Solved papers for RAJASTHAN ­ PET Rajasthan PET Solved Paper-2011

done Rajasthan PET Solved Paper-2011 Total Questions - 120

• question_answer1) The x and y coordinates of a particle at any time t are given\[x=7t+4{{t}^{2}}\]and\[y=5t,\]where\[x\]and y are in metre and t in second. The acceleration of particle at\[t=5s\]is
  A)
   zero            
  done clear
  B)
   \[\text{8 }m/{{s}^{2}}\]
  done clear
  C)
   \[20\text{ }m/{{s}^{2}}\]         
  done clear
  D)
   \[\text{40 }m/{{s}^{2}}\]
  done clear
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• question_answer2) Find the velocity of the particle moving in a circular path having a centripetal force of 10 N whose mass is 100 g and radius of circular path is 50 cm
  A)
   \[\sqrt{500}\]m/s       
  done clear
  B)
   \[\sqrt{50}\]m/s
  done clear
  C)
   \[\sqrt{30}\]m/s        
  done clear
  D)
   \[\sqrt{60}\]m/s
  done clear
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• question_answer3) A small object placed on a rotating horizontal turn-table just slips when it is placed at a distance of 4 cm from the axis of rotation. If the angular velocity of the turn-table is doubled the object slips when its distance from the axis of rotation is
  A)
   1 cm            
  done clear
  B)
   2 cm
  done clear
  C)
   4 cm            
  done clear
  D)
   8 cm
  done clear
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• question_answer4) A bullet moving with speed 200 m/s is just able to pierce a wooden block of 6 cm thickness. What velocity is required to just pierce a block of 8 cm?
  A)
   400\[\sqrt{3}\]m/s     
  done clear
  B)
   400 m/s
  done clear
  C)
   400/\[\sqrt{3}\]m/s    
  done clear
  D)
   400\[\sqrt{2}\]m/s
  done clear
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• question_answer5) A bullet of 5 g is fired with a velocity of 800 m/s. The velocity of bullet becomes 200 m/s when it pierces a wooden block 2 m thick. What is the average resistance offered by the wooden block?
  A)
   8.5 kN          
  done clear
  B)
   7.5 kN
  done clear
  C)
   6.5 kN          
  done clear
  D)
   30 kN
  done clear
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• question_answer6) On a massless rod four masses are fixed as shown in figure. What is the moment of inertia about an axis passing through centre of rod
  A)
   \[\frac{{{l}^{2}}}{2}\left( M+\frac{m}{4} \right)\]
  done clear
  B)
   \[\frac{{{l}^{2}}}{2}\left( \frac{M}{4}+m \right)\]
  done clear
  C)
   \[\frac{{{l}^{2}}}{4}\left[ M+\frac{m}{4} \right]\]
  done clear
  D)
   \[\frac{{{l}^{2}}}{4}\left[ \frac{M}{4}+m \right]\]
  done clear
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• question_answer7) The two waves, whose intensities are\[9:16\]are made to interfere. The ratio of maximum and minimum intensities in the interference pattern is
  A)
   16 : 9           
  done clear
  B)
   4 : 3
  done clear
  C)
   25 : 7           
  done clear
  D)
   49 : 1
  done clear
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• question_answer8) At what temperature is rms speed of air molecules double of that at NTP?
  A)
   \[819{}^\circ C\]          
  done clear
  B)
   \[719{}^\circ C\]
  done clear
  C)
   \[909{}^\circ C\]          
  done clear
  D)
   None of these
  done clear
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• question_answer9) A balloon contains\[500\text{ }{{m}^{3}}\]of helium at\[27{}^\circ C\]and 1 atmosphere pressure. The volume of the helium at\[-3{}^\circ C\]temperature and 0.5 atmosphere pressure will be
  A)
   \[500\,{{m}^{3}}\]
  done clear
  B)
   \[700\,{{m}^{3}}\]
  done clear
  C)
   \[900\,{{m}^{3}}\] 
  done clear
  D)
   \[1000\,{{m}^{3}}\]
  done clear
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• question_answer10) The rate of outflow of liquid through an orifice does not depend upon
  A)
   radius of the orifice
  done clear
  B)
   height of the liquid column
  done clear
  C)
   acceleration due to gravity
  done clear
  D)
   density of the liquid
  done clear
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• question_answer11) Two lamps of powers\[{{P}_{1}}\]and\[{{P}_{2}}\]are placed on either side of a paper having an oil spot. The lamps are at distances of 1 m and 2 m respectively on either side of the paper and the oil spot is invisible. What is the value of\[{{P}_{1}}/{{P}_{2}}\]?
  A)
   0.25            
  done clear
  B)
   0.40
  done clear
  C)
   0.50            
  done clear
  D)
   0.60
  done clear
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• question_answer12) A parallel plate capacitor of value 1.77 \[\mu \]F is to be designed using a dielectric material (dielectric constant = 200), breakdown strength of\[3\times {{10}^{6}}\] V/m. In order to make such a capacitor which can withstand a potential difference of 20 V across the plates, the separation between the plates d and area A of the plates respectively are
  A)
   \[6.6\times {{10}^{-6}}m,{{10}^{3}}{{m}^{2}}\]
  done clear
  B)
   \[6.6\times {{10}^{-5}}m,{{10}^{4}}{{m}^{2}}\]
  done clear
  C)
   \[6.6\times {{10}^{-4}}m,\text{ }{{10}^{5}}{{m}^{2}}\]
  done clear
  D)
   \[6.6\times {{10}^{-6}}m,\text{ }{{10}^{2}}{{m}^{2}}\]
  done clear
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• question_answer13) Mid way between the two equal and similar charges, we place the third equal and similar charge. Which of the following statements is correct?
  A)
   The third charge experiences a net force inclined to the line joining the charges
  done clear
  B)
   The third charge is in stable equilibrium
  done clear
  C)
   The third charge is in  unstable equilibrium
  done clear
  D)
   The third charge experience a net force perpendicular to the line joining the charges
  done clear
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• question_answer14) A magnetic field of 20 T is normal to a coil of 100 turns and area\[{{10}^{-2}}{{m}^{2}}\]. If the coil is removed from the magnetic field is 2 ms, what is the induced emf set up in the coil?
  A)
   2 kV            
  done clear
  B)
   5 kV
  done clear
  C)
   7 kV           
  done clear
  D)
   10 kV
  done clear
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• question_answer15) The first line of Balmer series has wavelength 6563 A. What will be the wavelength of the first member of Lyman seires?
  A)
   1215.4\[\overset{o}{\mathop{\text{A}}}\,\]         
  done clear
  B)
   2500\[\overset{o}{\mathop{\text{A}}}\,\]
  done clear
  C)
   7500\[\overset{o}{\mathop{\text{A}}}\,\]          
  done clear
  D)
   600\[\overset{o}{\mathop{\text{A}}}\,\]
  done clear
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• question_answer16) What will be the angular momentum in fourth orbit if L is the angular momentum of the electron in the second orbit of H-atom?
  A)
   \[\frac{2}{3}\]L              
  done clear
  B)
   \[\frac{L}{2}\]
  done clear
  C)
   2L               
  done clear
  D)
   \[\frac{3}{2}L\]
  done clear
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• question_answer17) If half-life of a radioactive atom is 2.3 days then its decay constant would be
  A)
   0.1              
  done clear
  B)
   0.2
  done clear
  C)
   0.3               
  done clear
  D)
   2.3
  done clear
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• question_answer18) The half-life period of a radioactive substance is 5 min. The amount of substance decayed in 20 min will be
  A)
   93.75%        
  done clear
  B)
   75%
  done clear
  C)
   25%           
  done clear
  D)
   6.25%
  done clear
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• question_answer19) The torque acting on a magnetic dipole of moment\[{{\mathbf{P}}_{m}}\]when placed in a magnetic field B is
  A)
   \[{{P}_{m}}B\]            
  done clear
  B)
   \[{{\mathbf{P}}_{m}}\times \mathbf{B}\]
  done clear
  C)
   \[{{\mathbf{P}}_{m}}.\text{ }B\]           
  done clear
  D)
   None of these
  done clear
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• question_answer20) A charged particle with velocity\[2\times {{10}^{3}}\]m/s passes undeflected through electric and magnetic field is 1.5 T. The electric field intensity would be
  A)
   \[2\times {{10}^{3}}N/C\]     
  done clear
  B)
   \[1.5\times {{10}^{3}}N/C\]
  done clear
  C)
   \[3\times {{10}^{3}}N/C\]     
  done clear
  D)
   \[\frac{4}{3}\times {{10}^{-3}}N/C\]
  done clear
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• question_answer21) An electron is accelerated through a potential difference of 45.5 V. The velocity acquired by it is (in m/s)
  A)
   \[{{10}^{6}}\]             
  done clear
  B)
   zero
  done clear
  C)
   \[4\times {{10}^{6}}\]          
  done clear
  D)
   \[4\times {{10}^{4}}\]
  done clear
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• question_answer22) What is the magnitude of the emf generated between the ends of the axle of a railway carriage 1 m in length when it is moving with a velocity of 30 km/h along horizontal track? Earth's horizontal magnetic field of induction\[=0.4\times {{10}^{-4}}T\]and angle of dip \[=60{}^\circ \]
  A)
   \[6.77\times {{10}^{-4}}V\]    
  done clear
  B)
   \[5.77\times {{10}^{-4}}V\]
  done clear
  C)
   \[5.23\times {{10}^{-4}}V\]    
  done clear
  D)
   \[5.47\times {{10}^{-4}}V\]
  done clear
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• question_answer23) Three identical charges placed at the vertices of an equilateral triangle. The force experienced by each charge \[\left( if\,k=\frac{1}{4}\pi {{\varepsilon }_{0}} \right)\] is
  A)
   \[2k\,\frac{{{q}^{2}}}{{{r}^{2}}}\]
  done clear
  B)
   \[\frac{k{{q}^{2}}}{2{{r}^{2}}}\]
  done clear
  C)
   \[\sqrt{3}k\frac{{{q}^{2}}}{{{r}^{2}}}\]
  done clear
  D)
   \[\frac{k{{q}^{2}}}{\sqrt{2{{r}^{2}}}}\]
  done clear
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• question_answer24) A capacitor of capacitance 6\[\mu \]F is charged upto 100 V. The energy stored in the capacitor is
  A)
   0.6 J            
  done clear
  B)
   0.06 J
  done clear
  C)
   0.03 J           
  done clear
  D)
   0.3 J
  done clear
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• question_answer25) The electric field due to an infinitely long thin wire at a distance R varies as
  A)
   1/R             
  done clear
  B)
   \[1/{{R}^{2}}\]
  done clear
  C)
   R               
  done clear
  D)
  \[{{R}^{2}}\]
  done clear
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• question_answer26) A magnet of magnetic moment M is freely suspended in a uniform magnetic field of strength B. The work done in rotating the magnet through \[60{}^\circ \]to\[90{}^\circ \]is
  A)
   \[-MB\text{ }(1-cos\text{ }90{}^\circ )\]
  done clear
  B)
   \[-MB(cos\text{ }60{}^\circ -cos\text{ }90{}^\circ )\]
  done clear
  C)
   \[-MB(0cos\text{ }60{}^\circ )\]
  done clear
  D)
   \[-MB(sin\text{ }60{}^\circ -cos\text{ }90{}^\circ )\]
  done clear
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• question_answer27) A 750 Hz, 20 V source is connected to a resistance of\[100\,\Omega ,\]an inductance of 0.1803 H and a capacitance of 10\[\mu \]F all in series. What is the time in which resistance (thermal capacity\[=2\text{ }J/{}^\circ C\]) will get heated by\[10{}^\circ C\]?
  A)
   380 s         
  done clear
  B)
   384 s
  done clear
  C)
   470 s         
  done clear
  D)
   479 s
  done clear
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• question_answer28) A capacitor discharges through an inductor of 0.02 H. If the frequency of discharge is 100 Hz then what is the capacitance of the capacitor?
  A)
   14.67 \[\mu \]F       
  done clear
  B)
   12.67 \[\mu \]F
  done clear
  C)
   9.67 \[\mu \]F         
  done clear
  D)
   4.67 \[\mu \]F
  done clear
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• question_answer29) Which of the following is the dimensional formula for capacitance X (potential) 2?
  A)
   \[[M{{L}^{2}}{{T}^{-1}}]\]       
  done clear
  B)
   \[[M{{L}^{2}}{{T}^{-2}}]\]
  done clear
  C)
   \[[M{{L}^{-2}}{{T}^{-3}}]\]       
  done clear
  D)
   \[[M{{L}^{-1}}{{T}^{-2}}]\]
  done clear
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• question_answer30) A bomb of 12 kg explods into two pieces of masses 4 kg and 8 kg. The velocity of 8 kg mass is 6 m/s. The kinetic energy of the other mass is
  A)
   48 J            
  done clear
  B)
   32 J
  done clear
  C)
   24 J            
  done clear
  D)
   288 J
  done clear
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• question_answer31) The path difference between the two waves \[{{y}_{1}}={{a}_{1}}\sin \left( \omega t-\frac{2\pi x}{\lambda } \right)\] and \[{{y}_{2}}={{a}_{2}}\sin \left( \omega t-\frac{2\pi x}{\lambda }+\phi  \right)is\]
  A)
   \[\frac{\lambda }{2\pi }\phi \]
  done clear
  B)
   \[\frac{\lambda }{2\pi }\left( \phi \frac{\pi }{2} \right)\]
  done clear
  C)
   \[\frac{2\pi }{\lambda }\left( \phi -\frac{\pi }{2} \right)\]
  done clear
  D)
   \[\frac{2\pi }{\lambda }\phi \]
  done clear
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• question_answer32) What is the relation between particle velocity (v), the wave velocity  and the slope (s) of the wave?
  A)
   \[v=-cs\]         
  done clear
  B)
   \[c=-vs\]
  done clear
  C)
   \[{{v}^{2}}={{c}^{2}}s\]       
  done clear
  D)
   \[{{c}^{2}}={{v}^{2}}s\]
  done clear
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• question_answer33) The velocity of sound in oxygen at NTP is v. The velocity of sound in helium at NTP should be
  A)
   4v             
  done clear
  B)
   \[v/2\sqrt{2}\]
  done clear
  C)
   2v             
  done clear
  D)
   None of these
  done clear
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• question_answer34) Two spheres have identical masses and moment of inertia. One of them is solid and the other is hollow. The ratio of the radius of solid sphere to that of hollow sphere is
  A)
   \[\sqrt{2}\]              
  done clear
  B)
   \[\sqrt{2/5}\]
  done clear
  C)
   \[\sqrt{5/3}\]          
  done clear
  D)
   \[\sqrt{2/3}\]
  done clear
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• question_answer35) A body cools in 7 min from\[60{}^\circ C\]to\[40{}^\circ C\]. What time does it take to cool from\[40{}^\circ C\]to\[28{}^\circ C\]if the surrounding temperature is\[10{}^\circ C\]?
  A)
   3.5 min        
  done clear
  B)
   14 min
  done clear
  C)
   7 min          
  done clear
  D)
   10 min
  done clear
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• question_answer36) Two metal spheres of radii\[{{r}_{1}}\]and\[{{r}_{2}}\]are charged to the same potential. The ratio of the charge on the two spheres is
  A)
   1                
  done clear
  B)
   \[\frac{1}{2}\]
  done clear
  C)
   \[{{r}_{1}}-{{r}_{2}}\]          
  done clear
  D)
   \[{{r}_{1}}/{{r}_{2}}\]
  done clear
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• question_answer37) What is the color of the interference fringe nearest to the white central maximum in case the source of light is white?
  A)
   Yellow
  done clear
  B)
   Red
  done clear
  C)
   Blue
  done clear
  D)
   Violet
  done clear
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• question_answer38) What will be the kinetic energy of an electron having de-Broglie wavelength\[2\overset{o}{\mathop{\text{A}}}\,\]?
  A)
   37.5 eV        
  done clear
  B)
   75 eV
  done clear
  C)
   150 eV         
  done clear
  D)
   30 eV
  done clear
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• question_answer39) Focal length of a convex lens will be maximum for
  A)
   blue light       
  done clear
  B)
   yellow light
  done clear
  C)
   green light      
  done clear
  D)
   red light
  done clear
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• question_answer40) Pitch of a node depends upon
  A)
   frequency
  done clear
  B)
   wavelength
  done clear
  C)
   amplitude      
  done clear
  D)
   None of these
  done clear
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• question_answer41) Mass of one atom of an element is \[6.64\times {{10}^{-23}}g.\] This is equal to
  A)
   \[6.64\times {{10}^{-23}}u\]
  done clear
  B)
   \[40.0u\]
  done clear
  C)
   \[\frac{1}{40}u\]
  done clear
  D)
   \[6.64u\]
  done clear
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• question_answer42) Point defects are present in
  A)
   ionic solids      
  done clear
  B)
   amorphous solid
  done clear
  C)
   molecular solids
  done clear
  D)
   liquids
  done clear
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• question_answer43) The average molecular speed is greatest in which of the following gas samples?
  A)
   1.0 mol of\[{{O}_{2}}\]at 560 K
  done clear
  B)
   0.50 mol of Neat 500 K
  done clear
  C)
   0.20 mol of\[C{{O}_{2}}\]at 440 K
  done clear
  D)
   2.0 mol of He at 140 K
  done clear
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• question_answer44) Elevation in boiling point of an aqueous urea solution is\[0.52{}^\circ C[{{K}_{b}}=0.52{}^\circ mo{{l}^{-1}}kg].\]Hence, mole fraction of urea in this solution is
  A)
   0.982           
  done clear
  B)
   0.567
  done clear
  C)
   0.943           
  done clear
  D)
   0.018
  done clear
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• question_answer45) Oxidation number of Cr in\[Cr{{O}_{5}}\]is
  A)
   +10           
  done clear
  B)
   +8
  done clear
  C)
   +6            
  done clear
  D)
   +4
  done clear
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• question_answer46) For the reaction \[{{H}_{2}}(g)+C{{O}_{2}}(g)CO(g)+{{H}_{2}}O(g)\] If the initial concentration of \[[{{H}_{2}}]=[C{{O}_{2}}]\]and \[x\] mol/L of hydrogen is consumed at equilibrium, the correct expression of\[{{K}_{p}}\]is
  A)
   \[\frac{{{x}^{2}}}{{{(1-x)}^{2}}}\]
  done clear
  B)
   \[\frac{{{x}^{2}}}{{{(2+x)}^{2}}}\]
  done clear
  C)
   \[\frac{{{x}^{2}}}{1-{{x}^{3}}}\]
  done clear
  D)
   \[\frac{{{(1+x)}^{2}}}{{{(1-x)}^{2}}}\]
  done clear
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• question_answer47) The solubility of\[AgI\]in\[NaI\]solution is less than that in pure water because
  A)
  \[AgI\]forms complex with \[NaI\]
  done clear
  B)
   of common ion effect
  done clear
  C)
   solubility product of\[AgI\]is less
  done clear
  D)
   the temperature of the solution decrease
  done clear
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• question_answer48) A buffer solution with pH 9 is to be prepared by mixing\[N{{H}_{4}}Cl\]and\[N{{H}_{4}}OH\]. Calculate the number of moles of\[N{{H}_{4}}Cl\]that should be added to 1 L of\[1.0\text{ }M\text{ }N{{H}_{4}}OH\].
  A)
   3.4              
  done clear
  B)
   2.6
  done clear
  C)
   1.5              
  done clear
  D)
   1.99
  done clear
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• question_answer49) The emf of the cell involving following changes, \[Zn(s)+N{{i}^{2+}}(1M)\xrightarrow[{}]{{}}Z{{n}^{2+}}(1M)+Ni(s)\] is 0.5105 V. The standard emf of the cell is
  A)
   0.540V        
  done clear
  B)
   0.4810V
  done clear
  C)
   0.5696V       
  done clear
  D)
   0.5105V
  done clear
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• question_answer50) Chlorination of toluene in presence of light and heat followed by treatment with aqueous \[NaOH\]gives
  A)
   o-cresol
  done clear
  B)
   p-cresol
  done clear
  C)
   mixture of o-cresol and p-cresol
  done clear
  D)
   benzoic acid
  done clear
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• question_answer51) Identify the product in the following sequence 3, 4, 5-tnbromoanilme \[\xrightarrow[(ii){{H}_{3}}P{{O}_{2}}]{(i)Diazotisation}\]
  A)
   3, 4, 5-tribromobenzene
  done clear
  B)
   1, 2, 3-tribromobenzene
  done clear
  C)
   3, 4, 5-tribromophenol
  done clear
  D)
   3, 4, 5-tribromonitrobenzene
  done clear
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• question_answer52) The order of first ionization energies of the elements \[Li,Be,B,Na\] is
  A)
   \[Li>Be>B>Na\]
  done clear
  B)
   \[Be>B>Li>Na\]
  done clear
  C)
   \[Na>Li>B>Be\]
  done clear
  D)
   \[Be>Li>B>Na\]
  done clear
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• question_answer53) Effective magnetic moment\[S{{c}^{3+}}\]ion is
  A)
   1.73           
  done clear
  B)
   zero
  done clear
  C)
   5.92            
  done clear
  D)
   2.83
  done clear
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• question_answer54) Potassium permanganate acts as an oxidant in alkaline and acidic medium. The final products formed from\[KMn{{O}_{4}}\]in the two conditions are respectively
  A)
   \[Mn{{O}^{2-}}\]and \[M{{n}^{3+}}\]
  done clear
  B)
   \[M{{n}^{3+}}\]and \[M{{n}^{2+}}\]
  done clear
  C)
   \[M{{n}^{2+}}\]and \[M{{n}^{3+}}\]
  done clear
  D)
   \[Mn{{O}_{2}}\]and \[M{{n}^{2+}}\]
  done clear
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• question_answer55) An alkene having the molecular formula \[{{C}_{9}}{{H}_{18}}\]on ozonolysis gives 2, 2-dimethyl propanal and butanone. The alkene is
  A)
   2, 2, 2-trimethyl-3-hexene
  done clear
  B)
   2, 2, 6-trimethyl-3-hexane
  done clear
  C)
   2, 2, 4-trimethyl 3-hexene
  done clear
  D)
   2, 3, 4-trimethyl-2-hexene
  done clear
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• question_answer56) The number of optical isomers of\[C{{H}_{3}}CH(OH)CH(OH)CHO\]is
  A)
   2            
  done clear
  B)
   3
  done clear
  C)
   6              
  done clear
  D)
   4
  done clear
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• question_answer57) The amine which will not liberate nitrogen on reaction with nitrous acid is
  A)
   trimethyl amine
  done clear
  B)
   ethyl amine
  done clear
  C)
   sec-butyl amine 
  done clear
  D)
   iso-propyi amine
  done clear
  View Answer play_arrow

• question_answer58) Find the two third life\[({{t}_{2/3}})\]a first order reaction in which\[k=5.48\times {{10}^{-14}}\]per second.
  A)
   \[2.01\times {{10}^{13}}s\]    
  done clear
  B)
   \[201\times {{10}^{13}}s\]
  done clear
  C)
   \[201\times {{10}^{20}}s\]    
  done clear
  D)
   \[0.201\times {{10}^{10}}s\]
  done clear
  View Answer play_arrow

• question_answer59) Identify the compound Z in this reaction sequence \[C{{H}_{3}}C{{H}_{2}}COOH\xrightarrow[{}]{N{{H}_{3}}}X\xrightarrow[{}]{B{{r}_{2}}+KOH}Y\xrightarrow[{}]{HN{{O}_{2}}}Z\]
  A)
   \[C{{H}_{3}}OH\]    
  done clear
  B)
   \[C{{H}_{3}}C{{H}_{2}}N{{H}_{2}}\]
  done clear
  C)
   \[C{{H}_{3}}C{{H}_{2}}OH\]    
  done clear
  D)
   \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}OH\]
  done clear
  View Answer play_arrow

• question_answer60) The orbital angular momentum of an electron revolving in p-orbital is
  A)
   zero 
  done clear
  B)
   \[\frac{h}{\sqrt{2\pi }}\]
  done clear
  C)
   \[\frac{h}{2\pi }\]
  done clear
  D)
   \[\frac{h}{2\sqrt{2\pi }}\]
  done clear
  View Answer play_arrow

• question_answer61) The pair whose both species are used in antiacid medicinal preparations is
  A)
   \[NaHC{{O}_{3}}\]and \[Mg{{(OH)}_{2}}\]
  done clear
  B)
   \[N{{a}_{2}}C{{O}_{3}}\]and \[Ca{{(HC{{O}_{3}})}_{2}}\]
  done clear
  C)
   \[Ca{{(HC{{O}_{3}})}_{2}}\]and \[Mg{{(OH)}_{2}}\]
  done clear
  D)
   \[Ca{{(OH)}_{2}}\]and \[NaHC{{O}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer62) \[{{F}_{2}}\]formed by reacting\[{{K}_{2}}Mn{{F}_{6}}\]with
  A)
   \[Sb{{F}_{5}}\]           
  done clear
  B)
   \[Mn{{F}_{3}}\]
  done clear
  C)
   \[KSb{{F}_{6}}\]         
  done clear
  D)
   \[Mn{{F}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer63) Four successive members of the first row of transition elements are listed below with their atomic numbers. Which one of them is expected to have the highest third ionization enthalpy?
  A)
   Vanadium \[(Z=23)\]
  done clear
  B)
   Chromium \[(Z=24)\]
  done clear
  C)
   Iron \[(Z=26)\]
  done clear
  D)
   Manganese \[(Z=25)\]
  done clear
  View Answer play_arrow

• question_answer64) Which of the following reactions is an example of redox reactions?
  A)
   \[AgN{{O}_{3}}+NaCl\xrightarrow[{}]{{}}AgCl+NaN{{O}_{3}}\]
  done clear
  B)
   \[N{{a}_{2}}C{{O}_{3}}+Si{{O}_{2}}\xrightarrow{{}}N{{a}_{2}}Si{{O}_{3}}+C{{O}_{2}}\]
  done clear
  C)
   \[Ca{{(HC{{O}_{3}})}_{3}}+Ca{{(OH)}_{2}}\xrightarrow[{}]{{}}\] \[2CaC{{O}_{3}}+2{{H}_{2}}O\]
  done clear
  D)
   \[10HN{{O}_{3}}+{{I}_{2}}\xrightarrow{{}}2HI{{O}_{3}}+10N{{O}_{2}}\] \[+4{{H}_{2}}O\]
  done clear
  View Answer play_arrow

• question_answer65) \[PC{{l}_{3}}\]and cold water reacts to produce which of the following?
  A)
   \[{{H}_{3}}P{{O}_{3}}\]
  done clear
  B)
   \[{{H}_{3}}P{{O}_{2}}\]
  done clear
  C)
   \[{{H}_{4}}{{P}_{2}}{{O}_{7}}\]
  done clear
  D)
   \[{{H}_{3}}P{{O}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer66) Which of the following is not an ore of magnesium?
  A)
   Magnesite
  done clear
  B)
   Dolomite
  done clear
  C)
   Gypsum
  done clear
  D)
   Camallite
  done clear
  View Answer play_arrow

• question_answer67) Brown ring in the test of\[NO_{3}^{-}\]is formed due to the formation of
  A)
   \[[Fe{{[{{H}_{2}}O]}_{5}}.NO]S{{O}_{4}}\]
  done clear
  B)
   \[[Fe{{[S{{O}_{4}}]}_{2}}.NO]{{H}_{2}}O\]
  done clear
  C)
   \[F{{e}_{2}}{{(S{{O}_{4}})}_{3}}.NO\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer68) Which one of the hollowing will most readily be dehydrated in acidic conditions?
  A)
   
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer69) Sulphide ores of metals are usually concentrated by froth floatation process. Which one of the following sulphide ores offers an exception and is concentrated by chemical leaching?
  A)
   Argentite       
  done clear
  B)
   Galena
  done clear
  C)
   Copper pyrite    
  done clear
  D)
   Sphalerite
  done clear
  View Answer play_arrow

• question_answer70) Soldiers of Napolean army which at Alps during freezing winter suffered a serious problem as regards to die tin buttons of their uniforms. White metallic tin buttons got covered to grey powder. This transformation is related to
  A)
   an interaction with nitrogen of the air at very low temperatures
  done clear
  B)
   a change in the partial pressure of oxygen in the air
  done clear
  C)
   a change in the crystalline structure of tin
  done clear
  D)
   an interaction with water vapour contained in the humid air
  done clear
  View Answer play_arrow

• question_answer71) Which of the following is a mixed oxide?
  A)
   \[F{{e}_{2}}{{O}_{3}}\]          
  done clear
  B)
   \[Pb{{O}_{2}}\]
  done clear
  C)
   \[Ba{{O}_{2}}\]          
  done clear
  D)
   \[P{{b}_{3}}{{O}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer72) The structure of\[XeO{{F}_{4}}\]is
  A)
   planar          
  done clear
  B)
   tetrahedral
  done clear
  C)
   square pyramidal
  done clear
  D)
   pyramidal
  done clear
  View Answer play_arrow

• question_answer73) A metal M forms chlorides in its +2 and +4 oxidation states. Which of the following statements about these chlorides is correct?
  A)
  \[MC{{l}_{2}}\]is more volatile than \[MC{{l}_{4}}\]
  done clear
  B)
  \[MC{{l}_{2}}\]is more soluble in anhydrous ethanol than\[MC{{l}_{4}}\]
  done clear
  C)
   \[MC{{l}_{2}}\]is more ionic than\[MC{{l}_{4}}\]
  done clear
  D)
  \[MC{{l}_{2}}\]is more easily hydrolysed than\[MC{{l}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer74) Atomic emission spectra of an element cannot be used to
  A)
   identify the atom
  done clear
  B)
   determine the mass number of the nucleus of atom
  done clear
  C)
   measure the difference in energy between pairs of stationary state of atom
  done clear
  D)
   All of the above
  done clear
  View Answer play_arrow

• question_answer75) For the reaction of one mole of zinc dust with one mole of sulphuric acid in a bomb calorimeter,\[\Delta U\]and W corresponds to
  A)
   \[\Delta U<0,W=0\]
  done clear
  B)
   \[\Delta U<0,W<0\]
  done clear
  C)
   \[\Delta U>0,W=0\]
  done clear
  D)
   \[\Delta U>0,W>0\]
  done clear
  View Answer play_arrow

• question_answer76) The enthalpy changes for the following processes are listed below \[C{{l}_{2}}(g)2Cl(g),242.3kJmo{{l}^{-1}}\] \[{{I}_{2}}(g)2I(g),151.0\,kJmo{{l}^{-1}}\] \[ICl(g)I(g)+Cl(g),211.3\,kJmo{{l}^{-1}}\] \[{{I}_{2}}(s){{I}_{2}}(g),62.76\,kJmo{{l}^{-1}}\] Given that the standard states for iodine and chlorine are\[{{I}_{2}}(s)\]and\[C{{l}_{2}}(g)\]the standard enthalpy of formation of\[ICI(g)\]is
  A)
   \[-14.6kJmo{{l}^{-1}}\]  
  done clear
  B)
   \[-16.8\text{ }kJ\text{ }mo{{l}^{-1}}\]
  done clear
  C)
   \[+\text{ }16.8\text{ }kJ\text{ }mo{{l}^{-1}}\]  
  done clear
  D)
   \[+\text{ }244.8\text{ }kJ\text{ }mo{{l}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer77) When glucose reacts with bromine water, the main product is
  A)
   acetic acid
  done clear
  B)
   saccharic acid
  done clear
  C)
   glyceraldehyde
  done clear
  D)
   gluconicacid
  done clear
  View Answer play_arrow

• question_answer78) Amylopectin is a polymer of
  A)
   \[\alpha -D-\]glucose     
  done clear
  B)
   \[\alpha -D-\]fructose
  done clear
  C)
   lactose        
  done clear
  D)
   amylose
  done clear
  View Answer play_arrow

• question_answer79) \[2C{{H}_{3}}-\overset{\begin{smallmatrix}  C{{H}_{3}} \\  | \end{smallmatrix}}{\mathop{C}}\,=O\xrightarrow[Reduction]{Mg-Hg+{{H}_{2}}O}A\xrightarrow[{}]{{{H}^{+}}}B\] Identify the B in the above sequence
  A)
   \[C{{H}_{3}}-\underset{\begin{smallmatrix}  | \\  OH \end{smallmatrix}}{\overset{\begin{smallmatrix}  C{{H}_{3}} \\  | \end{smallmatrix}}{\mathop{C}}}\,-\underset{\begin{smallmatrix}  | \\  OH \end{smallmatrix}}{\overset{\begin{smallmatrix}  C{{H}_{3}} \\  | \end{smallmatrix}}{\mathop{C}}}\,-C{{H}_{3}}\]
  done clear
  B)
   \[C{{H}_{3}}-\underset{\begin{smallmatrix}  || \\  OH \end{smallmatrix}}{\mathop{C}}\,-\underset{\begin{smallmatrix}  | \\  OH \end{smallmatrix}}{\overset{\begin{smallmatrix}  C{{H}_{3}} \\  | \end{smallmatrix}}{\mathop{C}}}\,-C{{H}_{3}}\]
  done clear
  C)
   \[C{{H}_{3}}-\underset{\begin{smallmatrix}  || \\  OH \end{smallmatrix}}{\mathop{C}}\,-\underset{\begin{smallmatrix}  | \\  C{{H}_{3}} \end{smallmatrix}}{\overset{\begin{smallmatrix}  C{{H}_{3}} \\  | \end{smallmatrix}}{\mathop{C}}}\,-C{{H}_{3}}\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer80) Which one of the following compound gives aspirin on reacting with acetic anhydride in presence of\[{{H}_{2}}S{{O}_{4}}\]?
  A)
   
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer81) If a plane meets the coordinate axes at A, B and C, in such a way that the centroid of \[\Delta ABC\]is at the point (1, 2, 3), the equation of the plane is
  A)
   \[\frac{x}{1}+\frac{y}{2}+\frac{z}{3}=1\]
  done clear
  B)
   \[\frac{x}{3}+\frac{y}{6}+\frac{z}{9}=1\]
  done clear
  C)
   \[\frac{x}{1}+\frac{y}{2}+\frac{z}{3}=1/3\]
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer82) Equation of a line passing through\[(-1,2,-3)\] and perpendicular to the plane \[2x+3y+z+5=0\]is
  A)
   \[\frac{x-1}{-1}=\frac{y+2}{1}=\frac{z-3}{-1}\]
  done clear
  B)
   \[\frac{x+1}{-1}=\frac{y-2}{1}=\frac{z+3}{1}\]
  done clear
  C)
   \[\frac{x+1}{2}=\frac{y-2}{3}=\frac{z+3}{1}\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer83) The equation of the plane containing the line\[r=i+j+\lambda 2i+j+4k)\]is
  A)
   \[r.(i+2j-k)=3\]
  done clear
  B)
   \[r.(i+2j-k)=6\]
  done clear
  C)
   \[r.(-i-2j+k)=3\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer84) If \[y=sin(sinx)\]and \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+\frac{dy}{dx}\tan x+f(x)=0,\]then\[f(x)\]equals to
  A)
   \[si{{n}^{2}}x.sin(cos\text{ }x)\]
  done clear
  B)
   sin2 x cos(sin x)
  done clear
  C)
   \[co{{s}^{2}}x.sin(\cos \text{ }x)\]
  done clear
  D)
   \[co{{s}^{2}}x\text{ }sin\text{ }(sin\text{ }x)\]
  done clear
  View Answer play_arrow

• question_answer85) The maximum value of the function \[f(x)=\sin (x+\pi /6)+\cos (x+\pi /6)\] in the interval\[(0,\text{ }\pi /2)\]occurs at
  A)
   \[\pi /12\]             
  done clear
  B)
   \[\pi /6\]
  done clear
  C)
   \[\pi /4\]              
  done clear
  D)
   \[\pi /3\]
  done clear
  View Answer play_arrow

• question_answer86) \[\underset{x\to 0}{\mathop{\lim }}\,{{\left\{ \tan \left( \frac{\pi }{4}+x \right) \right\}}^{1/x}}\]
  A)
   e               
  done clear
  B)
   \[{{e}^{2}}\]
  done clear
  C)
   \[\sqrt{e}\]             
  done clear
  D)
   \[1/\sqrt{e}\]
  done clear
  View Answer play_arrow

• question_answer87) The value of b for which the function \[f(x)=\left\{ \begin{matrix}    5x-4, & 0<x\le 1  \\    4{{x}^{2}}+3bx, & 1<x<2  \\ \end{matrix} \right.\]is continuous at every point of its domain is
  A)
   \[-1\]              
  done clear
  B)
   0
  done clear
  C)
   1              
  done clear
  D)
   13/3
  done clear
  View Answer play_arrow

• question_answer88) The area bounded by the x-axis, the curve\[y=f(x)\]and the lines\[x=1\]and\[x=b\]is equal to\[\sqrt{{{b}^{2}}+1}-\sqrt{2}\]for all\[b>1,\]then\[f(x)\]is
  A)
   \[\sqrt{x-1}\]         
  done clear
  B)
   \[\sqrt{x+1}\]
  done clear
  C)
   \[\sqrt{{{x}^{2}}+1}\]       
  done clear
  D)
   \[\frac{x}{\sqrt{1+{{x}^{2}}}}\]
  done clear
  View Answer play_arrow

• question_answer89) If\[{{I}_{n}}=\int_{0}^{\pi /4}{{{\tan }^{n}}\theta d\theta },\]then\[{{I}_{8}}+{{I}_{6}}\]is equal to
  A)
   1/4            
  done clear
  B)
   1/5
  done clear
  C)
   1/6            
  done clear
  D)
   1/7
  done clear
  View Answer play_arrow

• question_answer90) Equation of tangent to the curve\[x=a{{\cos }^{3}}t,\]\[y=a{{\sin }^{3}}t\]at\[t\]is
  A)
   \[x\sec t-y\cos ect=\alpha \]
  done clear
  B)
   \[x\sec t+y\cos ect=\alpha \]
  done clear
  C)
   \[x\cos ect+ysect=\alpha \]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer91) \[\underset{x\to \infty }{\mathop{\lim }}\,\frac{{{x}^{n}}}{{{e}^{x}}}=0\]for
  A)
   \[n=0\]only
  done clear
  B)
   n is any whole number
  done clear
  C)
  \[n=2\]only
  done clear
  D)
   no value of n
  done clear
  View Answer play_arrow

• question_answer92) Let\[p(x)={{a}^{2}}+bx,\]\[q(x)=l{{x}^{2}}+mx+n,\]if \[p(1)-q(1)=0,\]\[p(2)-q(2)=1\]and \[p(3)-q(3)=4,\]then\[p(2)-q(2)=1\]equals to
  A)
   0             
  done clear
  B)
   5
  done clear
  C)
   6             
  done clear
  D)
   9
  done clear
  View Answer play_arrow

• question_answer93) If\[a<0<b,\]then\[\int_{a}^{b}{\frac{|x|}{x}}dx\]
  A)
   \[a-b\]         
  done clear
  B)
   \[b-a\]
  done clear
  C)
   \[a+b\]         
  done clear
  D)
   \[-a-b\]
  done clear
  View Answer play_arrow

• question_answer94) \[\frac{d}{dx}\left\{ {{\sin }^{2}}{{\cot }^{-1}}\frac{1}{\sqrt{\frac{1+x}{1-x}}} \right\}\]
  A)
   0              
  done clear
  B)
   \[-1/2\]
  done clear
  C)
   1/2             
  done clear
  D)
   \[-1\]
  done clear
  View Answer play_arrow

• question_answer95) The integral \[\int_{-1/2}^{1/2}{\left\{ [x]+\log \left( \frac{1+x}{1-x} \right) \right\}dx}=?\] Where\[[.]\]is the greatest integer function.
  A)
   \[-1/2\]           
  done clear
  B)
   0
  done clear
  C)
   1             
  done clear
  D)
   \[2\log (1/2)\]
  done clear
  View Answer play_arrow

• question_answer96) \[\int{\frac{{{\sin }^{-1}}\sqrt{x}-{{\cos }^{-1}}\sqrt{x}}{{{\sin }^{-1}}\sqrt{x}+{{\cos }^{-1}}\sqrt{x}}}dx=?\]
  A)
   \[\frac{2}{\pi }[\sqrt{x-{{x}^{2}}}+(1-2x){{\sin }^{-1}}\sqrt{x}]x+C\]
  done clear
  B)
   \[\frac{2}{\pi }[\sqrt{x-{{x}^{2}}}-(1-2x){{\sin }^{-1}}\sqrt{x}]-x+C\]
  done clear
  C)
   \[\frac{2}{\pi }[\sqrt{x-{{x}^{2}}}+(1-2x){{\sin }^{-1}}\sqrt{x}]-x+C\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer97) Let\[f:R\to R,\text{ }g:R\to R,\]be two functions such that\[f(x)=2x-3,\text{ }g(x)={{x}^{3}}+5\]the function\[{{(fog)}^{-1}}(x)\]is equal to
  A)
   \[{{\left( \frac{x+7}{2} \right)}^{1/3}}\]
  done clear
  B)
   \[{{\left( x-\frac{7}{2} \right)}^{1/3}}\]
  done clear
  C)
   \[{{\left( \frac{x-2}{7} \right)}^{1/3}}\]
  done clear
  D)
   \[{{\left( \frac{x-7}{2} \right)}^{1/3}}\]
  done clear
  View Answer play_arrow

• question_answer98) If\[(a\text{ }sec\,\theta ,\text{ b }tan\,\theta )\]and\[(a\text{ }sec\phi ,\text{ b }tan\,\phi )\]are the ends of a focal chord of\[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1,\]then  \[\tan \theta /2\tan \phi /2\]is equal to
  A)
   \[\frac{e-1}{e+1}\]
  done clear
  B)
   \[\frac{1-e}{1+e}\]
  done clear
  C)
   \[\frac{1+e}{1-e}\]
  done clear
  D)
   \[\frac{e+1}{e-1}\]
  done clear
  View Answer play_arrow

• question_answer99) If the angle between tangents drawn to \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\]from (0, 0) is\[\pi /2,\]then
  A)
   \[{{g}^{2}}+{{f}^{2}}=3c\]
  done clear
  B)
   \[{{g}^{2}}+{{f}^{2}}=2c\]
  done clear
  C)
   \[{{g}^{2}}+{{f}^{2}}=5c\]
  done clear
  D)
   \[{{g}^{2}}+{{f}^{2}}=4c\]
  done clear
  View Answer play_arrow

• question_answer100) If\[a.b=b.c=c.a=0,\]then\[a.(b\times c)\]is equal to
  A)
   a lion-zero vector
  done clear
  B)
   1
  done clear
  C)
   \[-1\]              
  done clear
  D)
  \[|a|\,|b|\,|c|\]
  done clear
  View Answer play_arrow

• question_answer101) A variable line drawn through the point (1, 3) meets the\[x-\]axis at A and y-axis at B. If the rectangle OAPB is completed, where 0 is the origin, then locus of y is
  A)
   \[1/y+3/x=1\]
  done clear
  B)
   \[x+3y=1\]
  done clear
  C)
   \[1/x+3/y=1\]
  done clear
  D)
   \[3x+y=1\]
  done clear
  View Answer play_arrow

• question_answer102) If a, b, c are non-zero non-collinear vectors and\[a\times b=b\times c=c\times a,\]then\[a+b+c\]is equal to
  A)
   \[abc\]           
  done clear
  B)
   \[-1\]
  done clear
  C)
   2             
  done clear
  D)
   0
  done clear
  View Answer play_arrow

• question_answer103) The   two   parabolas\[{{y}^{2}}=4ax\]and\[{{y}^{2}}=4c(x-b)\]cannot have a common normal, other than the axis, unless
  A)
   \[\frac{a-c}{b}>2\]
  done clear
  B)
   \[\frac{b}{a-c}>2\]
  done clear
  C)
   \[\frac{b}{a+c}>2\]        
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer104) If the number\[\frac{{{(1-i)}^{n}}}{{{(1+i)}^{n-2}}}\]is real and positive, then n is
  A)
   any integer     
  done clear
  B)
   \[2\lambda \]
  done clear
  C)
   \[4\lambda +1\]          
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer105) The number of five digit telephone numbers having at least one of their digits repeated is
  A)
   90000         
  done clear
  B)
   100000
  done clear
  C)
   30240         
  done clear
  D)
   69760
  done clear
  View Answer play_arrow

• question_answer106) In the binomial expansion of\[{{(a-b)}^{n}},n\ge 5,\] the sum of the 5th and 6th terms is zero, then a/b equals
  A)
   \[\frac{n-5}{6}\]
  done clear
  B)
   \[\frac{n-4}{5}\]
  done clear
  C)
   \[\frac{5}{n-4}\]
  done clear
  D)
   \[\frac{6}{n-5}\]
  done clear
  View Answer play_arrow

• question_answer107) A value of\[\sqrt{i}+\sqrt{-i}\]is
  A)
   0               
  done clear
  B)
   \[\sqrt{2}\]
  done clear
  C)
   \[-i\]               
  done clear
  D)
   \[i\]
  done clear
  View Answer play_arrow

• question_answer108) Let\[{{z}_{1}}\]and\[{{z}_{2}}\]be complex numbers such that \[{{z}_{1}}\ne {{z}_{2}}\]and\[|{{z}_{1}}|=|{{z}_{2}}|.\]If\[{{z}_{1}}\]has positive real part and\[{{z}_{2}}\]has negative imaginary part, then\[\frac{{{z}_{1}}+{{z}_{2}}}{{{z}_{1}}-{{z}_{2}}}\]may be
  A)
   zero
  done clear
  B)
   real and positive
  done clear
  C)
   real and negative
  done clear
  D)
   purely imaginary or zero
  done clear
  View Answer play_arrow

• question_answer109) Let\[{{S}_{n}}\]denote the sum of first n terms of an AP, if\[{{S}_{2n}}=3{{S}_{n}},\]then the ratio -3n is equal to
  A)
   4                
  done clear
  B)
   6
  done clear
  C)
   \[\pm 3\]               
  done clear
  D)
   \[\pm 4\]
  done clear
  View Answer play_arrow

• question_answer110) In 324 throws of 4 dice, the expected number of times 3 sixes occur is
  A)
   81              
  done clear
  B)
   5
  done clear
  C)
   9              
  done clear
  D)
   31
  done clear
  View Answer play_arrow

• question_answer111) If the roots of the equation\[{{x}^{2}}+px+q=0\]differ by 1, then
  A)
   \[{{p}^{2}}=4q\]
  done clear
  B)
   \[{{p}^{2}}=4q+1\]
  done clear
  C)
   \[{{p}^{2}}=4q-1\]
  done clear
  D)
   \[{{p}^{2}}=q\]
  done clear
  View Answer play_arrow

• question_answer112) If\[\alpha ,\beta \]and\[\gamma \]are the roots of the equation \[{{x}^{3}}+px+q=0,\]then value of the determinant \[\left| \begin{matrix} \alpha  & \beta  & \gamma   \\ \beta  & \gamma  & \alpha   \\ \gamma  & \alpha  & \beta   \\ \end{matrix} \right|\]is
  A)
   \[p\]                
  done clear
  B)
   \[q\]
  done clear
  C)
   \[{{p}^{2}}-2q\]         
  done clear
  D)
   \[0\]
  done clear
  View Answer play_arrow

• question_answer113) If\[\frac{1}{a},\frac{1}{b},\frac{1}{c}\]are in AP, then\[\left( \frac{1}{a}+\frac{1}{b}-\frac{1}{c} \right)\left( \frac{1}{b}+\frac{1}{c}-\frac{1}{a} \right)\]is equal to
  A)
   \[\frac{4}{ac}-\frac{3}{{{b}^{2}}}\]
  done clear
  B)
   \[\frac{{{b}^{2}}-ac}{{{a}^{2}}{{b}^{2}}{{c}^{2}}}\]
  done clear
  C)
   \[\frac{4}{ac}-\frac{1}{{{b}^{2}}}\]         
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer114) If A and B are square matrices of the same order and A is non-singular, then for a positive integer n,\[{{({{A}^{-1}}BA)}^{n}}\]is equal to
  A)
   \[{{A}^{-n}}{{B}^{n}}{{A}^{n}}\]
  done clear
  B)
   \[{{A}^{n}}{{B}^{n}}{{A}^{-n}}\]
  done clear
  C)
   \[{{A}^{-1}}{{B}^{n}}A\]
  done clear
  D)
   \[n({{A}^{-1}}BA)\]
  done clear
  View Answer play_arrow

• question_answer115) Two numbers are a and b. What is the relation between their GP, AP and HP. If AP denotes A GP denotes G and HP denotes H?
  A)
   \[H=\frac{2AG}{A+G}\]   
  done clear
  B)
   \[A=H/{{G}^{2}}\]
  done clear
  C)
   \[H={{G}^{2}}/A\]     
  done clear
  D)
   \[G={{H}^{2}}/A\]
  done clear
  View Answer play_arrow

• question_answer116) The chance of throwing a total of 3 or 5 or 11 with two dice is
  A)
   5/36           
  done clear
  B)
   1/9
  done clear
  C)
   2/9            
  done clear
  D)
   19/36
  done clear
  View Answer play_arrow

• question_answer117) The number of roots of the equation \[x+2\text{ }\tan x=\pi /2\]in the interval\[[0,2\pi ]\]is
  A)
   1               
  done clear
  B)
   2
  done clear
  C)
   3               
  done clear
  D)
   infinite
  done clear
  View Answer play_arrow

• question_answer118) In a\[\Delta ABC,\]if\[\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}\]and the side\[a=2,\]then area of the triangle is
  A)
   1              
  done clear
  B)
   2
  done clear
  C)
   \[\sqrt{3}/2\]          
  done clear
  D)
  \[\sqrt{3}\]
  done clear
  View Answer play_arrow

• question_answer119) If\[{{\sin }^{-1}}\left( \frac{2a}{1+{{a}^{2}}} \right)+{{\sin }^{-1}}\left( \frac{2b}{1+{{b}^{2}}} \right)=2{{\tan }^{-1}}x,\] then\[x\]is equal to
  A)
   \[\frac{a-b}{1+ab}\]
  done clear
  B)
   \[\frac{b}{1+ab}\]
  done clear
  C)
   \[\frac{b}{1-ab}\]
  done clear
  D)
   \[\frac{a+b}{1-ab}\]
  done clear
  View Answer play_arrow

• question_answer120) If\[tan\text{ }A-tan\text{ }B=x\]and\[cot\text{ }B-cot\text{ }A=y,\]then \[cot(A-B)\]is equal to
  A)
   \[x+y\]            
  done clear
  B)
   \[x+\frac{1}{y}\]
  done clear
  C)
   \[\frac{1}{x}+\frac{1}{y}\]           
  done clear
  D)
   \[x+2y\]
  done clear
  View Answer play_arrow