JEE Main & Advanced Sample Paper

done JEE Main - Mock Test - 18 Total Questions - 75    [Download]

• question_answer1)
  The number of significant figures in the numbers \[4.8000\times {{10}^{4}}\] and 48000.50 are respectively
  A)
  5 and 6     
  done clear
  B)
   5 and 7
  done clear
  C)
  2 and 7            
  done clear
  D)
  2 and 6
  done clear
  View Answer play_arrow

• question_answer2)
  The length of a potentiometer wire is I. A cell of emf \[\varepsilon \] is balanced at a length \[l/5\]from the positive end of the wire. If length of the wire is increased by \[l/2\]. At what distance will the same cell give a balance point?
  A)
  \[\frac{2}{15}l\]            
  done clear
  B)
  \[\frac{3}{15}l\]
  done clear
  C)
  \[\frac{3}{10}l\]            
  done clear
  D)
  \[\frac{4}{10}l\]
  done clear
  View Answer play_arrow

• question_answer3)
  A body A starts from rest with an acceleration ay After 2 seconds, another body B starts from rest with an acceleration \[{{a}_{1}}\]. If they travel equal distances in the 5th second, after the start of A, then the ratio \[{{a}_{1}}:{{a}_{2}}\]is equal to
  A)
  5 : 9     
  done clear
  B)
  5 : 7  
  done clear
  C)
  9 : 5     
  done clear
  D)
  9 : 7
  done clear
  View Answer play_arrow

• question_answer4)
  A particle of charge q and mass m moves in a circular orbit of radius r with angular speed co. The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on
  A)
  \[\omega \] and q        
  done clear
  B)
  \[\omega q\] and m
  done clear
  C)
  q and m        
  done clear
  D)
    \[\omega \] and m
  done clear
  View Answer play_arrow

• question_answer5)
  A machine gun is mounted on a 2000 kg car on a horizontal frictionless surface. At some instant, the gun fires 10 bullets/second and each of mass 10 g with a velocity of \[500\,\text{m}\,{{\text{s}}^{-1}}\]. The acceleration of the car is
  A)
  \[0.025\,\text{m}\,{{\text{s}}^{-2}}\]   
  done clear
  B)
  \[0.25\,\text{m}\,{{\text{s}}^{-2}}\]
  done clear
  C)
  \[0.50\,\text{m}\,{{\text{s}}^{-2}}\]     
  done clear
  D)
  \[500\,\text{m}\,{{\text{s}}^{-2}}\]
  done clear
  View Answer play_arrow

• question_answer6)
  What will happen to the inductance L of a solenoid when the number of turns and the length are doubled keeping the area of cross- section same?
  A)
  \[\frac{L}{2}\]              
  done clear
  B)
  L
  done clear
  C)
  2L                   
  done clear
  D)
  4L
  done clear
  View Answer play_arrow

• question_answer7)
  A bomb moving with velocity \[(40\hat{i}+50\hat{j}-25\hat{k})m{{s}^{-1}}\]explode   into   two pieces of mass ratio 1 : 4. After explosion the smaller piece moves away with velocity\[(200\hat{i}+70\hat{j}+15\hat{k})m{{s}^{-1}}\]. The velocity of larger piece after explosion is
  A)
  \[45\hat{j}-35\hat{k}\]   
  done clear
  B)
  \[45\hat{i}-35\hat{j}\]
  done clear
  C)
  \[45\hat{k}-35\hat{j}\]   
  done clear
  D)
  \[-35\hat{i}+45\hat{k}\]
  done clear
  View Answer play_arrow

• question_answer8)
  A ray of light is incident normally on one of the faces of a prism of apex angle \[30{}^\circ \]and refractive index \[\sqrt{2}\]The angle of deviation of the ray is
  A)
  \[0{}^\circ \]   
  done clear
  B)
  \[12.5{}^\circ \]
  done clear
  C)
  \[15{}^\circ \]              
  done clear
  D)
  \[22.5{}^\circ \]
  done clear
  View Answer play_arrow

• question_answer9)
  Particles of masses m, 2m, 3m ... nm grams are placed on the same line at distance \[l,2l,3l...nlcm\] from a fixed point. The distance of centre of mass of the particles from the fixed point in centimetre is
  A)
  \[\frac{2n+1)l}{3}\]
  done clear
  B)
  \[\frac{l}{n+1}\]
  done clear
  C)
  \[\frac{n({{n}^{2}}+1)l}{2}\]  
  done clear
  D)
  \[\frac{2l}{n({{n}^{2}}+1)}\]
  done clear
  View Answer play_arrow

• question_answer10)
  When one of the slits of Youngs experiment is covered with a transparent sheet of thickness 4.8 mm, the central fringe shifts to a position originally occupied by the 30th bright fringe. What should be the thickness of the sheet if the central fringe has to shift to the position occupied by 20th bright fringe?
  A)
  3.8 mm
  done clear
  B)
           1.6 mm
  done clear
  C)
  7.6 mm         
  done clear
  D)
  3.2 mm
  done clear
  View Answer play_arrow

• question_answer11)
  A gas expands with temperature according to the relation \[V=K{{T}^{2/3}}\]. Calculate work done when the temperature changes by 60 K?
  A)
  10 R     
  done clear
  B)
  30 R 
  done clear
  C)
  40 R     
  done clear
  D)
  20 R
  done clear
  View Answer play_arrow

• question_answer12)
  The electric field (in \[\text{N}{{\text{C}}^{-1}}\]) in an electromagnetic wave is given by \[E=50\sin \omega \left( t-\frac{x}{c} \right)\]. The energy stored in a cylinder of cross- section \[10\text{c}{{\text{m}}^{2}}\]and length 100 cm along the x-axis will be
  A)
  \[5.5\times {{60}^{-12}}J\]      
  done clear
  B)
  \[1.1\times {{10}^{-11}}J\]
  done clear
  C)
  \[2.2\times {{10}^{-11}}J\]      
  done clear
  D)
  \[1.65\times {{10}^{-11}}J\]
  done clear
  View Answer play_arrow

• question_answer13)

  A liquid X of density \[3.36\,\text{g}\,\text{c}{{\text{m}}^{-3}}\]is poured in a U-tube, which contains Hg.

  Another liquid Y is poured in left arm with height 8 cm, upper levels of X and Y are same.

  What is the density of V?

   
  A)
  \[0.8\,\text{g}\,\text{c}{{\text{m}}^{-3}}\]     
  done clear
  B)
  \[1.2\,\text{g}\,\text{c}{{\text{m}}^{-3}}\]
  done clear
  C)
  \[1.4\,\text{g}\,\text{c}{{\text{m}}^{-3}}\]       
  done clear
  D)
  \[1.6\,\text{g}\,\text{c}{{\text{m}}^{-3}}\]
  done clear
  View Answer play_arrow

• question_answer14)
  A common emitter amplifier has a voltage gain of 50, an input impedance of \[100\Omega \]and an output impedance of \[200\Omega \]The power gain of the amplifier is
  A)
  500      
  done clear
  B)
  1000
  done clear
  C)
  1250    
  done clear
  D)
  100
  done clear
  View Answer play_arrow

• question_answer15)
  The Poisson?s ratio of a material is 0.4. If a force is applied to a wire of this material, there is a decrease of cross-sectional area by 2%. The percentage increase in its length is
  A)
  3%  
  done clear
  B)
    2.5%
  done clear
  C)
  1%       
  done clear
  D)
  0.5%
  done clear
  View Answer play_arrow

• question_answer16)
  A signal wave of frequency 12 kHz is modulated with a carrier wave of frequency 2.51 MHz. The upper and lower side band frequencies are respectively
  A)
  2512 kHz and 2508 kHz
  done clear
  B)
  2522 kHz and 2488 kHz
  done clear
  C)
  2502 kHz and 2498 kHz
  done clear
  D)
  2522 kHz and 2498 kHz
  done clear
  View Answer play_arrow

• question_answer17)

  Three rods of same dimensions have thermal conductivities 3K, 2K and K respectively.

  They are arranged as shown below

  What will be the temperature T of the junction?

  A)
  \[\frac{200}{3}\,{{\,}^{o}}C\] 
  done clear
  B)
  \[\frac{100}{3}\,{{\,}^{o}}C\]
  done clear
  C)
  \[75\,{{\,}^{o}}C\]      
  done clear
  D)
  \[\frac{50}{3}{{\,}^{o}}C\]
  done clear
  View Answer play_arrow

• question_answer18)
  The mass of deuteron \[{{(}_{1}}{{H}^{2}})\]nucleus is 2.014102 u. If the masses of proton and neutron are 1.007825 u and 1.008665 u respectively, nucleus the binding energy per nucleon of \[_{1}{{H}^{2}}\] nucleus is
  A)
  2.2 MeV       
  done clear
  B)
  1.1 MeV
  done clear
  C)
  0.5 MeV           
  done clear
  D)
  0.25 MeV
  done clear
  View Answer play_arrow

• question_answer19)
  An electric dipole of length 1 cm is placed with the axis making an angle of \[30{}^\circ \]with an electric field of strength \[{{10}^{4}}\text{N}\,{{\text{C}}^{-1}}\]. If it experiences a torque of \[10\sqrt{2}\,\text{N}\,\text{m,}\]the potential energy of the dipole is
  A)
  0.245 J          
  done clear
  B)
  2.45 J
  done clear
  C)
  0.0245 J         
  done clear
  D)
  24.5 J
  done clear
  View Answer play_arrow

• question_answer20)
  A rod is oscillating from a support, freely. The period is
  A)
  \[T=2\pi \sqrt{\frac{l}{g}}\]       
  done clear
  B)
  \[T=2\pi \sqrt{\frac{2l}{g}}\]
  done clear
  C)
  \[T=2\pi \sqrt{\frac{l}{3g}}\]     
  done clear
  D)
  \[T=2\pi \sqrt{\frac{2}{3}\frac{l}{g}}\]
  done clear
  View Answer play_arrow

• question_answer21)
  A parallel plate capacitor is maintained at a certain potential difference. When a 3 mm thick slab is introduced between the plates, in order to maintain the same potential difference, the distance between the plates is increased by 2.4 mm. The dielectric constant of the slab is __.
  View Answer play_arrow

• question_answer22)
  A silver sphere of radius 1 cm and work function 4.7 eV is suspended from an insulating thread in free-space. It is under continuous illumination of light of wavelength 200 nm. As photoelectrons are emitted, the sphere gets charged and acquires a potential. The maximum number of photoelectrons emitted from the sphere is \[A\times {{10}^{7}}\](where 1 < A < 10). The value of Z is ____.
  View Answer play_arrow

• question_answer23)
  The activity of a freshly prepared radioactive sample is \[{{10}^{10}}\]disintegrations per second, whose mean life is \[{{10}^{9}}\] s. The mass of an atom of this radioisotope is\[{{10}^{-25}}\] kg. The mass of the radioactive sample is ____ mg.        
  View Answer play_arrow

• question_answer24)
  The period of revolution of planet A around the sun is 8 times that of-B. The distance of A from the sun is ____ times that of B from the sun.
  View Answer play_arrow

• question_answer25)
  In a car race sound signals emitted by the two cars are detected by the detector on the straight track at the end point of the race. Frequency observed are 330 Hz and 360 Hz and the original frequency is 300 Hz of both cars. Race ends with the separation of 100 m between the cars. Assume both cars move with constant velocity and velocity of sound is 330\[\text{m}\,{{\text{s}}^{-1}}\]. The time taken by winning car is ____ s.
  View Answer play_arrow

• question_answer26)
  A solution containing \[2.675\text{ }g\]of \[CoC{{l}_{2}}.6N{{H}_{3}}\] was passed through a cation exchanger. The solution obtained gave \[4.305\text{ }g\]of \[AgCl\]precipitate with \[AgN{{O}_{3}}\]solution. Determine the formula of the complex. (\[{{M}_{wt}}\] of\[CoC{{l}_{3}}.6N{{H}_{3}}=267.5\])
  A)
  \[[Co{{(N{{H}_{3}})}_{6}}]C{{l}_{3}}\]  
  done clear
  B)
  \[[Co{{(N{{H}_{3}})}_{5}}Cl]C{{l}_{2}}\]
  done clear
  C)
         \[[Co{{(N{{H}_{3}})}_{4}}C{{l}_{2}}]Cl\]      
  done clear
  D)
  \[[Co{{(N{{H}_{3}})}_{3}}C{{l}_{3}}]\]
  done clear
  View Answer play_arrow

• question_answer27)
  In the following reactions A, B, C and D are, respectively, \[\underset{(blue)}{\mathop{CuS{{O}_{4}}.5{{H}_{2}}O}}\,\underset{(bluish\,\,white)}{\mathop{\xrightarrow{100{}^\circ C}A\xrightarrow{230{}^\circ C}}}\,B\underset{(Black)}{\mathop{\xrightarrow{800{}^\circ C}C+D}}\,+\frac{1}{2}{{O}_{2}}\]
  A)
                                                                                            A - \[CuS{{O}_{4}}.4{{H}_{2}}O\]                                B - \[CuS{{O}_{4}}\]   C - \[CuO\]        D - \[S{{O}_{3}}\]
  done clear
  B)
  A - \[CuS{{O}_{4}}.2{{H}_{2}}O\]                             B - \[CuS{{O}_{4}}.{{H}_{2}}O\]    C - \[CuS{{O}_{4}}\]                         D - \[CuO\]
  done clear
  C)
  A - \[CuS{{O}_{4}}.3{{H}_{2}}O\]                             B - \[CuS{{O}_{4}}.\]\[2{{H}_{2}}O\]         C - \[CuO\]                      D - \[S{{O}_{2}}\]
  done clear
  D)
  A - \[CuS{{O}_{4}}.{{H}_{2}}O\]                               B - \[CuO\]    C - \[S{{O}_{3}}\]        D - \[Cu{{O}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer28)
  Two flasks A and B have equal volumes. A is maintained at \[300\text{ }K\]and B at\[600\text{ }K\]. Flask A contains \[{{H}_{2}}\] gas, flask B has an equal mass of \[C{{H}_{4}}\]gas. Assuming ideal behaviour for both the gases. Select the INCORRECT statement
  A)
  \[{{N}_{A}}=8{{N}_{B}}\] (where \[{{N}_{A}}\]and \[{{N}_{B}}\] are the number of molecules in flask A and B respectively).
  done clear
  B)
  \[{{p}_{A}}=4{{p}_{B}}\] (where \[{{p}_{A}}\] and \[{{p}_{B}}\] are the pressure in flask A and B respectively)
  done clear
  C)
  \[{{({{\mu }_{av}})}_{A}}=4{{({{\mu }_{av}})}_{B}}\] and \[{{({{\mu }_{av}})}_{A}}\] are \[{{({{\mu }_{av}})}_{B}}\] average speed of molecules in flask A and B respectively)
  done clear
  D)
  \[{{X}_{A}}=16\,{{X}_{B}}\] (where \[{{X}_{A}}\] and \[{{X}_{B}}\] are the number of collisions per unit area per unit time in flask A and B respectively).
  done clear
  View Answer play_arrow

• question_answer29)
  The gas  and dibasic acid are, respectively,
  A)
  \[N{{O}_{2}},\,{{H}_{2}}{{N}_{2}}{{O}_{2}}\]    
  done clear
  B)
         \[{{N}_{2}}O,\,{{H}_{2}}{{N}_{2}}{{O}_{2}}\]    
  done clear
  C)
       \[{{N}_{2}}\,{{H}_{2}}{{N}_{2}}O\]       
  done clear
  D)
         \[NO,\,\,{{H}_{2}}{{N}_{2}}{{O}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer30)
  CORRECT statement about \[CO\]molecule and \[C{{O}^{\oplus }}\] ion is/are

  (I) Bond orders of \[CO\]and \[C{{O}^{\oplus }}\] are 3 and \[3.5\] respectively.

  (II) \[CO\]molecule is diamagnetic and \[C{{O}^{\oplus }}\]ion is paramagnetic with \[{{\mu }_{MM}}=\sqrt{8}\,BM.\].

  (III) \[CO\](g) is prepared by dehydration of formic acid with cone. \[{{H}_{2}}S{{O}_{4}}\] at\[373\text{ }K\].

  (IV) Mixture of \[CO(g)+{{H}_{2}}(g)\] is called water gas, whereas mixture of \[CO(g)+{{N}_{2}}(g)\] is called synthesis gas.

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

• question_answer31)
  Select the INCORRECT statement about biological importance of \[N{{a}^{\oplus }}\] and \[{{K}^{\oplus }}\] ions.
  A)
  Normal human being contains amount of potassium greater than the amount of sodium.
  done clear
  B)
  \[N{{a}^{\oplus }}\]ions are found primarily outside the cells in blood plasma and other interstitial fluids while K® ions are found inside the cell.
  done clear
  C)
  \[{{K}^{\oplus }}\] ions participate in the transmission of nerve signals and in the transport of sugars and amino acids into cells. \[N{{a}^{\oplus }}\] ions activate many enzymes, participate in the oxidation of glucose to produce ATP.
  done clear
  D)
  \[N{{a}^{\oplus }}\]ions are present to the extent of \[143\text{ }m\text{ }mol\text{ }{{L}^{-1}}\] in blood plasma whereas concentration of \[{{K}^{\oplus }}\] is only \[5\text{ }mmol\text{ }{{L}^{-1}}\] in RBC.
  done clear
  View Answer play_arrow

• question_answer32)
  Out of the following ions,

  (i) \[L{{i}^{\oplus }},\]

  (ii) \[M{{g}^{2+}},\]

  (iii) \[A{{l}^{+3}},\]

  (iv) \[C{{u}^{\oplus }},\]

  (v) \[C{{d}^{2+}},\]

  (vi) \[P{{t}^{4+}},\]

  (vii) \[\overset{\bigcirc -}{\mathop{O}}\,H,\]

  (viii) \[N{{O}_{3}}^{\bigcirc -},\]

  (ix) \[C{{O}_{3}}^{2-},\]

  (x) \[{{H}^{\bigcirc -}}\]

  (xi) \[{{I}^{\bigcirc -}},\]

  (xii) \[C{{N}^{\bigcirc -}},\]

  The total numbers of hard acids and soft acids are, respectively,

  A)
  3, 2                     
  done clear
  B)
         3, 3                    
  done clear
  C)
  4, 3                     
  done clear
  D)
         4, 4
  done clear
  View Answer play_arrow

• question_answer33)
  Calculate the potential of the following half-cells Given:
  A)
  \[-0.907V\]            
  done clear
  B)
         \[0.907V\]    
  done clear
  C)
  \[-0.313\]               
  done clear
  D)
        \[0.313\]
  done clear
  View Answer play_arrow

• question_answer34)
  In rutile structure coordination number of cation and anion are, respectively,
  A)
  \[6,\text{ }3\]            
  done clear
  B)
         \[3,\,\,6\]                   
  done clear
  C)
    \[6,\,\,4\]                   
  done clear
  D)
         \[4,\,\,6\]
  done clear
  View Answer play_arrow

• question_answer35)
  \[{{K}_{c}}\] for the following reaction is This reaction is set-up in aqueous medium. \[1\text{ }mol\]of \[{{I}_{2}}\] and \[0.5\text{ }mol\text{ }{{I}^{\bigcirc -}}\]in 1 L flask, after equilibrium is reached, excess of \[AgN{{O}_{3}}\]gave \[0.25\text{ }mol\]of yellow precipitate.
  A)
  \[1.33\]                   
  done clear
  B)
         \[2.66\]                  
  done clear
  C)
  \[2.00\]                  
  done clear
  D)
         \[3.00\]
  done clear
  View Answer play_arrow

• question_answer36)
  Two weak acids HX and HY have \[{{K}_{a}}\] values \[1.75\times {{10}^{-5}}\]and \[1.3\times {{10}^{-5}},\] respectively, at a certain temperature. An equimolar solution for mixture of two acids is partially neutralised by\[NaOH\]. How is the ratio of the contents of \[{{X}^{\bigcirc -}}\] and \[{{Y}^{\bigcirc -}}\] ions related to the values and molarity?
  A)
  \[\left[ \frac{\alpha }{1-\alpha } \right]=\frac{1.75}{1.3}\times \left[ \frac{\alpha '}{1-\alpha '} \right],\]\[0,\] where \[\alpha \] and \[\alpha \] are ionised fractions of the acids HX and HY respectively.
  done clear
  B)
  The ratio is unrelated to the \[{{K}_{a}}\] values.
  done clear
  C)
  The ratio is unrelated to the molarity.
  done clear
  D)
  The ratio is unrelated to the pH of the solution.
  done clear
  View Answer play_arrow

• question_answer37)
  In the case of a first order reaction, the time required for \[93.75%\] of reaction to take place is x times that required for half of the reaction. Find the value of x.
  A)
  2                      
  done clear
  B)
         3                     
  done clear
  C)
  4          
  done clear
  D)
         5
  done clear
  View Answer play_arrow

• question_answer38)
  An alkane, \[{{C}_{7}}{{H}_{16}}\] is produced by the reaction of di-(3-pentyl) lithium cuperate with \[{{C}_{2}}{{H}_{5}}Br\]. The alkane is
  A)
  3-Methylhexane 
  done clear
  B)
        2-Methylhexane 
  done clear
  C)
        3-Ethylpentane   
  done clear
  D)
       2, 3-Dimethylpentane'
  done clear
  View Answer play_arrow

• question_answer39)
  Product  and  are, respectively,
  A)
    and \[C{{H}_{2}}=C{{H}_{2}}\]
  done clear
  B)
    and \[C{{H}_{3}}-CH=C{{H}_{2}}\]
  done clear
  C)
   
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer40)
  Which of the following is an example of diastereomers?
  A)
  Two gauche forms of butane.
  done clear
  B)
  Products of bromination of cis-2-butene in the presence of \[CC{{l}_{4}}\].
  done clear
  C)
  Gauche and anti-forms of butane.
  done clear
  D)
  Both (a) and (c).
  done clear
  View Answer play_arrow

• question_answer41)
  The major product is
  A)
  Toluene           
  done clear
  B)
         o-Bromotoluene 
  done clear
  C)
        m-Bromo-toluene
  done clear
  D)
         p-Bromotoluene
  done clear
  View Answer play_arrow

• question_answer42)
  Which of the following compound has highest dipole moment?
  A)
  
  done clear
  B)
        
  done clear
  C)
           
  done clear
  D)
        
  done clear
  View Answer play_arrow

• question_answer43)
  One mole of \[HCHO\]and \[2\text{ }mol\]of \[PhCHO\]react with conc.\[NaOH\]. What are the product quantitatively?
  A)
  \[1\text{ }mol\]of \[HCOONa,\]\[1\text{ }mol\] of \[PhC{{H}_{2}}OH\] and \[1\text{ }mol\]of \[PhCOONa\]
  done clear
  B)
  \[1\text{ }mol\]of \[HCOONa,\]\[1\text{ }mol\] of  \[PhC{{H}_{2}}OH\]and \[0.5\text{ }mol\]of \[~PhCOONa\]
  done clear
  C)
  \[1\text{ }mol\]of \[HCOONa,\]\[1.5\text{ }mol\] of \[PhC{{H}_{2}}OH,\]and \[0.5\text{ }mol\]of \[PhCOONa\]
  done clear
  D)
  \[1\text{ }mol\]of \[HCOONa,\]\[2\text{ }mol\] of \[PhC{{H}_{2}}OH,\]and \[2\text{ }mol\]of \[PhCOONa\]
  done clear
  View Answer play_arrow

• question_answer44)
  Which of the following reagent is INCORRECT for the given reaction?
  A)
  i. \[NaN{{O}_{2}}+HCl,\,\,0-5{}^\circ C\] ii. \[{{H}_{3}}P{{O}_{2}}\]             
  done clear
  B)
  i. \[KN{{O}_{2}}+HBr,\,\,0-5{}^\circ C\]  ii. \[N{{a}_{2}}Sn{{O}_{2}}\]
  done clear
  C)
  i. \[HN{{O}_{2}}\] ii. \[{{C}_{2}}{{H}_{5}}OH\] and heat     
  done clear
  D)
  i. \[KN{{O}_{2}}+HCl\]         ii. \[{{H}_{2}}O\] (steam)
  done clear
  View Answer play_arrow

• question_answer45)
  There are two paths (A and B) for the preparation of phenyl-2,4-dinitro phenyl ether Which of the following statements is true?

  (I) Path  is feasible, whereas path  is not

  (II) Path  is feasible, whereas path  is not

  (III) The \[Cl\]of  undergoes \[SN\]reaction because it is activated by the two EWG \[(-N{{O}_{2}})\] groups.

  (IV) The nitration of (Z) does not give (V) but it gives

  because the first nitro groups is deactivated, so the second nitro group enters the other ring

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

• question_answer46)
  \[50\text{ }mL\]of ozone, \[({{O}_{3}})\] at STP was passed through \[50\text{ }mL\]of '5 volume' \[{{H}_{2}}{{O}_{2}}\] solution. The volume strength of \[{{H}_{2}}{{O}_{2}}\] after the reaction is ______.
  View Answer play_arrow

• question_answer47)
  Bond dissociation energy of XY, \[{{X}_{2}}\], and \[{{Y}_{2}}\] (all diatomic molecules) are in the ratio of \[1:1:0.5\]and \[\Delta {{H}_{f}}\] of XY is \[-100\,kJmo{{l}^{-1}},\] The bond dissociation energy of \[{{X}_{2}}\] is \[100x\]. Find the value of x.
  View Answer play_arrow

• question_answer48)
  Ratio of moles of oxidant to reductant in the following reaction is ______.
  View Answer play_arrow

• question_answer49)
  The energy required to ionise a helium atom is equal to\[24.6\text{ }eV\]. The energy required to remove both the electrons from the helium atom in eV is ______.
  View Answer play_arrow

• question_answer50)
  A certain substance A tetra merises in water to the extent of 80%. A solution of \[2.5\text{ }g\]of A in 100 g of water lowers the freezing point by\[0.3{}^\circ C\]. The molar mass of A is ______.
  View Answer play_arrow

• question_answer51)
  Let \[{{z}_{1}}\] and \[{{z}_{2}}\] be complex numbers, then \[|{{z}_{1}}+{{z}_{2}}{{|}^{2}}+|{{z}_{1}}-{{z}_{2}}{{|}^{2}}\]is equal to:
  A)
  \[|{{z}_{1}}{{|}^{2}}+|{{z}_{2}}{{|}^{2}}\]         
  done clear
  B)
    \[2(|{{z}_{1}}{{|}^{2}}+|{{z}_{2}}{{|}^{2}})\]
  done clear
  C)
  \[2(z_{1}^{2}+z_{2}^{2})\]        
  done clear
  D)
    \[4{{z}_{1}}{{z}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer52)
  If \[\cos \,\left( 2{{\sin }^{-1}}x \right)=\frac{1}{9},\]then; x=
  A)
  Only \[2/3\]          
  done clear
  B)
                Only \[-2/3\]
  done clear
  C)
  \[2/3,-2/3\]          
  done clear
  D)
     Neither \[2/3\] nor\[-2/3\]
  done clear
  View Answer play_arrow

• question_answer53)
  Area of the circle in which a chord of length \[\sqrt{2}\] makes an angle \[\frac{\pi }{2}\] at the centre is
  A)
  \[\frac{\pi }{2}\]                     
  done clear
  B)
    \[2\pi \]
  done clear
  C)
  \[\pi \]              
  done clear
  D)
    \[\frac{\pi }{4}\]
  done clear
  View Answer play_arrow

• question_answer54)
  The value of the determinant  is
  A)
  \[5(\sqrt{6}-5)\]          
  done clear
  B)
    \[5\sqrt{3}(\sqrt{6}-5)\]
  done clear
  C)
  \[5(\sqrt{6}-\sqrt{3})\]
  done clear
  D)
    \[\sqrt{2}(\sqrt{7}-\sqrt{5})\]
  done clear
  View Answer play_arrow

• question_answer55)
  The number of real roots of the following equation \[|x{{|}^{2}}-7|x|+12=0\]
  A)
  1
  done clear
  B)
    2         
  done clear
  C)
  3        
  done clear
  D)
    4
  done clear
  View Answer play_arrow

• question_answer56)
  Let \[h(x)=\min \,\{x,{{x}^{2}}\},\] for every real number of x,  Then
  A)
  h is continuous for all x
  done clear
  B)
  h differentiable for all x
  done clear
  C)
  \[h'(x)=2,\]for all \[x>1\]
  done clear
  D)
  h is not differentiable at three values of x.
  done clear
  View Answer play_arrow

• question_answer57)
  Let \[f(x)=a{{x}^{2}}+bx+c,\] \[g(x)=p{{x}^{2}}+qx+r,\] such that \[f(1)=g(1),\] \[f(2)=g(2)\] and \[f(3)-g(3)=2\]. Then \[f(4)-g(4)\] is
  A)
  4                     
  done clear
  B)
    5        
  done clear
  C)
  6         
  done clear
  D)
    7
  done clear
  View Answer play_arrow

• question_answer58)
  \[{{\int{\left\{ 1+2\tan x(\tan x+\sec x) \right\}}}^{1/2}}dx\] is equal to
  A)
  \[\log \,\sec \,x(\sec x-\tan x)+C\]
  done clear
  B)
  \[\log \,cosec\,x(\sec x+\tan x)+C\]
  done clear
  C)
  \[\log \,sec\,x(\sec x+\tan x)+C\]
  done clear
  D)
  \[\log \,(\sec x+\tan x)+C\]
  done clear
  View Answer play_arrow

• question_answer59)
  The point on the parabola \[{{y}^{2}}=8x\] at which the normal is parallel to the line \[x-2y+5=0\]is
  A)
  \[(-1/2,\,2)\]            
  done clear
  B)
  \[(1/2,\,-2)\]
  done clear
  C)
  \[(2,\,-1/2)\]           
  done clear
  D)
                \[(-2,\,1/2)\]
  done clear
  View Answer play_arrow

• question_answer60)
  If \[f:\left[ -6,6 \right]\to R\] is defined by \[f(x)={{x}^{2}}-3\]for \[x\in R\], then  \[\left( fofof \right)\,\left( -1 \right)+\left( fofof \right)\,\left( 0 \right)+\left( fofof \right)\,\left( 1 \right)\] is equal to
  A)
  \[f\left( 4\sqrt{2} \right)\]           
  done clear
  B)
    \[f\left( 3\sqrt{2} \right)\]
  done clear
  C)
  \[f\left( 2\sqrt{2} \right)\]           
  done clear
  D)
    \[f\left( \sqrt{2} \right)\]
  done clear
  View Answer play_arrow

• question_answer61)
  The number of values of x in the interval \[[0,\,3\pi ]\] satisfying the equation \[2{{\sin }^{2}}x+5\sin x-3=0\] is
  A)
  4                     
  done clear
  B)
    6
  done clear
  C)
  1                     
  done clear
  D)
    2
  done clear
  View Answer play_arrow

• question_answer62)
  Let \[\alpha \] and \[\beta \]be the roots of \[a{{x}^{2}}+bx+c=0,\] Then \[\underset{x\to \alpha }{\mathop{\lim }}\,\,\frac{1-\cos (a{{x}^{2}}+bx+c)}{{{(x-\alpha )}^{2}}}\]is equal to:
  A)
  \[0\]                 
  done clear
  B)
         \[\frac{1}{2}{{(\alpha -\beta )}^{2}}\]
  done clear
  C)
  \[\frac{{{a}^{2}}}{2}{{(\alpha -\beta )}^{2}}\]                       
  done clear
  D)
  none of these
  done clear
  View Answer play_arrow

• question_answer63)
  If \[4\hat{i}+7\hat{j}+8\hat{k},\] \[2\hat{i}+3\hat{j}+4\hat{k}\] and \[2\hat{i}+5\hat{j}+7\hat{k}\] are the position vectors of the vertices A, B and C respectively of triangle ABC. The position vector of the point where the bisector of angle A meets BC is :
  A)
  \[\frac{1}{3}(6\hat{i}+13\hat{j}+18\hat{k})\]
  done clear
  B)
  \[\frac{2}{3}(6\hat{i}+12\hat{j}-8\hat{k})\]
  done clear
  C)
  \[\frac{1}{3}(-6\hat{i}-8\hat{j}-9\hat{k})\]  
  done clear
  D)
  \[\frac{2}{3}(-6\hat{i}-12\hat{j}+8\hat{k})\]
  done clear
  View Answer play_arrow

• question_answer64)
  Given vertices \[A(1,1),\] \[B(4,-2)\] and \[C(5,5)\] of a triangle, then the equation of the perpendicular dropped from C to the interior bisector of the angle A is
  A)
  \[y-5=0\]           
  done clear
  B)
    \[x-5=0\]
  done clear
  C)
  \[y+5=0\]           
  done clear
  D)
    \[x+5=0\]
  done clear
  View Answer play_arrow

• question_answer65)
  The function \[f(x)=1+x\,(\sin x)\,[\cos x],\] \[0<x\le \frac{\pi }{2}\](where \[[.]\] is GLF.)
  A)
  is continuous on \[\left( 0,\frac{\pi }{2} \right)\]
  done clear
  B)
  is strictly increasing in \[\left( 0,\frac{\pi }{2} \right)\]
  done clear
  C)
  is strictly decreasing in \[\left( 0,\frac{\pi }{2} \right)\]
  done clear
  D)
  has global maximum value 2       
  done clear
  View Answer play_arrow

• question_answer66)
            The angular elevation of a tower CD at a point A due south of it is \[60{}^\circ \]and at a point B due west of A, the elevation is \[30{}^\circ \]. If \[AB=3\text{ }km,\]the height of the tower is
  A)
  \[2\sqrt{3}\,km\]
  done clear
  B)
                \[2\sqrt{6}\,km\]
  done clear
  C)
  \[\frac{3\sqrt{3}}{2}\,km\]          
  done clear
  D)
    \[\frac{3\sqrt{6}}{4}\,km\]
  done clear
  View Answer play_arrow

• question_answer67)
  The solution of the equation \[{{\sin }^{-1}}\left( \frac{dy}{dx} \right)=x+y\] is
  A)
  \[\tan (x+y)+\sec (x+y)=x+c\]
  done clear
  B)
  \[\tan (x+y)-\sec (x+y)=x+c\]
  done clear
  C)
  \[\tan (x+y)+\sec (x+y)=x+c=0\]
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer68)
  The contrapositive of \[p\to (\tilde{\ }q\to \tilde{\ }r)\] is -
  A)
  \[(\tilde{\ }q\wedge r)\to \tilde{\ }p\]
  done clear
  B)
    \[(q\to r)\to \tilde{\ }p\]
  done clear
  C)
  \[(q\vee \tilde{\ }r)\to \tilde{\ }p\]        
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer69)
  If \[(2,3,-1)\] is the foot of the perpendicular from \[(4,2,1)\] to a plane, then the equation of the plane
  A)
  \[2x-y-2z-3=0\]           
  done clear
  B)
  \[2x+y-2z-9=0\]
  done clear
  C)
  \[2x+y+2z-5=0\]       
  done clear
  D)
  \[2x-y+2z+1=0\]
  done clear
  View Answer play_arrow

• question_answer70)
  If \[\log \,2,\] \[\log \,({{2}^{x}}-1)\] and \[\log \,({{2}^{x}}+3)\] are in A. P., then the value of x is:
  A)
  \[5\]                    
  done clear
  B)
    \[3\]
  done clear
  C)
  \[{{\log }_{3}}2\]                
  done clear
  D)
    \[{{\log }_{2}}5\]
  done clear
  View Answer play_arrow

• question_answer71)
  Five digit number divisible by 3 is to be formed by using 0, 1, 2, 3, 4, 6 without repetition. Total number of such numbers are
  View Answer play_arrow

• question_answer72)
  A stone is dropped into a quiet lake and waves move in a circle at a speed of \[3.5\text{ }cm/sec.\]At the instant when the radius of the circular wave is\[7.5\text{ }cm\]. Then, the rate of increasing in the enclosed area is \[k\,\pi ,\] then k is
  View Answer play_arrow

• question_answer73)
  Let f: \[R\to R\]be a differentiable function and \[f(1)=4.\]. Then the value of \[\underset{x\to 1}{\mathop{\lim }}\,\,\frac{\int\limits_{4}^{f(x)}{2t\,dt}}{x-1}.\]if \[(1)=2\]is -
  View Answer play_arrow

• question_answer74)
  For natural numbers m, n if \[{{(1-y)}^{m}}{{(1+y)}^{n}}\] \[=1+{{a}_{1}}y+{{a}_{2}}{{y}^{2}}+...\]and \[{{a}_{1}}={{a}_{2}}=10,\] then \[(m+n)\] is
  View Answer play_arrow

• question_answer75)
  One dice is thrown three times and the sum of the thrown numbers is 15. If the probability for which number 4 appears in first throw is p, then \[\frac{1}{p}\] is:
  View Answer play_arrow