JEE Main & Advanced Sample Paper

done JEE Main Sample Paper-7 Total Questions - 90   

• question_answer1)
  Three amplifiers with amplification \[{{A}_{1}},\,{{A}_{2}}\] and \[{{A}_{3}}\] are connected in series. The output for unit input voltage supplied is:
  A)
   \[\frac{{{A}_{1}}{{A}_{2}}}{{{A}_{3}}}\]                
  done clear
  B)
   \[\frac{{{A}_{1}}{{A}_{3}}}{{{A}_{2}}}\]
  done clear
  C)
   \[{{A}_{1}}{{A}_{2}}{{A}_{3}}\]                 
  done clear
  D)
   \[{{A}_{1}}+{{A}_{2}}+{{A}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer2)
  In the Zener diode circuit used as a dc regulated power supply, the load current was 4.0 mA with an unregulated power of 10 volt. The Zener voltage is 6.0 volt and permissible current is five times the load current. The series resistance to be used \[({{R}_{s}})\] is
  A)
   \[100\,\Omega \]                           
  done clear
  B)
   \[169\,\Omega \]
  done clear
  C)
   \[167\,\Omega \]                           
  done clear
  D)
   \[200\,\Omega \]
  done clear
  View Answer play_arrow

• question_answer3)
  Myopic eye is corrected using a concave lens of suitable focal length, because it
  A)
   magnifies the object
  done clear
  B)
   brings the object nearer
  done clear
  C)
   reduces the size of the object
  done clear
  D)
   reduces the size and forms image at the far point
  done clear
  View Answer play_arrow

• question_answer4)
  A mobile phone of width 5 cm and length 10 cm, is placed parallel to its lengths, such that one of its lengths is along the principal axis of a concave mirror of focal length 30 cm. The far point of its length is at the centre of curvature of the mirror. The width of the image will be
  A)
   5 cm
  done clear
  B)
   varies from 5 to 7.5 cm
  done clear
  C)
   cannot be found
  done clear
  D)
   varies from 7.5 to 9 cm
  done clear
  View Answer play_arrow

• question_answer5)
  Equi-potential surfaces due to a point charge are shown here. The electric field created by these equi-potential surfaces can be best written as
  A)
   \[\frac{kq}{r}\]                                
  done clear
  B)
   \[\frac{kq}{{{r}^{2}}}\]
  done clear
  C)
   \[\frac{kq}{{{r}^{3}}}\]                                 
  done clear
  D)
   \[\frac{2kq}{{{r}^{3}}}\]
  done clear
  View Answer play_arrow

• question_answer6)
  The potential energy function of a diatomic molecule is given by \[U(x)=\frac{a}{{{x}^{12}}}-\frac{b}{{{x}^{6}}}\]. The position \[x\] of stable equilibrium is
  A)
   \[\sqrt{\frac{a}{b}}\]                                    
  done clear
  B)
   \[{{\left( \frac{2a}{b} \right)}^{1/3}}\]
  done clear
  C)
   \[{{\left( \frac{2a}{b} \right)}^{1/6}}\]                  
  done clear
  D)
   \[{{\left( \frac{a}{b} \right)}^{1/3}}\]
  done clear
  View Answer play_arrow

• question_answer7)
  A molecule of oxygen moving with a speed of 200 m/s collides elastically with another oxygen molecule at rest. After the collision, if one moves at an angle of \[42{}^\circ \] from the initial line, the other molecule will move at an angle on the other side of the initial line by
  A)
  \[42{}^\circ \]                                   
  done clear
  B)
  \[138{}^\circ \]
  done clear
  C)
  \[48{}^\circ \]
  done clear
  D)
   cannot be found
  done clear
  View Answer play_arrow

• question_answer8)
  Statement-1: A system of cylinder with non- accelerated motion of piston and large temperature gradient is called a Quasi-static process. Statement-2: In a Quasi-static process pressure and temperature of the surrounding and the cylinder are the same.
  A)
   Both statements are True and Statement-2 explains Statement-1.
  done clear
  B)
   Both statements are True but Statement-2 does not explain 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_answer9)
  Statement-1: Packing of mechanical wrist watches and sensitive instruments is done in soft-iron case. Statement-2: Soft iron permits magnetic field lines to pass through them.
  A)
   Both statements are True and Statement-2 explains Statement-1.
  done clear
  B)
   Both statements are True but Statement-2 does not explain 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_answer10)
  A point object approaches a convex mirror with a constant speed v along its optical axis. The speed of the image is always
  A)
   less than v        
  done clear
  B)
   greater than v
  done clear
  C)
   equal to v          
  done clear
  D)
   cannot be found
  done clear
  View Answer play_arrow

• question_answer11)
  A charged particle enters a unifrom magnetic field at an `angle of \[45{}^\circ \] with the magnetic field. The pitch of the helical path followed is P. The radius of the helix will be
  A)
   \[\frac{P}{\sqrt{2\pi }}\]                             
  done clear
  B)
   \[\sqrt{2P}\]
  done clear
  C)
   \[\frac{P}{2\pi }\]                                           
  done clear
  D)
   \[\frac{\sqrt{2}P}{\pi }\]
  done clear
  View Answer play_arrow

• question_answer12)
  A test tube of uniform cross-section A and length \[\ell \] is immersed inverted into a liquid of density \[\rho \]. The liquid rises to a height \[x(<\ell )\] in the tube. The excess pressure at the interface between trapped air and the liquid in the inverted tube is [Given : Atmospheric pressure is h column of mercury \[\left( {{\rho }_{m}} \right)\]]
  A)
   \[h{{\rho }_{m}}g\]                       
  done clear
  B)
   \[\frac{h({{\rho }_{m+\rho }})gx}{(\ell -x)}\]
  done clear
  C)
   \[h({{\rho }_{m}}-\rho )g\]                        
  done clear
  D)
   \[\frac{h{{\rho }_{m}}gx}{\ell -x}\]
  done clear
  View Answer play_arrow

• question_answer13)
  In a resonance tube apparatus, the first and the second resonating lengths are \[{{\ell }_{1}}\] and \[{{\ell }_{2}}\] respectively. If the velocity of the wave is \[{{v}_{1}}\] then the end correction is
  A)
   \[e=\frac{{{\ell }_{1}}-3{{\ell }_{2}}}{2}\]                             
  done clear
  B)
   \[e=\frac{{{\ell }_{2}}-3{{\ell }_{1}}}{2}\]
  done clear
  C)
   \[e=\frac{{{\ell }_{1}}-{{\ell }_{2}}}{2}\]                
  done clear
  D)
   \[e=\frac{{{\ell }_{2}}-{{\ell }_{1}}}{2v}\]
  done clear
  View Answer play_arrow

• question_answer14)
  A body of mass 6 kg moves in a straight line according to the equation \[x=({{t}^{3}}-8t)m\] where t is in second. The momentum of the body at the end of 4th second is (in kg m/s)
  A)
   560                       
  done clear
  B)
   192
  done clear
  C)
   240                       
  done clear
  D)
   6
  done clear
  View Answer play_arrow

• question_answer15)
  A SHM of a 2g mass is defined by \[\frac{{{d}^{2}}y}{d{{t}^{2}}}+0.2\frac{dy}{dt}+36y=0\]. Then the time period and quality factor Q are respectively:
  A)
   \[\frac{\pi }{3}s,\,30\]                  
  done clear
  B)
   \[\frac{\pi }{2},\,s,20\]
  done clear
  C)
   \[\pi \,s,\,10\]                 
  done clear
  D)
   \[2\pi s,\,10\]
  done clear
  View Answer play_arrow

• question_answer16)
  A triangular loop of equal sides of length \[\ell \] carries a current. The loop is kept in a magnetic field B, directed parallel to one side PQ (as shown). The torque on the loop is
  A)
   zero                                     
  done clear
  B)
   \[\sqrt{3}i\ell B\]
  done clear
  C)
   \[3i{{\ell }^{2}}B\]                          
  done clear
  D)
   \[\frac{\sqrt{3}}{4}i{{\ell }^{2}}B\]
  done clear
  View Answer play_arrow

• question_answer17)
  A capacitor \[1\,\mu F,\] a resistor 20 and a 4H inductor are connected in parallel to a conductor of length 2m sliding with a constant velocity of 1 m/s. If there exists a magnetic field of 2T directed into the plane of the coil, the power stored in the inductor at \[t=1\] second is [Assume that the Magnetic field was activated at \[t=0\]]
  A)
   4 W                                      
  done clear
  B)
   8 W
  done clear
  C)
   12 W                    
  done clear
  D)
   2 W
  done clear
  View Answer play_arrow

• question_answer18)
  In two surfaces of a lens (shown below) \[{{R}_{1}}\] and \[{{R}_{2}}\] are both 5 cm and is made of a material of refractive index 3/2. The power of the lens such formed is
  A)
   0                                            
  done clear
  B)
   500 D
  done clear
  C)
   20 D                                     
  done clear
  D)
   \[\infty \]
  done clear
  View Answer play_arrow

• question_answer19)
  The kinetic energies associated with a proton, an electron and an alpha particle each having the same de-Broglie wavelength are \[{{E}_{1}},\,{{E}_{2}}\] and \[{{E}_{3}}\] respectively. Then
  A)
   \[{{E}_{1}}>{{E}_{2}}>{{E}_{3}}\]                             
  done clear
  B)
   \[{{E}_{1}}<{{E}_{2}}<{{E}_{3}}\]
  done clear
  C)
   \[{{E}_{1}}>{{E}_{3}}>{{E}_{2}}\]                             
  done clear
  D)
   \[{{E}_{2}}>{{E}_{1}}>{{E}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer20)
  Two moles of a mono-atomic gas, undergoes a process such that the temperature changes from \[\theta \] to \[4\theta \]. The heat supplied to the system is
  A)
   \[15R\theta \]                 
  done clear
  B)
   \[\frac{3}{8}R\theta \]
  done clear
  C)
   \[\frac{2}{15}{{R}^{2}}\theta \]                
  done clear
  D)
   \[\frac{2}{15}R\theta \]
  done clear
  View Answer play_arrow

• question_answer21)
  A time varying force \[F=2t\] acts on a spool as shown. The angular momentum of the spool at time t about the lower most point in contact with the ground is
  A)
   \[\frac{{{r}^{2}}{{t}^{2}}}{R}\]                  
  done clear
  B)
   \[\frac{{{(R+r)}^{2}}{{t}^{2}}}{r}\]
  done clear
  C)
   \[(R+r){{t}^{2}}\]                            
  done clear
  D)
   Depends on mass
  done clear
  View Answer play_arrow

• question_answer22)
  The count rate of 100 cc of a radioactive liquid is R. After removing some liquid, the count rate becomes R/10 after three half-lives. The initial volume of the liquid available after removing some liquid is
  A)
   20 cc                    
  done clear
  B)
   40 cc
  done clear
  C)
   60 cc                                    
  done clear
  D)
   80 cc
  done clear
  View Answer play_arrow

• question_answer23)
  Statement-1: The shortest wavelength of X-rays emitted from an X-ray tube is independent of voltage applied to the tube. Statement-2: Wavelength of characteristic X-ray spectrum depends on atomic number of the target material.
  A)
   Both statements are True and Statement-2 explains Statement-1.
  done clear
  B)
   Both statements are True but Statement-2 does not explain 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_answer24)
  A bimetallic strip is formed of two identical strips of copper and brass, (\[{{\alpha }_{c}},\,{{\alpha }_{b}}\] are temperature coefficient of expansion of copper and brass respectively and \[{{\alpha }_{c}}>\,{{\alpha }_{b}}\]). When heated to a temperature t, the radius of curvature of the strip becomes proportional to
  A)
   \[{{({{\alpha }_{c}}-{{\alpha }_{b}})}^{-1}}\]                       
  done clear
  B)
   \[\frac{{{\alpha }_{b}}}{{{\alpha }_{c}}}\]
  done clear
  C)
   \[\frac{{{\alpha }_{b}}\times {{\alpha }_{c}}}{{{\alpha }_{b}}+{{\alpha }_{c}}}\]                 
  done clear
  D)
   \[({{\alpha }_{c}}-{{\alpha }_{b}})\]
  done clear
  View Answer play_arrow

• question_answer25)
  The \[I-V\] characteristic of a conductor at two different temperatures \[{{T}_{1}}\] and \[{{T}_{2}}\] are shown below. The difference in temperature is proportional to
  A)
   \[\tan \theta \]                               
  done clear
  B)
   \[\cot \theta \]
  done clear
  C)
   \[\cot 2\theta \]                             
  done clear
  D)
   \[\sin 2\theta \]
  done clear
  View Answer play_arrow

• question_answer26)
  A nucleus of mass number \[A=220\] at rest undergoes an a-decay. If the Q-value of the decay is 5.5 Me V, the kinetic energy of the a-particle is
  A)
   5.0 MeV             
  done clear
  B)
   5.4 MeV
  done clear
  C)
   5.6 MeV             
  done clear
  D)
   6.0 MeV
  done clear
  View Answer play_arrow

• question_answer27)
  Three rods of equal lengths and cross-sectional areas are joined in series. The thermal conductivities are in the ratio 2 : 4 : 3. The free ends consisting of the rods of least and second highest thermal conductivities are maintained at +473 K and \[18{}^\circ C\] respectively. Under steady conditions, the temperature at the junctions are
  A)
   \[{{116}^{o}}C,\,{{27}^{o}}C\]  
  done clear
  B)
   \[{{116}^{o}}C,\,{{74}^{o}}C\]
  done clear
  C)
   \[{{74}^{o}}C,\,{{27}^{o}}C\]                     
  done clear
  D)
   \[{{100}^{o}}C,\,{{27}^{o}}C\]
  done clear
  View Answer play_arrow

• question_answer28)
  A cylinder of mass 10 kg and radius 15 cm is undergoing pure rolling on an inclined plane of inclination\[30{}^\circ \]. The coefficient of friction is \[{{\mu }_{s}}=0.25\]. The force of friction on the cylinder is \[(g=10\,m/{{s}^{2}})\]
  A)
   10 N                     
  done clear
  B)
   15 N
  done clear
  C)
   16.3 N                 
  done clear
  D)
   25 N
  done clear
  View Answer play_arrow

• question_answer29)
  The component of \[(\hat{i}+\hat{j})\] along \[(\hat{i}-\hat{j})\] is
  A)
   0                                            
  done clear
  B)
   \[\frac{1}{\sqrt{2}}(\hat{i}-\hat{j})\]
  done clear
  C)
   \[\frac{1}{\sqrt{2}}(\hat{i}+\hat{j})\]                    
  done clear
  D)
   \[\frac{\hat{i}-\hat{j}}{2}\]
  done clear
  View Answer play_arrow

• question_answer30)
  The \[v-t\] graph given here represents a ball
  A)
   dropped from a height
  done clear
  B)
   thrown up from the ground
  done clear
  C)
   dropped ball bouncing to have second collision
  done clear
  D)
   cannot be found
  done clear
  View Answer play_arrow

• question_answer31)
  Which is the correct order of increasing dipole moment?
  A)
   \[ClF<BrCl<NO<HCl<Lil\]
  done clear
  B)
   \[LiI<BrCl<HCl<ClF<NO\]
  done clear
  C)
   \[BrCl<NO<HCl<ClF<LiI\]
  done clear
  D)
   \[NO<BrCl<HCl<LiI<ClF\]
  done clear
  View Answer play_arrow

• question_answer32)
  \[C{{H}_{3}}-\overset{\begin{smallmatrix}  O \\  || \end{smallmatrix}}{\mathop{C}}\,-\overset{18}{\mathop{O}}\,-\underset{\begin{smallmatrix}  | \\  C{{H}_{3}} \end{smallmatrix}}{\overset{\begin{smallmatrix}  C{{H}_{3}} \\  | \end{smallmatrix}}{\mathop{C}}}\,-C{{H}_{3}}\text{A}(\text{an}\,\text{acid})+\text{B}\]where A and B are respectively.
  A)
   \[C{{H}_{3}}-\overset{\begin{smallmatrix}  O \\  || \end{smallmatrix}}{\mathop{C}}\,-\underset{18}{\mathop{OH}}\,+C{{H}_{3}}-\underset{\begin{smallmatrix}  | \\  C{{H}_{3}} \end{smallmatrix}}{\overset{\begin{smallmatrix}  C{{H}_{3}} \\  | \end{smallmatrix}}{\mathop{C}}}\,-OH\]
  done clear
  B)
   \[C{{H}_{3}}-\overset{18}{\mathop{\overset{\begin{smallmatrix}  O \\  || \end{smallmatrix}}{\mathop{C}}\,}}\,-\underset{{}}{\mathop{OH}}\,+C{{H}_{3}}-\underset{\begin{smallmatrix}  | \\  C{{H}_{3}} \end{smallmatrix}}{\overset{\begin{smallmatrix}  C{{H}_{3}} \\  | \end{smallmatrix}}{\mathop{C}}}\,-OH\]
  done clear
  C)
   \[C{{H}_{3}}-\overset{\begin{smallmatrix}  O \\  || \end{smallmatrix}}{\mathop{C}}\,-\underset{{}}{\mathop{OH}}\,+C{{H}_{3}}-\underset{\begin{smallmatrix}  | \\  C{{H}_{3}} \end{smallmatrix}}{\overset{\begin{smallmatrix}  C{{H}_{3}} \\  | \end{smallmatrix}}{\mathop{C}}}\,-\overset{18}{\mathop{O}}\,-H\]
  done clear
  D)
   \[C{{H}_{3}}-\overset{18}{\mathop{\overset{\begin{smallmatrix}  O \\  || \end{smallmatrix}}{\mathop{C}}\,}}\,-\underset{{}}{\mathop{OH}}\,+C{{H}_{3}}-\underset{\begin{smallmatrix}  | \\  C{{H}_{3}} \end{smallmatrix}}{\overset{\begin{smallmatrix}  C{{H}_{3}} \\  | \end{smallmatrix}}{\mathop{C}}}\,-\overset{18}{\mathop{O}}\,H\]
  done clear
  View Answer play_arrow

• question_answer33)
  Given that \[{{E}^{o}}=\,+0.897\,V,\] calculate \[E\] at \[{{25}^{o}}C\] for  \[Pb(s)|P{{b}^{2+}}(0.040\,M)||F{{e}^{3+}}(0.20\,M),\] \[F{{e}^{2+}}(0.010M)|Pt(s)\]
  A)
   \[+0.779\,V\]                   
  done clear
  B)
   \[+0.935\,V\]
  done clear
  C)
   \[+1.015\,V\]                   
  done clear
  D)
   \[+1.134\,V\]
  done clear
  View Answer play_arrow

• question_answer34)
  If the radius of first Bohr's orbit is \[{{a}_{0}},\] then the radius of third Bohr's orbit would be
  A)
   \[3{{a}_{0}}\]                                   
  done clear
  B)
   \[6{{a}_{0}}\]
  done clear
  C)
   \[9{{a}_{0}}\]                                   
  done clear
  D)
   \[\frac{1}{9}{{a}_{0}}\]
  done clear
  View Answer play_arrow

• question_answer35)
  Correct order of stability of following carbocation is
  A)
   \[{{\left( {{C}_{6}}{{H}_{5}} \right)}_{3}}\overset{+}{\mathop{C}}\,>{{\left( C{{H}_{3}} \right)}_{3}}\overset{+}{\mathop{C}}\,>{{\left( CC{{l}_{3}} \right)}_{3}}\overset{+}{\mathop{C}}\,>{{\left( C{{F}_{3}} \right)}_{3}}\overset{+}{\mathop{C}}\,\]
  done clear
  B)
   \[{{\left( {{C}_{6}}{{H}_{5}} \right)}_{3}}\overset{+}{\mathop{C}}\,>{{\left( CC{{l}_{3}} \right)}_{3}}\overset{+}{\mathop{C}}\,>{{\left( C{{F}_{3}} \right)}_{3}}\overset{+}{\mathop{C}}\,>{{\left( C{{H}_{3}} \right)}_{3}}\overset{+}{\mathop{C}}\,\]
  done clear
  C)
   \[{{\left( C{{H}_{3}} \right)}_{3}}\overset{+}{\mathop{C}}\,>{{\left( {{C}_{6}}{{H}_{5}} \right)}_{3}}\overset{+}{\mathop{C}}\,>{{\left( C{{F}_{3}} \right)}_{3}}\overset{+}{\mathop{C}}\,>{{\left( CC{{l}_{3}} \right)}_{3}}\overset{+}{\mathop{C}}\,\]
  done clear
  D)
   \[{{\left( C{{H}_{3}} \right)}_{3}}\overset{+}{\mathop{C}}\,>{{\left( CC{{l}_{3}} \right)}_{3}}\overset{+}{\mathop{C}}\,>{{\left( {{C}_{6}}{{H}_{5}} \right)}_{3}}\overset{+}{\mathop{C}}\,>{{\left( C{{F}_{3}} \right)}_{3}}\overset{+}{\mathop{C}}\,\]
  done clear
  View Answer play_arrow

• question_answer36)
  Deviation from the ideal gas law is greatest at
  A)
   low temperature and low pressure
  done clear
  B)
   low temperature and high pressure
  done clear
  C)
   high temperature and high pressure
  done clear
  D)
   high temperature and low pressure
  done clear
  View Answer play_arrow

• question_answer37)
  Consider the following reaction. Which of the following alkenes is formed as the major product?
  A)
                                         
  done clear
  B)
  
  done clear
  C)
                                                   
  done clear
  D)
   \[C{{H}_{2}}=C{{H}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer38)
  Which of the following alkaline earth metal sulphates has hydration enthalpy higher than lattice enthalpy?
  A)
   \[CaS{{O}_{4}}\]                             
  done clear
  B)
   \[BeS{{O}_{4}}\]
  done clear
  C)
   \[BaS{{O}_{4}}\]                             
  done clear
  D)
   \[SrS{{O}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer39)
  Solubility of \[A{{g}_{2}}Cr{{O}_{4}}\] in water is \[2\times {{10}^{-3}}\,\text{mol}\,\text{1}{{\text{t}}^{-1}}\]. Solubility product of \[A{{g}_{2}}Cr{{O}_{4}}\] is
  A)
   \[3.2\times {{10}^{-8}}\]                             
  done clear
  B)
   \[4\times {{10}^{-6}}\]
  done clear
  C)
   \[4\times {{10}^{-9}}\]                 
  done clear
  D)
   \[3.2\times {{10}^{-9}}\]
  done clear
  View Answer play_arrow

• question_answer40)
  Which one of the following halides will not react with dimethyl sulphoxide?
  A)
   \[{{C}_{6}}{{H}_{5}}-CO-C{{H}_{2}}Br\] 
  done clear
  B)
   \[{{C}_{6}}{{H}_{5}}-\underset{\begin{smallmatrix}  | \\  Br \end{smallmatrix}}{\mathop{C}}\,H-C{{H}_{3}}\]
  done clear
  C)
   \[{{C}_{6}}{{H}_{5}}-C{{(C{{H}_{3}})}_{2}}-Br\]
  done clear
  D)
   \[{{C}_{6}}{{H}_{5}}-\underset{\begin{smallmatrix}  | \\  Br \end{smallmatrix}}{\mathop{C}}\,H-{{C}_{6}}{{H}_{5}}\]
  done clear
  View Answer play_arrow

• question_answer41)
  An \[\alpha -\]particle of mass 4.0026 amu has a velocity of 10% of the speed of light. What is its de-Broglie wavelength (in m)?
  A)
   \[3.32\times {{10}^{-15}}m\]    
  done clear
  B)
   \[3.3\times {{10}^{-18}}m\]
  done clear
  C)
   \[3.7\times {{10}^{-16}}m\]                       
  done clear
  D)
   \[1.22\times {{10}^{-15}}m\]
  done clear
  View Answer play_arrow

• question_answer42)
  A radioactive isotope X with half-life of \[6.93\times {{10}^{9}}\] years decays to Y which is stable. A sample of rock from the moon was found to contain both the elements X and Y in the mole ratio 1 : 7. What is the age of rock?
  A)
   \[2.079\times {{10}^{10}}\] years            
  done clear
  B)
   \[1.94\times {{10}^{9}}\] years
  done clear
  C)
   \[2\times {{10}^{15}}\] years    
  done clear
  D)
   \[{{10}^{15}}\] years
  done clear
  View Answer play_arrow

• question_answer43)
  
  A)
                                                   
  done clear
  B)
  
  done clear
  C)
                                          
  done clear
  D)
  
  done clear
  View Answer play_arrow

• question_answer44)
  Enthalpy of neutralization of \[HCl\] by \[NaOH\] is \[-55.84\,kJ\,mo{{l}^{-1}}\] and by \[N{{H}_{4}}OH\] is \[-51.34\,kJ\,mo{{l}^{-1}}\]. The enthalpy of ionization of \[N{{H}_{4}}OH\] is
  A)
   \[4.5\,kJ\,mo{{l}^{-1}}\]                              
  done clear
  B)
   \[-4.5kJ\,mo{{l}^{-1}}\]
  done clear
  C)
   \[1.8\,kJ\,mo{{l}^{-1}}\]                              
  done clear
  D)
   \[-1.8\,kJ\,mo{{l}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer45)
  The most stable canonical structure for diazomethane is
  A)
   \[{{H}_{2}}\overset{(-)}{\mathop{C}}\,-\overset{(+)}{\mathop{N}}\,\equiv N\]              
  done clear
  B)
   \[{{H}_{2}}\overset{(+)}{\mathop{C}}\,-N=\overset{(-)}{\mathop{N}}\,\]
  done clear
  C)
   \[{{H}_{2}}C=\overset{(+)}{\mathop{N}}\,=\overset{(-)}{\mathop{N}}\,\]         
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer46)
  Which of the following statements about the oxidizing property of \[KMn{{O}_{4}}\] in acidic medium is not correct?
  A)
   \[{{H}_{2}}S\] is oxidized to \[SO_{4}^{2-}\]
  done clear
  B)
   \[{{H}_{2}}S\] is oxidized to S
  done clear
  C)
   \[SO_{3}^{2-}\]gets oxidized to \[SO_{4}^{2-}\]
  done clear
  D)
   \[S{{n}^{2+}}\] gets oxidized to \[S{{n}^{4+}}\]
  done clear
  View Answer play_arrow

• question_answer47)
  Which of the following plot does not represent first order reaction? (\[r=\] rate at time t and \[{{r}_{0}}\] is the initial rate)
  A)
  
  done clear
  B)
  
  done clear
  C)
  
  done clear
  D)
  
  done clear
  View Answer play_arrow

• question_answer48)
    Solid \[PC{{l}_{5}}\] exists as
  A)
   \[PC{{l}_{5}}\]                 
  done clear
  B)
   \[[PCl_{4}^{+}]\]
  done clear
  C)
   \[[PCl_{6}^{-}]\]                             
  done clear
  D)
   \[[PCl_{4}^{+}][PCl_{6}^{-}]\]
  done clear
  View Answer play_arrow

• question_answer49)
  A 0.1 M solution of \[KN{{O}_{3}}\] has an osmotic pressure of 4.5 atm at\[27{}^\circ C\]. The degree of dissociation of \[KN{{O}_{3}}\] is
  A)
   0.25                      
  done clear
  B)
   0.79
  done clear
  C)
   0.82                      
  done clear
  D)
   0.49
  done clear
  View Answer play_arrow

• question_answer50)
  The colour of \[H{{g}_{2}}C{{l}_{2}}\] changes from white to black when treated with \[N{{H}_{3}}\]. This is due to formation of complex.
  A)
   \[Hg(N{{H}_{2}})Cl\]     
  done clear
  B)
   \[[Hg{{(N{{H}_{3}})}_{2}}]Cl\]
  done clear
  C)
   \[{{[Hg{{(N{{H}_{3}})}_{4}}]}^{+}}\]       
  done clear
  D)
   \[Hg(N{{H}_{3}})Cl\]
  done clear
  View Answer play_arrow

• question_answer51)
  Which metallurgy involves leaching?
  A)
   \[Ag\]                                 
  done clear
  B)
   \[Au\]
  done clear
  C)
   \[Fe\]                                  
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer52)
  Bond energy of \[C-C\] and \[C=C\] is 348 and 615 kJ mol-1 respectively. The enthalpy change for the isomerization of gaseous propene to gaseous cyclo propane is \[\text{Propen}{{\text{e}}_{\text{(g)}}}\xrightarrow{\,}\text{Cyclopropan}{{\text{e}}_{\text{(g)}}}\]
  A)
   \[-81\,kJ\,mo{{l}^{-1}}\]                             
  done clear
  B)
   \[-180\,kJ\,mo{{l}^{-1}}\]
  done clear
  C)
   \[-79\,kJ\,mo{{l}^{-1}}\]             
  done clear
  D)
   \[-89\,kJ\,mo{{l}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer53)
  Which pair gives \[C{{l}_{2}}\] at room temperature?
  A)
   Conc. \[HCl+KMn{{O}_{4}}\]     
  done clear
  B)
   \[NaCl+\] conc. \[{{H}_{2}}S{{O}_{4}}\]
  done clear
  C)
   \[NaCl+Mn{{O}_{2}}\]
  done clear
  D)
   \[NaCl+\] conc. \[HN{{O}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer54)
  \[n\]-butane on heating with \[AlC{{l}_{3}}\] in presence of \[HCl\] gives
  A)
   \[C{{H}_{3}}-\overset{\begin{smallmatrix}  C{{H}_{3}} \\  | \end{smallmatrix}}{\mathop{C}}\,H-C{{H}_{3}}\]
  done clear
  B)
   \[C{{H}_{3}}-C{{H}_{2}}-C{{H}_{2}}-C{{H}_{2}}-Cl\]
  done clear
  C)
   \[\]
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer55)
  The boiling point of an azeotropic mixture of water and ethyl alcohol is less than that of theoretical value of water and alcohol mixture. Hence, the mixture shows
  A)
   that solution is highly saturated
  done clear
  B)
   positive deviation from Raoult's law
  done clear
  C)
   negative deviation from Raoult's law
  done clear
  D)
   solution is ideal
  done clear
  View Answer play_arrow

• question_answer56)
  Which of the following statement is correct?
  A)
   \[{{[Co{{(N{{H}_{3}})}^{6}}]}^{2+}}\] is oxidized to diamagnetic \[{{[Co{{(N{{H}_{3}})}^{6}}]}^{3+}}\] by the oxygen in air.
  done clear
  B)
   \[{{[Fe{{(CN)}_{6}}]}^{3-}}\] is stable but \[{{[Fe{{F}_{6}}]}^{3-}}\] is unstable.
  done clear
  C)
   \[{{[NiC{{l}_{4}}]}^{2-}}\] is unstable with respect to \[{{[NiB{{r}_{4}}]}^{2-}}\].
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer57)
  Which of the following will act as best protective colloid?
  A)
   Gelatin (gold number = 0.005)
  done clear
  B)
   Starch (gold number = 25)
  done clear
  C)
   Garabic (gold number =0.15)
  done clear
  D)
   Egg albumin (gold number = 0.08)
  done clear
  View Answer play_arrow

• question_answer58)
  When heated with cone. \[HN{{O}_{3}},\] proteins give yellow colour. This test is called
  A)
   oxidising test
  done clear
  B)
   Xantho proteic test
  done clear
  C)
   Acid base test
  done clear
  D)
   Hoppe's test
  done clear
  View Answer play_arrow

• question_answer59)
  Ozonolysis of which of the following produces a tricarboxylic acid?
  A)
                                        
  done clear
  B)
  
  done clear
  C)
                                       
  done clear
  D)
  
  done clear
  View Answer play_arrow

• question_answer60)
  Degree of unsaturation in
  A)
   2                            
  done clear
  B)
   3
  done clear
  C)
   4                            
  done clear
  D)
   5
  done clear
  View Answer play_arrow

• question_answer61)
  If \[a,\,b,\,c\in R,\] and \[a\ne 0\] and the equation \[a{{x}^{2}}+bx+c=0\] has no real roots, then
  A)
   \[{{(a+c)}^{2}}<{{b}^{2}}\]                         
  done clear
  B)
   \[(a+{{c}^{2}})={{b}^{2}}\]
  done clear
  C)
   \[{{(a+c)}^{2}}>{{b}^{2}}\]                         
  done clear
  D)
   \[({{a}^{2}}+c)={{b}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer62)
  The value of \[\int\limits_{0}^{1}{\sqrt[3]{2{{x}^{3}}-3{{x}^{2}}-x+1}}\,dx\] is equal to
  A)
   \[5\sqrt{7}\]                     
  done clear
  B)
   1
  done clear
  C)
   1                                            
  done clear
  D)
   \[2\sqrt{2}\]
  done clear
  View Answer play_arrow

• question_answer63)
  If a and d are two complex numbers, then the sum to \[(n+1)\] terms of the following series \[a{{C}_{0}}-(a+d){{C}_{1}}+(a+2d){{C}_{2}}....\] is (Where \[{{C}_{r}}{{=}^{n}}{{C}_{r}})\]
  A)
   \[\frac{a}{{{2}^{n}}}\]                                  
  done clear
  B)
   \[na\]
  done clear
  C)
   \[0\]                                    
  done clear
  D)
   \[\frac{d}{{{2}^{n}}}\]
  done clear
  View Answer play_arrow

• question_answer64)
  If \[x\in \left( \frac{3\pi }{2},\,2\pi  \right),\] then value of the expression \[{{\sin }^{-1}}\left\{ \cos ({{\cos }^{-1}}(\cos x)+{{\sin }^{-1}}(\sin x)) \right\}\] is equal to
  A)
   \[-\frac{\pi }{2}\]                                            
  done clear
  B)
   \[\frac{\pi }{2}\]
  done clear
  C)
   0                                            
  done clear
  D)
   \[\frac{\pi }{2}-2x\]
  done clear
  View Answer play_arrow

• question_answer65)
  The parabola \[{{y}^{2}}=4ax\] and the circle \[{{x}^{2}}+{{y}^{2}}+2bx=0\] have more than one common tangents, if
  A)
   \[ab<0\]                             
  done clear
  B)
   \[ab>0\]
  done clear
  C)
   \[ab<-1\]                           
  done clear
  D)
   \[ab<-2\]
  done clear
  View Answer play_arrow

• question_answer66)
  If \[\vec{a}.\vec{a}=\vec{b}.\vec{b}=\vec{c}.\vec{c}=1;\]\[\vec{a}.\vec{b}=\frac{1}{2};\]\[\vec{b}.\vec{c}=\frac{1}{\sqrt{2}};\] \[\vec{c}.\vec{a}=\frac{\sqrt{3}}{2}\] then the value of \[\left[ \vec{a}\,\vec{b}\,\vec{c} \right]\] is
  A)
   \[\frac{\sqrt{3}-1}{2\sqrt{2}}\]                 
  done clear
  B)
   \[\frac{\sqrt{3}+1}{2\sqrt{2}}\]
  done clear
  C)
   \[\frac{\sqrt{\sqrt{6}+2}}{2}\]                  
  done clear
  D)
   \[\frac{\sqrt{\sqrt{6}-2}}{2}\]
  done clear
  View Answer play_arrow

• question_answer67)
  Let P be any point on the circle \[{{S}_{1}}:{{x}^{2}}+{{y}^{2}}-2x=1\]. AB be the chord of contact of this point w.r.t. circle \[{{S}_{2}}:{{x}^{2}}+{{y}^{2}}-2x=0\]. The locus of the cirumcentre of the triangle CAB (C being the centre of the circle \[{{S}_{2}}=0\]) is
  A)
   \[2{{x}^{2}}+2{{y}^{2}}-4x+1=0\]
  done clear
  B)
   \[{{x}^{2}}+{{y}^{2}}-4x+2=0\]
  done clear
  C)
   \[{{x}^{2}}+{{y}^{2}}-4x+1=0\]
  done clear
  D)
   \[2{{x}^{2}}+2{{y}^{2}}-4x+3=0\]
  done clear
  View Answer play_arrow

• question_answer68)
  If \[|z-4+3i|\le 1\]  and \[\alpha \] and \[\beta \] be the greatest and least value of |z| respectively and K be the least value of \[\frac{{{x}^{4}}+{{x}^{2}}+4}{x}\] on the interval \[\left( 0,\,\infty  \right)\] then K is equal to
  A)
   \[\alpha \]                                         
  done clear
  B)
   \[\beta \]
  done clear
  C)
   \[\alpha +\beta \]                          
  done clear
  D)
   \[\alpha -\beta \]
  done clear
  View Answer play_arrow

• question_answer69)
  Let \[f:R\to R\] be given by \[f(x)=\left\{ \begin{matrix}    |x-[x]|,\,\text{When}\,[x]\,\text{is}\,\text{odd}  \\    |x-[x]-1|,\,\text{When}\,[x]\,\text{is}\,\text{even}  \\ \end{matrix} \right.\] Where [.] denotes the greatest integer function, then \[\int\limits_{-4}^{4}{f(x)dx}\] is equal to
  A)
   5/2                                       
  done clear
  B)
   3/2
  done clear
  C)
   8                                            
  done clear
  D)
   4
  done clear
  View Answer play_arrow

• question_answer70)
  A function \[y=f(x)\] satisfies\[\left( x+1 \right)f'(x)-2\left( {{x}^{2}}+x \right)f(x)=\frac{{{e}^{{{x}^{2}}}}}{x+1}\forall x>-1\]. If \[f(0)=5,\] then\[f(x)\] is
  A)
   \[\left( \frac{3x+5}{x+1} \right).{{e}^{{{x}^{2}}}}\]                          
  done clear
  B)
   \[\left( \frac{6x+5}{x+1} \right).{{e}^{{{x}^{2}}}}\]
  done clear
  C)
   \[\left( \frac{6x+5}{{{(x+1)}^{2}}} \right).{{e}^{{{x}^{2}}}}\]       
  done clear
  D)
   \[\left( \frac{5-6x}{(x+1)} \right).{{e}^{{{x}^{2}}}}\]
  done clear
  View Answer play_arrow

• question_answer71)
  The area bounded by the curve \[f(x)=x+\sin x\] and its inverse function between the ordinates \[x=0\] and \[x=2\pi \] is
  A)
   \[4\pi \] sq. units            
  done clear
  B)
   \[8\pi \] sq. units
  done clear
  C)
   4 sq. units         
  done clear
  D)
   8 sq. units
  done clear
  View Answer play_arrow

• question_answer72)
  Total number of ways in which 256 identical balls can be placed in '16' numbered boxes (1, 2, 3 ....16) such that \[{{r}^{th}}\] box contains at least ?r? \[\left( 1\le r\le 16 \right)\] balls is
  A)
   \[^{120}{{C}_{15}}\]                      
  done clear
  B)
   \[^{135}{{C}_{15}}\]
  done clear
  C)
   \[^{256}{{C}_{15}}\]                      
  done clear
  D)
   \[^{255}{{C}_{15}}\]
  done clear
  View Answer play_arrow

• question_answer73)
  If  \[(1+\tan \,{{1}^{o}})\,(1+\tan {{2}^{o}})\,(1+\tan {{3}^{o}})\] \[...(1+\tan {{45}^{o}})={{2}^{n}},\] then n equals
  A)
   21                                         
  done clear
  B)
   22
  done clear
  C)
   23                                         
  done clear
  D)
   24
  done clear
  View Answer play_arrow

• question_answer74)
  If \[\{x,\,y\}\] is a subset of \[S=\left\{ 1,\,2,\,3,.........100 \right\}\] then probability that \[xy\] is a multiple of 3 is
  A)
   \[\frac{43}{100}\]                                           
  done clear
  B)
   \[\frac{87}{200}\]
  done clear
  C)
   \[\frac{61}{150}\]                                           
  done clear
  D)
   \[\frac{83}{150}\]
  done clear
  View Answer play_arrow

• question_answer75)
  If \[a,\,b,\,c\] are positive number such that \[{{a}^{{{\log }_{3}}7}}=27,\,{{b}^{{{\log }_{7}}11}}=49,\,{{c}^{{{\log }_{11}}25}}=\sqrt{11}\], then sum of digits of
  A)
   19                                         
  done clear
  B)
   17
  done clear
  C)
   15                                         
  done clear
  D)
   21
  done clear
  View Answer play_arrow

• question_answer76)
  Let \[f(x)={{x}^{2}}+xg'(1)+g''(2)\] and \[g(x)=f(1){{x}^{2}}+xf'(x)+f''(x)\] then the value of \[f'(1)+g'(1)\] is
  A)
   - 4                                         
  done clear
  B)
   0
  done clear
  C)
   2                                            
  done clear
  D)
   4
  done clear
  View Answer play_arrow

• question_answer77)
  Let \[f(x)\] be a continuous function such that \[f(0)=1\] and \[f(x)-f\left( \frac{x}{7} \right)=\frac{x}{7}\forall x\in R,\] then area bounded by the curve \[y=f(x)\] and the co-ordinate axes is
  A)
   4                            
  done clear
  B)
   3
  done clear
  C)
   2                            
  done clear
  D)
   1
  done clear
  View Answer play_arrow

• question_answer78)
  The value of \[\int\limits_{1}^{2011}{\prod\limits_{r=1}^{2011}{(x-r)}}dx\] is
  A)
   \[\frac{{{\left( 2011 \right)}^{2}}}{2}\]                  
  done clear
  B)
   \[\frac{\left( 2011 \right)\left( 2012 \right)\left( 4023 \right)}{2}\]
  done clear
  C)
   0
  done clear
  D)
   2010
  done clear
  View Answer play_arrow

• question_answer79)
  If the line passing through (-2, 1, b) and (4, 1, 2) is perpendicular to the vector \[\hat{i}+3\hat{j}-2\hat{k}\] and is parallel to the plane containing the vectors \[\hat{i}+c\hat{k}\] and \[c\hat{j}+b\hat{k},\] then the ordered pair \[(b,\,c)\] is
  A)
   \[(-1,\,-1/2)\]                  
  done clear
  B)
   \[(1,\,-6)\]
  done clear
  C)
   \[(-1,\,0)\]                        
  done clear
  D)
   \[(1,\,1/2)\]
  done clear
  View Answer play_arrow

• question_answer80)
  A continuous function \[y=f(x)\] satisfies the equation \[f(x)=\int\limits_{0}^{x}{(t)dt}\].  Then which of the following does not hold good?
  A)
   f is periodic
  done clear
  B)
   f is differentiable for all \[x\in R\]
  done clear
  C)
   Range of f is singleton
  done clear
  D)
   f is neither odd nor even
  done clear
  View Answer play_arrow

• question_answer81)
  If \[{{z}_{1}}\] and \[{{z}_{2}}\] are unimodular complex number that satisfy \[z_{1}^{2}+z_{2}^{2}=4\] and then \[\left( {{z}_{1}}+{{\overline{z}}_{1}} \right)+{{\left( {{z}^{2}}+{{\overline{z}}^{2}} \right)}^{2}}\] is equal to
  A)
   10                                         
  done clear
  B)
   12
  done clear
  C)
   14                                         
  done clear
  D)
   16
  done clear
  View Answer play_arrow

• question_answer82)
  If \[\int\limits_{{}}^{{}}{\frac{\cos x-\sin x+1-x}{{{e}^{x}}+\sin x+x}}dx=\ell n\,\left( fx \right)+g(x)+C,\]  where C is the constant of integration and \[f(x)\] is positive, then \[f(x)+g(x)\] has the value equal to
  A)
   \[{{e}^{x}}+\sin x+2x\]
  done clear
  B)
   \[{{e}^{x}}+\sin x\]
  done clear
  C)
   \[{{e}^{x}}-\sin x\]                        
  done clear
  D)
   \[{{e}^{x}}+\sin x+x\]
  done clear
  View Answer play_arrow

• question_answer83)
  The equation \[2{{\sin }^{2}}x-(p+3)\sin x+2p-2\]\[=0\] possesses a real solution, if
  A)
   \[0\le p\le 1\]                  
  done clear
  B)
   \[-1\le p\le 3\]
  done clear
  C)
   \[4\le p\le 6\]                  
  done clear
  D)
   \[p\ge 6\]
  done clear
  View Answer play_arrow

• question_answer84)
  The nearest point on the line \[3x-4y=25\] from origin is
  A)
   \[\left( -4,\,5 \right)\]                  
  done clear
  B)
   \[\left( 3,\,-4 \right)\]
  done clear
  C)
   \[\left( 3,\,4 \right)\]                    
  done clear
  D)
   \[\left( 3,\,5 \right)\]
  done clear
  View Answer play_arrow

• question_answer85)
  If centroid of an equilateral triangle is (1, 1) and its one vertex is (-1, 2), then the equation of its circumcircle is
  A)
   \[{{x}^{2}}+{{y}^{2}}-2x-2y-3=0\]
  done clear
  B)
   \[{{x}^{2}}+{{y}^{2}}+2x-2y-3=0\]
  done clear
  C)
   \[{{x}^{2}}+{{y}^{2}}+2x+2y-3=0\]
  done clear
  D)
   \[{{x}^{2}}+{{y}^{2}}-2x+2y-3=0\]
  done clear
  View Answer play_arrow

• question_answer86)
  Directions (Q. 86): Read the following questions and choose:

  Statement 1: Period of \[f(x)=\sin \,\frac{\pi x}{(n-1)!}\cos \frac{\pi x}{n!}\] is \[2(n!)\]

  Statement 2: Period of \[|\cos x|+|\sin x|+3\] is \[\pi \]

  A)
   Both statements are true, and Statement-2 explains Statement-1.
  done clear
  B)
   Both statements are true, but Statement-2 does not explain 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_answer87)
  Directions (Q. 87): Read the following questions and choose:

  Statement 1: Let \[f(x)=\underset{x\to \infty }{\mathop{\lim }}\,\,\frac{\text{In}(1+x)-{{x}^{2n}}(\sin 2x)}{1+{{x}^{2n}}}\], then \[f(x)\] is discontinuous at \[x=1\].

  Statement 2: \[LHL=RHL\ne f(1)\]

  A)
   Both statements are true, and Statement-2 explains Statement-1.
  done clear
  B)
   Both statements are true, but Statement-2 does not explain 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_answer88)
  Directions (Q. 88): Read the following questions and choose:

  Statement 1: Consider the function \[f(x)\] \[f\left( \frac{{{x}_{1}}+{{x}_{2}}}{2} \right)<\frac{f({{x}_{1}})+f({{x}_{2}})}{2}\]

  Statement 2: \[f'(x)>0,\,f''(x)>0\] where \[{{x}_{1}}<{{x}_{2}}\].

  A)
   Both statements are true, and Statement-2 explains Statement-1.
  done clear
  B)
   Both statements are true, but Statement-2 does not explain 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_answer89)
  Directions (Q. 89): Read the following questions and choose:

  Statement 1: Vectors \[\vec{a}=2\hat{i}+\hat{k},\,\vec{b}=3\hat{j}+4\hat{k}\] and \[\vec{c}=8\hat{i}-3\hat{j}\] are co-planar then \[\vec{c}=4\vec{a}-\vec{b}\].

  Statement 2: A set of vectors \[\overrightarrow{{{a}_{1}}},\,\overrightarrow{{{a}_{2}}},\,\overrightarrow{{{a}_{3}}}...\overrightarrow{{{a}_{n}}}\] is said to be linearly independent if every relation of the form \[{{\ell }_{1}}\overrightarrow{{{a}_{1}}}+{{\ell }_{2}}\,\overrightarrow{{{a}_{2}}}+{{\ell }_{3}}\,\overrightarrow{{{a}_{3}}}+.....+{{\ell }_{n}}\overrightarrow{{{a}_{n}}}=\vec{0}\] implies that \[{{\ell }_{1}}={{\ell }_{2}}={{\ell }_{3}}=....={{\ell }_{n}}=0\]

  A)
   Both statements are true, and Statement-2 explains Statement-1.
  done clear
  B)
   Both statements are true, but Statement-2 does not explain 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_answer90)
  Directions (Q. 90): Read the following questions and choose:

  Statement 1: If \[a,\,b,\,c\in R\] and the quadratic equation \[a{{x}^{2}}+bx+c=0\] and \[{{x}^{2}}+2x+3=0\] have a common root, \[a:b:c=1:2:3\].

  Statement 2: If \[a,\,b,\,c\in R\] and if one root is common then both the roots are common.

  A)
   Both statements are true, and Statement-2 explains Statement-1.
  done clear
  B)
   Both statements are true, but Statement-2 does not explain 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