JEE Main & Advanced Sample Paper

done JEE Main - Mock Test - 45 Total Questions - 75    [Download]

• question_answer1)
  The position vector of a particle is given as \[\vec{r}=\left( {{t}^{2}}-4t+6 \right)\hat{i}+\left( {{t}^{2}} \right)\hat{j}\]. The time after which the velocity vector and acceleration vector becomes perpendicular to each other is equal to
  A)
  1 sec     
  done clear
  B)
  2 sec                  
  done clear
  C)
  15 sec                 
  done clear
  D)
         Not possible
  done clear
  View Answer play_arrow

• question_answer2)
  A bullet of mass m moving with velocity \[{{v}_{0}}\] hits a wooden plank A of mass M placed on a smooth horizontal surface. The length of the plank is l. The bullet experiences a constant resistive force F inside the block. The minimum value of \[{{v}_{0}}\] such that it is able to come out of the plank is
  A)
  \[\sqrt{\frac{F/m}{{{M}^{2}}}}\]         
  done clear
  B)
         \[\sqrt{\frac{2F\ell (M+m)}{Mm}}\]
  done clear
  C)
  \[\sqrt{\frac{2F\ell m}{{{M}^{2}}}}\]               
  done clear
  D)
  \[\sqrt{\frac{F\ell (M+m)}{Mm}}\]
  done clear
  View Answer play_arrow

• question_answer3)
  A glass wind screen whose inclination with the vertical can be changed is mounted on a car. The car moves horizontally with a speed of\[2\text{ }m/s\]. At what angle \[\alpha \] with the vertical should the screen be placed so that the rain drops falling downwards with velocity \[6m/s\]strike the windscreen perpendicularly?
  A)
  \[{{\tan }^{-1}}(1/3)\]              
  done clear
  B)
  \[{{\tan }^{-1}}(3)\]         
  done clear
  C)
      \[{{\cos }^{-1}}(3)\]              
  done clear
  D)
        \[si{{n}^{-1}}(1/3)\]
  done clear
  View Answer play_arrow

• question_answer4)
  In the figure acceleration of A is \[1\text{ }m/{{s}^{2}}\]upwards, acceleration of C is \[7\text{ }m/{{s}^{2}}\]upwards and acceleration of C is \[\text{2 }m/{{s}^{2}}\] upwards. The acceleration of D will be
  A)
  \[7m/{{s}^{2}}\]downwards     
  done clear
  B)
  \[2m/{{s}^{2}}\] downwards     
  done clear
  C)
  \[10m/{{s}^{2}}\] downwards    
  done clear
  D)
  \[8m/{{s}^{2}}\] downwards
  done clear
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• question_answer5)
  Two particles A and 5 each of mass m are attached by a light inextensible string of length\[2l\] The whole system lies on a smooth horizontal surface. Now particle B starts moving with velocity u as shown. The velocity of particle A when the string jerks tight is
  A)
  \[\frac{u\sqrt{3}}{4}\]   
  done clear
  B)
  \[\frac{u}{\sqrt{3}}\]
  done clear
  C)
  \[\frac{u\sqrt{3}}{2}\]               
  done clear
  D)
  \[\frac{u}{2}\]
  done clear
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• question_answer6)
  An artificial satellite of mass m is moving in a circular orbit at a height equal to the radius R of the earth. Suddenly due to internal explosion the satellite breaks into two parts of equal masses. One part of the satellite stops just after the explosion. The increase in the mechanical energy of the system (satellite + earth) due to explosion will be (Given: acceleration due to gravity on the surface of earth is g).
  A)
  \[mgR\]      
  done clear
  B)
                     \[\frac{mgR}{2}\]                
  done clear
  C)
  \[\frac{mgR}{4}\]               
  done clear
  D)
         None of these
  done clear
  View Answer play_arrow

• question_answer7)
  Figure shows a cylinder \[1\text{ }m\]long with a thin massless piston clamped in such a way that it divides the cylinder into two equal parts. The whole system is placed in a large water bath maintained at temperature\[300\text{ }K\]. The wall of the cylinders is highly conducting. The left side of the cylinder contain 1 mole of helium gas at pressure \[4\times {{10}^{5}}Pa\] and the right side also contain helium gas at pressure\[{{10}^{5}}Pa\]. Now the piston is released. The piston finally attains the equilibrium position. How much heat will be transmitted by the water bath in the process? Take \[R=8.3\text{ }J/mole\text{ }K,\]ln \[(1.6)=0.47\] and ln \[(0.4)=-0.916\]]
  A)
  \[200\,J\]          
  done clear
  B)
         \[400\,J\]
  done clear
  C)
  \[600\,J\]          
  done clear
  D)
         \[800\,J\]
  done clear
  View Answer play_arrow

• question_answer8)
  A long train is moving on a circular track. The speed of train remains constant during motion. Engine of the train is emitting a sound of frequency \[{{f}_{0}}\]. The frequency observed by the guard at the rear end of the train is
  A)
  is equal to \[{{f}_{0}}\]
  done clear
  B)
  is less than \[{{f}_{0}}\]
  done clear
  C)
  is more than \[{{f}_{0}}\]
  done clear
  D)
  may be greater than, less than or equal to \[{{f}_{0}}\]depending on speed and length of train.
  done clear
  View Answer play_arrow

• question_answer9)
  A galvanometer of coil resistance\[1\Omega \]. is converted into voltmeter by using a resistance of \[5\Omega \]. in series and same galvanometer is converted into ammeter by using a shunt of \[1\Omega \]. Now ammeter and voltmeter are connected in circuit as shown, find the reading of voltmeter and ammeter.
  A)
  3 volt, 3 amp    
  done clear
  B)
  2 volt, 2 amp   
  done clear
  C)
  4 volt, 3 amp                
  done clear
  D)
  3 volt, 4 amp
  done clear
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• question_answer10)
  ABCD is a wire frame in the shape of an isosceles trapezium (i.e., length AR = length CD) enter a magnetic field with flux density B at \[t=0\]as shown in the figure. If the total resistance of wire frame is R, what is the value of the induced current in the wire frame after t seconds, assuming that the frame has not entered the field completely by then?
  A)
  zero                  
  done clear
  B)
         \[\frac{Bv}{R}(2vt\,\,\sin \theta +\ell )\]
  done clear
  C)
  \[\frac{Bv}{R}\left( \frac{2vt}{\tan \theta }+\ell  \right)\]
  done clear
  D)
         \[\frac{B}{v}\]
  done clear
  View Answer play_arrow

• question_answer11)
  In the following circuit, find \[{{I}_{1}}\] and \[{{I}_{2}}\]
  A)
              \[0,0\]               
  done clear
  B)
         \[5mA,\,5mA\]
  done clear
  C)
  \[5mA,\,0\]                    
  done clear
  D)
  \[0,\,5\,mA\]
  done clear
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• question_answer12)
  In the circuit shown the transformer is ideal with turn ratio \[\frac{{{N}_{1}}}{{{N}_{2}}}=\frac{5}{1}\]. The voltage of the source is \[{{V}_{s}}=300\]volt. The voltage measured across the load resistance \[{{R}_{L}}=100\Omega \]. is 50 volt. Find the value of resistance R in the primary circuit.
  A)
  \[250\Omega \]   
  done clear
  B)
                     \[500\Omega \]      
  done clear
  C)
  \[750\Omega \]                 
  done clear
  D)
         \[300\Omega \]
  done clear
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• question_answer13)
  A lamp emits monochromatic green light uniformly in all directions. The lamp is 3% efficient in converting electrical power to electromagnetic waves and consumes 100 W of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of 10 m from the lamp will be
  A)
  \[1.34\text{ }V/m\]
  done clear
  B)
  \[2.68\text{ }V/m\]
  done clear
  C)
  \[5.36\text{ }V/m\]
  done clear
  D)
  \[9.37\text{ }V/m\]
  done clear
  View Answer play_arrow

• question_answer14)
  A particle having specific charge \[\sigma \] is projected in \[xy\]plane with a speed V. There exists a uniform magnetic field in z-direction having a fixed magnitude\[{{B}_{0}}\]. The field \[2n\] is made to reverse its direction after every interval of \[\frac{2\sigma }{\sigma B}\]. The maximum separation between two positions of the particle during its course of motion will be
  A)
  \[\frac{2\sqrt{2}v}{\sigma {{B}_{0}}}\]             
  done clear
  B)
         \[\frac{4v}{\sigma {{B}_{0}}}\]    
  done clear
  C)
  \[\frac{2v}{\sigma {{B}_{0}}}\]              
  done clear
  D)
         \[\frac{v}{\sigma {{B}_{0}}}\]
  done clear
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• question_answer15)
  Six long parallel current carrying wires are perpendicular to the plane of the figure. They pass through the vertices of a regular hexagon of side length a. All wires have same current /. Direction of current is out of the plane of the figure in all the wires except the one passing through vertex F, which has current directed into the plane of the figure. The magnitude and direction of magnetic induction field at the centre of the hexagon will be
  A)
  \[\frac{{{\mu }_{0}}I}{\pi a}\]towards midpoint of side DE   
  done clear
  B)
   \[\frac{3{{\mu }_{0}}I}{\pi a}\] towards midpoint of side BC
  done clear
  C)
  \[\frac{3{{\mu }_{0}}I}{\pi a}\]towards midpoint of side DE                 
  done clear
  D)
  \[\frac{{{\mu }_{0}}I}{\pi a}\] towards midpoint of side BC
  done clear
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• question_answer16)
  A certain volume of copper is drawn into a wire of radius a and is wrapped in the shape of a helix having radius \[r(>>a)\]. The windings are as close as possible without overlapping. Self-inductance of the inductor so obtained is \[{{L}_{1}}\]. Another wire of radius \[2a\] is drawn using same volume of copper and wound in the fashion as described above. This time the inductance is \[{{L}_{2}}\] Find \[\frac{{{L}_{1}}}{{{L}_{2}}}\] .
  A)
              \[8\]                 
  done clear
  B)
  \[\frac{1}{8}\]
  done clear
  C)
  \[\frac{1}{6}\]                          
  done clear
  D)
  \[6\]
  done clear
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• question_answer17)
  A convex surface has a uniform radius of curvature equal to\[5R\]. A wheel of radius R is rolling without sliding on it with a constant speed v. Find the acceleration of the point (P) of the wheel which is in contact with the convex surface.
  A)
  \[\frac{3{{v}^{2}}}{5R}\]       
  done clear
  B)
                     \[\frac{2{{v}^{2}}}{3R}\]
  done clear
  C)
  \[\frac{5{{v}^{2}}}{6R}\]                   
  done clear
  D)
         \[\frac{{{v}^{2}}}{R}\]
  done clear
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• question_answer18)
  A disc of mass \[M=2m\]and radius R is pivoted at its centre. The disc is free to rotate in the vertical plane about its horizontal axis through its centre O. A particle of mass m is stuck on the periphery of the disc. Find the frequency of small oscillations of the system about its equilibrium position.
  A)
              \[\frac{1}{2\pi }\sqrt{\frac{g}{2R}}\]
  done clear
  B)
                     \[\frac{1}{\pi }\sqrt{\frac{g}{R}}\]
  done clear
  C)
  \[\frac{1}{2\pi }\sqrt{\frac{g}{R}}\]        
  done clear
  D)
         \[\frac{2}{\pi }\sqrt{\frac{g}{R}}\]
  done clear
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• question_answer19)
  A water tank has a circular hole at its base. A solid cone is used to plug the hole. Exactly half the height of the cone protrudes out of the hole. Water is filled in the tank to a height equal to height of the cone. Calculate the buoyancy force on the cone. Density of water is \[\rho \] and volume of cone is V.
  A)
  \[\frac{V\rho g}{8}\]      
  done clear
  B)
  \[\frac{V\rho g}{3}\]
  done clear
  C)
  \[\frac{V\rho g}{2}\]      
  done clear
  D)
         \[\frac{3V\rho g}{4}\]
  done clear
  View Answer play_arrow

• question_answer20)
  Sound of wavelength \[100\text{ }cm\]travels in air. At a given point the difference in maximum and minimum pressure is \[0.2\,N{{m}^{-2}}.\]If the bulk modulus of air is \[1.5\times 10h5N{{m}^{-2}},\] find the amplitude of vibration of the particles of the medium.
  A)
  \[1.2\times {{10}^{-7}}m\] 
  done clear
  B)
                     \[2.4\times {{10}^{-7}}m\]
  done clear
  C)
  \[2.0\times {{10}^{-7}}m\]       
  done clear
  D)
         \[1.0\times {{10}^{-7}}m\]
  done clear
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• question_answer21)
  A uniform disc of radius 'R? is rotating about vertical axis /passing through the centre in horizontal plane with constant angular speed. A massless pole AB is fixed on its circumference as shown in the figure. A light string of length 2R is tied at A and a small bob at its other end. In equilibrium string makes an angle \[37{}^\circ \] with vertical. What is the angular speed (in rad/sec) of disc? (Take \[R=\frac{3}{11}m,\,\,g=10m/{{s}^{2}}\])
  View Answer play_arrow

• question_answer22)
  A soap bubble in vacuum has a radius of \[3\text{ }cm\]and another soap bubble in vacuum has a radius of \[\text{4 }cm\]. If the two bubbles coalesce under isothermal conditions, what is the radius (in cm) of the new bubble?
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• question_answer23)
  A cylinder of ideal gas is closed by an \[8.00\text{ }kg\]movable piston (area\[=60\text{ }c{{m}^{2}}\]) as shown in figure. Atmospheric pressure is\[100\text{ }kPa\]. When the gas is heated from \[30.0{}^\circ C\]to \[100.0{}^\circ C,\] the piston rises by\[20.0\text{ }cm\]. The piston is then fastened in place, and the gas is cooled back to\[30.0{}^\circ C\]. If \[\Delta {{Q}_{1}}\] is the heat added to the gas in the heating process and \[\Delta {{Q}_{2}}\] is the heat lost during cooling, find the difference \[\left| \Delta {{Q}_{1}} \right|-\,\left| \Delta {{Q}_{2}} \right|\](in calories).
  View Answer play_arrow

• question_answer24)
  Three plates A, B and C each of area \[0.1\text{ }{{m}^{2}}\]are separated by a distance of \[0.885\text{ }mm\]from each other as shown in the figure. A 10 V battery is used to charge the system. What is the energy stored in the system (in\[\mu J\])?
  View Answer play_arrow

• question_answer25)
  In a Young's double slit experiment, the slits are \[2\text{ }mm\]apart and are illuminated with a mixture of two wavelengths \[{{\lambda }_{0}}=750nm\]and\[\lambda =900nm\]. What is the minimum distance (in mm) from the common central bright fringe on a screen 2 m from the slits where a bright fringe from one interference pattern coincides with a bright fringe from the other?
  View Answer play_arrow

• question_answer26)
  Beryllium shows diagonal relationship with aluminium. Which of the following similarity is incorrect?
  A)
  \[B{{e}_{2}}C\] like \[A{{l}_{4}}{{C}_{3}}\] yields methane on hydrolysis.
  done clear
  B)
  \[Be\]like \[Al\] is rendered passive by \[HN{{O}_{3}}\].
  done clear
  C)
  \[Be{{(OH)}_{2}}\] like \[Al{{(OH)}_{3}}\] is basic.
  done clear
  D)
  \[Be\]forms beryllates and \[Al\]forms aluminates.
  done clear
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• question_answer27)
  Bromination of toluene gives
  A)
  only w-substituted product
  done clear
  B)
  only p-substituted product
  done clear
  C)
  mixture of o-and p-substituted products
  done clear
  D)
  mixture of o-and m-substituted products
  done clear
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• question_answer28)
  Schottky defects occurs mainly in electrovalent compounds where:
  A)
  Positive ions and negative ions are of different size.
  done clear
  B)
  Positive ions and negative ions are of same size.
  done clear
  C)
  Positive ions are small and negative ions are big.
  done clear
  D)
  Positive ions are big and negative ions are small.
  done clear
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• question_answer29)
  Hydrogenation of the given compound in the presence of poisoned palladium catalyst gives
  A)
  An optically active compound
  done clear
  B)
  An optically inactive compound
  done clear
  C)
  A racemic mixture
  done clear
  D)
  A diastereomeric mixture
  done clear
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• question_answer30)
  The de Broglie wavelength of an electron in the ground state of hydrogen atom is : \[[K.E.=13.6\,eV=1.602\times {{10}^{-19}}J]\]
  A)
  \[33.28\text{ }nm\]
  done clear
  B)
  \[3.328\text{ }nm\]
  done clear
  C)
  \[0.3328\text{ }nm\]
  done clear
  D)
         \[0.0332\text{ }nm\]
  done clear
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• question_answer31)
  The substance which is a primary pollutant?
  A)
  \[{{H}_{2}}S{{O}_{4}}\]
  done clear
  B)
         \[CO\]
  done clear
  C)
  \[PAN\]
  done clear
  D)
         Aldehydes
  done clear
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• question_answer32)
  A solution of sucrose (molar mass\[=342\text{ }g\text{ }mol\]) is prepared by dissolving \[68.4\text{ }g\]of it per litre of the  solution, what is its osmotic pressure \[(r=0.082\,L\,atm\,{{K}^{-1}}\,mo{{l}^{-1}})\] at 273K
  A)
  \[6.02\,atm\]
  done clear
  B)
         \[4.48\,atm\]
  done clear
  C)
  \[4.04\,atm\]
  done clear
  D)
         \[5.32\,atm\]
  done clear
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• question_answer33)
  \[{{t}_{1/4}}\] can be taken as the time taken for the concentration of a reactant to drop to \[\frac{3}{4}\] of its initial value. If the rate constant for a first order reaction is k, the \[{{t}_{1/4}}\] can be written as
  A)
  \[0.75/k\]
  done clear
  B)
         \[0.69/k\]
  done clear
  C)
  \[0.29/k\]
  done clear
  D)
         \[0.10/k\]
  done clear
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• question_answer34)
  Which one of the following esters cannot undergo Claisen self-condensation?
  A)
  \[C{{H}_{3}}-C{{H}_{2}}-C{{H}_{2}}-C{{H}_{2}}-COO{{C}_{2}}{{H}_{5}}\]
  done clear
  B)
  \[{{C}_{6}}{{H}_{5}}COO{{C}_{2}}{{H}_{5}}\]
  done clear
  C)
  \[{{C}_{6}}{{H}_{5}}C{{H}_{2}}COO{{C}_{2}}{{H}_{5}}\]
  done clear
  D)
  \[{{C}_{6}}{{H}_{11}}C{{H}_{2}}COO{{C}_{2}}{{H}_{5}}\]
  done clear
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• question_answer35)
  A pair of species of oxygen and their magnetic behaviours are noted below. Which of the following presents the correct description?
  A)
   \[O_{2}^{-},O_{2}^{2-}\]- Both diamagnetic
  done clear
  B)
  \[O_{2}^{+},O_{2}^{2-}\] - Both paramagnetic
  done clear
  C)
  \[O_{2}^{+},{{O}_{2}}\]   - Both paramagnetic
  done clear
  D)
  None of these
  done clear
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• question_answer36)
  For the reaction: \[{{H}_{2}}(g)+C{{O}_{2}}(g)CO(g)+{{H}_{2}}O(g),\]if the initial concentration of \[[{{H}_{2}}]=[C{{O}_{2}}]\] and \[x\text{ }mol/Litre\]of hydrogen is consumed at equilibrium, the correct expression of \[{{K}_{p}}\] is
  A)
  \[\frac{{{x}^{2}}}{{{(1-x)}^{2}}}\]   
  done clear
  B)
         \[\frac{{{(1+x)}^{2}}}{{{(1-x)}^{2}}}\]
  done clear
  C)
  \[\frac{{{x}^{2}}}{{{(2+x)}^{2}}}\]
  done clear
  D)
         \[\frac{{{x}^{2}}}{1-{{x}^{2}}}\]
  done clear
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• question_answer37)
  Arrange the following metals in order in which they displace each other from the solutions of their salts in decreasing order. \[Al,\text{ }Cu,\text{ }Fe,\text{ }Mg\]and\[Zn\]. \[[E{{{}^\circ }_{A{{l}^{3+}}/Al}}=-1.66V,\,\,E{{{}^\circ }_{C{{u}^{2+}}/Cu}}=+0.34\,V,\] \[E{{{}^\circ }_{F{{e}^{2+}}/Fe}}=-0.44V,\,\,E{{{}^\circ }_{M{{g}^{2+}}/Mg}}=-2.36V,\]and \[E{{{}^\circ }_{Z{{n}^{2+}}/Zn}}=-0.76V\]]
  A)
  \[Cu,\text{ }Fe,\text{ }Zn,\text{ }Al,\text{ }Mg\]
  done clear
  B)
  \[Fe,\text{ }Zn,\text{ }Cu,\text{ }Al,\text{ }Mg\]
  done clear
  C)
  \[Mg,Cu,Fe,Zn,Al\]    
  done clear
  D)
  \[Mg,\text{ }Al,\text{ }Zn,\text{ }Fe,\text{ }Cu\]
  done clear
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• question_answer38)
  Corrosion of iron is essentially an electrochemical phenomenon where the cell reactions are
  A)
  \[Fe\]is oxidised to \[F{{e}^{2+}}\] and dissolved oxygen in water is reduced to \[^{-}OH\]
  done clear
  B)
  \[Fe\]is oxidised to \[F{{e}^{3+}}\] and \[{{H}_{2}}O\] is reduced to \[O_{2}^{2-}\]
  done clear
  C)
  \[Fe\]is oxidised to \[F{{e}^{2+}}\] and \[{{H}_{2}}O\] is reduced to \[O_{2}^{-}\]
  done clear
  D)
  \[Fe\]is oxidised to \[F{{e}^{2+}}\] and \[{{H}_{2}}O\] is reduced to \[{{O}_{2}}\]
  done clear
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• question_answer39)
  Keto-enol tautomerism is observed in:
  A)
  \[{{H}_{5}}{{C}_{6}}-\overset{O}{\mathop{\overset{||}{\mathop{C}}\,}}\,-C{{H}_{2}}-\overset{O}{\mathop{\overset{||}{\mathop{C}}\,}}\,-{{C}_{6}}{{H}_{5}}\]
  done clear
  B)
  \[{{H}_{5}}{{C}_{6}}-\overset{O}{\mathop{\overset{||}{\mathop{C}}\,}}\,-C{{H}_{3}}\]
  done clear
  C)
  \[{{H}_{5}}{{C}_{6}}-\overset{O}{\mathop{\overset{||}{\mathop{C}}\,}}\,-H\]
  done clear
  D)
  Both [a] and [b]
  done clear
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• question_answer40)
  Blackened oil painting can be restored into original form by the action of                                          
  A)
  Chlorine
  done clear
  B)
         \[Ba{{O}_{2}}\]
  done clear
  C)
  \[{{H}_{2}}{{O}_{2}}\]
  done clear
  D)
         \[Mn{{O}_{2}}\]
  done clear
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• question_answer41)
  An organic amino compound reacts with aqueous nitrous acid at low temperature to produce an oily nitrosoamine. The compound is                               
  A)
  \[C{{H}_{3}}N{{H}_{2}}\]
  done clear
  B)
  \[C{{H}_{3}}C{{H}_{2}}N{{H}_{2}}\]
  done clear
  C)
  \[C{{H}_{3}}C{{H}_{2}}NHC{{H}_{2}}C{{H}_{3}}\]
  done clear
  D)
  \[{{(C{{H}_{3}}C{{H}_{2}})}_{3}}N\]
  done clear
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• question_answer42)
  Which one of the following compounds is a peroxide?
  A)
  \[K{{O}_{2}}\]
  done clear
  B)
         \[Ba{{O}_{2}}\]
  done clear
  C)
  \[Mn{{O}_{2}}\]
  done clear
  D)
         \[N{{O}_{2}}\]
  done clear
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• question_answer43)
  The rms velocity of hydrogen is \[\sqrt{7}\] times the rms velocity of nitrogen. If T is the temperature of the gas, then    
  A)
  \[T({{H}_{2}})=T({{N}_{2}})\]
  done clear
  B)
         \[T({{H}_{2}})>T({{N}_{2}})\]
  done clear
  C)
  \[T({{H}_{2}})<T({{N}_{2}})\]
  done clear
  D)
         \[T({{H}_{2}})=\sqrt{7}\,T({{N}_{2}})\]
  done clear
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• question_answer44)
  \[C{{H}_{3}}-Mg-Br\]is an organometallic compound due to
  A)
  \[Mg-Br\] bond
  done clear
  B)
         \[C-Mg\]bond
  done clear
  C)
  \[C-Br\]bond
  done clear
  D)
        \[C-H\]bond.
  done clear
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• question_answer45)
  Which of the following is most powerful to coagulate the negative colloid?
  A)
  \[ZnS{{O}_{4}}\]
  done clear
  B)
         \[N{{a}_{3}}P{{O}_{4}}\]
  done clear
  C)
  \[AlC{{l}_{3}}\]
  done clear
  D)
         \[{{K}_{4}}[Fe{{(CN)}_{6}}]\]
  done clear
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• question_answer46)
  What is the sum of coordination number and oxidation number of the metal M in the complex \[[M{{(en)}_{2}}({{C}_{2}}{{O}_{4}})]Cl\]. (where en is ethylenediamine)?
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• question_answer47)
  How many iodides are produced in more than \[5%\]yield?
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• question_answer48)
  A conductivity cell has been calibrated with a \[0.01\text{ }M\text{ }1:1\] electrolyte solution (specific conductance, \[k=1.25\times {{10}^{-3}}S\,c{{m}^{-1}}\]) in the cell and the measured resistance was 800 ohms at\[25{}^\circ C\]. What is the value of constant in \[c{{m}^{-1}}\]?
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• question_answer49)
  \[2\text{ }g\]of metal in \[{{H}_{2}}S{{O}_{4}}\]gives \[4.51\text{ }g\]of the metal sulphate. The specific heat of metal is\[0.057\text{ }cal/g\]. Calculate the atomic weight of metal.
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• question_answer50)
  In acidic medium, \[{{H}_{2}}{{O}_{2}}\]changes \[C{{r}_{2}}O_{7}^{-2}\] to \[Cr{{O}_{5}}\] which has two \[(-O-O)\] bonds. What is the oxidation state of \[Cr\]in \[Cr{{O}_{5}}\]?
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• question_answer51)
  The total number of matrices formed with the help of 6 different numbers are-
  A)
  6!              
  done clear
  B)
                     3(6)!
  done clear
  C)
  2(6)!                 
  done clear
  D)
         4(6)!
  done clear
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• question_answer52)
  If an integer p is chosen at random in the interval\[0\le p\le 5\], then the probability that the roots of the equation \[{{x}^{2}}+px+\frac{p}{4}+\frac{1}{2}=0\] are real is-
  A)
  \[\frac{4}{5}\]              
  done clear
  B)
         \[\frac{2}{3}\]
  done clear
  C)
  \[\frac{3}{5}\]              
  done clear
  D)
         None of these
  done clear
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• question_answer53)
  If p and q are two statements, then the truth values of compound statement \[p\leftrightarrow \left( p\wedge -q \right)\] is-
  A)
  F, F, T, T      
  done clear
  B)
         T, T, F, F
  done clear
  C)
  F, T, T, T   
  done clear
  D)
         None
  done clear
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• question_answer54)
  \[\sum\limits_{r=0}^{10}{r{{.}^{10}}{{C}_{r}}{{.3}^{r}}.{{(-2)}^{10-r}}}\] is-
  A)
  20                    
  done clear
  B)
         10
  done clear
  C)
  30     
  done clear
  D)
         300
  done clear
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• question_answer55)
  A candidate has to reach the examination centre in time. Probability of him going by bus or scooter or by other means of transport are \[\frac{3}{10},\frac{1}{10},\frac{3}{5}\] respectively. The probability that he will be late is \[\frac{1}{4}\] and \[\frac{1}{3}\] respectively, if he travels by bus or scooter. But he reaches in time if the uses any mode of transport. He reached late at the centre. The probability that he travelled by bus is -
  A)
  \[\frac{1}{9}\]              
  done clear
  B)
         \[\frac{2}{13}\]
  done clear
  C)
  \[\frac{9}{13}\] 
  done clear
  D)
         None of these
  done clear
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• question_answer56)
  If the slope of chord PQ of \[f\left( x \right)={{x}^{3}}-2{{x}^{-3}}+10\] is 9, then relation between the AMand GM(G) of abscissae of points P and Q is-
  A)
  \[9{{G}^{2}}-\left( 7{{A}^{2}}-{{G}^{2}} \right)\left( {{G}^{6}}+2 \right)=0\]
  done clear
  B)
  \[6{{G}^{6}}-\left( 7{{A}^{2}}-{{G}^{2}} \right)\left( {{G}^{6}}+2 \right)=0\]
  done clear
  C)
  \[9{{G}^{6}}-\left( 4{{A}^{2}}-{{G}^{2}} \right)\left( {{G}^{6}}+2 \right)=0\]
  done clear
  D)
  \[6{{G}^{6}}-(4{{A}^{2}}-{{G}^{2}})\left( {{G}^{6}}+2 \right)=0\]
  done clear
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• question_answer57)
  Dual of \[\left( x'\wedge y' \right)'=x\vee y\] is-
  A)
  \[\left( x'\wedge y' \right)=x\wedge y\]  
  done clear
  B)
         \[\left( x'\vee y' \right)'=x\wedge y\]
  done clear
  C)
  \[\left( x'\vee y' \right)'=xy\]     
  done clear
  D)
         None of these
  done clear
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• question_answer58)
  The locus of the centre of a circle which passes through the point (0, 0) and cuts off a length 2b from the line x = c is-
  A)
  \[{{y}^{2}}+2cx={{b}^{2}}+{{c}^{2}}\]
  done clear
  B)
         \[{{x}^{2}}+cx={{b}^{2}}+{{c}^{2}}\]
  done clear
  C)
  \[{{y}^{2}}+2cy={{b}^{2}}+{{c}^{2}}\]  
  done clear
  D)
  None of these
  done clear
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• question_answer59)
  Circles drawn on the diameter as focal distance of any point lying on the parabola \[{{x}^{2}}-4x+6y+10=0\] will touch a fixed line whose equation is-
  A)
  \[y=2\]             
  done clear
  B)
         \[y=-1\]
  done clear
  C)
  \[x+y=2\]       
  done clear
  D)
         \[x-y=2\]
  done clear
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• question_answer60)
  The distance of a point P, on the ellipse \[{{x}^{2}}+3{{y}^{2}}=6\] lying in the first quadrant, from the centre of the ellipse is 2 units. The eccentric angle of the point P is-
  A)
  \[\frac{\pi }{3}\]            
  done clear
  B)
         \[\frac{\pi }{4}\]
  done clear
  C)
  \[\frac{\pi }{6}\]            
  done clear
  D)
         None of these
  done clear
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• question_answer61)
  Total number of integral values of 'a' so that \[{{x}^{2}}-\left( a+1 \right)x+a-1=0\] has integral roots, is equal to:
  A)
  2                     
  done clear
  B)
         1
  done clear
  C)
  4                     
  done clear
  D)
         None of these
  done clear
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• question_answer62)
  If a, b, c, d are such unequal real numbers that \[({{a}^{2}}+{{b}^{2}}+{{c}^{2}}){{p}^{2}}-2(ab+bc+cd)p+({{b}^{2}}+{{c}^{2}}+{{d}^{2}})\le 0,\]  then a, b, c, d are in-
  A)
  A.P.              
  done clear
  B)
         G.P.
  done clear
  C)
  H.P.              
  done clear
  D)
         None of these
  done clear
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• question_answer63)
  If [x] denotes the greatest integer \[\le x\], then the value of \[\int\limits_{4}^{10}{\frac{[{{x}^{2}}]}{[{{x}^{2}}-28x+196]+[{{x}^{2}}]}dx}\] is-
  A)
  3          
  done clear
  B)
         2
  done clear
  C)
  1                     
  done clear
  D)
         0
  done clear
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• question_answer64)
  The area of the portion of the circle \[{{x}^{2}}+{{y}^{2}}=1,\] which lies inside the parabola\[{{y}^{2}}=1-x\], is-
  A)
  \[\frac{\pi }{2}-\frac{2}{3}\]      
  done clear
  B)
         \[\frac{\pi }{2}+\frac{2}{3}\]
  done clear
  C)
  \[\frac{\pi }{2}+\frac{4}{3}\]    
  done clear
  D)
         \[\frac{\pi }{2}-\frac{4}{3}\]
  done clear
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• question_answer65)
  Solution of the differential equation \[x\,dy-y\,dx=0\] represents-
  A)
  parabola whose vertex is at origin
  done clear
  B)
  Circle whose centre is at origin
  done clear
  C)
  A rectangular hyperbola
  done clear
  D)
  Straight line passing through origin
  done clear
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• question_answer66)
  \[K=\underset{x\to \infty }{\mathop{\lim }}\,\left[ \frac{\sum\limits_{K=1}^{1000}{{{(x+k)}^{m}}}}{{{X}^{m}}+{{10}^{1000}}} \right](m>101)\]is-
  A)
  10                    
  done clear
  B)
         \[{{10}^{2}}\]
  done clear
  C)
  \[{{10}^{3}}\]             
  done clear
  D)
         \[{{10}^{4}}\]
  done clear
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• question_answer67)
  If roots of \[a{{x}^{2}}+bx+c=0\] where \[a\in {{R}^{+}}\], are two positive consecutive even integers, then
  A)
  \[|b|\le 6a\]          
  done clear
  B)
         \[\left| b \right|\ge 6a\]
  done clear
  C)
  \[\left| b \right|=6a\]          
  done clear
  D)
         None of these
  done clear
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• question_answer68)
  If\[co{{s}^{-1}}\left( cosx \right)=\sqrt{1+sin2x}\forall \,x\in (0,2\pi )\], then no. of solution =
  A)
  2                     
  done clear
  B)
         4     
  done clear
  C)
  3                     
  done clear
  D)
         5
  done clear
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• question_answer69)
  For what value(s) of a, will the two points (1, a, 1) and \[(-3,0,a)\] lie on opposite sides of the plane\[3x+4y-12x+13=0\]?
  A)
  \[a<-1\,or\,a>1/3\]
  done clear
  B)
         \[a=0\]only
  done clear
  C)
  0 < a < 1         
  done clear
  D)
         \[-1<a<1\]
  done clear
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• question_answer70)
  The number of integer values of x for which the inequality \[lo{{g}_{10}}\left( \frac{2x-2007}{x+1} \right)~\ge 0\], is true, is
  A)
  1004            
  done clear
  B)
         1005
  done clear
  C)
  2007                
  done clear
  D)
         infinite
  done clear
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• question_answer71)
  In a throw of a dice find the probability of getting one in even number of throw.
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• question_answer72)
  A set of 7 observations has mean 10 and another set of 3 observations has mean 5. Find the mean of combined set.
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• question_answer73)
  Find the number of solution of the equation \[3\tan x+{{x}^{3}}=2\] in\[\left( 0,\frac{\pi }{4} \right)\].
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• question_answer74)
  If \[{{x}_{n}}=cos\left( \frac{\pi }{{{2}^{n}}} \right)+i\,sin\left( \frac{\pi }{{{2}^{n}}} \right)\], then \[{{X}_{1}}{{X}_{2}}{{X}_{3}}....\] is equal to
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• question_answer75)
  If f (x) is a polynomial function such that\[f\left( x \right).\text{ }f\left( 1/x \right)=f\left( x \right)+f\left( 1/x \right)\] and \[f\left( 2 \right)=9\] then f(4) is equal to-
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