Solved papers for RAJASTHAN ­ PET Rajasthan PET Solved Paper-2012

done Rajasthan PET Solved Paper-2012 Total Questions - 120

• question_answer1) The unit of permittivity of free space\[{{\varepsilon }_{0}}\]is
  A)
   \[{{C}^{2}}/N-{{m}^{2}}\]
  done clear
  B)
   \[{{C}^{2}}/{{(N-m)}^{2}}\]
  done clear
  C)
   \[N-{{m}^{2}}/{{C}^{2}}\]
  done clear
  D)
   \[C/N-m\]
  done clear
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• question_answer2) How are the numerical value (N) and unit (U) of a physical quantity related to each other?
  A)
   \[N\propto \sqrt{U}\]
  done clear
  B)
   \[N\propto \frac{1}{\sqrt{U}}\]
  done clear
  C)
   \[N\propto \frac{1}{U}\]
  done clear
  D)
   \[N\propto U\]
  done clear
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• question_answer3) If a ball is thrown vertically upwards with speed\[u,\]the distance covered during the last t second of its ascent is
  A)
   \[ut-\frac{1}{2}g{{t}^{2}}\]
  done clear
  B)
   \[\frac{1}{2}g{{t}^{2}}\]
  done clear
  C)
   \[(u+gt)t\]
  done clear
  D)
   \[ut\]
  done clear
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• question_answer4) An electron starting from rest has a velocity\[v\] that increases linearly with time t as\[v=kt,\] where\[k=2\text{ }m{{s}^{-2}}\]. The distance covered by electron in first 3 s is
  A)
   9m          
  done clear
  B)
   11 m
  done clear
  C)
   33m         
  done clear
  D)
   40m
  done clear
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• question_answer5) The excess of pressure inside a drop of soap solution is pj and that inside a soap bubble of same radius is\[{{p}_{b}}\]. The correct relation between \[{{p}_{d}}\]and\[{{p}_{b,}}\]is given by
  A)
   \[2{{p}_{d}}={{p}_{b}}\]
  done clear
  B)
   \[{{p}_{d}}={{p}_{b}}\]
  done clear
  C)
   \[{{p}_{d}}=2{{p}_{b}}\]      
  done clear
  D)
   None of these
  done clear
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• question_answer6) Two vectors A and B are such that,\[A+B=C\] and\[{{A}^{2}}+{{B}^{2}}={{C}^{2}}\]. If 9 is the angle between positive directions of A and B, then
  A)
   \[\theta =\frac{2\pi }{3}\]
  done clear
  B)
   \[\theta =\frac{\pi }{2}\]
  done clear
  C)
   \[\theta =\pi \]
  done clear
  D)
   \[\theta =0\]
  done clear
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• question_answer7) Let two satellites X and Y revolves around a planet P in circular orbits of radii 4R and R respectively. If the speed of the satellite X is 3v, then the speed of satellite Y will be
  A)
   \[6v\]
  done clear
  B)
   \[\frac{3v}{4}\]
  done clear
  C)
   \[12v\]           
  done clear
  D)
   \[\frac{3v}{2}\]
  done clear
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• question_answer8) A bimetallic strip is made of two strips A and B having coefficient of linear expansion as\[{{\alpha }_{A}}\]and da. If\[{{\alpha }_{A}}>{{\alpha }_{B}},\] which one of the following describes the behaviour of the metallic strip when heated?
  A)
   Strip will bend only when \[\frac{{{\alpha }_{A}}+{{\alpha }_{B}}}{2}>({{\alpha }_{A}}-{{\alpha }_{B}})\]
  done clear
  B)
   Strip will bend but will not elongate
  done clear
  C)
   Strip will bend with metal A as the outer side
  done clear
  D)
   Strip will bend with metal B as The outer side
  done clear
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• question_answer9) An electron accelerated through a potential difference of V volts has a wavelength\[\lambda \] associated with it. Mass of proton is nearly 2000 times that of an electron. In order to have the same wavelength\[\lambda \]for the proton, it must be accelerated through a potential difference of
  A)
   2000 V volt   
  done clear
  B)
   20 V volt
  done clear
  C)
   V/2000 volt   
  done clear
  D)
   \[\sqrt{2000}\]V volt
  done clear
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• question_answer10) Two points charges of\[+3C\]and\[+9C\]repel each other with a force of 27 N. If charges of\[-3C\] are given to each of these charges, then the new force of interaction will be
  A)
   zero         
  done clear
  B)
   9 N
  done clear
  C)
   18 N         
  done clear
  D)
   2 N
  done clear
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• question_answer11) In Young's double slit experiment the 7th maximum with wavelength\[{{\lambda }_{1}}\]is at a distance\[{{d}_{1}}\]and that with wavelength\[{{\lambda }_{2}}\]is at distance\[{{d}_{2}}.\]Then, \[{{d}_{1}}/{{d}_{2}}=\]
  A)
   \[{{\lambda }_{2}}/{{\lambda }_{1}}\]
  done clear
  B)
   \[{{\lambda }_{1}}/{{\lambda }_{2}}\]
  done clear
  C)
   \[\lambda _{2}^{2}/\lambda _{1}^{2}\]
  done clear
  D)
   \[\lambda _{1}^{2}/\lambda _{2}^{2}\]
  done clear
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• question_answer12) The plates of a parallel air capacitor are 2 cm apart. If a slab of dielectric constant 5 and thickness 1 cm is placed between its plates, then to keep the capacitance of the capacitor unchanged. The plates of the capacitor should moved by a distance of
  A)
   3.2 cm        
  done clear
  B)
   3.0 cm
  done clear
  C)
   2.8 cm       
  done clear
  D)
   2.2 cm
  done clear
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• question_answer13) If\[W\]units of works is required to turn a magnetic needle through\[60{}^\circ \]when it is lying parallel to a magnetic field, then amount of torque needed to maintain needle in this position will be
  A)
   \[W\]           
  done clear
  B)
   \[2\,W\]
  done clear
  C)
   \[\sqrt{3}W\]        
  done clear
  D)
   \[\frac{\sqrt{3}W}{2}\]
  done clear
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• question_answer14) If two stars radiates maximum energy at wavelengths\[316\times {{10}^{-7}}m\]and\[4.8\times {{10}^{-7}}m\] respectively, then ratio of their temperatures T/T? will be
  A)
   \[\frac{2}{3}\]
  done clear
  B)
   \[\frac{4}{3}\]
  done clear
  C)
   \[\frac{3}{4}\]
  done clear
  D)
   \[\frac{3}{2}\]
  done clear
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• question_answer15) The diameter of the moon is\[3.5\times {{10}^{3}}\]km and its distance from the earth is\[3.8\times {{10}^{5}}\]km seen by a telescope having focal lengths of the objective and eye piece as 4 m and 10 cm respectively, the diameter of image of the moon will be approximately
  A)
   \[10{}^\circ \]          
  done clear
  B)
   \[20{}^\circ \]
  done clear
  C)
   \[35{}^\circ \]           
  done clear
  D)
   \[50{}^\circ \]
  done clear
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• question_answer16) The rms velocity of oxygen molecule at\[27{}^\circ C\]is (Atomic weight of oxygen =16)
  A)
   \[402.5\,m{{s}^{-1}}\]   
  done clear
  B)
   \[400.5\text{ }m{{s}^{-1}}\]
  done clear
  C)
   \[483.5\text{ }m{{s}^{-1}}\]   
  done clear
  D)
   \[532.5\text{ }m{{s}^{-1}}\]
  done clear
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• question_answer17) If a constant volume gas thermometer records a pressure of 20 kPa at tripple point of water and pressure of 14.3 kPa at the dry ice, then the temperature of dry ice will be
  A)
   \[-77.85{}^\circ C\]    
  done clear
  B)
   \[+77.85{}^\circ C\]
  done clear
  C)
   \[-66.05{}^\circ C\]    
  done clear
  D)
   None of these
  done clear
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• question_answer18) Two discs have same mass and thickness but are made, up of different materials having different densities. Which one of them will have larger moment of inertia?
  A)
   Both disc have same moment of inertia
  done clear
  B)
   disc having less density have larger moment of inertia
  done clear
  C)
   disc having more density have larger moment of inertia
  done clear
  D)
   None of the above
  done clear
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• question_answer19) If a resistor of\[30\,\Omega ,\]is bent in the form of a circle as shown in figure, then the effective resistance' between points X and Y will be
  A)
   \[\frac{5}{6}\Omega \]
  done clear
  B)
   \[\frac{6}{5}\Omega \]
  done clear
  C)
   \[\frac{6}{25}\Omega \]
  done clear
  D)
   \[\frac{25}{6}\Omega \]
  done clear
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• question_answer20) A radioactive nuclide decays to form a stable nuclide. If the half-life of nuclide is 3 min, then what fraction of its 1 g will remain radioactive after 9 min?
  A)
   0.125         
  done clear
  B)
   0.875
  done clear
  C)
   1.125         
  done clear
  D)
   1.875
  done clear
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• question_answer21) If an\[\alpha -\]particle of energy 10 MeV is deflected back when its distance from the nucleus is \[4\times {{10}^{-14}}m,\]then the atomic number of the atom is
  A)
   129          
  done clear
  B)
   130
  done clear
  C)
   139          
  done clear
  D)
   120
  done clear
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• question_answer22) Which of the following spectral series in hydrogen atom give spectral line of\[4860\overset{o}{\mathop{\text{A}}}\,\]?
  A)
   Brackett      
  done clear
  B)
   Paschen
  done clear
  C)
   Lyman       
  done clear
  D)
   Balmer
  done clear
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• question_answer23) A bus starts from rest with an acceleration\[1\,m{{s}^{-2}}\]. A man who is 48 m behind the bus starts with a uniform velocity of\[10\text{ }m{{s}^{-1}}\]. Then the minimum rime after which the man will reach the bus
  A)
   4 s            
  done clear
  B)
   8 s
  done clear
  C)
   10 s           
  done clear
  D)
   15 s
  done clear
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• question_answer24) The gravitational constant G is called universal constant because
  A)
   It has no dimensions
  done clear
  B)
   It has no unit
  done clear
  C)
   It has same value in different systems of unit
  done clear
  D)
   It does not depend upon the nature of the medium in which the bodies lie
  done clear
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• question_answer25) If a metallic block had no potential difference applied across it, then the average velocity of free electrons in it
  A)
   zero
  done clear
  B)
   proportional to T
  done clear
  C)
   proportional to\[\sqrt{T}\]
  done clear
  D)
   finite but independent of temperature
  done clear
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• question_answer26) A particle describes a horizontal circle on the smooth surface of an inverted cone. If the height of the plane of the circle above the vertex is 9.8 cm, then the speed of the particle will be (Take\[g=9.8\text{ }m/{{s}^{2}}\])
  A)
   \[0.98\text{ }m{{s}^{-1}}\]    
  done clear
  B)
   \[19.6\text{ }m{{s}^{-1}}\]
  done clear
  C)
   \[4.9\,m{{s}^{-1}}\]     
  done clear
  D)
   None of these
  done clear
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• question_answer27) The equation of a wave is represented by \[y={{10}^{-4}}\sin \left( 100t-\frac{x}{10} \right)m,\]the velocity of the wave will be
  A)
   \[0.1\text{ }m{{s}^{-1}}\]     
  done clear
  B)
   \[10\text{ }m{{s}^{-1}}\]
  done clear
  C)
   \[100\text{ }m{{s}^{-1}}\]     
  done clear
  D)
   \[1000\text{ }m{{s}^{-1}}\]
  done clear
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• question_answer28) If two vessels of different materials identical in size and wall thickness are filled with equal quantities of ice at\[0{}^\circ C\]and ice melts completely in 10 and 25 min respectively, then the ratio of coefficients of thermal conductivies of the materials of the vessels will be
  A)
   \[\frac{5}{7}\]
  done clear
  B)
   \[\frac{5}{2}\]
  done clear
  C)
   \[\frac{2}{5}\]
  done clear
  D)
   \[\frac{7}{5}\]
  done clear
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• question_answer29) The stress for elastic limit of a material is\[3.5\times {{10}^{8}}N-{{m}^{-2}}\]. The minimum diameter of a rod made of this material which can support 500 N load without exceeding elastic limit will be
  A)
   1.35 mm     
  done clear
  B)
   1.35 cm
  done clear
  C)
   \[1.35\times {{10}^{-6}}m\] 
  done clear
  D)
   2mm
  done clear
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• question_answer30) A ray of light passing through a prism having\[\mu =\sqrt{2}\]suffers minimum deviation. If the angle of incidence is double the angle of refraction within the prism, then the angle of the prism is
  A)
   \[45{}^\circ \]          
  done clear
  B)
   \[90{}^\circ \]
  done clear
  C)
   \[60{}^\circ \]          
  done clear
  D)
   None of these
  done clear
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• question_answer31) A drop of olive oil is introduced in a mixture of alcohol and water. The density of the mixture is same as that of olive oil. The upward thrust on the drop is
  A)
   zero
  done clear
  B)
   equal to weight of the drop
  done clear
  C)
   less than the weight of the drop
  done clear
  D)
   more than the weight of the drop
  done clear
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• question_answer32) A Carnot engine whose low temperature reservoir is at\[7{}^\circ C\]has an efficiency of 50%. If the efficiency of heat engine is to be increased more by 10% then the temperature of high temperature reservoir should be increased by
  A)
   107 K        
  done clear
  B)
   500 K
  done clear
  C)
   140 K        
  done clear
  D)
   200 K
  done clear
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• question_answer33) An AC source of frequency 50 Hz is connected to 50 mH inductor and a bulb. To get the maximum brightness from the bulb, what should be the capacitance of a capacitor connected in series with the circuit?
  A)
   \[50\times {{10}^{-4}}F\]
  done clear
  B)
   \[1\times {{10}^{-4}}F\]
  done clear
  C)
   \[2.03\times {{10}^{-4}}F\]
  done clear
  D)
   \[3\times {{10}^{-4}}F\]
  done clear
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• question_answer34) Two long straight wires are connected by a circular section that has a radius r as shown in figure. All segments of the wire lie in the same place and carry steady current I. The magnetic field at centre O of the circular segment will be
  A)
   \[\frac{B{{\mu }_{0}}I}{4\pi r}\]
  done clear
  B)
   \[\frac{B{{\mu }_{0}}I}{r}\]
  done clear
  C)
   \[\frac{B{{\mu }_{0}}I}{2\pi r}\]
  done clear
  D)
   \[\frac{{{\mu }_{0}}I}{4\pi r}\]
  done clear
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• question_answer35) If two wires made of tinned copper having identical cross-section but different lengths \[{{l}_{1}}\]and\[{{l}_{2}}\]respectively are used as fuse wires, then the fuses will melt at same value of current in both of them
  A)
   True
  done clear
  B)
   False
  done clear
  C)
   Insufficient data
  done clear
  D)
   None of the above
  done clear
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• question_answer36) A wave is represented by \[y=a\cos (\omega t+kx+\phi )\] where\[\omega ,\phi \]and\[\phi \]are three constants. The dimensions of\[\omega ,k\]and\[\phi \]are respectively
  A)
   \[[T],[{{L}^{-1}}],[{{M}^{0}}{{L}^{0}}{{T}^{0}}]\]
  done clear
  B)
   \[[T],[L],[M]\]
  done clear
  C)
   \[[T],[{{L}^{-1}}],[{{M}^{0}}{{L}^{0}}{{T}^{0}}]\]
  done clear
  D)
   \[[{{T}^{-1}}],[L],[{{M}^{0}}{{L}^{0}}{{T}^{0}}]\]
  done clear
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• question_answer37) Two blocks of masses \[{{m}_{1}}\] and \[{{m}_{2}}\] are placed in contact with each other on a rough horizontal surface having coefficient of friction\[\mu \]as shown in figure. The minimum horizontal force F required to move the block\[{{m}_{1}}\]
  A)
   \[\mu ({{m}_{1}}-{{m}_{2}})g\]
  done clear
  B)
   \[\mu ({{m}_{2}}-{{m}_{1}})g\]
  done clear
  C)
   \[\mu {{m}_{1}}g\]
  done clear
  D)
   \[\mu ({{m}_{1}}+{{m}_{2}})g\]
  done clear
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• question_answer38) A ball of mass m moving with a velocity\[\mu \]collides head-on with another ball of mass m initially at rest. If the coefficient of restitution be e, then the ratio of the final and initial velocities of the first ball is
  A)
   \[\frac{1-e}{2}\]
  done clear
  B)
   \[\frac{1+e}{2}\]
  done clear
  C)
   \[\frac{1-e}{1+e}\]
  done clear
  D)
   \[\frac{1+e}{1-e}\]
  done clear
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• question_answer39) If\[{{I}_{A}},{{K}_{A}}\]and\[{{I}_{B}},{{K}_{B}}\]are the moments of interia and kinetic energies of two freely rotating bodies A and B respectively, such that\[{{I}_{A}}>{{I}_{B}}\]and their angular mements are equal, then
  A)
   \[{{K}_{A}}<{{K}_{B}}\]
  done clear
  B)
   \[{{K}_{A}}>{{K}_{B}}\]
  done clear
  C)
   \[{{K}_{A}}={{K}_{B}}\]
  done clear
  D)
   \[{{K}_{A}}=2{{K}_{B}}\]
  done clear
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• question_answer40) The angular frequency and the amplitude of a simple pendulum are\[\omega \]and a respectively. If the pendulum is displaced through a distance\[x\] from the mean position then the ratio of its kinetic energy (K) and potential energy (U) will be
  A)
   \[\frac{K}{U}=\frac{{{a}^{2}}-{{x}^{2}}{{\omega }^{2}}}{{{x}^{2}}{{\omega }^{2}}}\]
  done clear
  B)
   \[\frac{K}{U}=\frac{{{a}^{2}}-{{x}^{2}}}{{{x}^{2}}}\]
  done clear
  C)
   \[\frac{K}{U}=\frac{{{x}^{2}}}{{{a}^{2}}-{{x}^{2}}}\]
  done clear
  D)
   \[\frac{K}{U}=\frac{{{x}^{2}}{{\omega }^{2}}}{{{a}^{2}}-{{\omega }^{2}}{{x}^{2}}}\]
  done clear
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• question_answer41) Self-condensation of two moles of ethyl acetate in presence of sodium ethoxide yields
  A)
   ethyl butyrate
  done clear
  B)
   acetoacetic ester
  done clear
  C)
   methyl acetoacetate
  done clear
  D)
   ethyl propionate
  done clear
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• question_answer42) End product of the following reaction is\[C{{H}_{3}}C{{H}_{2}}COOH\xrightarrow[red\,P]{C{{l}_{2}}}\xrightarrow[{}]{Alcoholic\text{ }KOH}\]
  A)
   \[\underset{\begin{smallmatrix}  | \\  OH \end{smallmatrix}}{\mathop{C{{H}_{3}}CHCOO}}\,\]
  done clear
  B)
   \[\underset{\begin{smallmatrix}  | \\  OH \end{smallmatrix}}{\mathop{C{{H}_{2}}C{{H}_{2}}COO}}\,H\]
  done clear
  C)
   \[C{{H}_{2}}=CHCOOH\]
  done clear
  D)
   \[\underset{\begin{smallmatrix}  | \\  Cl \end{smallmatrix}}{\mathop{C{{H}_{2}}}}\,\underset{\begin{smallmatrix}  | \\  OH \end{smallmatrix}}{\mathop{CH}}\,COOH\]
  done clear
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• question_answer43) \[{{S}_{N}}1\]reaction is feasible in
  A)
   
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
   
  done clear
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• question_answer44) Maximum dehydration takes place in that of
  A)
   
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
   
  done clear
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• question_answer45) The volume of 2.8 g of CO at\[27{}^\circ C\]and 0.821 atm pressure is (R = 0.0821 L atm mol\[{{s}^{-1}}{{K}^{-1}}\])
  A)
   30 mL        
  done clear
  B)
   3 L
  done clear
  C)
   0.3 L
  done clear
  D)
   1.5 L
  done clear
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• question_answer46) An electron having highest energy in the set
  A)
   \[3,2,1,\frac{1}{2}\]
  done clear
  B)
   \[4,2,-1,\frac{1}{2}\]
  done clear
  C)
   \[4,1,0,-\frac{1}{2}\]
  done clear
  D)
   \[5,0,0,\frac{1}{2}\]
  done clear
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• question_answer47) On heating benzyl amine with chloroform and ethanolic KOH, product obtained is
  A)
   benzyl alcohol
  done clear
  B)
   benzaldehyde
  done clear
  C)
   benzonitrile
  done clear
  D)
   benzyl isocyanide
  done clear
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• question_answer48) In which of the following pairs are both the ions coloured in aqueous solution? (At. no. : Sc = 21, Ti = 22, Ni = 28, Cu = 29, Co =27)
  A)
   \[N{{i}^{2+}},T{{i}^{3+}}\]
  done clear
  B)
   \[S{{c}^{3+}},T{{i}^{3+}}\]
  done clear
  C)
   \[S{{c}^{3+}},C{{o}^{2+}}\]
  done clear
  D)
   \[N{{i}^{2+}},C{{u}^{+}}\]
  done clear
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• question_answer49) The number of lone pairs on\[Xe\]in\[Xe{{F}_{2}},Xe{{F}_{4}},\] arid\[Xe{{F}_{5}}\]respectively are
  A)
   3, 2, 1       
  done clear
  B)
   2, 4, 6
  done clear
  C)
   1, 2, 3       
  done clear
  D)
   6, 4, 2
  done clear
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• question_answer50) A solution of Baeyer's reagent
  A)
   contains cold dilute\[CuC{{l}_{2}}\]and\[HCl\]
  done clear
  B)
   contains cold dilute alkaline\[KMn{{O}_{4}}\]solution
  done clear
  C)
   can be used for reduction purpose
  done clear
  D)
   can be used to detect unsaturation in phenol
  done clear
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• question_answer51) Gold number is the index for
  A)
   protective colloid
  done clear
  B)
   purity of gold
  done clear
  C)
   metallic gold
  done clear
  D)
   electroplated gold
  done clear
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• question_answer52) The standard emf of the cell \[Zn+C{{u}^{2+}}\xrightarrow[{}]{{}}Cu+Z{{n}^{2+}}\]is 1.10 at\[25{}^\circ C\]. The emf of the cell when\[0.1\text{ }M\,C{{u}^{2+}}\]and\[0.1\text{ }M\,Z{{n}^{2+}}\]solution are used will be
  A)
   1.10V
  done clear
  B)
   \[+\text{ }0.110\text{ }V\]
  done clear
  C)
   \[-1.10V\]
  done clear
  D)
   \[-0.11\,V\]
  done clear
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• question_answer53) Given: The mass of electron is\[9.11\times {{10}^{-31}}kg\]and Planck constant is\[6.626\times {{10}^{-34}}Js,\]the uncertainty involved in the measurement of velocity within a distance of\[0.1\overset{o}{\mathop{\text{A}}}\,\]is
  A)
   \[5.79\times {{10}^{6}}m{{s}^{-1}}\]
  done clear
  B)
   \[5.79\times {{10}^{7}}m{{s}^{-1}}\]
  done clear
  C)
   \[5.79\times {{10}^{8}}m{{s}^{-1}}\]
  done clear
  D)
   \[5.79\times {{10}^{5}}m{{s}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer54) If \[E_{F{{e}^{2+}}/Fe}^{o}=-0.441V\] and       \[E_{F{{e}^{3+}}/F{{e}^{2+}}}^{o}=0.771V\]the standard emf of the reaction \[Fe+3F{{e}^{3+}}\xrightarrow[{}]{{}}3F{{e}^{2+}}\]will be
  A)
   0.330V      
  done clear
  B)
   1.653V
  done clear
  C)
   1.212V      
  done clear
  D)
   0.111 V
  done clear
  View Answer play_arrow

• question_answer55) The enthalpy of combustion of\[{{H}_{2}},\]cyclohexene\[({{C}_{6}}{{H}_{10}})\]and  cyclohexane\[({{C}_{6}}{{H}_{12}})\]are\[-241,~-3800\] and\[-3920\text{ }kJ\]per  mol respectively. Heat of hydrogenation of cyclohexene is
  A)
   \[-121\text{ }kJ\] per mol
  done clear
  B)
   \[+121\text{ }kJ\] per mol
  done clear
  C)
   \[+242\text{ }kJ\] per mol
  done clear
  D)
   \[-242\text{ }kJ\] per mol
  done clear
  View Answer play_arrow

• question_answer56) In which of the following molecules are all the bonds not equal?
  A)
   \[CI{{F}_{3}}\]          
  done clear
  B)
   \[B{{F}_{3}}\]
  done clear
  C)
   \[Al{{F}_{3}}\]          
  done clear
  D)
   \[N{{F}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer57) Half-life period of a substance is 1600 min. How much fraction of the substance will remain after 6400mm?
  A)
   \[\frac{1}{16}\]
  done clear
  B)
   \[\frac{1}{4}\]
  done clear
  C)
   \[\frac{1}{8}\]
  done clear
  D)
   \[\frac{1}{2}\]
  done clear
  View Answer play_arrow

• question_answer58) Compound A given below is
  A)
   antiseptic     
  done clear
  B)
   antibiotic
  done clear
  C)
   analgesic     
  done clear
  D)
   pesticide
  done clear
  View Answer play_arrow

• question_answer59) For the following cell with hydrogen electrodes at two different pressures\[{{p}_{1}}\]and\[{{p}_{2}},\]emf is given by \[\underset{{{p}_{1}}}{\mathop{pt({{H}_{2}})}}\,|\underset{1M}{\mathop{{{H}^{+}}(aq)}}\,|\underset{{{p}_{2}}}{\mathop{Pt({{H}_{2}})}}\,\]
  A)
   \[\frac{RT}{F}{{\log }_{e}}\frac{{{p}_{1}}}{{{p}_{2}}}\]
  done clear
  B)
   \[\frac{RT}{2F}{{\log }_{e}}\frac{{{p}_{1}}}{{{p}_{2}}}\]
  done clear
  C)
   \[\frac{RT}{F}{{\log }_{e}}\frac{{{p}_{2}}}{{{p}_{1}}}\]
  done clear
  D)
   \[\frac{RT}{2F}{{\log }_{e}}\frac{{{p}_{2}}}{{{p}_{1}}}\]
  done clear
  View Answer play_arrow

• question_answer60) Consider the following two reactions, \[A\xrightarrow[{}]{{}}\]Product; \[-\frac{d[A]}{dt}={{k}_{1}}{{[A]}^{0}}\] \[B\xrightarrow[{}]{{}}\]Product; \[-\frac{d[B]}{dt}={{k}_{2}}[B]\] \[{{k}_{1}}\]and\[{{k}_{2}}\]are expressed in terms of molarity (mol\[{{L}^{-1}}\]) and time\[({{s}^{-1}})\]as
  A)
   \[{{s}^{-1}},M\,{{s}^{-1}}{{L}^{-1}}\]
  done clear
  B)
   \[M\,{{s}^{-1}}M\,{{s}^{-1}}\]
  done clear
  C)
   \[{{s}^{-1}}{{M}^{-1}}{{s}^{-1}}\]
  done clear
  D)
   \[M\,{{s}^{-1}}{{s}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer61) \[CsBr\]crystallises in a body centred cubic lattice. The unit cell length is 436.6 pm. Given that the atomic mass of Cs = 133 u and that of Br = 80 u and Avogadro number being \[6.0.2\times {{10}^{23}}mo{{l}^{-1}},\] the density of\[CsBr\]is
  A)
   \[42.5g/c{{m}^{3}}\]  
  done clear
  B)
   \[0.425g/c{{m}^{3}}\]
  done clear
  C)
   \[8.25\text{ }g/c{{m}^{3}}\] 
  done clear
  D)
   \[4.25\text{ }g/c{{m}^{3}}\]
  done clear
  View Answer play_arrow

• question_answer62) \[-[NH(C{{H}_{2}})NHCO{{(C{{H}_{2}})}_{4}}CO]{{-}_{n}}\]is a
  A)
   copolymer
  done clear
  B)
   addition polymer
  done clear
  C)
   thermosetting polymer
  done clear
  D)
   homopolymer
  done clear
  View Answer play_arrow

• question_answer63) During the process of digestion, the proteins present in food materials are hydrolysed to amino acids. The two enzymes involved in the process Proteins \[\xrightarrow[{}]{Enzyme(A)}\]Polypeptides are respectively
  A)
   amylase and maltase
  done clear
  B)
   diastase and lipase
  done clear
  C)
   pepsin and trypsin
  done clear
  D)
   invertase and zymase
  done clear
  View Answer play_arrow

• question_answer64) Hybridisation of the underlined atom changes in
  A)
  \[\underline{Al}{{H}_{3}}\]changes to \[AlH_{4}^{-}\]
  done clear
  B)
  \[{{H}_{2}}\underline{O}\]changes to\[{{H}_{3}}{{O}^{+}}\]
  done clear
  C)
  \[\underline{N}{{H}_{3}}\]changes to\[NH_{4}^{-}\]
  done clear
  D)
   All the above cases
  done clear
  View Answer play_arrow

• question_answer65) A metal M forms water soluble MS 04 and inert MO. MO in aqueous solution forms insoluble \[M{{(OH)}_{2}}\]which is soluble in\[NaOH\]. Metal M is
  A)
   \[Be\]          
  done clear
  B)
  \[Mg\]
  done clear
  C)
   \[Ca\]          
  done clear
  D)
  \[Si\]
  done clear
  View Answer play_arrow

• question_answer66) In an organic compound of molar mass 108g \[mo{{l}^{-1}},C,H\]and N atoms are present in 9 : 1: 3.5 by weight. Molecular formula can be
  A)
   \[{{C}_{6}}{{H}_{8}}{{N}_{2}}\]
  done clear
  B)
   \[{{C}_{7}}{{H}_{10}}N\]
  done clear
  C)
   \[{{C}_{5}}{{H}_{6}}{{N}_{3}}\]
  done clear
  D)
   \[{{C}_{4}}{{H}_{18}}{{N}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer67) \[[Co{{(N{{H}_{3}})}_{4}}{{(N{{O}_{2}})}_{2}}]Cl\]exhibits
  A)
   linkage isomerism, ionisation isomerism and optical isomerism
  done clear
  B)
   linkage isomerism, ionisation isomerism and geometrical isomerism
  done clear
  C)
   Ionisation    isomerism,    geometrical isomerism and optical isomerism
  done clear
  D)
   linkage isomerism, geometrical isomerism and optical isomerism
  done clear
  View Answer play_arrow

• question_answer68) The correct order of the mobility of the alkali metal ions in aqueous solution is
  A)
   \[L{{i}^{+}}>N{{a}^{+}}>{{K}^{+}}>R{{b}^{+}}\]
  done clear
  B)
   \[N{{a}^{+}}>{{K}^{+}}>R{{b}^{+}}>L{{i}^{+}}\]
  done clear
  C)
   \[{{K}^{+}}>R{{b}^{+}}>N{{a}^{+}}>L{{i}^{+}}\]
  done clear
  D)
   \[R{{b}^{+}}>{{K}^{+}}>N{{a}^{+}}>L{{i}^{+}}\]
  done clear
  View Answer play_arrow

• question_answer69) Cyanide process is used for the extraction of
  A)
   barium       
  done clear
  B)
   silver
  done clear
  C)
   boron         
  done clear
  D)
   zinc
  done clear
  View Answer play_arrow

• question_answer70) For an aqueous solution, freezing point is\[-0.186{}^\circ C\]. Elevation of the boiling point of the same solution is (\[{{K}_{f}}=1.86{}^\circ mo{{l}^{-1}}kg\]and\[{{K}_{b}}=0.512{}^\circ mo{{l}^{-1}}kg\])
  A)
   \[0.186{}^\circ C\]
  done clear
  B)
   \[0.0512{}^\circ C\]
  done clear
  C)
   \[1.86{}^\circ C\]
  done clear
  D)
   \[5.12{}^\circ C\]
  done clear
  View Answer play_arrow

• question_answer71) Assume each reaction is carried out in an open container. For which reaction will\[\Delta H=\Delta E\]?
  A)
   \[{{H}_{2}}(g)+B{{r}_{2}}(g)\xrightarrow[{}]{{}}2HBr(g)\]
  done clear
  B)
   \[C(s)+2{{H}_{2}}O(g)\xrightarrow[{}]{{}}2{{H}_{2}}(g)+C{{O}_{2}}(g)\]
  done clear
  C)
   \[PC{{l}_{5}}(g)\xrightarrow[{}]{{}}PC{{l}_{3}}(g)+C{{l}_{2}}(g)\]
  done clear
  D)
   \[2CO(g)+{{O}_{2}}(g)\xrightarrow[{}]{{}}2C{{O}_{2}}(g)\]
  done clear
  View Answer play_arrow

• question_answer72) The hydrogen ion concentration of a \[{{10}^{-8}}M\,HCl\]aqueous solution at 298 K\[({{K}_{w}}={{10}^{-14}})\]
  A)
   \[1.0\times {{10}^{-6}}M\]
  done clear
  B)
   \[1.0525\times {{10}^{-7}}M\]
  done clear
  C)
   \[9.525\times {{10}^{-8}}M\]
  done clear
  D)
   \[1.0\times {{10}^{-8}}M\]
  done clear
  View Answer play_arrow

• question_answer73) Proteins are composed of
  A)
  \[\alpha -\]amino acids
  done clear
  B)
   carbohydrates
  done clear
  C)
   vitamins
  done clear
  D)
   mineral salts
  done clear
  View Answer play_arrow

• question_answer74) A carbonyl compound reacts with hydrogen cyanide to form cyanbhydrin which on hydrolysis forms a racemic mixture of a\[\alpha -\]ydroxy acid. The carbonyl compound is
  A)
   acetaldehyde
  done clear
  B)
   acetone
  done clear
  C)
   diethyl ketone
  done clear
  D)
   formaldehyde
  done clear
  View Answer play_arrow

• question_answer75) Following reaction \[{{(C{{H}_{3}})}_{2}}CBr+{{H}_{2}}O\xrightarrow[{}]{{}}{{(C{{H}_{3}})}_{3}}COOH+HBr\] is an example of
  A)
   elimination reaction
  done clear
  B)
   free radical substitution
  done clear
  C)
   nucleophilic substitution
  done clear
  D)
   elecrophilic substitution
  done clear
  View Answer play_arrow

• question_answer76) Acetylene does not react with
  A)
   Na
  done clear
  B)
   \[HCl\]
  done clear
  C)
   ammoniacal \[AgN{{O}_{3}}\]
  done clear
  D)
   \[NaOH\]
  done clear
  View Answer play_arrow

• question_answer77) The following reaction is described as
  A)
   \[{{S}_{E}}2\]         
  done clear
  B)
   \[{{S}_{N}}2\]
  done clear
  C)
   \[{{S}_{N}}1\]         
  done clear
  D)
   \[{{S}_{E}}1\]
  done clear
  View Answer play_arrow

• question_answer78) Refining of impure copper with zinc impurity is to be done by electrolysis using electrodes as
  A)
   Cathode-pure copper        Anode-pure zinc
  done clear
  B)
   Cathode-pure zinc          Anode- pure copper
  done clear
  C)
   Cathode-pure copper       Anode-impure copper
  done clear
  D)
   Cathode-pure zinc           Anode- impure zinc
  done clear
  View Answer play_arrow

• question_answer79) \[A{{l}_{2}}{{O}_{3}}\]can be converted to anhydrous\[AlC{{l}_{3}}\]by heating
  A)
  \[A{{l}_{2}}{{O}_{3}}\]with\[HCl\]gas
  done clear
  B)
  \[A{{l}_{2}}{{O}_{3}}\]with\[NaCl\]in solid state
  done clear
  C)
   a mixture of\[A{{l}_{2}}{{O}_{3}}\] and carbon in dry\[C{{l}_{2}}\]gas
  done clear
  D)
  \[A{{l}_{2}}{{O}_{3}}\]with\[C{{l}_{2}}\]gas
  done clear
  View Answer play_arrow

• question_answer80) Which one of the following is a redox reaction?
  A)
   \[NaCl+KN{{O}_{3}}\xrightarrow[{}]{{}}NaN{{O}_{3}}+KCl\]
  done clear
  B)
   \[Ca{{C}_{2}}{{O}_{4}}+2HCl\xrightarrow[{}]{{}}CaC{{l}_{2}}+{{H}_{2}}{{C}_{2}}{{O}_{4}}\]
  done clear
  C)
   \[Ca{{(OH)}_{2}}+2N{{H}_{4}}Cl\xrightarrow[{}]{{}}CaC{{l}_{2}}+2N{{H}_{3}}\] \[+2{{H}_{2}}O\]
  done clear
  D)
   \[2K[Ag{{(CN)}_{2}}]+Zn\xrightarrow[{}]{{}}2Ag\] \[+{{K}_{2}}[Zn{{(CN)}_{4}}]\]
  done clear
  View Answer play_arrow

• question_answer81) The region of the argand diagram defined by\[|z-1|+|z+1|\le 4\]is
  A)
   interior of an ellipse
  done clear
  B)
   exterior of a circle
  done clear
  C)
   interior and boundary of an ellipse
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer82) The smallest positive integer n for which\[{{(1+i)}^{2n}}={{(1-i)}^{2n}}\]is
  A)
   1        
  done clear
  B)
   2
  done clear
  C)
   3    
  done clear
  D)
   4
  done clear
  View Answer play_arrow

• question_answer83) If\[a=\cos \alpha +i\sin \alpha ,\]\[b=\cos \beta +i\sin \beta ,\] \[c=\cos \gamma +i\sin \gamma \]and\[\frac{b}{c}+\frac{c}{a}+\frac{a}{b}=1,\]then \[\cos (\beta -\gamma )+\cos (\gamma -\alpha )+\cos (\alpha +\beta )\]is equal to
  A)
   0
  done clear
  B)
   1
  done clear
  C)
   -1
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer84) If one root of the equation\[lx+mx+n=0\]is\[\frac{9}{2}\] \[(l,m\]and n are positive integers) and\[\frac{m}{4n}=\frac{l}{m},\]then\[l+n\]is equal to
  A)
   80           
  done clear
  B)
   85
  done clear
  C)
   90           
  done clear
  D)
   95
  done clear
  View Answer play_arrow

• question_answer85) If\[\alpha \]and\[\beta \]are the roots of the equation \[a{{x}^{2}}+bx+c=0,\]then\[\frac{\alpha }{\alpha \beta +b}+\frac{\beta }{a\alpha +b}\]is equal to
  A)
   \[\frac{2}{a}\]
  done clear
  B)
   \[\frac{2}{b}\]
  done clear
  C)
   \[\frac{2}{c}\]
  done clear
  D)
   \[\frac{-2}{a}\]
  done clear
  View Answer play_arrow

• question_answer86) If\[{{H}_{1}}\]and\[{{H}_{2}}\]are two harmonic means between two positive numbers a and\[b(a\ne b),\]and G are the arithmetic and geometric means between a and b, then\[\frac{{{H}_{2}}+{{H}_{1}}}{{{H}_{2}}{{H}_{1}}}\]is
  A)
   \[\frac{A}{G}\]
  done clear
  B)
   \[\frac{2A}{{{G}^{2}}}\]
  done clear
  C)
   \[\frac{A}{2{{G}^{2}}}\]
  done clear
  D)
   \[\frac{A}{{{G}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer87) Let\[{{S}_{n}}=\frac{1}{{{1}^{3}}}+\frac{1+2}{{{1}^{3}}+{{2}^{3}}}+...+\]\[\frac{1+2+....+n}{{{1}^{3}}+{{2}^{3}}+...+{{n}^{3}}},n=1,2,3,.....\]Then\[{{S}_{n}}\]is not greater than
  A)
   \[\frac{1}{2}\]              
  done clear
  B)
   1
  done clear
  C)
   2              
  done clear
  D)
   4
  done clear
  View Answer play_arrow

• question_answer88) p points are chosen on each of the three coplanar lines. The maximum number of triangles formed with vertices at these points is
  A)
   \[{{p}^{3}}+3{{p}^{2}}\]
  done clear
  B)
   \[\frac{1}{2}({{p}^{3}}+p)\]
  done clear
  C)
   \[\frac{{{p}^{2}}}{2}(5p-3)\]
  done clear
  D)
   \[{{p}^{2}}(4p-3)\]
  done clear
  View Answer play_arrow

• question_answer89) If\[p(n):2+4+6+....+(2n),n\in N,\]then\[p(k)=k(k+1)+2\]implies\[p(k+1)=\] \[(k+1)(k+2)+2\]is true for all\[k\in N\]. So, statement\[p(n)=n(n+1)+2\]is true for
  A)
   \[n\ge 1\]       
  done clear
  B)
   \[n\ge 2\]
  done clear
  C)
   \[n\ge 3\]        
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer90) If in the expansion of\[{{(1+x)}^{m}}{{(1-x)}^{n}},\]the coefficient of \[x\]and\[{{x}^{2}}\]are 3 and\[-6\]respectively, then m is
  A)
   6            
  done clear
  B)
   9
  done clear
  C)
   12           
  done clear
  D)
   24
  done clear
  View Answer play_arrow

• question_answer91) If A and B are square matrices of size\[n\times n\]such that\[{{A}^{2}}-{{B}^{2}}=(A\text{ }B)(A+B)\]then which of the following will be always true?
  A)
   \[AB=BA\]
  done clear
  B)
   Either\[A=O\]or\[B=O\]
  done clear
  C)
   Either\[A=I\]or\[B=I\]
  done clear
  D)
   \[A=B\]
  done clear
  View Answer play_arrow

• question_answer92) The values of \[x\] for which the given matrix will be non-singular, are
  A)
   \[-2\le x\le 2\]
  done clear
  B)
   for all\[x\]other than 2 and\[-2\]
  done clear
  C)
   \[x\ge 2\]
  done clear
  D)
   \[x\le -2\]
  done clear
  View Answer play_arrow

• question_answer93) If\[f(\theta )=\left| \begin{matrix} {{\cos }^{2}}\theta  & \cos \theta \sin \theta  & -\sin \theta   \\ \cos \theta  & {{\sin }^{2}}\theta  & \cos \theta   \\ \sin \theta  & -\cos \theta  & 0  \\ \end{matrix} \right|\]Then, for all\[\theta \]
  A)
   \[f(\theta )=0\]     
  done clear
  B)
   \[f(\theta )=1\]
  done clear
  C)
   \[f(\theta )=-1\]   
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer94) The system of equations\[2x+y-5=0,\] \[x-2y+1=0\]and\[2x-14y-a=0\]is consistent. Then, a is equal to
  A)
   1            
  done clear
  B)
   2
  done clear
  C)
   5            
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer95) Find imaginary part of\[{{\sin }^{-1}}(\cos ec\theta )\].
  A)
   \[\log \left( \cot \frac{\theta }{2} \right)\]
  done clear
  B)
   \[\frac{\pi }{2}\]
  done clear
  C)
   \[\frac{1}{2}\log \left( \cot \frac{\theta }{2} \right)\] 
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer96) If\[\tan \left( \frac{x}{2} \right).\coth \left( \frac{x}{2} \right)=1,\]then the value of\[\cos x.\cosh \,x\]is
  A)
   1             
  done clear
  B)
   \[-1\]
  done clear
  C)
   \[co{{s}^{2}}\text{ }x\]        
  done clear
  D)
  \[sin{{h}^{2}}\text{ }x\]
  done clear
  View Answer play_arrow

• question_answer97) The\[x-\]axis, y-axis and a line passing through the point A(6, 0) form a\[\Delta ABC\]. If\[\angle A=30{}^\circ ,\] then the area of the triangle (in sq unit) is
  A)
   \[6\sqrt{3}\]         
  done clear
  B)
   \[12\sqrt{3}\]
  done clear
  C)
   \[4\sqrt{3}\]        
  done clear
  D)
   \[8\sqrt{3}\]
  done clear
  View Answer play_arrow

• question_answer98) The equation of perpendicular bisectors of sides AB and AC of a\[\Delta ABC\]are\[x-y+5=0\]and\[x+2y=0,\]respectively. If the coordinates of vertex A are\[(1,-2),\]the equation of BC is
  A)
   \[14x+23y-40=0\]
  done clear
  B)
   \[14x-23y+40=0\]
  done clear
  C)
   \[23x+14y-40=0\]
  done clear
  D)
   \[23x-14y+40=0\]
  done clear
  View Answer play_arrow

• question_answer99) If two chords having lengths\[{{a}^{2}}-1\]and\[3(a+1),\]where a is a constant of a circle bisect each other, then the radius of the circle is
  A)
   6             
  done clear
  B)
   \[\frac{15}{2}\]
  done clear
  C)
   8              
  done clear
  D)
   \[\frac{19}{2}\]
  done clear
  View Answer play_arrow

• question_answer100) For an equilateral triangle the centre is the origin and the length of altitude is a. Then, the equation of the circumcircle is
  A)
   \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]
  done clear
  B)
   \[3{{x}^{2}}+3{{y}^{2}}=2{{a}^{2}}\]
  done clear
  C)
   \[9{{x}^{2}}+9{{y}^{2}}=4{{a}^{2}}\]
  done clear
  D)
   \[{{x}^{2}}+{{y}^{2}}=4{{a}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer101) The equation of the plane passing through the mid-point of the line of join of the points (1, 2, 3) and (3, 4, 5) and perpendicular to it, is
  A)
   \[x+y+z=9\]
  done clear
  B)
   \[x+y+z=-9\]
  done clear
  C)
   \[2x+3y+4z=9\]
  done clear
  D)
   \[2x+3y+4z=-9\]
  done clear
  View Answer play_arrow

• question_answer102) The direction cosines\[l,m\]and n of two lines are connected by the relation\[l+m+n=0,\text{ }lm=0,\]then the angle between them is
  A)
   \[\frac{\pi }{3}\]
  done clear
  B)
   \[\frac{\pi }{4}\]
  done clear
  C)
   \[\frac{\pi }{2}\]
  done clear
  D)
   0
  done clear
  View Answer play_arrow

• question_answer103) If\[f(x)=\frac{{{4}^{x}}}{{{4}^{x}}+2},\]then \[f\left( \frac{1}{97} \right)+f\left( \frac{2}{97} \right)+....+f\left( \frac{96}{97} \right)\] is equal to
  A)
   1            
  done clear
  B)
   48
  done clear
  C)
   \[-48\]         
  done clear
  D)
   \[-1\]
  done clear
  View Answer play_arrow

• question_answer104) The range of the function \[f(x)=\tan \sqrt{\frac{{{\pi }^{2}}}{9}-{{x}^{2}}}\]is
  A)
   \[[0,3]\]        
  done clear
  B)
   \[[0,\sqrt{3}]\]
  done clear
  C)
   \[(-\infty ,\infty )\]      
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer105) If\[f(x)=|\log |x||,\]then
  A)
  \[f(x)\]is continuous and differentiable for all \[x\]in its domain
  done clear
  B)
  \[f(x)\]is continuous for all\[x\]in its domain but not differentiable at\[x=\pm 1\]
  done clear
  C)
  \[f(x)\]is neither continuous nor differentiable at\[x=\pm 1\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer106) If\[f(x)={{\cot }^{-1}}[(3x-{{x}^{3}})/(1-3{{x}^{2}})]\]and \[g(x)={{\cos }^{-1}}[(1-{{x}^{2}})/(1+{{x}^{2}})],\] then \[\underset{x\to a}{\mathop{\lim }}\,\frac{f(x)-f(a)}{g(x)-g(a)}\left[ 0<a<\frac{1}{2} \right]\]is
  A)
   \[-\frac{3}{2}\]           
  done clear
  B)
   \[\frac{1}{2}\]
  done clear
  C)
   \[\frac{3}{2}\]            
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer107) If\[f(x)=(x-2)(x-4)(x-6)...(x-2n),\]then \[f'(2)\]is
  A)
   \[{{(-1)}^{n}}{{2}^{n-1}}.(n-1)!\]
  done clear
  B)
   \[{{(-2)}^{n-1}}(n-1)!\]
  done clear
  C)
   \[{{(-2)}^{n}}n!\]
  done clear
  D)
   \[{{(-1)}^{n-1}}{{2}^{n}}(n-1)!\]
  done clear
  View Answer play_arrow

• question_answer108) The derivative of\[f(\tan x)\]w.r.t.\[g(\sec x)\]at \[x=\frac{\pi }{4},\]where\[f'(1)=2\]and\[g'(\sqrt{2})=4\]is
  A)
   \[\frac{1}{\sqrt{2}}\]           
  done clear
  B)
   \[\sqrt{2}\]
  done clear
  C)
   1            
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer109) The minimum value of\[{{e}^{(2{{x}^{2}}-2x+1){{\sin }^{2}}x}}\]is
  A)
   0           
  done clear
  B)
   1
  done clear
  C)
   2            
  done clear
  D)
   3
  done clear
  View Answer play_arrow

• question_answer110) The function\[f(x)={{\cot }^{-1}}x+x\]increases in the interval
  A)
   \[(1,\infty )\]
  done clear
  B)
   \[(-1,\infty )\]
  done clear
  C)
   \[(-\infty ,\infty )\]
  done clear
  D)
   \[(0,\infty )\]
  done clear
  View Answer play_arrow

• question_answer111) If\[u=-f''(\theta ).\sin \theta +f'(\theta ).\cos \theta \]and\[v=f''(\theta ).\cos \theta +f'(\theta ).\sin \theta ,\]then \[{{\int{\left[ {{\left( \frac{du}{d\theta } \right)}^{2}}+{{\left( \frac{dv}{d\theta } \right)}^{2}} \right]}}^{1/2}}d\theta \]is equal to
  A)
   \[f(\theta )-f''(\theta )+C\]
  done clear
  B)
   \[f(\theta )+f''(\theta )+C\]
  done clear
  C)
   \[f'(\theta )+f''(\theta )+C\]
  done clear
  D)
   \[f'(\theta )-f''(\theta )+C\]
  done clear
  View Answer play_arrow

• question_answer112) If for every integer\[n,\int_{n}^{n+1}{f(x)}\,dx={{n}^{2}},\]then the value of\[\int_{-2}^{4}{f(x)}\,dx\]is
  A)
   16           
  done clear
  B)
   14
  done clear
  C)
   19           
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer113) If\[f(x)=\int_{-1}^{x}{|t|dt},\]then for any\[x\ge 0,f(x)\]is equal to
  A)
   \[1-{{x}^{2}}\]
  done clear
  B)
   \[\frac{1}{2}(1+{{x}^{2}})\]
  done clear
  C)
   \[1+{{x}^{2}}\]
  done clear
  D)
   \[\frac{1}{2}(1-{{x}^{2}})\]
  done clear
  View Answer play_arrow

• question_answer114) The area bounded by the parabola\[{{y}^{2}}=8x\] and its latusrectum, is
  A)
   \[\frac{16}{3}\]sq units
  done clear
  B)
   \[\frac{32}{3}\]sq units
  done clear
  C)
   \[\frac{8}{3}\]sq units
  done clear
  D)
   \[\frac{64}{3}\]sq units
  done clear
  View Answer play_arrow

• question_answer115) The area bounded by the curve\[y=2x-{{x}^{2}}\]and the line\[y=-x\]is
  A)
   \[\frac{3}{2}\]sq units     
  done clear
  B)
   \[\frac{9}{3}\]sq units
  done clear
  C)
   \[\frac{9}{2}\]sq units    
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer116) If a, b and c are non-coplanar and\[(a+\lambda b).[(b+3c)\times (c-4a)]=0,\]then the value of\[\lambda \]is equal to
  A)
   0
  done clear
  B)
   \[\frac{1}{12}\]
  done clear
  C)
   \[\frac{5}{12}\]
  done clear
  D)
   \[3\]
  done clear
  View Answer play_arrow

• question_answer117) If a and b are unit vectors such that\[[a\,b\,a\times b]=\frac{1}{4},\]then angle between a and b is
  A)
   \[\frac{\pi }{3}\]
  done clear
  B)
   \[\frac{\pi }{4}\]
  done clear
  C)
   \[\frac{\pi }{6}\]
  done clear
  D)
   \[\frac{\pi }{2}\]
  done clear
  View Answer play_arrow

• question_answer118) The area of the triangle having vertices as \[i-2j+3k,-2i+3j-k,4i-7j+7k\]is
  A)
   36 sq units   
  done clear
  B)
   0 sq unit
  done clear
  C)
   39 sq units   
  done clear
  D)
   11 sq units
  done clear
  View Answer play_arrow

• question_answer119) If\[P(A)=P(B)=x\]and \[P(A\cap B)=P(A'\cap B')=\frac{1}{3},\] then\[x\]is equal to
  A)
   \[\frac{1}{2}\]
  done clear
  B)
   \[\frac{1}{3}\]
  done clear
  C)
   \[\frac{1}{4}\]
  done clear
  D)
   \[\frac{1}{6}\]
  done clear
  View Answer play_arrow

• question_answer120) A fair die is tossed eight times. The probability that a third six is observed on the eight throw is
  A)
   \[\frac{^{7}{{C}_{2}}\times {{5}^{5}}}{{{6}^{7}}}\]
  done clear
  B)
   \[\frac{^{7}{{C}_{2}}\times {{5}^{5}}}{{{6}^{8}}}\]
  done clear
  C)
   \[\frac{^{7}{{C}_{2}}\times {{5}^{5}}}{{{6}^{6}}}\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow