\varepsilon }_{0}}}\] done clear
D) \[{{\varepsilon }_{0}}\,({{\phi }_{1}}+{{\phi }_{2}})\] done clear
View Answer play_arrowquestion_answer9) In the propagation of light waves, the angle between the direction of vibration and plane of polarization is
A) \[{{0}^{o}}\] done clear
B) \[{{90}^{o}}\] done clear
C) \[{{45}^{o}}\] done clear
D) \[{{80}^{o}}\] done clear
View Answer play_arrowquestion_answer10) A light emitting diode (LED) has a voltage drop of 2 V across it and passes a current of 10 mA. When it operates with a 6 V battery through a limiting resistor R, the value of R is
A) \[40\,k\Omega \] done clear
B) \[4\,k\Omega \] done clear
C) \[200\,\Omega \] done clear
D) \[400\,\Omega \] done clear
View Answer play_arrowquestion_answer11) The minimum potential difference between the base and emitter required to switch a silicon transistor ON is approximately
A) 1 V done clear
B) 3 V done clear
C) 5 V done clear
D) 4.2 V done clear
View Answer play_arrowquestion_answer12) Two stones are projected with the same speed but making different angles with the horizontal. Their horizontal ranges are equal. The angle of projection of one is \[\pi /3\]and the maximum height reached by it is 102 m. Then the maximum height reached by the other in metre is
A) 336 done clear
B) 224 done clear
C) 56 done clear
D) 34 done clear
View Answer play_arrowquestion_answer13) Which one of the following is a possible nuclear reaction?
A) \[_{5}^{10}B+_{2}^{4}He\xrightarrow{{}}_{7}^{13}N+_{1}^{1}H\] done clear
B) \[_{11}^{23}Na+_{1}^{1}H\xrightarrow{{}}_{10}^{20}Ne+_{2}^{4}He\] done clear
C) \[_{93}^{239}Np+\xrightarrow{{}}_{94}^{239}Pu+{{\beta }^{-}}+\bar{v}\] done clear
D) \[_{7}^{11}N+_{1}^{1}H\xrightarrow{{}}_{6}^{12}C+{{\beta }^{-}}+v\] done clear
View Answer play_arrowquestion_answer14) Two circular discs A and B with equal radii are blackened. They are heated to same temperature and are cooled under identical conditions. What inference do you draw from their cooling curves?
A) A and B have same specific heats done clear
B) Specific heat of A is less done clear
C) Specific heat of B is less done clear
D) Nothing can be said done clear
View Answer play_arrowquestion_answer15) During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio \[{{C}_{p}}/{{C}_{v}}\]for the gas is
A) 4/3 done clear
B) 2 done clear
C) 5/3 done clear
D) 3/2 done clear
View Answer play_arrowquestion_answer16) The sum of two vectors \[\vec{A}\] and \[\vec{B}\] is at right angles to their difference. Then
A) \[A=B\] done clear
B) \[A=2B\] done clear
C) \[B=2A\] done clear
D) \[\vec{A}\] and \[\vec{B}\] have the same direction done clear
View Answer play_arrowquestion_answer17) A ball is thrown up at an angle with the horizontal. Then the total change of momentum by the instant it returns to ground is
A) acceleration due to gravity \[\times \] total time of flight done clear
B) weight of the ball \[\times \] half the time of flight done clear
C) weight of the ball \[\times \]total time of flight done clear
D) weight of the ball \[\times \]horizontal range done clear
View Answer play_arrowquestion_answer18) When a spring is stretched by a distance \[x,\]it exerts a force, given by \[F=(-5x-16{{x}^{3}})N\] The work done, when the spring is stretched from 0.1 m to 0.2 m is
A) \[8.7\times {{10}^{-2}}J\] done clear
B) \[12.2\times {{10}^{-2}}J\] done clear
C) \[8.7\times {{10}^{-1}}J\] done clear
D) \[12.2\times {{10}^{-1}}J\] done clear
View Answer play_arrowquestion_answer19) Time period of a simple pendulum of length\[l\] is \[{{T}_{1}}\]and time period of a uniform rod of the same length \[l\] pivoted about one end and oscillating in a vertical plane is \[{{T}_{2}}.\]Amplitude of oscillations in both the cases is small. Then\[{{T}_{1}}/{{T}_{2}}\]is
A) \[\frac{1}{\sqrt{3}}\] done clear
B) \[1\] done clear
C) \[\sqrt{\frac{4}{3}}\] done clear
D) \[\sqrt{\frac{3}{2}}\] done clear
View Answer play_arrowquestion_answer20) An insulator plate is passed between the plates of a capacitor. Then current
A) first flows from A to Band then from B to A done clear
B) first flows from B to A and then from A to B done clear
C) always flows from B to A done clear
D) always flows from A to B done clear
View Answer play_arrowquestion_answer21) Two parallel large thin metal sheets have equal surface charge densities \[(\sigma =26.4\times {{10}^{-12}}C/{{m}^{2}})\] of opposite signs. The electric field between these sheets is
A) \[1.5\,N/C\] done clear
B) \[1.5\times {{10}^{-10}}\,N/C\] done clear
C) \[3\,N/C\] done clear
D) \[3\times {{10}^{-10}}\,N/C\] done clear
View Answer play_arrowquestion_answer22) The electric current passes through a metallic wire produces heat because of
A) collisions of conduction electrons with each other done clear
B) collisions of the atoms of the metal with each other done clear
C) the energy released in the ionization of the atoms of the metal done clear
D) collisions of the conduction electrons with the atoms of the metallic wire done clear
View Answer play_arrowquestion_answer23) Two concentric circular coils of ten turns each are situated in the same plane. Their radii are 20 cm and 40 cm and they carry respectively 0.2 A and 0.3 A currents in opposite direction. The magnetic field in tesla at the centre is
A) \[35\,{{\mu }_{0}}/4\] done clear
B) \[\,{{\mu }_{0}}/80\] done clear
C) \[7\,{{\mu }_{0}}/80\] done clear
D) \[5\,{{\mu }_{0}}/4\] done clear
View Answer play_arrowquestion_answer24) Electromagnetic waves with frequencies greater than the critical frequency of ionosphere cannot be used for communication using sky wave propagation, because
A) the refractive Index of the ionosphere becomes very high for \[f>{{f}_{c}}\] done clear
B) the refractive index of the ionosphere becomes very low for \[f>{{f}_{c}}\] done clear
C) the refractive index of the ionosphere becomes very high for \[f<{{f}_{c}}\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer25) In a choke coil, the reactance \[{{X}_{L}}\]and resistance R are such that
A) \[{{X}_{L}}=R\] done clear
B) \[{{X}_{L}}>>R\] done clear
C) \[{{X}_{L}}<<R\] done clear
D) \[{{X}_{L}}=\infty \] done clear
View Answer play_arrowquestion_answer26) Reverberation time does not depend upon
A) temperature done clear
B) volume of room done clear
C) size of window done clear
D) carpet and curtain done clear
View Answer play_arrowquestion_answer27) In a potentiometer, the null point is received at 7th wire. If now we have to change the null point at 9th wire, what should we do?
A) Attach resistance in series with battery done clear
B) Increase resistance in main circuit done clear
C) Decrease resistance in main circuit done clear
D) Decrease applied emf done clear
View Answer play_arrowquestion_answer28) If average velocity becomes 4 times then what will be the effect on rms velocity at that temperature?
A) 1.4 times done clear
B) 4 times done clear
C) 2 times done clear
D) \[\frac{1}{4}\] times done clear
View Answer play_arrowquestion_answer29) What is the Q-value of the reaction \[p+{{\,}^{7}}Li\xrightarrow{{}}{{\,}^{4}}He+{{\,}^{4}}He\] The atomic masses of \[{{\,}^{1}}H,{{\,}^{4}}He\] and \[{{\,}^{7}}Li\] are 1.007825u, 4.002603 u and 7.016004 u respectively
A) 17.35 MeV done clear
B) 18.06 MeV done clear
C) 177.35 MeV done clear
D) 170.35 MeV done clear
View Answer play_arrowquestion_answer30) A Carots engine has an efficiency of 50% at sink temperature \[50{{\,}^{o}}C.\] Calculate the temperature of source.
A) \[133{{\,}^{o}}C\] done clear
B) \[143{{\,}^{o}}C\] done clear
C) \[100{{\,}^{o}}C\] done clear
D) \[373{{\,}^{o}}C\] done clear
View Answer play_arrowquestion_answer31) \[4{{m}^{3}}\]of water is to be pumped to a height of 20 m and forced into a reservoir at a pressure of \[2\times {{10}^{5}}N/{{m}^{2}}.\] The work done by the motor is (external pressure\[={{10}^{5}}\,N/{{m}^{2}}\])
A) \[8\times {{10}^{5}}J\] done clear
B) \[16\times {{10}^{5}}\,J\] done clear
C) \[12\times {{10}^{5}}\,J\] done clear
D) \[32\times {{10}^{5}}\,J\] done clear
View Answer play_arrowquestion_answer32) Moment of inertia of ring about its diameter is \[I.\] Then, moment of inertia about an axis passing through centre perpendicular to its plane is
A) \[2I\] done clear
B) \[\frac{I}{2}\] done clear
C) \[\frac{3}{2}I\] done clear
D) \[I\] done clear
View Answer play_arrowquestion_answer33) When both the listener and source are moving towards each other, then which of the following is true regarding frequency and wavelength of wave observed by the observer?
A) More frequency, less wavelength done clear
B) More frequency, more wavelength done clear
C) Less frequency, less wavelength done clear
D) More frequency, constant wavelength done clear
View Answer play_arrowquestion_answer34) The coefficient of friction between the tyres and the road is 0.25. The maximum speed with which car can be driven round a curve of radius 40 m without skidding is (assume\[g=10\,m{{s}^{-2}}\])
A) \[40\,m{{s}^{-1}}\] done clear
B) \[20\,m{{s}^{-1}}\] done clear
C) \[15\,m{{s}^{-1}}\] done clear
D) \[10\,m{{s}^{-1}}\] done clear
View Answer play_arrowquestion_answer35) A bomb of mass 3.0 kg explodes in air into two pieces of masses 2.0 kg and 1.0 kg. The smaller mass goes at a speed of 80 m/s. The total energy-.imparted, to the two fragments is
A) 1.07 kJ done clear
B) 2.14 kJ done clear
C) 2.4 kJ done clear
D) 4.8 kJ done clear
View Answer play_arrowquestion_answer36) If distance between earth and sun become four times, then time period becomes
A) 4 times done clear
B) 8 times done clear
C) 1/4 times done clear
D) 1/8 times done clear
View Answer play_arrowquestion_answer37) An air bubble is contained inside water. It behaves as a
A) concave lens done clear
B) convex lens done clear
C) Neither convex nor concave done clear
D) Cannot say done clear
View Answer play_arrowquestion_answer38) The power dissipated across resistance R which is connected across a battery of potential V is P. If resistance is doubled, then the power becomes
A) 1/2 done clear
B) 2 done clear
C) 1/4 done clear
D) 4 done clear
View Answer play_arrowquestion_answer39) A 100 V, AC source of frequency 500 Hz is connected to an LCR circuit with\[L=8.1\,mH,\]\[C=12.5\mu F,R=10\,\Omega \]all connected in series as shown in figure. What is the quality factor of circuit?
A) \[2.02\] done clear
B) \[2.5434\] done clear
C) \[20.54\] done clear
D) \[200.54\] done clear
View Answer play_arrowquestion_answer40) The inductance of a coil is \[L=10\,H\]and resistance \[R=5\,\Omega .\]If applied voltage of battery is 10 V and it switches off in 1 millisecond, find induced emf of inductor,
A) \[2\times {{10}^{4}}V\] done clear
B) \[1.2\times {{10}^{4}}V\] done clear
C) \[2\times {{10}^{-4}}V\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer41) A proton is moving in a uniform magnetic field in a circular path of radius a in a direction perpendicular to z-axis along which field B exists. Calculate the angular momentum, if the radius is a charge on proton is e.
A) \[\frac{Be}{{{a}^{2}}}\] done clear
B) \[e{{B}^{2}}a\] done clear
C) \[{{a}^{2}}eB\] done clear
D) \[aeB\] done clear
View Answer play_arrowquestion_answer42) We wish to see inside an atom. Assuming the atom to have a diameter of 100 pm, this means that one must be able to resolve a width of say 10 pm. If an electron microscope is used, the minimum electron energy required is about
A) 1.5 keV done clear
B) 15 keV done clear
C) 150 keV done clear
D) 1.5 MeV done clear
View Answer play_arrowquestion_answer43) A body from height h is dropped. If the coefficient of restitution is e, then calculate the height achieved after one bounce.
A) \[{{h}_{1}}={{e}^{2}}h\] done clear
B) \[{{h}_{1}}={{e}^{4}}h\] done clear
C) \[{{h}_{1}}=eh\] done clear
D) \[{{h}_{1}}=\frac{h}{e}\] done clear
View Answer play_arrowquestion_answer44) A beam of light travelling along \[x-\]axis is described by the electric field\[{{E}_{y}}=(600\,V{{m}^{-1}})\sin \omega (t-x/c)\] then maximum magnetic force on a charge \[q=2e,\]moving along \[y-\]axis with a speed of \[3.0\times {{10}^{7}}\,m{{s}^{-1}}\] is \[(e=1.6\times {{10}^{-19}}C)\]
A) \[19.2\times {{10}^{-17}}N\] done clear
B) \[1.92\times {{10}^{-17}}\,N\] done clear
C) \[0.192\,N\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer45) Equipotential surfaces associated with an electric field which is increasing in magnitude along the \[x-\]direction are
A) planes parallel to \[yz-\]plane done clear
B) planes parallel to \[xy-\]plane done clear
C) planes parallel to \[xz-\]plane done clear
D) coaxial cylinders of increasing radii around the \[x-\]axis done clear
View Answer play_arrowquestion_answer46) If 200 MeV energy is released in the fission of a single nucleus of \[{{\,}_{92}}U{{\,}^{235}},\] how many fissions must occur per second to produce a power 1 kW?
A) \[3.12\times {{10}^{13}}\] done clear
B) \[3.12\times {{10}^{3}}\] done clear
C) \[3.1\times {{10}^{17}}\] done clear
D) \[3.12\times {{10}^{19}}\] done clear
View Answer play_arrowquestion_answer47) Find ratio of acceleration due to gravity g depth d and at height h, where d = 2h.
A) \[1:1\] done clear
B) \[1:2\] done clear
C) \[2:1\] done clear
D) \[1:4\] done clear
View Answer play_arrowquestion_answer48) A convex lens of focal length 40 cm is in contact with a concave lens of focal length 25 cm. The power of combination is
A) \[-1.5\,D\] done clear
B) \[-6.5\,D\] done clear
C) \[+6.5D\] done clear
D) \[+\,6.67D\] done clear
View Answer play_arrowquestion_answer49) In a Youngs experiment, two coherent sources are placed 0.90 mm apart and the fringes are observed one metre away. If it produces the second dark fringe at a distance of 1 mm from the central fringe, the wavelength monochromatic light used would be
A) \[60\times {{10}^{-4}}cm\] done clear
B) \[10\times {{10}^{-4}}cm\] done clear
C) \[10\times {{10}^{-5}}cm\] done clear
D) \[6\times {{10}^{-5}}cm\] done clear
View Answer play_arrowquestion_answer50) A bar magnet when placed at an angle of \[{{30}^{o}}\] the direction of magnetic field induction of \[5\times {{10}^{-2}}T,\]experiences a moment of couple \[25\times {{10}^{-6}}\,N-m.\] If the length of the magnet is 5 cm its pole strength is
A) \[2\times {{10}^{-2}}A-m\] done clear
B) \[5\times {{10}^{-2}}A-m\] done clear
C) \[2\,A-m\] done clear
D) \[5\,A-m\] done clear
View Answer play_arrowquestion_answer51) The number of moles of \[\text{KMn}{{\text{O}}_{\text{4}}}\]reduced by one mole of KI in alkaline medium is
A) 1 done clear
B) 5 done clear
C) 1/2 done clear
D) 1/5 done clear
View Answer play_arrowquestion_answer52) Value of \[x\] in potash alum, \[{{K}_{2}}S{{O}_{4}}.A{{l}_{x}}{{(S{{O}_{4}})}_{3}}.24{{H}_{2}}O\]
A) 4 done clear
B) 1 done clear
C) 2 done clear
D) None of these done clear
View Answer play_arrowquestion_answer53) Ozone is used for purifying water because
A) it dissociates and release oxygen done clear
B) do not leave any foul smell like chlorine done clear
C) kills bacteria, cyst, fungi and acts as a biocide done clear
D) All of the above done clear
View Answer play_arrowquestion_answer54) Internal energy is sum of
A) kinetic energy and potential energy done clear
B) all types of energy of the system done clear
C) energy of internal system done clear
D) None of the above done clear
View Answer play_arrowquestion_answer55) Total volume of atoms present in a face centred cubic unit cell of a metal is (\[r=\]atomic radius)
A) \[\frac{20}{3}\pi {{r}^{3}}\] done clear
B) \[\frac{24}{3}\pi {{r}^{3}}\] done clear
C) \[\frac{12}{3}\pi {{r}^{3}}\] done clear
D) \[\frac{16}{3}\pi {{r}^{3}}\] done clear
View Answer play_arrowquestion_answer56) If two molecules of A and B having mass 100 kg and 64 kg and rate of diffusion of A is \[12\times {{10}^{-3}},\] then what will be the rate of diffusion of B?
A) \[15\times {{10}^{-3}}\] done clear
B) \[64\times {{10}^{-3}}\] done clear
C) \[~5\times {{10}^{-3}}\] done clear
D) \[~46\times {{10}^{-3}}\] done clear
View Answer play_arrowquestion_answer57) Aniline is prepared in presence of Fe/HCl from
A) benzene done clear
B) nitrobenzene done clear
C) dinitrobenzene done clear
D) None of these done clear
View Answer play_arrowquestion_answer58) Difference between S and \[{{S}^{2-}}\]as \[{{S}^{2-}}\]has
A) larger radii and larger size done clear
B) smaller radii and larger size done clear
C) larger radii and smaller size done clear
D) smaller radii and smaller size done clear
View Answer play_arrowquestion_answer59) Which of the following is not correct?
A) \[{{t}_{1/2}}=\frac{0.693}{k}\] done clear
B) \[N={{N}_{0}}{{e}^{-kt}}\] done clear
C) \[\frac{1}{N}=\frac{1}{{{N}_{0}}}=\ln \,k{{t}_{1/2}}\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer60) Which is not in accordance to aufbau principle?
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer61) \[C{{H}_{3}}C{{H}_{2}}Cl\]undergoes homolytic fission, produces
A) \[C{{H}_{3}}\overset{\centerdot }{\mathop{C}}\,{{H}_{2}}\]and \[\overset{\centerdot }{\mathop{C}}\,l\] done clear
B) \[C{{H}_{3}}\overset{\oplus }{\mathop{C}}\,{{H}_{2}}\]and \[C{{l}^{\text{o}-}}\] done clear
C) \[C{{H}_{3}}\overset{\oplus }{\mathop{C}}\,{{H}_{2}}\]and \[\overset{\centerdot }{\mathop{C}}\,l\] done clear
D) \[C{{H}_{3}}\overset{\centerdot }{\mathop{C}}\,{{H}_{2}}\]and \[C{{l}^{\text{o}-}}\] done clear
View Answer play_arrowquestion_answer62) \[C-C\]bond order in benzene is
A) 1 done clear
B) 2 done clear
C) between 1 and 2 done clear
D) None of these done clear
View Answer play_arrowquestion_answer63) In colloid particles, range of diameter is
A) 1 to 100 nm done clear
B) 1 to 1000 cm done clear
C) 1 to 1000 mm done clear
D) 1 to 100 km done clear
View Answer play_arrowquestion_answer64) \[Z{{n}^{2+}}\xrightarrow{{}}Zn(s);{{E}^{o}}=-0.76\,V\] \[C{{u}^{2+}}\xrightarrow{{}}Cu(s);{{E}^{o}}=-0.34\,V\] Which of the following is spontaneous?
A) \[Z{{n}^{2+}}+Cu\xrightarrow{{}}Zn+C{{u}^{2+}}\] done clear
B) \[C{{u}^{2+}}+Zn\xrightarrow{{}}Cu+Z{{n}^{2+}}\] done clear
C) \[Z{{n}^{2+}}+C{{u}^{2+}}\xrightarrow{{}}Zn+Cu\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer65) Highest electron affinity among the following is
A) fluorine done clear
B) chlorine done clear
C) sulphur done clear
D) xenon done clear
View Answer play_arrowquestion_answer66) Which of the following noble gases is most reactive?
A) He done clear
B) Ne done clear
C) Ar done clear
D) Xe done clear
View Answer play_arrowquestion_answer67) Which one of the following is a correct set with respect to molecule, hybridisation and shape?
A) \[BeC{{l}_{2}},\text{ }s{{p}^{2}},\,\]linear done clear
B) \[BeC{{l}_{2}},\text{ }s{{p}^{2}},\]triangular planar done clear
C) \[~BC{{l}_{3}},\text{ }s{{p}^{2}},\] triangular planar done clear
D) \[BC{{l}_{3}},s{{p}^{3}},\]tetrahedral done clear
View Answer play_arrowquestion_answer68) \[{{H}_{2}}S\]is not a/an
A) reducing agent done clear
B) acidic done clear
C) oxidizing agent done clear
D) None of the above done clear
View Answer play_arrowquestion_answer69) On doubling p and V with constant temperature, the equilibrium constant will
A) remain constant done clear
B) become double done clear
C) become one-fourth done clear
D) None of the above done clear
View Answer play_arrowquestion_answer70) What is the electronic configuration of\[M{{n}^{2+}}\]?
A) \[~[Ne]\text{ }3{{d}^{5}},\text{ }4{{s}^{o}}\] done clear
B) \[\text{ }\!\![\!\!\text{ }Ar\text{ }\!\!]\!\!\text{ }3{{d}^{5}},\text{ }4{{s}^{2}}\] done clear
C) \[\text{ }\!\![\!\!\text{ }Ar\text{ }\!\!]\!\!\text{ }3{{d}^{5}},\text{ }4{{s}^{0}}\] done clear
D) \[\text{ }\!\![\!\!\text{ }Ne\text{ }\!\!]\!\!\text{ }3{{d}^{5}},\text{ }4{{s}^{2}}\] done clear
View Answer play_arrowquestion_answer71) Increase in atomic size down the group is due to
A) increase in number of electrons done clear
B) increase in number of protons and neutrons done clear
C) increase in number of protons done clear
D) increase in number of protons, neutrons and electrons done clear
View Answer play_arrowquestion_answer72) Which is tribasic acid?
A) \[{{H}_{3}}P{{O}_{2}}\] done clear
B) \[{{H}_{3}}P{{O}_{4}}\] done clear
C) \[{{H}_{4}}{{P}_{2}}{{O}_{7}}\] done clear
D) \[{{H}_{3}}P{{O}_{3}}\] done clear
View Answer play_arrowquestion_answer73) Highest ionizing power is exhibited by
A) \[\alpha -\] rays done clear
B) \[\beta -\]rays done clear
C) \[\gamma -\]rays done clear
D) \[X-\]rays done clear
View Answer play_arrowquestion_answer74) Blister copper is
A) impure \[Cu\] done clear
B) \[Cu\]alloy done clear
C) pure \[Cu\] done clear
D) Cu having 1% impurity done clear
View Answer play_arrowquestion_answer75) Claisen condensation is not given by
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer76) \[AgN{{O}_{3}}\]does not give precipitate with \[CHC{{l}_{3}}\] because
A) \[CHC{{l}_{3}}\] does not ionize in water done clear
B) \[Agn{{O}_{3}}\] is chemically inert done clear
C) \[CHC{{l}_{3}}\] is chemically inert done clear
D) None of the above done clear
View Answer play_arrowquestion_answer77) \[_{90}T{{h}^{228}}\xrightarrow{{}}{{\,}_{83}}B{{i}^{212}}\]by
A) \[4\alpha ,1\beta \] done clear
B) \[4\alpha ,2\beta ,\] done clear
C) \[5\alpha ,1\beta \] done clear
D) \[5\alpha ,2\beta ,\] done clear
View Answer play_arrowquestion_answer78) Blood cells do not shrink in blood because blood is
A) hypotonic done clear
B) isotonic done clear
C) equimolar done clear
D) hypeitonic done clear
View Answer play_arrowquestion_answer79) The compound in which underlined carbon uses only its \[s{{p}^{3}}\]hybrid orbitals for bond formation is
A) \[C{{H}_{3}}\underset{\scriptscriptstyle-}{C}OOH\] done clear
B) \[C{{H}_{3}}\underline{C}ON{{H}_{2}}\] done clear
C) \[C{{H}_{3}}\underline{C}{{H}_{2}}OH\] done clear
D) \[C{{H}_{3}}\underline{C}H=C{{H}_{2}}\] done clear
View Answer play_arrowquestion_answer80) t-butyl alcohol is
A) 2-methyl propan-2-ol done clear
B) 2-methyl propan-1-ol done clear
C) 3-methyl butan-1-ol done clear
D) 3-methyl butan-2-ol done clear
View Answer play_arrowquestion_answer81) Optical isomerism is shown by
A) propanol-2 done clear
B) butanol-2 done clear
C) ethanol done clear
D) methanol done clear
View Answer play_arrowquestion_answer82) When \[{{C}_{2}}{{H}_{2}},C{{H}_{4}}\]and \[{{C}_{2}}{{H}_{4}}\]passes through a test tube which have ammoniacal \[C{{u}_{2}}C{{l}_{2}},\]find out which gas comes out unaffected from test tube?
A) \[{{C}_{2}}{{H}_{2}}\]and \[C{{H}_{4}}\] done clear
B) \[{{C}_{2}}{{H}_{2}}\]and \[{{C}_{2}}{{H}_{4}}\] done clear
C) \[{{C}_{2}}{{H}_{4}}\]and \[C{{H}_{4}}\] done clear
D) \[{{C}_{2}}{{H}_{2}}\] done clear
View Answer play_arrowquestion_answer83) When hydrogen molecules decomposed into its atoms which conditions gives maximum yield of H atoms?
A) High temperature and low pressure done clear
B) Low temperature and high pressure done clear
C) High temperature and high pressure done clear
D) Low temperature and low pressure done clear
View Answer play_arrowquestion_answer84) Natural rubber is a polymer of
A) styrene done clear
B) chloroprene done clear
C) \[C{{H}_{2}}=\underset{C{{H}_{3}}}{\mathop{\underset{|}{\mathop{C}}\,}}\,-CH=C{{H}_{2}}\]or isoprene done clear
D) 1, 3-butadiene done clear
View Answer play_arrowquestion_answer85) Which of the following compounds is aromatic?
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer86) The value of \[\Lambda _{eq}^{\infty }\] for\[N{{H}_{4}}Cl,NaOH\] and\[NaCl\] are respectively, 149.74, 248.1 and \[126.4\,oh{{m}^{-1}}\,c{{m}^{2}}e{{q}^{-1}}.\] The value of \[A_{eq}^{\infty }\]of \[N{{H}_{4}}OH\]is
A) 371.44 done clear
B) 271.44 done clear
C) 71.44 done clear
D) Cannot be predicted from given data done clear
View Answer play_arrowquestion_answer87) Number of atoms of He in 100 u of He (atomic wt of He is 4) are
A) 25 done clear
B) 100 done clear
C) 50 done clear
D) \[100\times 6\times {{10}^{-23}}\] done clear
View Answer play_arrowquestion_answer88) Which has least gold number?
A) Gelatin done clear
B) Starch done clear
C) Albumin done clear
D) Blood done clear
View Answer play_arrowquestion_answer89) In a compound C, H and N are present in 9 : 1 : 3.5 by weight. If molecular weight of the compound is 108, then the molecular formula of the compound is
A) \[{{C}_{2}}{{H}_{6}}{{N}_{2}}\] done clear
B) \[{{C}_{3}}{{H}_{4}}N\] done clear
C) \[{{C}_{6}}{{H}_{8}}{{N}_{2}}\] done clear
D) \[{{C}_{9}}{{H}_{12}}{{N}_{3}}\] done clear
View Answer play_arrowquestion_answer90) In the following reaction \[{{C}_{2}}{{H}_{2}}\xrightarrow[HgS{{O}_{4}}/{{H}_{2}}S{{O}_{4}}]{{{H}_{2}}O}X\rightleftharpoons C{{H}_{3}}CHO,\]What is \[X\]?
A) \[C{{H}_{3}}C{{H}_{2}}OH\] done clear
B) \[C{{H}_{3}}-O-C{{H}_{3}}\] done clear
C) \[C{{H}_{3}}C{{H}_{2}}CHO\] done clear
D) \[C{{H}_{2}}=CHOH\] done clear
View Answer play_arrowquestion_answer91) Which one of the following will most readily be dehydrated in acidic conditions?
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer92) Which of the following solutions will have \[pH=9\]at 298 K?
A) \[1\times {{10}^{-9}}\,M\,HCl\]solution done clear
B) \[1\times {{10}^{-5}}\,M\,NaOH\]solution done clear
C) \[1\times {{10}^{-9}}\,M\,KOH\]solution done clear
D) Both (a) and (b) done clear
View Answer play_arrowquestion_answer93) The following data are for the decomposition of ammonium nitrite in aqueous solution.
Vol. of \[{{N}_{2}}\]in cc | Times (min) |
6.25 | 10 |
9.00 | 15 |
11.40 | 20 |
13.65 | 25 |
35.65 | Infinity |
A) zero done clear
B) one done clear
C) two done clear
D) three done clear
View Answer play_arrowquestion_answer94) An alkyl halide by formation of its Grignard reagent and heating with water yields propane. What is the original alkyl halide?
A) Methyl iodide done clear
B) Ethyl iodide done clear
C) Ethyl bromide done clear
D) Propyl bromide done clear
View Answer play_arrowquestion_answer95) The following reaction is known as
A) Perkin reaction done clear
B) Gattermann reaction done clear
C) Kolbe reaction done clear
D) Gattermann-aldehyde reaction done clear
View Answer play_arrowquestion_answer96) Aldehyde with \[N{{H}_{2}}.N{{H}_{2}}\]forms
A) hydrazones done clear
B) aniline done clear
C) nitrobenzene done clear
D) None of these done clear
View Answer play_arrowquestion_answer97) Van t Hoff factor of \[Ca{{(N{{O}_{3}})}_{2}}\]us
A) one done clear
B) two done clear
C) three done clear
D) four done clear
View Answer play_arrowquestion_answer98) 1 mole of \[{{H}_{2}}\]and 2 moles of \[{{I}_{2}}\]are taken initially in a two litre vessel. The number of moles of \[{{H}_{2}}\]at equilibrium is 0.2. Then, the number of moles of \[{{I}_{2}}\]and HI at equilibrium are
A) 1.2, 1.6 done clear
B) 1.8, 1.0 done clear
C) 0.4, 2.4 done clear
D) 0.8, 2.0 done clear
View Answer play_arrowquestion_answer99) The volume of water to be added to 100 cm3 of \[0.5\text{ }N\text{ }{{H}_{2}}S{{O}_{4}}\]to get decinormal concentration is
A) \[400\,c{{m}^{3}}\] done clear
B) \[450\,c{{m}^{3}}\] done clear
C) \[~500\,c{{m}^{3}}\] done clear
D) \[100\,c{{m}^{3}}\] done clear
View Answer play_arrowquestion_answer100) 1.520 g of hydroxide of a metal on ignition gave 0.995 g of oxide. The equivalent weight of metal is
A) 1.52 done clear
B) 0.995 done clear
C) 190 done clear
D) 9 done clear
View Answer play_arrowquestion_answer101) If \[f:R\to R\]is defined by \[f(x)=[2x]-2[x]\] for all \[x\in R,\]where \[[x]\]is the greatest integer not exceeding x, then the range of\[f\]is
A) \[\{x\in R:0\le x\le 1\}\] done clear
B) \[(0,1)\] done clear
C) \[\{x\in R:x>0\}\] done clear
D) \[\{x\in R:x\le 0\}\] done clear
View Answer play_arrowquestion_answer102) If \[x=\sqrt{\frac{2+\sqrt{3}}{2-\sqrt{3}},}\]then \[{{x}^{2}}{{(x-4)}^{2}}\] is equal to
A) 7 done clear
B) 4 done clear
C) 2 done clear
D) 1 done clear
View Answer play_arrowquestion_answer103) For all integers \[n\ge 1,\]which of the following is divisible by 9?
A) \[{{8}^{n}}+1\] done clear
B) \[{{4}^{n}}-3n-1\] done clear
C) \[{{3}^{2n}}+3n+1\] done clear
D) \[{{10}^{n}}+1\] done clear
View Answer play_arrowquestion_answer104) Eight different letters of an alphabet are given Words of four letters from these are formed The number of such words with at least one letter repeated is
A) \[\left( _{4}^{8} \right)-{{\,}^{8}}{{P}_{4}}\] done clear
B) \[{{8}^{4}}+\left( _{4}^{8} \right)\] done clear
C) \[{{8}^{4}}-{{\,}^{8}}{{P}_{4}}\] done clear
D) \[{{8}^{4}}-\left( _{4}^{8} \right)\] done clear
View Answer play_arrowquestion_answer105) The number of natural numbers less than 1000, in which no two digits are repeated is
A) 738 done clear
B) 792 done clear
C) 837 done clear
D) 720 done clear
View Answer play_arrowquestion_answer106) \[1+\frac{2}{4}+\frac{2.5}{4.8}+\frac{2.5.8}{4.8.12}+\frac{2.5.8.11}{4.8.12.16}+...\]is equal to
A) \[{{4}^{-2/3}}\] done clear
B) \[\sqrt[3]{16}\] done clear
C) \[\sqrt[3]{4}\] done clear
D) \[{{4}^{3/2}}\] done clear
View Answer play_arrowquestion_answer107) The coefficient of \[{{x}^{n}}\]in\[\frac{1-2x}{{{e}^{x}}}\]is
A) \[\frac{(1+2n)}{n!}\] done clear
B) \[{{(-1)}^{n}}.\frac{\left( 1+2n \right)}{n!}\] done clear
C) \[{{(-1)}^{n}}.\frac{(1-2n)}{n!}\] done clear
D) \[{{(-1)}^{n}}.\frac{(1+4n)}{n!}\] done clear
View Answer play_arrowquestion_answer108) If \[\sqrt{9{{x}^{2}}+6x+1}<(2-x),\]then
A) \[x\in \left( -\frac{3}{2},\frac{1}{4} \right)\] done clear
B) \[x\in \left( -\frac{3}{2},\frac{1}{4} \right]\] done clear
C) \[x\in \left[ -\frac{3}{2},\frac{1}{4} \right)\] done clear
D) \[x<\frac{1}{4}\] done clear
View Answer play_arrowquestion_answer109) The difference between two roots of the equation \[{{x}^{3}}-13{{x}^{2}}+15x+189=0\] is\[2.\]Then, the roots of the equation are
A) \[-3,5,7\] done clear
B) \[-3,-7,-9\] done clear
C) \[3,-5,7\] done clear
D) \[-3,7,9\] done clear
View Answer play_arrowquestion_answer110) If \[\alpha ,\beta ,\gamma \]are the roots of the equation \[{{x}^{3}}-6{{x}^{2}}+11x+6=0,\]then \[\sum {{\alpha }^{2}}\beta +\sum {{\alpha }^{2}}\beta +\sum \alpha {{\beta }^{2}}\]is equal to
A) 80 done clear
B) 84 done clear
C) 90 done clear
D) - 84 done clear
View Answer play_arrowquestion_answer111) If A is an inverrible matrix of order n, then the determinant of \[adj\,(A)\] is equal to
A) \[|A{{|}^{n}}\] done clear
B) \[|A{{|}^{n+1}}\] done clear
C) \[|A{{|}^{n-1}}\] done clear
D) \[|A{{|}^{n+2}}\] done clear
View Answer play_arrowquestion_answer112) \[\left| \begin{matrix} \log e & \log {{e}^{2}} & \log {{e}^{3}} \\ \log {{e}^{2}} & \log {{e}^{3}} & \log {{e}^{4}} \\ \log {{e}^{3}} & \log {{e}^{4}} & \log {{e}^{5}} \\ \end{matrix} \right|\]is equal to
A) 0 done clear
B) 1 done clear
C) 4 loge done clear
D) 5 loge done clear
View Answer play_arrowquestion_answer113) The equation of the locus of \[z\] such that \[\left| \frac{z-i}{z+i} \right|=2,\]where \[z=x+iy\]is a complex number, is
A) \[3{{x}^{2}}+\text{ }3{{y}^{2}}+10y\text{ }-3=0\] done clear
B) \[~3{{x}^{2}}+3{{y}^{2}}+10y+3=0\] done clear
C) \[3{{x}^{2}}-3{{y}^{2}}-10y-3=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}-5y+3=0\] done clear
View Answer play_arrowquestion_answer114) If \[5\cos x+12\cos y=13,\] then the maximum value of \[5\,\sin x+12\sin y\]is
A) 12 done clear
B) \[\sqrt{120}\] done clear
C) \[\sqrt{20}\] done clear
D) 13 done clear
View Answer play_arrowquestion_answer115) The quadratic equation whose roots are \[{{\sin }^{2}}{{18}^{o}}\]and \[{{\cos }^{2}}{{36}^{o}}\]is
A) \[~16{{x}^{2}}-12x+1=0\] done clear
B) \[16{{x}^{2}}+12x+1=0\] done clear
C) \[16{{x}^{2}}-12x-1=0\] done clear
D) \[16{{x}^{2}}+\text{10}x+1=0\] done clear
View Answer play_arrowquestion_answer116) For all values of \[\theta ,\] the values of \[3-\cos \theta +\cos \left( \theta +\frac{\pi }{3} \right)\] lie in the interval
A) \[[-2,3]\] done clear
B) \[[-2,1]\] done clear
C) \[[2,4]\] done clear
D) \[[1,5]\] done clear
View Answer play_arrowquestion_answer117) If \[x=\tan {{15}^{o}},y=\cos ec{{75}^{o}}\]and \[z=4\sin {{18}^{o}},\]then
A) \[x<y<z\] done clear
B) \[y<z<x\] done clear
C) \[z<x<\text{ }y\] done clear
D) \[~x<z<\text{ }y\] done clear
View Answer play_arrowquestion_answer118) If in \[\Delta \,ABC,\,\,\tan \frac{A}{2}=\frac{5}{6}\] and \[\tan \frac{C}{2}=\frac{2}{5},\]then\[a,b,c\] are such that
A) \[{{b}^{2}}=ac\] done clear
B) \[2b=a+c\] done clear
C) \[2ac=b(a+c)\] done clear
D) \[a+b=c\] done clear
View Answer play_arrowquestion_answer119) If \[b+c=3a,\]then \[\cot \frac{B}{2}\cot \frac{C}{2}\]is equal to
A) 3 done clear
B) 1 done clear
C) 4 done clear
D) 2 done clear
View Answer play_arrowquestion_answer120) The elevation of an object on a hill is observed from a certain point in the horizontal plane through its base, to be \[{{30}^{o}}.\] After walking 120 m towards it on level ground the elevation is found to be \[{{60}^{o}}.\] Then the height of the object (in metres) is
A) 120 done clear
B) \[60\sqrt{3}\] done clear
C) \[120\sqrt{3}\] done clear
D) \[60\] done clear
View Answer play_arrowquestion_answer121) If \[\vec{a}+\vec{b}+\vec{c}=\vec{o}\]and \[|\vec{a}|=3,|\vec{b}|=4\]and \[|\vec{c}|=\sqrt{37},\]then the angle between \[\vec{a}\]and \[\vec{b}\] is
A) \[\frac{\pi }{4}\] done clear
B) \[\frac{\pi }{2}\] done clear
C) \[\frac{\pi }{6}\] done clear
D) \[\frac{\pi }{3}\] done clear
View Answer play_arrowquestion_answer122) The position vector of a point lying on the line joining the points whose position vectors are \[\hat{i}+\hat{j}-\hat{k}\]and \[\hat{i}-\hat{j}+\hat{k}\]is
A) \[\hat{j}\] done clear
B) \[\hat{i}\] done clear
C) \[\hat{k}\] done clear
D) \[\vec{o}\] done clear
View Answer play_arrowquestion_answer123) If the volume of parallelepiped with\[4\hat{i}+5\hat{j}+\hat{k},-\hat{j}+\hat{k}\]with coterminous edges \[4\hat{i}+5\hat{j}+\hat{k},-\hat{j}+\hat{k}\] and \[3\hat{i}+9\hat{j}+p\hat{k}\]is 34 cubic unit, then? is equal to
A) 4 done clear
B) -13 done clear
C) 13 done clear
D) 6 done clear
View Answer play_arrowquestion_answer124) If A and B are two independent events such that \[P(B)=\frac{2}{7},P(A\cup {{B}^{c}})=0.8,\]then \[P(A)\] is equal to
A) 0.1 done clear
B) 0.2 done clear
C) 0.3 done clear
D) 0.4 done clear
View Answer play_arrowquestion_answer125) Seven balls are drawn simultaneoulsy from a bag containing 5 white and 6 green balls. The probability of drawing 3 white and 4 green balls is
A) \[\frac{7}{{{\,}^{11}}{{C}_{7}}}\] done clear
B) \[\frac{{{\,}^{5}}{{C}_{3}}+{{\,}^{6}}{{C}_{4}}}{{{\,}^{11}}{{C}_{7}}}\] done clear
C) \[\frac{{{\,}^{5}}{{C}_{2}}+{{\,}^{6}}{{C}_{2}}}{{{\,}^{11}}{{C}_{7}}}\] done clear
D) \[\frac{{{\,}^{6}}{{C}_{3}}+{{\,}^{5}}{{C}_{4}}}{{{\,}^{11}}{{C}_{7}}}\] done clear
View Answer play_arrowquestion_answer126) The equation of the line passing through the point of intersection of the lines\[~x-3y+2=0\] and and perpendicular to the line \[2x+5y-7=0\] is
A) \[2x-3y+1=0\] done clear
B) \[~6x-9y+11=0\] done clear
C) \[~2x-3y+5=0\] done clear
D) \[3x-2y+1=0\] done clear
View Answer play_arrowquestion_answer127) Let O be the origin and A be a point on the curve \[{{y}^{2}}=4x.\]Then the locus of the mid point of OA, is
A) \[{{x}^{2}}=4y\] done clear
B) \[{{x}^{2}}=2y\] done clear
C) \[{{x}^{2}}=16y\] done clear
D) \[{{y}^{2}}=2x\] done clear
View Answer play_arrowquestion_answer128) The lines represented by the equation \[{{x}^{2}}-\text{ }{{y}^{2}}-\text{ }x+3y-2=0\]are
A) \[x+y-1=0,\,x-y+2=0\] done clear
B) \[x-y-2=0,x+y+1=0\] done clear
C) \[x+y+2=,0,x-y-1=0\] done clear
D) \[x-y+1=0,x+y-2=0\] done clear
View Answer play_arrowquestion_answer129) If OA is equally inclined to OX, OY and OZ and if A is \[\sqrt{3}\]unit from the origin, then A is
A) \[(3,3,3)\] done clear
B) \[(-1,1,-1)\] done clear
C) \[(-1,1,1)\] done clear
D) \[(1,1,1)\] done clear
View Answer play_arrowquestion_answer130) If the direction cosines of two lines are such that \[l+m+n=0,{{l}^{2}}+{{m}^{2}}-{{n}^{2}}=,0\]then the angle between them is
A) \[\pi \] done clear
B) \[\pi /3\] done clear
C) \[\pi /4\] done clear
D) \[\pi /6\] done clear
View Answer play_arrowquestion_answer131) The number of common tangents to the two circles \[{{x}^{2}}+\text{ }{{y}^{2}}-\text{ }8x+2y=0\] and \[{{x}^{2}}+{{y}^{2}}-2x-16y+25=0\]is
A) 1 done clear
B) 2 done clear
C) 3 done clear
D) 4 done clear
View Answer play_arrowquestion_answer132) The length of the tangent drawn to the circle \[{{x}^{2}}+{{y}^{2}}-2x+4y-11=0\]from the point \[(1,3)\]is
A) 1 done clear
B) 2 done clear
C) 3 done clear
D) 4 done clear
View Answer play_arrowquestion_answer133) Equation of the latusrectum of the ellipse \[9{{x}^{2}}+4{{y}^{2}}-18x-8y-23=0\text{ }\]are
A) \[y=\pm \text{ }\sqrt{5}\] done clear
B) \[x=\pm \text{ }\sqrt{5}\] done clear
C) \[y=1\pm 5\] done clear
D) \[x=-1\pm \sqrt{5}\] done clear
View Answer play_arrowquestion_answer134) If the eccentricity of a hyperbola is\[\sqrt{3},\], then the eccentricity of its conjugate hyperbola is
A) \[\sqrt{2}\] done clear
B) \[\sqrt{3}\] done clear
C) \[\sqrt{\frac{3}{2}}\] done clear
D) \[2\sqrt{3}\] done clear
View Answer play_arrowquestion_answer135) If \[{{x}^{y}}={{y}^{x}},\]then \[x(x-y\log x)\frac{dy}{dx}\]is equal to
A) \[y(y-x\log \,y)\] done clear
B) \[y(y+x\,\log \,y)\] done clear
C) \[x(x+y\log x)\] done clear
D) \[x(y-x\log y)\] done clear
View Answer play_arrowquestion_answer136) \[f(x)={{e}^{x}}\sin x,\]then \[f(x)\]is equal to
A) \[{{e}^{6x}}\sin 6x\] done clear
B) \[2{{e}^{x}}\cos x\] done clear
C) \[8{{e}^{x}}\sin x\] done clear
D) \[8{{e}^{x}}\cos x\] done clear
View Answer play_arrowquestion_answer137) If \[0<p<q,\]then \[\underset{n\to \infty }{\mathop{\lim }}\,{{({{q}^{n}}+{{p}^{n}})}^{1/n}}\]is equal to
A) \[e\] done clear
B) \[p\] done clear
C) \[q\] done clear
D) 0 done clear
View Answer play_arrowquestion_answer138) \[\underset{x\to \infty }{\mathop{\lim }}\,[{{x}^{2}}+2x-1]\]is equal to
A) \[\infty \] done clear
B) \[\frac{1}{2}\] done clear
C) 4 done clear
D) 1 done clear
View Answer play_arrowquestion_answer139) If \[f(x)=\left\{ \begin{matrix} \frac{1-\sqrt{2}\sin x}{\pi -4x}, & if\,x\ne \frac{\pi }{4} \\ a & if\,x=\frac{\pi }{4} \\ \end{matrix} \right.\] is continuous at \[\frac{\pi }{4},\] then a is equal to
A) 4 done clear
B) 2 done clear
C) 1 done clear
D) 1/4 done clear
View Answer play_arrowquestion_answer140) If \[\theta \]is the angle between the curves \[xy=2\]and \[{{x}^{2}}+4y=0,\]then \[\tan \theta \]is equal to
A) 1 done clear
B) -1 done clear
C) 2 done clear
D) 3 done clear
View Answer play_arrowquestion_answer141) In the interval \[(-3,3)\] the function \[f(x)=\frac{x}{3}+\frac{3}{x},x\ne 0\]is
A) increasing done clear
B) decreasing done clear
C) neither increasing nor decreasing done clear
D) partly increasing and partly decreasing done clear
View Answer play_arrowquestion_answer142) If \[\int_{{}}^{{}}{\,\sqrt{\frac{x}{{{a}^{3}}-{{x}^{3}}}}dx}=g(x)+c,\]then \[g(x)\]is equal to
A) \[\frac{2}{3}{{\cos }^{-1}}x\] done clear
B) \[\frac{2}{3}{{\sin }^{-1}}\left( \frac{{{x}^{3}}}{{{a}^{3}}} \right)\] done clear
C) \[\frac{2}{3}{{\sin }^{-1}}\left( \sqrt{\frac{{{x}^{3}}}{{{a}^{3}}}} \right)\] done clear
D) \[\frac{2}{3}{{\cos }^{-1}}\left( \frac{x}{a} \right)\] done clear
View Answer play_arrowquestion_answer143) If \[\frac{dx}{{{x}^{2}}+2x+2}=f(x)+c,\]then \[f(x)\]is equal to
A) \[{{\tan }^{-1}}(x+1)\] done clear
B) \[2{{\tan }^{-1}}(x+1)\] done clear
C) \[-{{\tan }^{-1}}(x+1)\] done clear
D) \[3{{\tan }^{-1}}(x+1)\] done clear
View Answer play_arrowquestion_answer144) \[\int_{0}^{\pi /2}{\frac{dx}{1+{{\tan }^{3}}x}}\]is equal to
A) \[\pi \] done clear
B) \[\frac{\pi }{2}\] done clear
C) \[\frac{\pi }{4}\] done clear
D) \[\frac{3\pi }{2}\] done clear
View Answer play_arrowquestion_answer145) The solution of\[(1+{{x}^{2}})\frac{dy}{dx}+2xy-4{{x}^{2}}=0\]is
A) \[3x(1+{{y}^{2}})=4{{y}^{3}}+c\] done clear
B) \[3y(1+{{x}^{2}})=4{{x}^{3}}+c\] done clear
C) \[3x(1-{{y}^{2}})=4{{y}^{3}}+c\] done clear
D) \[3y(1+{{y}^{2}})=4{{x}^{3}}+c\] done clear
View Answer play_arrowquestion_answer146) The function \[f(x)=\log (x+\sqrt{{{x}^{2}}+1})\]is
A) an even function done clear
B) an odd function done clear
C) a periodic function done clear
D) neither an even nor an odd function done clear
View Answer play_arrowquestion_answer147) If p, q and rare simple propositions with truth values T, F, T, then the truth value of\[(\tilde{\ }p\vee q)\wedge \tilde{\ }q\Rightarrow p\]is
A) true done clear
B) false done clear
C) true, if r is false done clear
D) None of these done clear
View Answer play_arrowquestion_answer148) The dual of \[x+(yx)=x\]is
A) \[(x+y).(x+x)=x\] done clear
B) \[x.(y+x)=x\] done clear
C) \[x.(y.x)=x\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer149) Forces of magnitudes 5N, 10N, 15N and 20 N act on a particle in the direction of North, South, East and West respectively. The magnitude of their resultant is
A) \[15\sqrt{2}N\] done clear
B) \[10\,N\] done clear
C) \[25\sqrt{2}\,N\] done clear
D) \[5\sqrt{2}\,N\] done clear
View Answer play_arrowquestion_answer150) The value of \[\int_{-\pi /2}^{\pi /2}{\log \left( \frac{2-\sin \theta }{2+\sin \theta } \right)}d\theta \]is
A) 0 done clear
B) 1 done clear
C) 2 done clear
D) None of these done clear
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