JEE Main & Advanced Sample Paper

done JEE Main Sample Paper-1 Total Questions - 105   

• question_answer1)
  An object is tossed vertically into the air with an initial velocity of 8 m/s. Using the sign convention up as positive, how does the vertical component of the acceleration ay of the object (after leaving the hand) vary during the flight of object?
  A)
  On the way up \[{{a}_{y}}>0,\]on the way down\[{{a}_{y}}>0\]
  done clear
  B)
   On the way up \[{{a}_{y}}>0,\] on the way down\[{{a}_{y}}<0,\]
  done clear
  C)
   On the way up \[{{a}_{y}}<0,\] on the way down\[{{a}_{y}}>0\]
  done clear
  D)
   On the way up \[{{a}_{y}}<0,\] on the way down\[{{a}_{y}}<0\]
  done clear
  View Answer play_arrow

• question_answer2)
  Which equation is dimensionally incorrect, where symbol represent their usual-meaning?
  A)
   \[I=p+mgt\]                     
  done clear
  B)
   \[\tau =(m{{v}^{2}}/2)+Fr\]
  done clear
  C)
   \[mvr=I\omega +Fr\]
  done clear
  D)
   \[\frac{L}{R}=RC+t\frac{r}{(1/\sqrt{{{\mu }_{0}}{{\in }_{0}}})}\]
  done clear
  View Answer play_arrow

• question_answer3)
  Why the capacitance of a capacitor is not affected by surrounding conducting bodies?
  A)
   From the formula C = q/V, if q changes, V changes and hence, C remains same
  done clear
  B)
   The plates of the capacitor are arranged in such a way that the field created by charges accumulated on the plate is concentrated almost completely inside the capacitor
  done clear
  C)
   Capacitance changes due to induction phenomenon                     
  done clear
  D)
   Both a and b
  done clear
  View Answer play_arrow

• question_answer4)
  The source voltage is 9V and the source resistance is \[1k\Omega \] The current through the diode is
  A)
   3.8 mA                                
  done clear
  B)
   4.2 mA
  done clear
  C)
   0.833mA                            
  done clear
  D)
   8.3mA
  done clear
  View Answer play_arrow

• question_answer5)
  The velocity versus time graph for two particles A and B are plotted as shown in figure. The relative velocity of A with respect to B is
  A)
   positive and continuously increasing.
  done clear
  B)
   negative and continuously increasing
  done clear
  C)
   positive and continuously decreasing
  done clear
  D)
   negative and continuously decreasing
  done clear
  View Answer play_arrow

• question_answer6)
  A ray is incident at an angle of \[20{}^\circ \] to a plane mirror as shown in figure. If mirror is rotated by \[10{}^\circ \] in anticlockwise direction and incident ray is rotated by \[10{}^\circ \] in clockwise direction then through what angle the reflected ray will turn?
  A)
   \[30{}^\circ \], clockwise             
  done clear
  B)
  \[10{}^\circ \], anticlockwise                     
  done clear
  C)
  \[30{}^\circ \], anticlockwise    
  done clear
  D)
   \[10{}^\circ \], clockwise
  done clear
  View Answer play_arrow

• question_answer7)
  Two spherical vessels of equal volume are connected by a narrow tube. The apparatus contains an ideal gas at 1 atm and 300 K. Now, if one vessel is immersed in a bath of constant temperature 600K and other in a bath of constant temperature 300K, then common pressure will be
  A)
   1 atm                                   
  done clear
  B)
   4/5 atm
  done clear
  C)
   4/3 atm                              
  done clear
  D)
   3/2 atm
  done clear
  View Answer play_arrow

• question_answer8)
  A compass needle is placed in the gap of a parallel plate capacitor. The capacitor is connected to a battery through a resistance. The compass needle
  A)
   does not deflect
  done clear
  B)
   deflects for a very short time and then comes back to the original position
  done clear
  C)
   deflects and remains deflected as long as the battery is connected
  done clear
  D)
   deflects and gradually comes to the original position in a time which is large compared to the time constant
  done clear
  View Answer play_arrow

• question_answer9)
  A block moves up a \[30{}^\circ \] incline under the action of certain forces, three of which are shown in figure. \[\overrightarrow{{{F}_{1}}}\]is horizontal and of magnitude 40 N. \[\overrightarrow{{{F}_{2}}}\]is normal to the .plane and of magnitude 20 N. \[\overrightarrow{{{F}_{3}}}\]is parallel to the plane and of magnitude 30 N. Determine the work done by each force as the block (and point of application of each force) moves 80 cm up the incline.
  A)
   28 J, 34.6 J, 24 J
  done clear
  B)
   28 J, 0 J, 24 J
  done clear
  C)
   24 J, 44 J, 15 J   
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer10)
  The minimum kinetic energy needed to project a body of mass m from the earth's surface to infinity is [g is acceleration due to gravity at earth's surface]
  A)
   \[\frac{1}{4}\]mgR                         
  done clear
  B)
   \[\frac{1}{2}\]mgR
  done clear
  C)
   mgR                                     
  done clear
  D)
   2 mgR
  done clear
  View Answer play_arrow

• question_answer11)
  A player hits a football at some angle and runs on the ground to trap it before it hits the ground. In the above case
  A)
   displacement of football > displacement of player
  done clear
  B)
   displacement of football < displacement of player
  done clear
  C)
   displacement of football < displacement of player
  done clear
  D)
   Can't say anything
  done clear
  View Answer play_arrow

• question_answer12)
  Mark the correct option.
  A)
   Frequency of a wave is the characteristic property of source and it changes when medium changes
  done clear
  B)
    Frequency of wave is the characteristic property of source and its value does not changes when medium changes
  done clear
  C)
   Wavelength and velocity of light remain same when medium changes
  done clear
  D)
   Wavelength is the property of medium
  done clear
  View Answer play_arrow

• question_answer13)
  Electric conduction in discharge tube takes place due to
  A)
   positive ions and negative ions
  done clear
  B)
   positive ions and electrons
  done clear
  C)
   positive ions, negative ions and electrons
  done clear
  D)
   negative ions and electrons
  done clear
  View Answer play_arrow

• question_answer14)
  A block is moving with constant velocity on a horizontal surface, then which one is incorrect
  A)
   some force must act on the body
  done clear
  B)
   some forces may act on the body
  done clear
  C)
   net force on the body must be zero
  done clear
  D)
   the body is in equilibrium
  done clear
  View Answer play_arrow

• question_answer15)
  Acceleration of each block is given as \[g/5\sqrt{2}\]. Find the magnitude and direction of force exerted by string on pulley.
  A)
   6 mg/5, downward direction
  done clear
  B)
   6 mg/5, upward direction
  done clear
  C)
   6 mg/5, horizontal direction
  done clear
  D)
   Not possible to have acceleration
  done clear
  View Answer play_arrow

• question_answer16)
  Write down the expression for capacitance of a spherical capacitor whose conductors radii are \[{{R}_{1}}\] and \[{{R}_{2}}({{R}_{1}}>{{R}_{2}}),\]when inner sphere is grounded
  A)
   \[\frac{4\pi {{\varepsilon }_{0}}{{R}_{1}}{{R}_{2}}}{{{R}_{2}}-{{R}_{1}}}\]                              
  done clear
  B)
   \[\frac{4\pi {{\varepsilon }_{0}}R_{1}^{2}}{{{R}_{2}}-{{R}_{1}}}\]
  done clear
  C)
   \[\frac{4\pi {{\varepsilon }_{0}}R_{2}^{2}}{{{R}_{2}}-{{R}_{1}}}\]                              
  done clear
  D)
   \[\frac{4\pi {{\varepsilon }_{0}}R_{1}^{2}{{R}_{2}}}{{{({{R}_{2}}-{{R}_{1}})}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer17)
  Find the magnetic field at point O due to    semi-infinite wire shown in figure.
  A)
   \[\frac{\sqrt{2}{{\mu }_{0}}I}{(4\pi R)}\]out of plane of paper
  done clear
  B)
   \[\frac{\sqrt{2}{{\mu }_{0}}I}{4\pi R}\]into the plane of paper
  done clear
  C)
   \[\frac{(\sqrt{2}-1){{\mu }_{0}}I}{4\pi R}\]out of plane of paper
  done clear
  D)
   \[\frac{(\sqrt{2}-1){{\mu }_{0}}I}{4\pi R}\]into the plane of paper
  done clear
  View Answer play_arrow

• question_answer18)
  A particle is moving along X-axis, under the action of a variable force which is providing position varying acceleration described by the equation, d = 3x - 4. At t = 0, \[x=\frac{4}{3}m\]and v = 0, Find the velocity and position of particle at t = 5 s.
  A)
   0 m/s, 0 m         
  done clear
  B)
   \[0,-\frac{8}{3}m\]
  done clear
  C)
   0 m/s, 4/3m      
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer19)
  Mark the correct one.
  A)
  Work function is defined as the minimum energy needed to make the electron free from the atom
  done clear
  B)
   Photoelectric effect can take place if light has been incident on a free electron
  done clear
  C)
   Photon works on the principle of all or nothing while energy transfer
  done clear
  D)
   All of the above
  done clear
  View Answer play_arrow

• question_answer20)
  Two circular loops of equal radii are placed coaxially at some separation. The first is cut and a battery is inserted in between to drive a current in it. The current changes slightly because of the variation in resistance with temperature. During the period, the two loops:
  A)
   attract each other
  done clear
  B)
   repel each other
  done clear
  C)
   do not exert any force on each other
  done clear
  D)
   attract or repel each other depending on the sense of the current
  done clear
  View Answer play_arrow

• question_answer21)
  Mark the correct options.
  A)
   For positive charge carrier current flows from higher potential to lower potential. While for negative charge carrier, it flows from lower to higher potential
  done clear
  B)
   For both positive and negative charge carriers current flows from higher to lower potential                         
  done clear
  C)
   For both positive and negative charge carriers current flows from lower to higher potential
  done clear
  D)
   For negative charge carriers current flows from higher to lower potential while for positive charge carrier it flows from lower to higher potential
  done clear
  View Answer play_arrow

• question_answer22)
  A\[\alpha -\] particle passes through a potential difference of \[2\times {{10}^{6}}V\] and then it becomes incident on a silver foil. The charge number of silver is 47. The energy of incident particles will be: (in joule)
  A)
   \[5\times {{10}^{-12}}\]                              
  done clear
  B)
   \[6.4\times {{10}^{-13}}\]
  done clear
  C)
   \[5.8\times {{10}^{-14}}\]                           
  done clear
  D)
   \[9.1\times {{10}^{-15}}\]
  done clear
  View Answer play_arrow

• question_answer23)
  The deflection in moving coil galvanometer falls from 80 division to 40 division when a shunt of \[20\Omega \]is connected across it. Determine the galvanometer resistance.
  A)
   \[40\,\Omega \]                             
  done clear
  B)
   \[30\,\Omega \]
  done clear
  C)
   \[20\,\Omega \]                                             
  done clear
  D)
   \[15\,\Omega \]
  done clear
  View Answer play_arrow

• question_answer24)
  A barometer reads 74 cm on a steel scale; the room temperature is \[25{}^\circ C\]. The scale is correctly graduated for \[0{}^\circ C\]. Find the true atmospheric pressure, \[({{\alpha }_{steel}}=1.2\times {{10}^{-5}}{{/}^{o}}C,\]\[{{\gamma }_{Hg}}=1.8\times {{10}^{-4}}{{/}^{o}}C)\]
  A)
   74.0042 cm        
  done clear
  B)
   76 cm
  done clear
  C)
   74.878 cm          
  done clear
  D)
   74.0222 cm
  done clear
  View Answer play_arrow

• question_answer25)
  Mark the correct option.
  A)
   Behaviour of moving charge along the circle is equivalent to current carrying circular coil for instantaneous value as well as for average value of magnetic field on its axis
  done clear
  B)
   If two identical charge particles are moving symmetrically along a circle then its behaviour with respect to magnetic field on the axis is equivalent to current carrying coil for both average and instantaneous value
  done clear
  C)
   For instantaneous value of magnetic field on the axis, the charge moving along a circle is equivalent to current carrying circular coil
  done clear
  D)
   Both b and c
  done clear
  View Answer play_arrow

• question_answer26)
  A particle has been projected from the top of tower as shown in figure. Find the time taken by the particle to reach the ground. Take \[g=10\,\,m/{{s}^{2}}\]
  A)
   8s                                          
  done clear
  B)
   6.28 s
  done clear
  C)
   5.6s                                      
  done clear
  D)
   7.07s
  done clear
  View Answer play_arrow

• question_answer27)
  A block of mass 10 kg is suspended through two light spring balances as  shown in figure    
  A)
  both the scales will read 10 kg                 
  done clear
  B)
   both the scales will read 5 kg                    
  done clear
  C)
   the upper scale will read 10 kg and the lower zero
  done clear
  D)
   the readings may be anything but their sum will be 10 kg
  done clear
  View Answer play_arrow

• question_answer28)
  A tuning fork of frequency 512 Hz is vibrated with a sonometer wire and 6 beats/s are heard. The beat frequency reduces, if the tension in the string is slightly increased. The original frequency of vibration of the string is
  A)
   506 Hz                                 
  done clear
  B)
   512 Hz
  done clear
  C)
   518 Hz                                 
  done clear
  D)
   524 Hz
  done clear
  View Answer play_arrow

• question_answer29)
  Direction: Question No. 29 are based on the following paragraph. A wire of length L, mass m and carrying a current is suspended from point O as shown. An infinitely long wire carrying the same current I is at a distance L below the lower end of the wire. Given, I = 2A, L= 1m and m = 0.1 kg (ln 2 = 0.693) What is angular acceleration of the wire just after it is released from the position shown?
  A)
   \[6.2\times {{10}^{-8}}\frac{\text{rad}}{{{\text{s}}^{\text{2}}}}\]            
  done clear
  B)
   \[2.1\times {{10}^{-4}}\frac{\text{rad}}{{{\text{s}}^{\text{2}}}}\]
  done clear
  C)
   \[4.5\times {{10}^{-5}}\frac{\text{rad}}{{{\text{s}}^{\text{2}}}}\]                            
  done clear
  D)
   \[9.3\times {{10}^{-6}}\frac{\text{rad}}{{{\text{s}}^{\text{2}}}}\]
  done clear
  View Answer play_arrow

• question_answer30)
  Direction: Question No. 30 are based on the following paragraph. A wire of length L, mass m and carrying a current is suspended from point O as shown. An infinitely long wire carrying the same current I is at a distance L below the lower end of the wire. Given, I = 2A, L= 1m and m = 0.1 kg (ln 2 = 0.693) We want to keep the suspended wire stationary by placing a third infinitely long wire carrying an upward current. Then this wire should be placed.
  A)
   to the left of suspended wire
  done clear
  B)
   to the right of suspended wire
  done clear
  C)
   We can't of suspended wire stationary be placing a third wire to the right or to the left of it
  done clear
  D)
   we can keep it either to the right or to the left. It will depend on the magnitude of the current in the third wire
  done clear
  View Answer play_arrow

• question_answer31)
  Direction: Question No. 31 are based on the following paragraph. A wire of length L, mass m and carrying a current is suspended from point O as shown. An infinitely long wire carrying the same current I is at a distance L below the lower end of the wire. Given, I = 2A, L= 1m and m = 0.1 kg (ln 2 = 0.693) At what distance r from the suspended wire, the new wire (having the same current) should be placed to keep it stationary.
  A)
   2.9 m                                   
  done clear
  B)
   1.9 m
  done clear
  C)
   1.3 m                                   
  done clear
  D)
   2.4 m
  done clear
  View Answer play_arrow

• question_answer32)
  The length of a cube is measured with the help of a vernier callipers. The observations are shown in figure. The length of the cube with these observation is
  A)
   5.06cm                                
  done clear
  B)
   5.6cm
  done clear
  C)
   5.06mm                              
  done clear
  D)
   5.60mm
  done clear
  View Answer play_arrow

• question_answer33)
  If \[{{l}_{1}}\]and \[{{l}_{2}}\] be the length of the air column for the first and the second resonance respectively with a tuning fork of frequency v, then the velocity of sound is given by
  A)
   \[v=v({{l}_{2}}-{{l}_{1}})\]          
  done clear
  B)
   \[v=2v({{l}_{2}}-{{l}_{1}})\]
  done clear
  C)
   \[v=\frac{2v}{{{l}_{2}}-{{l}_{1}}}\]                           
  done clear
  D)
   \[v=\frac{v}{2({{l}_{2}}-{{l}_{1}})}\]
  done clear
  View Answer play_arrow

• question_answer34)
  Directions: Question No. 34 are Assertion - Reaction type each of these contains two statements: Statement I (Assertion), Statement II (Reason) Each of these questions also has four alternative choices, only one of which is correct. You have to select the correct choices from the codes a, b, c and d given below:

  Statement I: The isothermal curves intersect each other at a certain point.

  Statement II: The isothermal changes takes place slowly, so the eso thermal curves have very little slope.

  A)
  Statement I is true; Statement II is true; Statement II is not a correct explanation for Statement I.
  done clear
  B)
   Statement I is true; Statement II is false.
  done clear
  C)
   Statement I is false; Statement II is true.
  done clear
  D)
   Statement I is true; Statement II is true; Statement II is not a correct explanation for Statement I.
  done clear
  View Answer play_arrow

• question_answer35)
  Directions: Question No. 35 are Assertion - Reaction type each of these contains two statements: Statement I (Assertion), Statement II (Reason) Each of these questions also has four alternative choices, only one of which is correct. You have to select the correct choices from the codes a, b, c and d given below:

  Statement I: Balmer series lies in the visible region of electromagnetic spectrum.

  Statement II: \[\frac{1}{\lambda }=R\left( \frac{1}{{{2}^{2}}}-\frac{1}{{{n}^{2}}} \right).\]where n = 3,4,5.

  A)
  Statement I is true; Statement II is true; Statement II is not a correct explanation for Statement I.
  done clear
  B)
   Statement I is true; Statement II is false.
  done clear
  C)
   Statement I is false; Statement II is true.
  done clear
  D)
   Statement I is true; Statement II is true; Statement II is not a correct explanation for Statement I.
  done clear
  View Answer play_arrow

• question_answer36)
  Hall and Heroult's process is used for
  A)
   extraction of Al
  done clear
  B)
   purification of \[A{{l}_{2}}{{O}_{3}}\]
  done clear
  C)
   refining of Al
  done clear
  D)
  None of the above
  done clear
  View Answer play_arrow

• question_answer37)
  Which is not true about \[O{{F}_{2}}\]and \[C{{l}_{2}}O\]?
  A)
   Both are sp3 hybridized
  done clear
  B)
   Bond angle in \[O{{F}_{2}}\]is less than \[109{}^\circ 28'\]
  done clear
  C)
   Bond angle in \[C{{l}_{2}}O\]is greater than \[O{{F}_{2}}\]
  done clear
  D)
   Bond angle in both cases are \[109{}^\circ 28'\]
  done clear
  View Answer play_arrow

• question_answer38)
  Which of the following could be added to water to make 0.10 M solution of\[\text{MH}_{\text{4}}^{\text{+}}\]?
  A)
   \[N{{H}_{3}}\]                                 
  done clear
  B)
  \[N{{H}_{4}}Cl\]
  done clear
  C)
   \[KN{{H}_{4}}\]                               
  done clear
  D)
   None m these
  done clear
  View Answer play_arrow

• question_answer39)
  The number of electrons lost during electrolysis of 2g\[\overset{\Theta }{\mathop{\text{Cl}}}\,\]ion
  A)
   \[3.39\times {{10}^{22}}\]                          
  done clear
  B)
   \[6.023\times {{10}^{23}}\]
  done clear
  C)
   \[1.20\times {{10}^{23}}\]                          
  done clear
  D)
   \[2.46\times {{10}^{23}}\]
  done clear
  View Answer play_arrow

• question_answer40)
  The substance used as an activator in froth floatation process is
  A)
   potassium ethyl xanthate
  done clear
  B)
   sodium cyanide
  done clear
  C)
   copper sulphate             
  done clear
  D)
   pine oil
  done clear
  View Answer play_arrow

• question_answer41)
  Carbon monoxide acts as a Lewis base because it has
  A)
   a double bond between C and O atoms
  done clear
  B)
   a triple bond between C and O atoms
  done clear
  C)
   a lone pair of electrons on the C atom
  done clear
  D)
   two lone pairs of electrons on the O atom
  done clear
  View Answer play_arrow

• question_answer42)
  The decreasing order of catenation of group 16 elements is
  A)
   O > S > Se >Te 
  done clear
  B)
   S > O > Se > Te
  done clear
  C)
   S > Se > O > Te
  done clear
  D)
   O > S >Te > Se
  done clear
  View Answer play_arrow

• question_answer43)
  Mark out the correct order of stability(decreasing order) for the following molecules
  A)
   I > II > III > IV    
  done clear
  B)
   I > II \[\approx \] III > IV
  done clear
  C)
   IV > III >\[\approx \] I                  
  done clear
  D)
   III > I \[\approx \]II > IV
  done clear
  View Answer play_arrow

• question_answer44)
  Increasing value of magnetic moments of \[I:Ni{{(CO)}_{4}},\]                        \[II:{{[Ti{{({{H}_{2}}O)}_{6}}]}^{2+}}\] \[III:{{[V{{({{H}_{2}}O)}_{6}}]}^{2+}}\]    \[IV:{{[Fe{{({{H}_{2}}O)}_{6}}]}^{2+}}\]is
  A)
   I < II < III < IV                    
  done clear
  B)
   IV < III < II < I
  done clear
  C)
   II < III < I < IV    
  done clear
  D)
   II < I < III < IV
  done clear
  View Answer play_arrow

• question_answer45)
  \[A\xrightarrow[{}]{{{O}_{3}};Zn,C{{H}_{3}}COOH}2C{{H}_{3}}-\overset{\begin{smallmatrix}  \text{O} \\  \text{ }\!\!|\!\!\text{  }\!\!|\!\!\text{ } \end{smallmatrix}}{\mathop{\text{C}}}\,-C{{H}_{3}}+C{{O}_{2}}\]Original molecule' A' is
  A)
    
  done clear
  B)
  
  done clear
  C)
                                 
  done clear
  D)
  
  done clear
  View Answer play_arrow

• question_answer46)
  The dipeptide glycylalanine contains
  A)
   glycine as C-terminal residue
  done clear
  B)
   glycine as N-terminal residue
  done clear
  C)
   alanine as N-terminal residue
  done clear
  D)
   either a or b
  done clear
  View Answer play_arrow

• question_answer47)
  IUPAC name of the compound \[\text{C}{{\text{H}}_{\text{3}}}-\text{C}{{\text{H}}_{\text{2}}}-\overset{\begin{smallmatrix}  \text{C} \\  \text{ }\!\!|\!\!\text{  }\!\!|\!\!\text{ } \end{smallmatrix}}{\mathop{\text{C}}}\,{{\text{H}}_{\text{2}}}-\overset{\begin{smallmatrix}  \text{C} \\  \text{ }\!\!|\!\!\text{  }\!\!|\!\!\text{ } \end{smallmatrix}}{\mathop{\text{C}}}\,{{\text{H}}_{\text{2}}}-\text{C}{{\text{H}}_{\text{3}}}\]
  A)
   3-eAyl-2- methyl buta-1, 3-diene
  done clear
  B)
   2-ethyl-3-methyl buta- 1,3-diene
  done clear
  C)
   2,3-dimethylidene pentane
  done clear
  D)
   2-methyl-3-methylidenepent-l-ene
  done clear
  View Answer play_arrow

• question_answer48)
   ?X? is
  A)
   HCOOH                               
  done clear
  B)
   HCHO
  done clear
  C)
   \[C{{H}_{2}}{{I}_{2}}\]                  
  done clear
  D)
   \[C{{H}_{2}}=C{{H}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer49)
  In benzilic acid rearrangement
  A)
   benzaldehyde is converted into benzoin
  done clear
  B)
   benzoin is converted into benzilic acid
  done clear
  C)
   benzilic acid is converted into benzil
  done clear
  D)
   benzil is converted into benzilic acid
  done clear
  View Answer play_arrow

• question_answer50)
  Direction: Question No. 50 is assertion reason type. These question contains two statements Statement I (Assertion), Statement II (Reason). These question also has four alternative choices, only one of which is correct. You have to select the correct choices from the codes (a), (b), (c) and (d) given below:

  Statement I: 4 moles of \[KCl{{O}_{3}}\](50% pure) gave 3 moles of \[{{O}_{2}}\]on heating strongly and thus, yield is 100%.\[2KCl{{O}_{3}}\to 2KCl+3{{O}_{2}}\]

  Statement II: 3 moles of\[{{O}_{2}}\] are Obtained from 2 moles of\[KCl{{O}_{3}}\].

  A)
   Statement I is true; Statement II is true; Statement II is not a correct explanation for Statement I.
  done clear
  B)
   Statement I is true; Statement II is false.
  done clear
  C)
   Statement I is false; Statement II is true.
  done clear
  D)
   Statement I is true; Statement II is true; Statement II is not a correct explanation for Statement I.
  done clear
  View Answer play_arrow

• question_answer51)
  Direction: Question No. 51 is assertion reason type. These question contains two statements Statement I (Assertion), Statement II (Reason). These question also has four alternative choices, only one of which is correct. You have to select the correct choices from the codes (a), (b), (c) and (d) given below:

  Statement I: Detection of chlorine in 2, 4, 6 -trinitrochlorobenzene can be done directly by addition of aq. \[AgN{{O}_{3}}\]solution.

  Statement II: \[C-Cl\] bond is weakened by electron withdrawing - \[N{{O}_{2}}\] group.

   
  A)
   Statement I is true; Statement II is true; Statement II is not a correct explanation for Statement I.
  done clear
  B)
   Statement I is true; Statement II is false.
  done clear
  C)
   Statement I is false; Statement II is true.
  done clear
  D)
   Statement I is true; Statement II is true; Statement II is not a correct explanation for Statement I.
  done clear
  View Answer play_arrow

• question_answer52)
  The amount of work done, when one mole of an ideal gas contained in a bulb of 10 L capacity at 1 atm is allowed to expand into an evacuated container of 100 L capacity, is
  A)
   1.013 kJ                              
  done clear
  B)
   101.3 kJ
  done clear
  C)
   0                                            
  done clear
  D)
   10 kJ
  done clear
  View Answer play_arrow

• question_answer53)

  Gas	CO	CH4	HCl	SO2
  Critical temperatur\[{{\text{T}}_{\text{c}}}\text{(K)}\]	134	190	324	430

  In the context of given values of critical temperature, the decreasing order of adsorption of various gases at charcoal is
  A)
  \[S{{O}_{2}}>HCl>C{{H}_{4}}>CO\]
  done clear
  B)
  \[CO>C{{H}_{4}}>HCl>S{{O}_{2}}\]
  done clear
  C)
  \[HCl>S{{O}_{2}}>CO>C{{H}_{4}}\]
  done clear
  D)
  \[C{{H}_{4}}>CO>S{{O}_{2}}>HCl\]
  done clear
  View Answer play_arrow

• question_answer54)
  Calculate the mole fraction of toluene in the vapour phase which is in equilibrium with asolution of benzene and toluene having a mole fraction of toluene 0.500. The vapour pressure of pure benzene is 119 Torr, that of toluene is37.0 Torr at the same temperature.
  A)
   0.237                                   
  done clear
  B)
   0.76
  done clear
  C)
   0.50                                      
  done clear
  D)
   0.75
  done clear
  View Answer play_arrow

• question_answer55)
  The only cations present in a slightly acidic solution are \[F{{e}^{3+}},Z{{n}^{2+}}\]and \[C{{u}^{2+}}\]. The reagent that when added in excess to this solution would identify and separate \[F{{e}^{3+}}\] in one, step is
  A)
  \[2M\,HCl\]                       
  done clear
  B)
  \[6M\,N{{H}_{3}}\]
  done clear
  C)
  \[6M\,NaOH\]                  
  done clear
  D)
  \[{{H}_{2}}S\,gas\]
  done clear
  View Answer play_arrow

• question_answer56)
  The stability constants of the complexes formed by a metal ion \[({{M}^{2+}})\] with \[N{{H}_{3}},\]\[C{{N}^{-}},{{H}_{2}}O\]and en are of the order \[{{10}^{11}},{{10}^{27}},{{10}^{15}}\]and \[{{10}^{18}}\] respectively. Then
  A)
   en is the strongest ligand
  done clear
  B)
   \[\text{C}{{\text{N}}^{-}}\]is the strongest ligand
  done clear
  C)
   these values cannot predict the strength of the ligand
  done clear
  D)
   all ligands are equally strong
  done clear
  View Answer play_arrow

• question_answer57)
  A silvery white metal, lighter than water can be produced only by the electrolysis of its fused chloride with difficulty. The metal is used as coolant in nuclear reactors. The metal is
  A)
   K                                           
  done clear
  B)
   Mg
  done clear
  C)
   Ca                                         
  done clear
  D)
   Na
  done clear
  View Answer play_arrow

• question_answer58)
  In analogy to \[O_{2}^{+}{{[Pt{{F}_{6}}]}^{-}}\] a compound \[N_{2}^{+}{{[Pt{{F}_{6}}]}^{-}}\]will not be formed because
  A)
   the ionisation enthalpy of \[{{\text{N}}_{\text{2}}}\]gas is higher than that of \[{{\text{O}}_{\text{2}}}\] gas
  done clear
  B)
   the ionisation enthalpy of \[{{\text{N}}_{\text{2}}}\] gas is lower than that \[{{\text{O}}_{\text{2}}}\] gas
  done clear
  C)
   the ionisation enthalpy of\[{{\text{N}}_{\text{2}}}\] gas is higher than that of N atom
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer59)
  n-butyraldehyde can be synthesized from n-propyl magnesium bromide and
  A)
   ethyl orthoformate       
  done clear
  B)
   acetyl chloride
  done clear
  C)
   n-butyl formate              
  done clear
  D)
   formic acid
  done clear
  View Answer play_arrow

• question_answer60)
  Which of the following sequence of reaction is the best means to furnish the conversion\[RC{{H}_{2}}OH\xrightarrow[{}]{{}}RC{{H}_{2}}N{{H}_{2}}\]
  A)
  \[KMn{{O}_{4}};SOC{{l}_{2}}:N{{H}_{3}};OB{{r}^{-}}\]
  done clear
  B)
  \[PB{{r}_{3}}:NaCN;{{H}_{2}}/Ni\]
  done clear
  C)
   Collins reagent;\[N{{H}_{3}},{{H}_{2}}/Ni\]
  done clear
  D)
   All of the above
  done clear
  View Answer play_arrow

• question_answer61)
  The reaction of primary aliphatic amines with nitrous acid gives a quantitative yield of nitrogen gas and is the basis of the van Slyke determination of amino nitrogen. What volume of nitrogen gas at STP would be liberated from mole of proline?
  A)
   44.8 mL                               
  done clear
  B)
   73.1 mL
  done clear
  C)
   123.01 mL          
  done clear
  D)
   0
  done clear
  View Answer play_arrow

• question_answer62)
  Directions: Questions No. 62 are based on the following paragraph. When ammonium vanadate is heated with oxalic add solution, a compound Z is formed. A sample of Z was titrated with\[KMn{{O}_{4}}\] solution in hot acidic solution. The resulting liquid was reduced with \[S{{O}_{2}}\], the excess \[S{{O}_{2}}\]boiled off, and the liquid again titrated with \[KMn{{O}_{4}}\]. The ratio of the volumes of \[KMn{{O}_{4}}\] used in the two titrations was 5 : 1. \[KMn{{O}_{4}}\] oxidises all oxidation state of vanadium to Vanadium (+V) and \[S{{O}_{2}}\] reduces vanadium (+V) to vanadium (+IV). Read the above experiment and answer the following questions.                                      What is the oxidation state of vanadium in the compound Z?
  A)
   +2                                         
  done clear
  B)
   +1
  done clear
  C)
   0
  done clear
  D)
   -1
  done clear
  View Answer play_arrow

• question_answer63)
  Directions: Questions No. 63 are based on the following paragraph. When ammonium vanadate is heated with oxalic add solution, a compound Z is formed. A sample of Z was titrated with\[KMn{{O}_{4}}\] solution in hot acidic solution. The resulting liquid was reduced with \[S{{O}_{2}}\], the excess \[S{{O}_{2}}\]boiled off, and the liquid again titrated with \[KMn{{O}_{4}}\]. The ratio of the volumes of \[KMn{{O}_{4}}\] used in the two titrations was 5 : 1. \[KMn{{O}_{4}}\] oxidises all oxidation state of vanadium to Vanadium (+V) and \[S{{O}_{2}}\] reduces vanadium (+V) to vanadium (+IV). Read the above experiment and answer the following questions. If vanadium exists as \[VO_{4}^{3-}\], reduced species by\[S{{O}_{2}}\] would be
  A)
  \[VO_{4}^{2-}\]                                               
  done clear
  B)
  \[VO_{3}^{2-}\]
  done clear
  C)
  \[VO_{2}^{2-}\]                                               
  done clear
  D)
  \[VO_{{}}^{2-}\]
  done clear
  View Answer play_arrow

• question_answer64)
  Directions: Questions No. 64 are based on the following paragraph. When ammonium vanadate is heated with oxalic add solution, a compound Z is formed. A sample of Z was titrated with\[KMn{{O}_{4}}\] solution in hot acidic solution. The resulting liquid was reduced with \[S{{O}_{2}}\], the excess \[S{{O}_{2}}\]boiled off, and the liquid again titrated with \[KMn{{O}_{4}}\]. The ratio of the volumes of \[KMn{{O}_{4}}\] used in the two titrations was 5 : 1. \[KMn{{O}_{4}}\] oxidises all oxidation state of vanadium to Vanadium (+V) and \[S{{O}_{2}}\] reduces vanadium (+V) to vanadium (+IV). Read the above experiment and answer the following questions. Consider following redox reaction\[VO_{3}^{2-}+MnO_{4}^{-}\to M{{n}^{2+}}+VO_{4}^{3-}\]1 mole of\[VO_{3}^{2-}\] is oxidised by x mole of\[MnO_{4}^{-}\] Thus, x is
  A)
   0. 2                                       
  done clear
  B)
   0. 4
  done clear
  C)
   0. 8                                       
  done clear
  D)
   1. 0
  done clear
  View Answer play_arrow

• question_answer65)
  In which case the wavelength emitted is minimum?
  A)
   An electron jumps from 2nd to 1st level
  done clear
  B)
   An electron jumps from 3rd to 2nd level
  done clear
  C)
   An electron jumps from 4th to 3rd level
  done clear
  D)
   An electron jumps from 5th to 4th level
  done clear
  View Answer play_arrow

• question_answer66)
  3.7g of an oxide of a metal was heated with charcoal. The liberated \[C{{O}_{2}}\]was absorbed in caustic soda solution and weighed 1.0 g. If the specific gravity of the metal is 0.095, the exact atomic weight of the metal is
  A)
   170.8                                   
  done clear
  B)
   32.7
  done clear
  C)
   67.37                                   
  done clear
  D)
   65.4
  done clear
  View Answer play_arrow

• question_answer67)
  In a cubic dosed packed structure of mixed oxides, the lattice is made up of oxide ions, one eighth of tetrahedral/voids are occupied by divalent ions \[({{A}^{2+}})\], while one half of the octahedral voids are occupied by trivalent ions\[({{B}^{3+}})\]What is the formula of the oxide ?
  A)
  \[{{A}_{3}}{{B}_{2}}{{O}_{4}}\]                  
  done clear
  B)
  \[{{A}_{2}}{{B}_{2}}{{O}_{4}}\]
  done clear
  C)
  \[A{{B}_{2}}{{O}_{5}}\]                 
  done clear
  D)
  \[A{{B}_{2}}{{O}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer68)
  The standard heat of combustion of carbon(s), sulphur (s) and carbon disulphide \[(l)\] are-393.3, -293.72 and - 1108.76 kJ/mol respectively. The standard heat of formation of carbon disulphide (0 is
  A)
  -128.02 kJ                           
  done clear
  B)
  +128.02kJ
  done clear
  C)
  -218.42 kJ                           
  done clear
  D)
   + 218.42 kJ
  done clear
  View Answer play_arrow

• question_answer69)
  The decomposition of \[{{N}_{2}}O\]into \[{{N}_{2}}\] and O in the presence of gaseous argon follows second order kinetics with \[k=(5.0\times {{10}^{11}}L\,mo{{l}^{-1}}{{s}^{-1}}){{e}^{-29000k/T}}\] Activation energy of the reaction is
  A)
  \[\text{121}\,\text{kJ}\,\text{mo}{{\text{l}}^{\text{-1}}}\]                         
  done clear
  B)
  \[241\,\text{kJ}\,\text{mo}{{\text{l}}^{\text{-1}}}\]
  done clear
  C)
  \[201\,\text{kJ}\,\text{mo}{{\text{l}}^{\text{-1}}}\]                       
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer70)
  In which of the following case, increase in concentration of ion cause increase in \[{{\text{E}}_{\text{cell}}}\]?
  A)
  \[Pt({{H}_{2}})|{{H}^{+}}(Ag)\]
  done clear
  B)
  \[Ag,AgCl|C{{l}^{-}}(aq)\]
  done clear
  C)
  \[Pt|\]Quinhydrone\[|{{H}^{+}}(aq)\]
  done clear
  D)
  \[Ag|A{{g}^{+}}(aq)\]
  done clear
  View Answer play_arrow

• question_answer71)
  Which one of the following is wrong?
  A)
   The elements on the main diagonal of a symmetric marix are all zero.
  done clear
  B)
   The elements on the main diagonal of a skew-symmetric matrix are all zero.
  done clear
  C)
   For any square matrix \[A,\frac{1}{2}(A+A')\] is symmetric.
  done clear
  D)
   For any square matrix \[A,\frac{1}{2}(A+A')\] is skew-symmetric.
  done clear
  View Answer play_arrow

• question_answer72)
  Let .R be set of real numbers. If \[f:R\to R\] is defined by \[f(x)={{e}^{x}}\], then f is
  A)
   surJective but not injecrive
  done clear
  B)
   injective but not surjective
  done clear
  C)
   bijective
  done clear
  D)
   neither suqective nor injective
  done clear
  View Answer play_arrow

• question_answer73)
  \[\frac{\tan 3x}{\tan x}\]never lies between
  A)
   \[-\frac{1}{3}\]and 0                     
  done clear
  B)
   \[\frac{1}{3}\]and 0
  done clear
  C)
   \[-\frac{1}{3}\]and \[\frac{1}{3}\]                           
  done clear
  D)
   - 3 and 3
  done clear
  View Answer play_arrow

• question_answer74)
  If \[\sin x+\sqrt{3}\cos x=\sqrt{2},\]then x is
  A)
   \[2n\pi +\frac{\pi }{12},2n\pi -\frac{\pi }{3}\]
  done clear
  B)
   \[2n\pi +\frac{5\pi }{12},2n\pi -\frac{\pi }{12}\]
  done clear
  C)
   \[2n\pi -\frac{\pi }{12},2n\pi -\frac{\pi }{12}\]
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer75)
  Directions: Question No. 75 are based on the following paragraph. Let \[\overrightarrow{a},\overrightarrow{b}\]and \[\overrightarrow{c}\]be three vectors such that \[|\overrightarrow{a}|=|\overrightarrow{b}|=|\overrightarrow{c}|=4\]and angel between \[\overrightarrow{a}\]and \[\overrightarrow{b}\]is \[\frac{\pi }{3}\]and angel between \[\overrightarrow{b}\]and \[\overrightarrow{c}\]is \[\frac{\pi }{3}\]and angle between \[\overrightarrow{c}\]and \[\overrightarrow{a}\]is \[\frac{\pi }{3}\] The volume of the  parallelepiped whose adjacent edges are represented by the vectors \[\overrightarrow{a},\overrightarrow{b}\] and \[\overrightarrow{c}\] is                                     
  A)
   \[24\sqrt{3}\]                  
  done clear
  B)
   \[32\sqrt{3}\]
  done clear
  C)
   \[24\sqrt{2}\]                  
  done clear
  D)
   \[32\sqrt{2}\]
  done clear
  View Answer play_arrow

• question_answer76)
  Directions: Question No. 76 are based on the following paragraph. Let \[\overrightarrow{a},\overrightarrow{b}\]and \[\overrightarrow{c}\]be three vectors such that \[|\overrightarrow{a}|=|\overrightarrow{b}|=|\overrightarrow{c}|=4\]and angel between \[\overrightarrow{a}\]and \[\overrightarrow{b}\]is \[\frac{\pi }{3}\]and angel between \[\overrightarrow{b}\]and \[\overrightarrow{c}\]is \[\frac{\pi }{3}\]and angle between \[\overrightarrow{c}\]and \[\overrightarrow{a}\]is \[\frac{\pi }{3}\] The volume of the tetrahedron whose adjacent edges are represented by the vectors \[\overrightarrow{a},\overrightarrow{b}\] and \[\overrightarrow{c}\]is
  A)
   \[\frac{16\sqrt{2}}{3}\]                
  done clear
  B)
   \[2\sqrt{\frac{2}{3}}\]
  done clear
  C)
   \[3\sqrt{\frac{2}{3}}\]                  
  done clear
  D)
   \[4\sqrt{\frac{2}{3}}\]
  done clear
  View Answer play_arrow

• question_answer77)
  The function \[f(x)={{\sin }^{-1}}(\cos x)\] is
  A)
   continuous at x = 0
  done clear
  B)
   discontinuous at x = 0
  done clear
  C)
   differentiable at x = 0
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer78)
  A line segment has length 63 and direction ratios < 3, - 2, 6 >. If the line makes an obtuse angle with x -axis, then the components of the vector are
  A)
   27, -18, 54                          
  done clear
  B)
   27,18, - 54
  done clear
  C)
   - 27,18, - 54       
  done clear
  D)
   27, -18, - 54
  done clear
  View Answer play_arrow

• question_answer79)
  In a football championship, there were played 153 matches. Every two teams played one match with each other. The number of teams participating in the championship is
  A)
   14                                         
  done clear
  B)
   22
  done clear
  C)
   18                                         
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer80)
  The equation \[|z-i|+|z+i|=k,k>0,\]  can represent an ellipse, if k2 is
  A)
   < 1                                        
  done clear
  B)
   < 2
  done clear
  C)
   > 4                                        
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer81)
  If \[({{\lambda }^{2}}+\lambda -2){{x}^{2}}+(\lambda +2)x<1\] for all \[x\in R\], then X belongs to the interval
  A)
   \[(-2,1)\]                            
  done clear
  B)
   \[\left( -2,\frac{2}{5} \right)\]
  done clear
  C)
   \[\left( \frac{2}{5},1 \right)\]                    
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer82)
  A ladder rests against a wall at an angle a to the horizontal. Its foot is pulled away from the wall through a distance a, so that it slides a distance b down the wall making an angle \[\text{ }\!\!\beta\!\!\text{ }\] with the horizontal. Then a is equal to
  A)
   \[b\tan \frac{1}{2}(\alpha +\beta )\]     
  done clear
  B)
   \[b\tan \frac{1}{2}(\alpha -\beta )\]
  done clear
  C)
   \[a\tan \frac{1}{2}(\alpha -\beta )\]      
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer83)
  The distance between the point (1, 1) and the tangent to the curve \[y={{e}^{2x}}+{{x}^{2}}\] drawn from the point x = 0 is
  A)
   \[\frac{1}{\sqrt{5}}\]                                    
  done clear
  B)
   \[-\frac{1}{\sqrt{5}}\]
  done clear
  C)
   \[\frac{2}{\sqrt{5}}\]                                    
  done clear
  D)
   \[-\frac{2}{\sqrt{5}}\]
  done clear
  View Answer play_arrow

• question_answer84)
  The value 6f a for which the function  f(x) = sin x - cos x - ax + b decreases for \[x\in R\]is given by                        
  A)
   \[a\ge \sqrt{2}\]                             
  done clear
  B)
   \[a\ge 1\]
  done clear
  C)
   \[a<\sqrt{2}\]                  
  done clear
  D)
   \[a<1\]    
  done clear
  View Answer play_arrow

• question_answer85)
  If \[f(x)=\frac{1}{{{x}^{2}}}\int_{4}^{x}{\{(4{{t}^{2}}-2f'(t)\}}\]dt, then f'(4) is equal to
  A)
  32                                          
  done clear
  B)
   \[\frac{32}{3}\]
  done clear
  C)
   \[\frac{32}{9}\]                               
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer86)
  If \[{{A}_{1}}\]  is the area of the parabola \[{{y}^{2}}=4ax\] lying between vertex and the latusrectum and \[{{A}_{2}}\] is the area between the latusrectum and the double ordinate x = 2a, then \[{{A}_{1}}/{{A}_{2}}\]is equal to
  A)
   \[(2\sqrt{2}-1)\]                             
  done clear
  B)
   \[\frac{1}{7}(2\sqrt{2}+1)\]
  done clear
  C)
   \[\frac{1}{7}(2\sqrt{2}-1)\]                        
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer87)
  A man and his wife appear for an interview for two posts. The probability of the man's selection is 1/5 and that of his wife's selection is 1/7. The probability that at least one of them is selected, is
  A)
   9/35                                     
  done clear
  B)
   12/35
  done clear
  C)
   2/7                                       
  done clear
  D)
   11/35
  done clear
  View Answer play_arrow

• question_answer88)
  If the coordinates of the vertex A of a \[\Delta ABC\] are (1, 2) and equation of the perpendicular bisectors of AB and AC are 3x + 4y -1 = 0 and 4x + 3y - 5 = 0, then the area of \[\Delta ABC\] is
  A)
   2 sq unit                             
  done clear
  B)
   3 sq unit
  done clear
  C)
   1 sq unit                             
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer89)
  If from any point P on the circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\],  tangents are drawn to the circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c{{\sin }^{2}}a+({{g}^{2}}+{{f}^{2}}){{\cos }^{2}}a=0\] , then angle between the tangents is
  A)
   \[\alpha \]
  done clear
  B)
   \[2\alpha \]
  done clear
  C)
  \[\frac{\alpha }{2}\]                                       
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer90)
  Area of the triangle formed by the tangents and chord of contact of the   circle \[{{x}^{2}}+{{y}^{2}}+6x+8y=0\], if tangents, are drawn from the point (1, 1), is
  A)
   \[\frac{340}{41}\]sq unit             
  done clear
  B)
    \[\frac{360}{41}\]sq unit
  done clear
  C)
   \[\frac{320}{41}\]sq unit             
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer91)
  Direction: Question No. 91 is Assertion-Reason type question. These question contains two statements: Statement I (Assertion) and Statement II (Reason). These question also has four alternative choices, only one of which is the correct answer. You have to select the correct choice in the cedes (a), (b), (c) and (d) in the given below:  

  Statement I: A bag has contains 23 balls in which 7 are identical, then the number of ways of selecting 12 balls from bag is \[^{18}{{C}_{6}}{{+}^{18}}{{C}_{8}}.\]

  Statement II: In a group has n things in which are identical, then the number of ways of selecting r things from a group is \[\sum\limits_{r=0}^{r}{^{n=p}{{C}_{r}}.}\]

   
  A)
   Statement I is true. Statement II is true; Statement B is not a correct explanation for Statement I.
  done clear
  B)
   Statement I is true. Statement II is false.
  done clear
  C)
   Statement 1 is false. Statement S is true.
  done clear
  D)
   Statement I is true, Statement H is true; Statement H is a correct explanation for Statement I.
  done clear
  View Answer play_arrow

• question_answer92)
  Direction: Question No. 92 is Assertion-Reason type question. These question contains two statements: Statement I (Assertion) and Statement II (Reason). These question also has four alternative choices, only one of which is the correct answer. You have to select the correct choice in the cedes (a), (b), (c) and (d) in the given below:  

  Statement I: If A is obtuse angle in \[\Delta ABC\], then tan B tan C > 1.

  Statement II: In \[\Delta ABC\] \[\tan A=\frac{\tan B+\tan C}{\tan B\tan C-1}\]

   
  A)
   Statement I is true. Statement J fin true; Statement B is not a correct explanation for Statement I.
  done clear
  B)
   Statement I is true. Statement II is false.
  done clear
  C)
   Statement 1 is false. Statement S is true.
  done clear
  D)
   Statement I is true, Statement H is true; Statement H is a correct explanation for Statement I.
  done clear
  View Answer play_arrow

• question_answer93)
  Direction: Question No. 93 is Assertion-Reason type question. These question contains two statements: Statement I (Assertion) and Statement II (Reason). These question also has four alternative choices, only one of which is the correct answer. You have to select the correct choice in the cedes (a), (b), (c) and (d) in the given below:  

  Statement I: \[\int_{-1}^{1}{|x|dx}\] can be found while \[\int_{{}}^{{}}{|x|dx}\] cannot be found.

  Statement II: |x| is non-differentiable at x = 0.

  A)
   Statement I is true. Statement J fin true; Statement B is not a correct explanation for Statement I.
  done clear
  B)
   Statement I is true. Statement II is false.
  done clear
  C)
   Statement 1 is false. Statement S is true.
  done clear
  D)
   Statement I is true, Statement H is true; Statement H is a correct explanation for Statement I.
  done clear
  View Answer play_arrow

• question_answer94)
  In \[\Delta ABC,\angle B={{90}^{o}}\]  and b + a = 4, the area of the triangle is the maximum, when \[\angle C\] is
  A)
   \[\frac{\pi }{4}\]                                             
  done clear
  B)
   \[\frac{\pi }{6}\]
  done clear
  C)
   \[\frac{\pi }{3}\]                                             
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer95)
  The sum of the digits in the unit place of all the numbers formed with the help of 3, 4, 5, 8 taken all at a time, is
  A)
   432                                       
  done clear
  B)
   120
  done clear
  C)
   36                                         
  done clear
  D)
   18     
  done clear
  View Answer play_arrow

• question_answer96)
  The proposition is a \[(p\Rightarrow \tilde{\ }p)\wedge (\tilde{\ }p\Rightarrow p)\]is a
  A)
   tautology and contradiction
  done clear
  B)
   neither tautology nor contradiction
  done clear
  C)
   contradiction   
  done clear
  D)
   tautology
  done clear
  View Answer play_arrow

• question_answer97)
  If \[(1+x)(1+{{x}^{2}})(1={{x}^{4}})....(1+{{x}^{128}})\] \[=\sum\limits_{r=0}^{n}{{{x}^{r}},}\]then n is
  A)
   255                                       
  done clear
  B)
   127
  done clear
  C)
   60                                         
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer98)
  An elevator starts with m passengers and stops at n floors \[(m\le n)\]. The probability that no two passengers alight at the same floor, is
  A)
   \[\frac{^{n}{{P}_{m}}}{{{m}^{n}}}\]                       
  done clear
  B)
   \[\frac{^{n}{{P}_{m}}}{{{n}^{m}}}\]
  done clear
  C)
   \[\frac{^{n}{{C}_{m}}}{{{m}^{n}}}\]                       
  done clear
  D)
   \[\frac{^{n}{{C}_{m}}}{{{m}^{n}}}\]
  done clear
  View Answer play_arrow

• question_answer99)
  \[\int_{{}}^{{}}{\sqrt{\frac{\cos x-{{\cos }^{3}}x}{1-{{\cos }^{3}}x}}}dx\] ax is equal to
  A)
   \[\frac{2}{3}{{\sin }^{-1}}({{\cos }^{3/2}}x)+c\]
  done clear
  B)
   \[\frac{3}{2}{{\sin }^{-1}}({{\cos }^{3/2}}x)+c\]
  done clear
  C)
   \[\frac{2}{3}{{\cos }^{-1}}({{\cos }^{3/2}}x)+c\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer100)
  The function \[f(\theta )=\frac{d}{d\theta }\int_{0}^{\theta }{\frac{dx}{1-\cos \theta \cos x}}\] satisfies
  A)
  \[\frac{df}{d\theta }+2f(\theta )\cot \theta =0\]
  done clear
  B)
   \[\frac{df}{d\theta }-2f(\theta )\cot \theta =0\]
  done clear
  C)
   \[\frac{2}{3}{{\cos }^{-1}}({{\cos }^{3/2}}x)+c\]
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer101)
  A rectangular hyperbola whose centre is C is cut by any circle of radius r in four points P, Q, R and 5. Then, \[C{{P}^{2}}+C{{Q}^{2}}+C{{R}^{2}}+C{{S}^{2}}\] is  equal to
  A)
   r2                                           
  done clear
  B)
   2r2
  done clear
  C)
   3r2                                        
  done clear
  D)
   4r2
  done clear
  View Answer play_arrow

• question_answer102)
  The shortest distance between the lines \[\overrightarrow{r}=(5\hat{i}+7\hat{j}+3\hat{k})+\lambda (5\hat{i}-16\hat{j}+7\hat{k})\]and \[\overrightarrow{r}=(9\hat{i}+13\hat{j}+15\hat{k})+\mu (3\hat{i}+8\hat{j}-5\hat{k})\]is
  A)
   14 unit                                
  done clear
  B)
   12 unit
  done clear
  C)
   10 unit                                
  done clear
  D)
   8 unit
  done clear
  View Answer play_arrow

• question_answer103)
  Let \[f(x)=x-|x-{{x}^{2}}|,x\in [-1,1]\]Then, the number of points at which f(x) is discontinuous, is
  A)
   1                                            
  done clear
  B)
   2
  done clear
  C)
   0                                            
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer104)
  The number of real solutions of the equation \[{{2}^{x/2}}+{{(\sqrt{2}+1)}^{x}}={{(5+2\sqrt{2})}^{x/2}}\] is
  A)
   1                                            
  done clear
  B)
   2
  done clear
  C)
   4                                            
  done clear
  D)
   infinite
  done clear
  View Answer play_arrow

• question_answer105)
  If \[{{\cot }^{-1}}(\sqrt{\cos x})-{{\tan }^{-1}}(\sqrt{\cos \alpha })=x\], then sin x is equal to
  A)
   \[{{\cot }^{2}}\left( \frac{\alpha }{2} \right)\]                    
  done clear
  B)
   \[{{\tan }^{2}}\left( \frac{\alpha }{2} \right)\]
  done clear
  C)
   \[\tan \alpha \]
  done clear
  D)
   \[{{\cot }^{2}}\left( \frac{\alpha }{2} \right)\]
  done clear
  View Answer play_arrow