JEE Main & Advanced Sample Paper

done JEE Main Sample Paper-36 Total Questions - 90   

• question_answer1)
  An atom X belongs to 4th period of the periodic table and has highest number of unpaired electrons in comparison to the other elements of the period. The atomic number of X is
  A)
   23                               
  done clear
  B)
   25
  done clear
  C)
   24    
  done clear
  D)
   33
  done clear
  View Answer play_arrow

• question_answer2)
  The quantum number not obtained from Schrodinger 's wave equation is
  A)
   n                                
  done clear
  B)
   l
  done clear
  C)
   m                               
  done clear
  D)
   s
  done clear
  View Answer play_arrow

• question_answer3)
  Aluminothermy used for on the spot welding of large iron structure is based on the fact that-
  A)
   As compared to iron, aluminium has greater affinity for oxygen.
  done clear
  B)
   As compared to aluminium, iron has greater affinity for oxygen,                                              
  done clear
  C)
   Reaction between aluminium and oxygen is endothermic.
  done clear
  D)
   Reaction between iron and oxygen is endothermic.        
  done clear
  View Answer play_arrow

• question_answer4)
  Which of the following shows the tendency to form peroxide?
  A)
   Lithium                       
  done clear
  B)
   Magnesium                
  done clear
  C)
   Beryllium                     
  done clear
  D)
   Radium              
  done clear
  View Answer play_arrow

• question_answer5)
  A \[1.0\text{ }M\] solution with respect to each of the metal halides \[A{{X}_{3}},B{{X}_{2}},C{{X}_{3}}\] and \[D{{X}_{2}}\] is electro lysed using platinum electrodes. If \[{{E}^{o}}_{{{A}^{3+}}/A}=1.50V,\,{{E}^{o}}_{{{B}^{2+}}/B}=0.3V,\,{{E}^{o}}_{{{C}^{3+}}/C}=-0.74V,{{E}^{o}}_{{{D}^{2+}}/D}=-23.7V.\] The correct sequence in which the various metals are deposited at the cathode is
  A)
   A, B, C, D                   
  done clear
  B)
   A, B, C
  done clear
  C)
   D, C, B, A                   
  done clear
  D)
   C, B, A
  done clear
  View Answer play_arrow

• question_answer6)
  Arrange hypo phosphorous acid \[({{H}_{3}}P{{O}_{2}}),\] phosphorous acid \[({{H}_{3}}P{{O}_{3}})\] and Phosphoric acid \[({{H}_{3}}P{{O}_{4}})\] in the decreasing order of acidic strength
  A)
   \[{{H}_{3}}P{{O}_{3}}>{{H}_{3}}P{{O}_{4}}>{{H}_{3}}P{{O}_{2}}\]
  done clear
  B)
   \[{{H}_{3}}P{{O}_{4}}>{{H}_{3}}P{{O}_{3}}>{{H}_{3}}P{{O}_{2}}\]
  done clear
  C)
   \[{{H}_{3}}P{{O}_{4}}>{{H}_{3}}P{{O}_{2}}>{{H}_{3}}P{{O}_{3}}\]
  done clear
  D)
   \[{{H}_{3}}P{{O}_{4}}\approx {{H}_{3}}P{{O}_{3}}\approx {{H}_{3}}P{{O}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer7)
  Which of the following reactions corresponds to the definition of enthalpy of formation?
  A)
   C (diamond) \[+{{O}_{2}}(g)\to C{{O}_{2}}(g)\]
  done clear
  B)
   C (graphite) \[+{{O}_{2}}(I)\to C{{O}_{2}}(g)\]
  done clear
  C)
   C (graphite) \[+{{O}_{2}}(g)\to C{{O}_{2}}(g)\]
  done clear
  D)
   \[C(g)+{{O}_{2}}(g)\to C{{O}_{2}}(g)\]
  done clear
  View Answer play_arrow

• question_answer8)
  Among the reactions given below for \[{{B}_{2}}{{H}_{6}},\] the one which does not take place is
  A)
   \[{{B}_{2}}{{H}_{6}}+HCl\xrightarrow{{}}{{B}_{2}}{{H}_{5}}Cl+{{H}_{2}}\]
  done clear
  B)
   \[2{{B}_{2}}{{H}_{6}}+6N{{H}_{3}}\xrightarrow{\Delta }{{B}_{3}}{{N}_{3}}{{H}_{6}}\,\,(borazine)\]
  done clear
  C)
   \[{{B}_{2}}{{H}_{6}}+2N{{(C{{H}_{3}})}_{3}}\xrightarrow{{}}2{{(C{{H}_{3}})}_{3}}NB{{H}_{3}}\]
  done clear
  D)
   \[{{B}_{2}}{{H}_{6}}+6{{C}_{2}}{{H}_{4}}\xrightarrow{{{H}_{3}}{{O}^{+}}}3{{C}_{2}}{{H}_{5}}OH+2B{{(OH)}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer9)
  The pure crystalline substance on being heated gradually first forms a turbid liquid at constant temperature and still at higher temperature turbidity completely disappears. The behaviour is a characteristic of substance forming.
  A)
   Allotropic crystals
  done clear
  B)
   Liquid crystals
  done clear
  C)
   Isomeric crystals
  done clear
  D)
   Isomorphous crystals.
  done clear
  View Answer play_arrow

• question_answer10)
  Which of the following ions are optically active?

  (I)

  (II)

  (III)

  (IV)

  A)
   I only                          
  done clear
  B)
   II only
  done clear
  C)
   II and III
  done clear
  D)
   IV only
  done clear
  View Answer play_arrow

• question_answer11)
  Which of the following can be termed as a mixed complex?
  A)
   \[{{K}_{4}}[Fe{{(CN)}_{6}}]\]         
  done clear
  B)
   \[[Cu{{(N{{H}_{3}})}_{4}}]S{{O}_{4}}\]
  done clear
  C)
   \[[Co{{(N{{H}_{3}})}_{4}}N{{O}_{2}}Cl]Cl\]  
  done clear
  D)
   \[{{K}_{2}}Fe{{O}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer12)
  Consider a \[0.1M\]solution of two solutes A and B. Abe haves as a non-electrolyte while 80% of B dimerises. Which of the following statement is correct regarding these solutions?
  A)
   The b.pt of A will be less than B
  done clear
  B)
   The osmotic pressure of B will be more than that of A
  done clear
  C)
   The freezing point of solution A will be less than that of B
  done clear
  D)
   Boiling points of both solutions will be same.
  done clear
  View Answer play_arrow

• question_answer13)
  A metal gives two chlorides A and B. A gives black precipitate with and B gives white. With KI, B gives a red precipitate soluble in excess of \[KI\]. A and B are respectively
  A)
   \[HgC{{l}_{2}}\]and \[H{{g}_{2}}C{{l}_{2}}\]
  done clear
  B)
   \[H{{g}_{2}}C{{l}_{2}}\] and \[HgC{{l}_{2}}\]
  done clear
  C)
   \[HgC{{l}_{2}}\]and \[ZnC{{l}_{2}}\]      
  done clear
  D)
   \[ZnC{{l}_{2}}\]and \[HgC{{l}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer14)
  In which reaction, there is change in oxidation number of N
  A)
   \[2N{{O}_{2}}\to {{N}_{2}}{{O}_{4}}\]
  done clear
  B)
   \[N{{H}_{4}}OH\to N{{H}_{4}}^{+}+O{{H}^{-}}\]
  done clear
  C)
   \[{{N}_{2}}{{O}_{5}}+{{H}_{2}}O\to 2HN{{O}_{3}}\]
  done clear
  D)
   \[2N{{O}_{2}}+{{H}_{2}}O\to HN{{O}_{3}}+HN{{O}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer15)
  Potassium permanganate acts as an oxidant in neutral, alkaline as well as acidic media. The final products obtained from it in the three conditions are, respectively             
  A)
   \[MnO_{4}^{2-},\,M{{n}^{3+}}\] and \[M{{n}^{2+}}\]
  done clear
  B)
   \[Mn{{O}_{2}},Mn{{O}_{2}}\]and \[M{{n}^{2+}}\]
  done clear
  C)
   \[Mn{{O}_{2}},Mn{{O}_{2}}^{+}\]and \[M{{n}^{3+}}\]
  done clear
  D)
    \[MnO,Mn{{O}_{2}}\] and \[M{{n}^{2+}}\]
  done clear
  View Answer play_arrow

• question_answer16)
  The number of \[\pi \] electrons present in 6.4 g of calcium carbide is - (\[{{N}_{A}}=\] Avagadro's number)
  A)
   \[4\,{{N}_{A}}\]                      
  done clear
  B)
   \[0.4\,{{N}_{A}}\]
  done clear
  C)
   \[0.1\,{{N}_{A}}\]                   
  done clear
  D)
   \[0.2\,{{N}_{A}}\]
  done clear
  View Answer play_arrow

• question_answer17)
  An organic compound 'X' on ozonolysis followed by reduction with \[Zn/{{H}_{2}}O\]gives 2 moles of \[H-\overset{O}{\mathop{\overset{||}{\mathop{C}}\,}}\,-H\]and \[H-\overset{O}{\mathop{\overset{||}{\mathop{C}}\,}}\,-C{{H}_{2}}-\overset{O}{\mathop{\overset{||}{\mathop{C}}\,}}\,-H.\]?X? is
  A)
   \[C{{H}_{2}}=CH-C{{H}_{2}}-CH=C{{H}_{2}}\]
  done clear
  B)
   \[C{{H}_{2}}=CH-C{{H}_{2}}-C{{H}_{2}}-CH=C{{H}_{2}}\]
  done clear
  C)
   \[H-C\equiv C-C\equiv C-H\]
  done clear
  D)
   \[C{{H}_{2}}=CH-CH=C{{H}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer18)
  The rate of \[{{S}_{N}}1\] reaction is fastest in the hydrolysis of which of the following halides?
  A)
   \[{{C}_{6}}{{H}_{5}}C{{H}_{2}}Br\]        
  done clear
  B)
   \[C{{H}_{3}}Br\]
  done clear
  C)
   \[{{(C{{H}_{3}})}_{2}}CHBr\]        
  done clear
  D)
   \[{{(C{{H}_{3}})}_{3}}CBr\]
  done clear
  View Answer play_arrow

• question_answer19)
  Two elements A & B form compounds having molecular formulae \[A{{B}_{2}}\] and \[A{{B}_{4}}\]. When dissolved in \[20.0\text{ }g\] of benzene \[1.00g\] of \[A{{B}_{2}}\] lowers f.p. by \[{{2.3}^{o}}C\] whereas \[1.00g\] of \[A{{B}_{4}}\]lowers f.p. by\[{{1.3}^{o}}C\]. The molal depression constant for benzene in \[1000g\] is \[5.1\]. The atomic masses of A and B are
  A)
   \[52,48\]                      
  done clear
  B)
   \[42,25\]
  done clear
  C)
   \[25,42\]                      
  done clear
  D)
   None
  done clear
  View Answer play_arrow

• question_answer20)
  To detect iodine in presence of bromine, the sodium extract is treated with \[NaN{{O}_{2}}+\] glacial acetic acid \[+CC{{l}_{4}}\] Iodine is detected by the appearance of
  A)
   yellow colour of \[CC{{l}_{4}}\]layer
  done clear
  B)
   purple colour of \[CC{{l}_{4}}\]
  done clear
  C)
   brown colour in the organic layer of \[CC{{l}_{4}}\]
  done clear
  D)
   deep blue colour in \[CC{{l}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer21)
  An element (atomic mass \[=100g/mol\]) having bcc structure has unit cell edge 400pm. The density (in \[g/c{{m}^{3}}\]) of the element is
  A)
   \[10.376\]                    
  done clear
  B)
   \[5.19\]
  done clear
  C)
   \[7.289\]                      
  done clear
  D)
   \[2.144\]
  done clear
  View Answer play_arrow

• question_answer22)
  An organic compound A \[({{C}_{4}}{{H}_{10}}O)\] has two enantiomeric forms and on dehydration it gives B(major product) and C  (minor product). B and C are treated with HBr/ Peroxide and  the compounds so produced were subjected to alkaline hydrolysis then-                                          
  A)
   B will give an isomer of A                            
  done clear
  B)
   C will give an isomer of A                          
  done clear
  C)
   Neither of them will give isomer of A                 
  done clear
  D)
   Both B and C will give isomer of A
  done clear
  View Answer play_arrow

• question_answer23)
  A reaction is found to be second order wr.t. one of the reactants & has rate constant of\[0.5\text{ }mo{{l}^{-1}}\text{ }d{{m}^{3}}\text{ }mi{{n}^{1}}\]. If initial  concentration is \[0.2\text{ }mol\text{ }d{{m}^{-3}}\]then \[{{t}_{1/2}}\] of reaction is       
  A)
   \[5\,\min \]                   
  done clear
  B)
   \[10\,\min \]              
  done clear
  C)
   \[15\,\min \]                 
  done clear
  D)
   \[20\,\min \]                
  done clear
  View Answer play_arrow

• question_answer24)
  The above shown polymer is obtained when a carbonyl compound is allowed to stand. It is a white solid. The polymer is
  A)
   Trioxane             
  done clear
  B)
   Formose
  done clear
  C)
   Paraformaldehyde     
  done clear
  D)
   met aldehyde.
  done clear
  View Answer play_arrow

• question_answer25)
  Concentration of \[N{{H}_{4}}Cl\] and \[N{{H}_{4}}OH\] in a buffer solution is in the ratio of \[1:1,\,{{K}_{b}}\] for \[N{{H}_{4}}OH\]is \[{{10}^{-10}}\]. The pH of the buffer is
  A)
   4                                
  done clear
  B)
   5
  done clear
  C)
   9                                
  done clear
  D)
   11
  done clear
  View Answer play_arrow

• question_answer26)
  Aniline when diazotized in cold and when treated with dimethyl aniline gives a coloured product. Its structure would be
  A)
    
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer27)
   \[\xrightarrow[(ii)\,CuCl]{(i)\,NaN{{O}_{2}}HCl}A.\] Compound ?A? is
  A)
                         
  done clear
  B)
   
  done clear
  C)
                
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer28)
  The standard reduction potential of\[L{{i}^{+}}/Li,B{{a}^{2+}}/Ba,\,N{{a}^{+}}/Na\]and \[M{{g}^{2+}}/Mg\]are--\[-3.05,-2.73,-2.71\]and \[-2.37\]volts respectively Which one of the following is strongest oxidising agent?
  A)
   \[N{{a}^{+}}\]             
  done clear
  B)
   \[L{{i}^{+}}\]
  done clear
  C)
   \[B{{a}^{2+}}\]                    
  done clear
  D)
   \[M{{g}^{2+}}\]
  done clear
  View Answer play_arrow

• question_answer29)
  Phospholipids are esters of glycerol with
  A)
   two carboxylic acid residues and one phosphate group
  done clear
  B)
   one carboxylic acid residue and two phosphate groups
  done clear
  C)
   three phosphate groups
  done clear
  D)
   three carboxylic acid residues
  done clear
  View Answer play_arrow

• question_answer30)
  \[{{C}_{6}}{{H}_{5}}MgBr\xrightarrow{Ether}A\xrightarrow{{{H}_{3}}{{O}^{+}}}Ba\]
  A)
            
  done clear
  B)
   
  done clear
  C)
           
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer31)
  A bullet comes out of a gun with a velocity of \[600\text{ }m/s.\]At what height from the target should the gun be aimed in order to hit the target situated at a distance of 200 m from the gun ?
  A)
   \[0.55\,m\]                   
  done clear
  B)
   \[55\,m\]
  done clear
  C)
   \[5.5\,m\]                     
  done clear
  D)
   \[55\,\times {{10}^{-4}}m\]
  done clear
  View Answer play_arrow

• question_answer32)
  A gramophone record is revolving with an angular velocity co. A coin is placed at a distance r from the center of the record. The static coefficient of friction is p. The coin will revolve with the record if
  A)
   \[r<\frac{\mu g}{{{\omega }^{2}}}\] only
  done clear
  B)
   \[r>\frac{\mu g}{{{\omega }^{2}}}\] only
  done clear
  C)
   \[r=\frac{\mu g}{{{\omega }^{2}}}\] only
  done clear
  D)
   \[r\le \frac{\mu g}{{{\omega }^{2}}}\] only
  done clear
  View Answer play_arrow

• question_answer33)
  A pendulum consists of a wooden bob of mass m and length \['\ell '\]. A bullet of mass \[{{m}_{1}}\] is fired towards the pendulum with a speed \[{{v}_{1}}\]. The bullet emerges out of the bob with a speed \[{{v}_{1}}/3,\] and the bob just completes motion along a vertical circle. Then \[{{v}_{1}}\] is
  A)
   \[\left( \frac{m}{{{m}_{1}}} \right)\sqrt{5g\ell }\]           
  done clear
  B)
   \[\frac{3}{2}\left( \frac{m}{{{m}_{1}}} \right)\sqrt{5g\ell }\]
  done clear
  C)
   \[\frac{2}{3}\left( \frac{{{m}_{1}}}{m} \right)\sqrt{5g\ell }\]        
  done clear
  D)
   \[\left( \frac{{{m}_{1}}}{m} \right)\sqrt{g\ell }\]
  done clear
  View Answer play_arrow

• question_answer34)

  Statement-1: If some portion of a disc is taken out, the centre of mass shifts to the opposite side of the removed portion.

  Statement-2: The position of centre of mass depends on the position of individual masses only

  A)
   Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  done clear
  B)
   Statement-1 is true, Statement-2 is true; Statement-2 not a correct explanation for Statement-1.          
  done clear
  C)
   Statement-1 is true, Statement-2 is false.          
  done clear
  D)
   Statement-1 is false, Statement-2 is true.          
  done clear
  View Answer play_arrow

• question_answer35)
  A particle of mass \[m{{  }_{1}}\] collides head-on with another stationary particle of mass \[{{m}_{2}}({{m}_{2}}>{{m}_{1}})\]. The collision is perfectly inelastic. The fraction of kinetic energy which is converted into heat in this collision is
  A)
   \[{{m}_{2}}/({{m}_{1}}+{{m}_{2}})\]
  done clear
  B)
   \[{{m}_{1}}/({{m}_{1}}+{{m}_{2}})\]
  done clear
  C)
   \[{{m}_{1}}/({{m}_{1}}-{{m}_{2}})\]        
  done clear
  D)
   \[{{m}_{2}}/({{m}_{1}}-{{m}_{2}})\]
  done clear
  View Answer play_arrow

• question_answer36)
  The correct graph between the gravitational potential \[({{V}_{s}})\]due to a hollow sphere and distance from its centre will be
  A)
   
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer37)
  A beaker containing a liquid of density p moves up with an acceleration a. The pressure due to the liquid at a depth h below the free surface of the liquid is
  A)
   \[h\,\rho g\]                  
  done clear
  B)
   \[h\,\rho (g-a)\]
  done clear
  C)
   \[h\,\rho (g+a)\]            
  done clear
  D)
   \[2h\,\rho \left( \frac{g+a}{g-a} \right)\]
  done clear
  View Answer play_arrow

• question_answer38)
  A wooden block of volume \[1000\text{ }cc\] is suspended from a spring balance. It weighs 12 N in air. It is then held suspended in water with half of it inside water. What would be the reading in spring balance now?
  A)
   \[10\,N\]                      
  done clear
  B)
   \[9\,N\]
  done clear
  C)
   \[8\,N\]                        
  done clear
  D)
   \[7\,N\]
  done clear
  View Answer play_arrow

• question_answer39)
  A square wire frame of size L is dropped in a liquid. On taking out, a membrane is formed. If the surface tension of &the liquid is T, force acting on the frame will be
  A)
   \[2T.L\]                       
  done clear
  B)
   \[4T.L\]
  done clear
  C)
   \[8T.L\]
  done clear
  D)
   \[10T.L\]
  done clear
  View Answer play_arrow

• question_answer40)

  Statement-1: Two different gas molecules having same temperature will have the same K.E.

  Statement-2: KE of gas molecules follows the Boltzmann's law

                                                 
  A)
   Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  done clear
  B)
   Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  done clear
  C)
   Statement-1 is true, Statement-2 is false.
  done clear
  D)
   Statement-1 is false, Statement-2 is true.
  done clear
  View Answer play_arrow

• question_answer41)
  1/2 mole of helium gas is contained in a container at S.T.P. The heat energy needed to double the pressure of the gas, keeping the volume constant (heat capacity of the gas \[=3\,J{{g}^{-1}}{{K}^{-1}}\]) is
  A)
   \[3276\text{ }J\]                       
  done clear
  B)
   \[1638\text{ }J\]
  done clear
  C)
   \[819\text{ }J\]                         
  done clear
  D)
   \[409.5\text{ }J\]
  done clear
  View Answer play_arrow

• question_answer42)
  A sphere, a cube and a thin circular plate all made of the same material and having the same mass, are initially heated to a temperature of\[{{200}^{o}}C\]. Which of these objects will cool slowest when left in air at room temperature?
  A)
   the sphere            
  done clear
  B)
   the cube
  done clear
  C)
   the circular plate      
  done clear
  D)
    all will cool at same rate
  done clear
  View Answer play_arrow

• question_answer43)
  A system changes from the state \[({{P}_{1}},\,{{V}_{1}})\] to \[({{P}_{2}},\,{{V}_{2}})\] as shown in the figure below. What is the work done by the system?
  A)
   \[7.5\times {{10}^{5}}\,joule\]
  done clear
  B)
   \[7.5\times {{10}^{5}}\,ergs\]
  done clear
  C)
   \[12\times {{10}^{5}}\,joule\]
  done clear
  D)
   \[6\times {{10}^{5}}\,joule\]
  done clear
  View Answer play_arrow

• question_answer44)
  A cylinder of radius R made of a material of thermal conductivity \[{{K}_{1}}\] is surrounded by a cylindrical shell of inner radius R & outer radius 2R made of a material of thermal conductivity \[{{K}_{2}}\] The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is
  A)
   \[{{K}_{1}}+{{K}_{2}}\]
  done clear
  B)
   \[{{K}_{1}}{{K}_{2}}/({{K}_{1}}+{{K}_{2}})\]
  done clear
  C)
   \[({{K}_{1}}+3{{K}_{2}})/4\]
  done clear
  D)
   \[(3{{K}_{1}}+{{K}_{2}})/4\]
  done clear
  View Answer play_arrow

• question_answer45)
  Figure shows a closed surface which intersects a conducting sphere. If a positive charge is placed at the point P, the flux of the electric field through the closed surface
  A)
   will remain zero       
  done clear
  B)
   will become positive
  done clear
  C)
   will become negative  
  done clear
  D)
   will become undefined
  done clear
  View Answer play_arrow

• question_answer46)
  In the circuit shown, the total current supplied by the battery is
  A)
   2 ampere                     
  done clear
  B)
   4 ampere
  done clear
  C)
   1 ampere                     
  done clear
  D)
   6 ampere
  done clear
  View Answer play_arrow

• question_answer47)
  Parallel plate capacitors \[{{C}_{1}}\] & \[{{C}_{2}}\] have the same area with \[{{C}_{1}}\]having half the plate separation as \[{{C}_{2}}\] . \[{{C}_{1}}\] is inserted wholly inside \[{{C}_{2}}\] as shown with their plates joined as shown. The capacitance across terminals AB will be
  A)
   \[{{C}_{1}}+{{C}_{2}}\]                   
  done clear
  B)
   \[\frac{{{C}_{1}}{{C}_{2}}}{{{C}_{1}}+{{C}_{2}}}\]
  done clear
  C)
   \[{{C}_{1}}\]                                   
  done clear
  D)
   \[{{C}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer48)
  In the figure battery B supplies \[12\,V\]. Take \[{{C}_{1}}=1\mu F,\,{{C}_{2}}=2\,\mu F,\,{{C}_{3}}=3\mu F,{{C}_{4}}=4\mu F.\]Charge on capacitor \[{{C}_{1}}\] when only \[{{S}_{1}}\] is closed is
  A)
   \[3\,\mu C\]                 
  done clear
  B)
   \[9\,\mu C\]
  done clear
  C)
   \[6\,\mu C\]                 
  done clear
  D)
   \[12\,\mu C\]
  done clear
  View Answer play_arrow

• question_answer49)
  The instantaneous values of current and voltage in an A.C. circuit are \[I=4\,\sin \omega t\] and \[E=100\cos \left( \omega t+\frac{\pi }{3} \right)\] respectively.     The phase difference between voltage and current is  
  A)
   \[\frac{\pi }{3}\]                                   
  done clear
  B)
   \[\frac{2\pi }{3}\]
  done clear
  C)
   \[\frac{5\pi }{6}\]                              
  done clear
  D)
   \[\frac{7\pi }{6}\]     
  done clear
  View Answer play_arrow

• question_answer50)
  An alternating voltage E (in volt) \[200\sqrt{2}\sin \]  \[100t\] connected to one microfarad capacitor through an A.C. ammeter. The reading of the ammeter shall be
  A)
   \[20\sqrt{2}mA\]                      
  done clear
  B)
   \[20\,mA\]
  done clear
  C)
   \[40\,mA\]                    
  done clear
  D)
   \[80\,mA\]
  done clear
  View Answer play_arrow

• question_answer51)
  In fig, what is the magnetic field induction at point O?
  A)
   \[\frac{{{\mu }_{0}}i}{4\pi r}\]                        
  done clear
  B)
   \[\frac{{{\mu }_{0}}i}{4\pi r}+\frac{{{\mu }_{0}}i}{2\pi r}\]
  done clear
  C)
   \[\frac{{{\mu }_{0}}i}{4r}+\frac{{{\mu }_{0}}i}{4\pi r}\]
  done clear
  D)
   \[\frac{{{\mu }_{0}}i}{4r}-\frac{{{\mu }_{0}}i}{4\pi r}\]
  done clear
  View Answer play_arrow

• question_answer52)
  A proton, a deutron and an a particle accelerated through the same potential difference enter a region of uniform magnetic field, moving at right angles to B. What is the ratio of their K.E.?
  A)
   \[1:2:2\]                       
  done clear
  B)
   \[2:2:1\]
  done clear
  C)
   \[1:2:1\]                       
  done clear
  D)
   \[1:1:2\]
  done clear
  View Answer play_arrow

• question_answer53)
  A simple pendulum with a bob of mass 'm' oscillates from A to C and back to A such that PB is H. If the acceleration due to gravity is' g\ then the velocity of the bob as it passes through B is
  A)
   zero                
  done clear
  B)
   \[2\,gH\]
  done clear
  C)
   \[mgH\]                       
  done clear
  D)
   \[\sqrt{2\,g\,H}\]
  done clear
  View Answer play_arrow

• question_answer54)
  A ray of light is incident at an angle of \[{{60}^{o}}\] on one face of a prism of angle \[{{30}^{o}}\]. The ray emerging out of the prism makes an angle of \[{{30}^{o}}\] with the incident ray The emergent ray is
  A)
   Normal to the face through which it emerges
  done clear
  B)
   Inclined at \[{{30}^{o}}\] to the face through which it emerges
  done clear
  C)
   Inclined at \[{{60}^{o}}\] to the face through which it emerges
  done clear
  D)
   Inclined at \[{{90}^{o}}\] to the normal at face through which it emerges
  done clear
  View Answer play_arrow

• question_answer55)

  Statement 1: A current flows in a conductor only when there is an electric field within the conductor.

  Statement 2: The drift velocity of electron in presence of electric field decreases.

  A)
   Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  done clear
  B)
   Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  done clear
  C)
   Statement-1 is true, Statement-2 is false.
  done clear
  D)
   Statement-1 is false, Statement-2 is true.
  done clear
  View Answer play_arrow

• question_answer56)
  Two periodic waves of intensities \[{{I}_{1}}\] and \[{{I}_{2}}\] pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is
  A)
   \[2({{I}_{1}}+{{I}_{2}})\]                  
  done clear
  B)
   \[{{I}_{1}}+{{I}_{2}}\]
  done clear
  C)
   \[{{(\sqrt{{{I}_{1}}}+\sqrt{{{I}_{2}}})}^{2}}\]         
  done clear
  D)
   \[{{(\sqrt{{{I}_{1}}}-\sqrt{{{I}_{2}}})}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer57)
  Range of frequencies alloted for commercial FM radio broadcast is
  A)
   88 to 108 MHz        
  done clear
  B)
   88 to 108 kHz
  done clear
  C)
   8 to 108 MHz         
  done clear
  D)
   88 to 108 GHz
  done clear
  View Answer play_arrow

• question_answer58)
  A hydrogen-like atom has one electron revolving around a stationary nucleus. The energy required to excite the electron from the second orbit to the third orbit is\[47.2\text{ }eV\]. The atomic number of the atom is
  A)
   3                    
  done clear
  B)
   4         
  done clear
  C)
   5                                
  done clear
  D)
   6
  done clear
  View Answer play_arrow

• question_answer59)
  In Millikan oil drop experiment, a charged drop of mass \[1.8\times {{10}^{-14}}kg\] is stationary between its plates. The distance between its plates is \[0.90\text{ }cm\] and potential difference is \[2.0\] kilovolts. The number of electrons on the drop is
  A)
   500                             
  done clear
  B)
   50      
  done clear
  C)
   5                    
  done clear
  D)
   0
  done clear
  View Answer play_arrow

• question_answer60)
  For the determination of the focal length of a convex mirror, a convex lens is required because
  A)
   it is not possible to obtain the image produced by a convex mirror on the screen
  done clear
  B)
   a convex lens has high resolving power so it helps to measure the focal length correctly
  done clear
  C)
   a convex mirror always forms a real image which is diminished by the convex lens
  done clear
  D)
   none of these
  done clear
  View Answer play_arrow

• question_answer61)
  Let\[f(x)=[{{(\tan x+\sin x)}^{2}}]\]. Then
  A)
   \[\underset{x\to 0}{\mathop{\lim }}\,f(x)\]does not exist.
  done clear
  B)
   \[f(x)\] is not continuous at x=0
  done clear
  C)
   \[f(x)\] is not differentiable at x = 0
  done clear
  D)
   \[f'(0)=0\]
  done clear
  View Answer play_arrow

• question_answer62)
  The two curves \[y={{x}^{2}}+ax-1\] and \[y=6{{x}^{2}}+b\] touch each other at a point having \[\text{abscissca}\,\,1\] when
  A)
  \[a=3,\,\,b=-3\]                      
  done clear
  B)
  \[a=9,\,\,b=3\]
  done clear
  C)
  \[a=0,\,\,b=-6\]                      
  done clear
  D)
  \[a=3,\,\,b=9\]
  done clear
  View Answer play_arrow

• question_answer63)
  If\[\int{\frac{({{x}^{2}}-1)dx}{({{x}^{4}}+3{{x}^{2}}+1){{\tan }^{-1}}\left( \frac{{{x}^{2}}+1}{x} \right)}=\log |{{\tan }^{-1}}f(x)|+C}\], then
  A)
  \[f(x)={{x}^{2}}+1\]                     
  done clear
  B)
  \[f(x)=\frac{{{x}^{2}}+1}{2x}\]
  done clear
  C)
  \[f(x)=\frac{{{x}^{2}}+1}{x}\]     
  done clear
  D)
  \[f(x)=\frac{1}{2}({{x}^{2}}+1)\]
  done clear
  View Answer play_arrow

• question_answer64)
  If the function \[f(x)=P{{e}^{2x}}+Q{{e}^{x}}+Rx\] satisfies the conditions \[f(0)=-1,\,\,f'(\log 2)=31\] and
  A)
  \[P=5,\,\,Q=-6,\,\,R=3\]
  done clear
  B)
  \[P=-5,\,\,Q=6,\,\,R=3\]
  done clear
  C)
  \[P=-5,\,\,Q=6,\,\,R=3\]
  done clear
  D)
  \[P=3,\,\,Q=2,\,\,R=3\]
  done clear
  View Answer play_arrow

• question_answer65)

  Statement-1: The area of the ellipse \[2{{x}^{2}}+3{{y}^{2}}=6\] is more than the area of the circle\[{{x}^{2}}+{{y}^{2}}-2x+4y+4=0\].

  Statement-2: If the length of the major axis of an ellipse is more than the diameter of a circle then the area of the ellipse will be more than the area of the circle.

  A)
   Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  done clear
  B)
   Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  done clear
  C)
   Statement-1 is true, Statement-2 is false.
  done clear
  D)
   Statement-1 is false, Statement-2 is true.
  done clear
  View Answer play_arrow

• question_answer66)
  Area included between \[y=\frac{{{x}^{2}}}{4a}\] and\[y=\frac{8{{a}^{3}}}{{{x}^{2}}+4{{a}^{2}}}\] is
  A)
  \[\frac{{{a}^{2}}}{3}(6\pi -4)\]                 
  done clear
  B)
  \[\frac{{{a}^{2}}}{3}(4\pi +3)\]
  done clear
  C)
  \[\frac{{{a}^{2}}}{3}(8\pi +3)\]               
  done clear
  D)
   none of these
  done clear
  View Answer play_arrow

• question_answer67)
  Given that \[\overrightarrow{a}\] is \[1\] to \[\overrightarrow{b}\] and \[p\] is a nonzero scalar if \[p\overrightarrow{r}+(\overrightarrow{r}+\overrightarrow{b})\overrightarrow{a}=\overrightarrow{c}\] then \[\overrightarrow{r}\] equals
  A)
  \[\overrightarrow{c}/p-\left[ (\overrightarrow{b}.\overrightarrow{c})\overrightarrow{a} \right]/{{p}^{2}}\]
  done clear
  B)
  \[\overrightarrow{a}/p-\left[ (\overrightarrow{c}.\overrightarrow{a})\overrightarrow{b} \right]/{{p}^{2}}\]
  done clear
  C)
  \[\overrightarrow{b}/p-\left[ (\overrightarrow{a}.\overrightarrow{b})\overrightarrow{c} \right]/{{p}^{2}}\]
  done clear
  D)
   None
  done clear
  View Answer play_arrow

• question_answer68)

  Statement-1: The domain of the function\[f(x)=\sqrt{{{\log }_{2}}\sin x}\]is\[(4n+1)\frac{\pi }{2},\,\,n\in N\].

  Statement-1: Expression under even root should be\[\ge 0\].

  A)
   Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  done clear
  B)
   Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  done clear
  C)
   Statement-1 is true, Statement-2 is false.
  done clear
  D)
   Statement-1 is false, Statement-2 is true.
  done clear
  View Answer play_arrow

• question_answer69)
  If the \[S.D.\] of a variable \[X\] is \[\sigma \], then the \[S.D.\] of\[(a,\,\,\,b,\,\,\,c\] are constant) is
  A)
  \[\frac{a}{c}\sigma \]                         
  done clear
  B)
  \[\left| \frac{a}{c} \right|\sigma \]
  done clear
  C)
  \[\left| \frac{c}{a} \right|\sigma \]                             
  done clear
  D)
  \[\frac{c}{a}\sigma \]
  done clear
  View Answer play_arrow

• question_answer70)

  Statement 1: The determinant of a matrix  is zero.

  Statement 2: The determinant of a skew symmetric matrix of odd order is zero.

  A)
   Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  done clear
  B)
   Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  done clear
  C)
   Statement-1 is true, Statement-2 is false.
  done clear
  D)
   Statement-1 is false, Statement-2 is true.
  done clear
  View Answer play_arrow

• question_answer71)
  If \[A\] and \[B\] are two sets, then \[A\cap (A\cup B)'\] equals:
  A)
  \[A\]                            
  done clear
  B)
  \[B\]
  done clear
  C)
  \[\phi \]                        
  done clear
  D)
   None
  done clear
  View Answer play_arrow

• question_answer72)
  \[f(x)={{x}^{2}}[x]\]
  A)
   increases in\[(0,\,\,1)\]            
  done clear
  B)
   decreases in\[(0,\,\,1)\]
  done clear
  C)
   increases in\[(-1,\,\,0)\]   
  done clear
  D)
   none of these
  done clear
  View Answer play_arrow

• question_answer73)
  If\[y={{e}^{x}}+\sin x\], then\[{{d}^{2}}x/d{{y}^{2}}\]is equal to
  A)
  \[{{e}^{x}}-\sin x\]
  done clear
  B)
  \[-{{({{e}^{x}}+\cos x)}^{-2}}\]
  done clear
  C)
  \[-({{e}^{x}}-\sin x){{({{e}^{x}}+\cos x)}^{-2}}\]
  done clear
  D)
  \[(\sin x-{{e}^{x}}){{(\cos x+{{e}^{x}})}^{-3}}\]
  done clear
  View Answer play_arrow

• question_answer74)
  The sum to n terms of the series\[\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+.....\]is
  A)
  \[n-1-{{2}^{-n}}\]               
  done clear
  B)
  \[1\]
  done clear
  C)
  \[n-1+{{2}^{-n}}\]             
  done clear
  D)
  \[1+{{2}^{-n}}\]
  done clear
  View Answer play_arrow

• question_answer75)

  Statement-1:\[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{2}^{1/x}}}{1+{{2}^{1/x}}}=1.\]

  Statement-2:\[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{\cos }^{-1}}\left( 1-x \right)}{\sqrt{x}}=\sqrt{2}.\]

  A)
   Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  done clear
  B)
   Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  done clear
  C)
   Statement-1 is true, Statement-2 is false.
  done clear
  D)
   Statement-1 is false, Statement-2 is true.
  done clear
  View Answer play_arrow

• question_answer76)
  Two finite sets have \[m\] and \[n\] elements. The total number of subsets of the first set is \[56\] more than the total number of subsets of the second set. Then:
  A)
  \[m=3,\,\,n=6\]                      
  done clear
  B)
  \[m=6,\,\,n=3\]
  done clear
  C)
  \[m=5,\,\,n=6\]                      
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer77)
  A set \[A\] has \[3\] elements and another set \[B\] has \[6\] elements. Then
  A)
  \[3\le n(A\cup B)\le 6\]
  done clear
  B)
  \[3\le n(A\cup B)\le 9\]
  done clear
  C)
  \[6\le n(A\cup B)\le 9\]
  done clear
  D)
  \[0\le n(A\cup B)\le 9\]
  done clear
  View Answer play_arrow

• question_answer78)
  If\[g=\{(1,\,\,1),\,\,(2,\,\,3),\,\,(3,\,\,5),\,\,(4,\,\,7)\}\] described by the formula, \[g(x)=\alpha \,\,x+\beta \] then what values should be assigned to \[\alpha \] and\[\beta ?\]
  A)
  \[\alpha =1,\,\,\beta =1\]                    
  done clear
  B)
  \[\alpha =2,\,\,\beta =-1\]
  done clear
  C)
  \[\alpha =1,\,\,\beta =-2\]      
  done clear
  D)
  \[\alpha =-2,\,\,\beta =-1\]
  done clear
  View Answer play_arrow

• question_answer79)
  The roots \[\alpha \] and \[\beta \] of the quadratic equation\[p{{x}^{2}}+qx+r=0\]are real and of opposite signs. The roots of \[\alpha {{(x-\beta )}^{2}}+\beta {{(x-\alpha )}^{2}}=0\] are
  A)
   positive                      
  done clear
  B)
   negative
  done clear
  C)
   of opposite signs        
  done clear
  D)
   non real
  done clear
  View Answer play_arrow

• question_answer80)
  The value of \[x\] for which \[({{\cot }^{-1}}(1+x))=\cos ({{\tan }^{-1}}x)\]is
  A)
  \[1/2\]                          
  done clear
  B)
  \[1\]
  done clear
  C)
  \[0\]                             
  done clear
  D)
  \[-1/2\]
  done clear
  View Answer play_arrow

• question_answer81)
  The equation \[k\sin \theta +\cos 2\theta =2k-7\] possesses a solution if:
  A)
  \[2\le k\le 6\]                
  done clear
  B)
  \[k>2\]
  done clear
  C)
  \[k>6\]            
  done clear
  D)
  \[k<2\]
  done clear
  View Answer play_arrow

• question_answer82)
  The value of\[\underset{x\to 0}{\mathop{\lim }}\,\frac{1-{{\cos }^{3}}x}{x\sin x\cos x}\]is
  A)
  \[\frac{2}{5}\]                        
  done clear
  B)
  \[\frac{3}{5}\]
  done clear
  C)
  \[\frac{3}{2}\]                        
  done clear
  D)
  \[\frac{3}{4}\]
  done clear
  View Answer play_arrow

• question_answer83)
  If \[y={{\sin }^{-1}}\frac{2x}{1+{{x}^{2}}}\], then which of the following is not correct?
  A)
   \[\frac{dy}{dx}=\frac{2}{1+{{x}^{2}}}\]for\[|x|\,\,<1\]
  done clear
  B)
   \[\frac{dy}{dx}=\frac{-2}{1+{{x}^{2}}}\]for\[|x|\,>1\]
  done clear
  C)
   \[\frac{dy}{dx}=2\]for\[x=-1\]
  done clear
  D)
   \[\frac{dy}{dx}\]does not exist at\[|x|=1\]
  done clear
  View Answer play_arrow

• question_answer84)
  If\[f(x)=\frac{1}{1-x}\], the number of points of discontinuity of\[f\{f[f(x)]\}\]is:
  A)
  \[2\]                             
  done clear
  B)
  \[1\]
  done clear
  C)
  \[0\]                             
  done clear
  D)
   infinite
  done clear
  View Answer play_arrow

• question_answer85)

  Statement-1: The period of\[f(x)=\sin 2x\cos [2x]-\cos 2x\sin [2x]\]is\[\frac{1}{2}\]

  Statement-2: The period of\[x-[x]\]is\[1\]

  A)
  Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
  done clear
  B)
   Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  done clear
  C)
   Statement-1 is true, Statement-2 is false.
  done clear
  D)
   Statement-1 is false, Statement-2 is true.
  done clear
  View Answer play_arrow

• question_answer86)
  If the slope of the tangent at\[(x,\,\,y)\]to a curve passing through\[\left( 1,\,\,\frac{\pi }{4} \right)\]is given by\[\frac{y}{x}-{{\cos }^{2}}\left( \frac{y}{x} \right)\], then the equation of the curve is
  A)
  \[y={{\tan }^{-1}}\log (e/x)\]          
  done clear
  B)
  \[y={{e}^{1+\cot (y/x)}}\]
  done clear
  C)
  \[y=x{{\tan }^{-1}}\log (e/x)\]        
  done clear
  D)
  \[y={{e}^{1+\tan y(y/x)}}\]
  done clear
  View Answer play_arrow

• question_answer87)
  If\[y={{\tan }^{-1}}\left( \frac{{{2}^{x}}}{1+{{2}^{2x+1}}} \right)\], then\[\frac{dy}{dx}\]at\[x=0\]is:
  A)
  \[-\frac{3}{5}\log 2\]              
  done clear
  B)
  \[\frac{2}{5}\log 2\]
  done clear
  C)
  \[-\frac{3}{2}\log 2\]              
  done clear
  D)
   None
  done clear
  View Answer play_arrow

• question_answer88)
  If and the vectors \[\overrightarrow{A}=(1,\,\,a,\,\,{{a}^{2}});\] \[\overrightarrow{B}=(1,\,\,b,\,\,{{b}^{2}});\] \[\overrightarrow{C}=(1,\,\,c,\,\,{{c}^{2}})\] are non-coplanar then the product\[abc=\]
  A)
  \[0\]                             
  done clear
  B)
  \[1\]
  done clear
  C)
  \[-1\]                           
  done clear
  D)
   None
  done clear
  View Answer play_arrow

• question_answer89)
  \[A\] and \[B\] are two independent witnesses \[(i.e.\] there is no collusion between them) in a case. The probability that \[A\] will speak the truth is \[x\] and the probability that \[B\] will speak the truth is\[y\]. \[A\] and \[B\] agree in a certain statement. The probability that the statement is true is
  A)
  \[\frac{x-y}{x+y}\]                
  done clear
  B)
  \[\frac{xy}{1+x+y+xy}\]
  done clear
  C)
  \[\frac{x-y}{1-x-y+2xy}\]      
  done clear
  D)
  \[\frac{xy}{1-x-y+2xy}\]
  done clear
  View Answer play_arrow

• question_answer90)
  Complex number \[z\] satisfies \[|z-a+ia|\,\,=1\] and has the least absolute value. Its absolute value is
  A)
  \[a\sqrt{2}-1\]                         
  done clear
  B)
  \[a\sqrt{2}+1\]
  done clear
  C)
  \[0\]                                         
  done clear
  D)
  \[a\]
  done clear
  View Answer play_arrow