Solved papers for RAJASTHAN ­ PET Rajasthan PET Solved Paper-2006

done Rajasthan PET Solved Paper-2006 Total Questions - 150

• question_answer1) An \[\alpha \]-particle is emitted with velocity v from \[_{92}{{U}^{238}}\]nucleus placed at rest. The rebound velocity of the remaining nucleus will be
  A)
   \[-\left( \frac{4v}{234} \right)\]
  done clear
  B)
   \[\left( \frac{v}{234} \right)\]
  done clear
  C)
   \[\left( \frac{v}{238} \right)\]
  done clear
  D)
   \[\frac{4v}{238}\]
  done clear
  View Answer play_arrow

• question_answer2) \[_{90}{{X}^{200}}\,\xrightarrow[{}]{{}}{{\,}_{80}}{{Y}^{168}}.\]In this reaction how many \[\alpha \] and \[\beta \]-particles are emitted?
  A)
   6, 8              
  done clear
  B)
   8, 6
  done clear
  C)
   12, 8            
  done clear
  D)
   8, 12
  done clear
  View Answer play_arrow

• question_answer3) The count rate of Geigez -Muller counter for the radiation of a radioactive material of half life of 30 min decreases to\[5{{s}^{-1}}\]after 2 h the initial count rate was
  A)
   \[25{{s}^{-1}}\]           
  done clear
  B)
   \[80{{s}^{-1}}\]
  done clear
  C)
   \[625{{s}^{-1}}\]          
  done clear
  D)
   \[20{{s}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer4) When hydrogen atom makes a transition from ground state to excited state, then
  A)
  its kinetic and potential energies decrease.
  done clear
  B)
  potential energy increases and kinetic energy decreases
  done clear
  C)
  potential energy decreases and kinetic energy increases
  done clear
  D)
  its kinetic and potential energies increase
  done clear
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• question_answer5) The figure represents the observed intensity of X-rays emitted by an X-ray tube as a function of wavelength. The sharp peaks A and B denote
  A)
   band spectrum
  done clear
  B)
   continuous spectrum
  done clear
  C)
   characteristic radiation
  done clear
  D)
   white radiation
  done clear
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• question_answer6) If we consider wavelength of electron and photon are same. They will have same
  A)
   velocity         
  done clear
  B)
   energy
  done clear
  C)
   momentum      
  done clear
  D)
   angular momentum
  done clear
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• question_answer7) An electric field is in the X- direction. If the work done to displace 0.2 C charge to 2m at an angle of \[60{}^\circ \]from X-axis along a straight line is 4 J, then the value of E will be
  A)
   8 N/C            
  done clear
  B)
   4 N/C
  done clear
  C)
   \[\sqrt{3}\] N/C           
  done clear
  D)
   20 N/C
  done clear
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• question_answer8) In the circuit shown in the figure, each of the resistance is equal to 2 0. The resistance between the points and B is              
  A)
   3\[\Omega \]         
  done clear
  B)
   2\[\Omega \]
  done clear
  C)
   4\[\Omega \]
  done clear
  D)
   1\[\Omega \]
  done clear
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• question_answer9) A heater coil is labelled 100 W, 220 V. The coil is cut into two equal halves and the two pieces are joined in parallel to the same source. The energy now liberated per second is
  A)
   50 J             
  done clear
  B)
   40 J
  done clear
  C)
   4000 J           
  done clear
  D)
   400 J
  done clear
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• question_answer10) A straight conductor of length 0.4 m is moved with a speed of 7 m/s perpendicular to the magnetic field of intensity of\[0.9Wb/{{m}^{2}}\]. The induced emf across the conductor will be
  A)
   3.52 V           
  done clear
  B)
   25.2 V
  done clear
  C)
   2.52 V           
  done clear
  D)
   0.252 V
  done clear
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• question_answer11) When the key K is pressed at tune\[t=0,\]which of the following statements about the current I in the resistor AB of the given circuit is true
  A)
  \[i=2\text{ }mA\]at all t
  done clear
  B)
   \[i\]oscillates between 1mA and 2mA
  done clear
  C)
   \[i=1\text{ }mA\] at all t
  done clear
  D)
   at \[t=0,i=2\text{ }mA\]and with time it goes to 1mA
  done clear
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• question_answer12) Dimension of RC is
  A)
   square of time
  done clear
  B)
   equal to time
  done clear
  C)
   inverse of time
  done clear
  D)
   inverse of square of time
  done clear
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• question_answer13) The figure indicates the energy level diagram of an atom and the origin of six spectral line in emission (.e.g., line no. 5 aries from the transition from level B to A). The following spectral lines will also occur in the absorption spectrum
  A)
   1, 4, 5            
  done clear
  B)
   1, 2, 3, 4, 5
  done clear
  C)
   2, 3, 5           
  done clear
  D)
   1, 2, 3
  done clear
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• question_answer14) A lens is placed between a source of light and wall. It forms image of area\[{{A}_{1}}\]and\[{{A}_{2}}\]on the wall for its two different positions. The area of the source of light is
  A)
   \[\frac{{{A}_{1}}+{{A}_{2}}}{2}\]
  done clear
  B)
   \[\sqrt{{{A}_{1}}{{A}_{2}}}\]
  done clear
  C)
   \[{{\left[ \frac{\sqrt{{{A}_{1}}}\,+\,\sqrt{{{A}_{2}}}}{2} \right]}^{2}}\]
  done clear
  D)
   \[{{\left[ \frac{1}{{{A}_{1}}}+\frac{1}{{{A}_{2}}} \right]}^{-1}}\]
  done clear
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• question_answer15) Efficiency of a Carnot engine is 40% when temperature of outlet is 500 K. In order to increase efficiency up to 50% keeping temperature of intake the same. What is temperature of outlet?
  A)
   700 K           
  done clear
  B)
   600 K
  done clear
  C)
   400 K           
  done clear
  D)
   500 K
  done clear
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• question_answer16) The heat is flowing through two cylindrical rods of same material. The diameters of the rods are in the ratio 1:2 and their lengths are in the ratio 2 : 1. If the temperature difference between their ends is the same, the ratio of rate of flow of heat through them will be
  A)
   1 : 4             
  done clear
  B)
   1 : 2
  done clear
  C)
   1 : 8             
  done clear
  D)
   1 : 3
  done clear
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• question_answer17) Which of the following is used to produce radio waves of constant amplitude
  A)
   oscillator
  done clear
  B)
   FET
  done clear
  C)
   Rectifier
  done clear
  D)
   Amplifier
  done clear
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• question_answer18) A hospital uses an ultrasonic a scanner to locate tumours in a tissue. The operating frequency of the scanner is 4.2 MHz. The speed of sound in a tissue is 1.7 km/s. The wavelength of sound in the tissue is close to
  A)
   \[2\times {{10}^{-4}}m\]       
  done clear
  B)
   \[6\times {{10}^{-3}}m\]
  done clear
  C)
   \[2\times {{10}^{-3}}m\]       
  done clear
  D)
   \[4\times {{10}^{-4}}m\]
  done clear
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• question_answer19)  A bucket full of water is kept in a room and it cools from\[80{}^\circ C\]to\[70{}^\circ C\]in\[{{t}_{1}}\]min from\[75{}^\circ C\]to \[70{}^\circ C\]in\[{{t}_{2}}\]min and from\[70{}^\circ C\]to\[65{}^\circ C\]in\[{{t}_{3}}\]min then
  A)
   \[{{t}_{1}}<{{t}_{2}}<{{t}_{3}}\]       
  done clear
  B)
   \[{{t}_{1}}>{{t}_{2}}>{{t}_{3}}\]
  done clear
  C)
   \[{{t}_{2}}<{{t}_{1}}<{{t}_{3}}\]         
  done clear
  D)
   \[{{t}_{1}}>{{t}_{2}}>{{t}_{3}}\]
  done clear
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• question_answer20) The earth of mass\[6\times {{10}^{24}}\]kg. with\[2\times {{10}^{-7}}\]rad/s angular velocity is moves around the sun at \[15\times {{10}^{8}}\]km radius. The force on the earth by sun is
  A)
   zero           
  done clear
  B)
   \[16\times {{10}^{24}}N\]
  done clear
  C)
   \[25\times {{10}^{16}}N\]
  done clear
  D)
   \[36\times {{10}^{21}}N\]
  done clear
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• question_answer21) Water drops fall at regular intervals from a tap which is 5m above the ground. The third drop is learning the tap at the instant the first drop touches the ground. How for above the ground is the second drop at that instant?
  A)
   2.50 m
  done clear
  B)
   3.75 m
  done clear
  C)
   4.00 m          
  done clear
  D)
   1.25 m
  done clear
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• question_answer22) A particle is moving on circular path. The centripetal force is inversely proportional to distance r. The velocity of particle will
  A)
   be proportional to r
  done clear
  B)
   not depend upon r
  done clear
  C)
   be inversely proportional to r
  done clear
  D)
   be proportional to\[{{r}^{2}}\]
  done clear
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• question_answer23) A simple pendulum with a bob of mass m oscillates from A to C and back to A such that PB is H. If the acceleration due to gravity is g, then the velocity of the bob as it passes through B is
  A)
   \[mgH\]            
  done clear
  B)
   \[\sqrt{2gH}\]
  done clear
  C)
   \[2gH\]             
  done clear
  D)
   zero
  done clear
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• question_answer24) The gravitational constant is G and radius of earth is\[{{R}_{e}},\]The relation between average density \[\rho \] of earth to gravitational acceleration will be
  A)
   \[\rho =\left[ \frac{g}{G} \right]/\left[ \frac{4\pi }{3}R_{e}^{2} \right]\]
  done clear
  B)
   \[\rho =\left[ \frac{g}{G} \right]/\left[ \frac{4\pi }{3}R_{e}^{3} \right]\]
  done clear
  C)
   \[\rho =\left[ \frac{g}{G} \right]/\left[ \frac{4\pi }{3}R_{e}^{3} \right]\]
  done clear
  D)
   \[\rho =\left[ \frac{g}{G} \right]/\left[ \frac{4\pi }{3}R_{e}^{{}} \right]\]
  done clear
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• question_answer25) The position vector of the particle is\[r=(a\cos \,\,\omega t\,)\,\overset{\hat{\ }}{\mathop{i}}\,\,(a\,\sin \,\omega t)\,\overset{\hat{\ }}{\mathop{j}}\,.\] The velocity of particle is
  A)
   parallel to position vector
  done clear
  B)
   perpendicular to position vector
  done clear
  C)
   along the origin
  done clear
  D)
   along to opposite of origin
  done clear
  View Answer play_arrow

• question_answer26) The position of a particle at time (t) is given by \[x(t)=({{v}_{0}}/\alpha )(1-{{e}^{-\alpha t}})\]. Here v0 and\[\alpha \]are constants and\[a>0\]. The dimension of v0 and \[\alpha \] are
  A)
   \[\left[ {{M}^{0}}L{{T}^{-1}} \right]\]and\[\left[ L{{T}^{-1}} \right]\]
  done clear
  B)
   \[\left[ {{M}^{0}}L{{T}^{-1}} \right]and\left[ {{T}^{-1}} \right]\]  
  done clear
  C)
   \[\left[ {{M}^{0}}L{{T}^{-1}} \right]and\,\left[ T \right]\]
  done clear
  D)
   \[\left[ {{M}^{0}}L{{T}^{0}} \right]and\,\left[ {{T}^{-1}} \right]\]
  done clear
  View Answer play_arrow

• question_answer27) In the case of forward biasing of p-n junction. Which one of the following figures correctly depicts the direction of flow of charge carries?
  A)
   
  done clear
  B)
   
  done clear
  C)
    
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer28) The binding energies per nucleon for a deuteron and an \[\alpha \]-particle are\[{{x}_{1}}\]and\[{{x}_{2}}\]respectively. What will be the energy Q released in the reaction? \[_{1}{{H}^{2}}{{+}_{1}}{{H}^{2}}{{\xrightarrow[{}]{{}}}_{2}}H{{e}^{4}}+Q\]
  A)
   \[4({{x}_{1}}+{{x}_{2}})\]       
  done clear
  B)
   \[({{x}_{1}}{{x}_{2}})\]
  done clear
  C)
   \[({{x}_{1}}+{{x}_{2}})\]         
  done clear
  D)
   \[4({{x}_{2}}{{x}_{1}})\]
  done clear
  View Answer play_arrow

• question_answer29) An electron makes a transition from orbit\[n=4\]to be the orbit\[n=2\]of a hydrogen atom. The wave number of the emitted radiations (R = R vdberg's constant) will be
  A)
   7/16 R           
  done clear
  B)
   3R/16
  done clear
  C)
   16/3 R           
  done clear
  D)
   9R/16
  done clear
  View Answer play_arrow

• question_answer30) The bond present in conductors are
  A)
   covalent         
  done clear
  B)
   metallic
  done clear
  C)
   van der Waals    
  done clear
  D)
   ionic
  done clear
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• question_answer31) An electron of mass m when accelerated through a potential difference V has de-Broglie wavelength\[\lambda \]. The de- Broglie wavelength associated with a proton of mass M accelerated through the same potenial difference will be
  A)
   \[\lambda \sqrt{\frac{m}{M}}\]
  done clear
  B)
   \[\frac{\lambda M}{m}\]
  done clear
  C)
   \[\frac{\lambda m}{M}\]
  done clear
  D)
   \[\lambda \sqrt{\frac{M}{m}}\]
  done clear
  View Answer play_arrow

• question_answer32) A charge q is placed at the centre of the line joining two equal charges Q. The system of the three charges will be in equilibrium, if q is equal to
  A)
   \[-\frac{Q}{2}\]             
  done clear
  B)
   \[-\frac{Q}{4}\]
  done clear
  C)
   \[+\frac{Q}{4}\]              
  done clear
  D)
   \[+\frac{Q}{2}\]
  done clear
  View Answer play_arrow

• question_answer33) Two metals sphere of 1 cm and 20 cm radii are given charges\[{{10}^{-2}}C\]and\[5\times {{10}^{-2}}C\]respectively. If both the spheres are connected to metal wire, the final charge on the smaller sphere will be
  A)
   \[4\times {{10}^{2}}C\]       
  done clear
  B)
   \[5\times {{10}^{-2}}C\]
  done clear
  C)
   \[2\times {{10}^{-2}}C\]       
  done clear
  D)
   \[4\times {{10}^{-2}}C\]
  done clear
  View Answer play_arrow

• question_answer34) Two wires of same metal have the same length but their cross-section are in the ratio 3:1. They are joined in series. The resistance of the thicker wire is 10\[\Omega \]. The total resistance of the combination will be
  A)
   \[40\,\Omega \]
  done clear
  B)
   \[\frac{40}{3}\Omega \]
  done clear
  C)
   \[\frac{5}{2}\,\Omega \]
  done clear
  D)
   \[100\,\Omega \]
  done clear
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• question_answer35) Two particles X and Y hiving equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field and describes circular path of radius \[{{R}_{1}}\] and \[{{R}_{2}}\] respectively. The ratio of mases of X to that of Y is
  A)
   \[{{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{2}}\]
  done clear
  B)
   \[\frac{{{R}_{1}}}{{{R}_{2}}}\]
  done clear
  C)
   \[{{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{3}}\]
  done clear
  D)
   \[{{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{1/2}}\]
  done clear
  View Answer play_arrow

• question_answer36) In an AC circuit V and i are given by \[V=200\text{ }sin\](100t) V, \[i=5\text{ }sin\]\[\left( 10t-\frac{\pi }{2} \right)A.\] The power dissipated in circuit will be
  A)
   1000 W          
  done clear
  B)
   zero
  done clear
  C)
   40 W            
  done clear
  D)
   20 W
  done clear
  View Answer play_arrow

• question_answer37) The work done in turning a magnet of magnetic moment M by angle of \[90{}^\circ \] from the meridian is n times the corresponding work done to turn it through an angle of \[60{}^\circ \] where n is given by
  A)
   4               
  done clear
  B)
   2
  done clear
  C)
   1/2             
  done clear
  D)
   1
  done clear
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• question_answer38) A star of emitting radiation 5000\[\overset{o}{\mathop{\text{A}}}\,\]is coming towards the earth with velocity\[1.5\times {{10}^{6}}m/s\]. The change of wavelength of radiation on earth will be
  A)
   250\[\overset{o}{\mathop{\text{A}}}\,\]           
  done clear
  B)
   25\[\overset{o}{\mathop{\text{A}}}\,\]
  done clear
  C)
   2.5\[\overset{o}{\mathop{\text{A}}}\,\]             
  done clear
  D)
   zero
  done clear
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• question_answer39) The exposure time of a camera lens at the \[\frac{f}{2.8}\]setting is \[\frac{1}{200}\]sec. The correct time of exposure at \[\frac{f}{5.6}\] is
  A)
   0.02 s             
  done clear
  B)
   0.2 s
  done clear
  C)
   0.4 s              
  done clear
  D)
   0.04 s
  done clear
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• question_answer40) The compressibility of water is\[5\times {{10}^{-10}}{{m}^{2}}/\text{ }N\]. If the pressure at volume 100 ml is\[15\times {{10}^{6}}Pa,\]then the change of volume will be
  A)
   zero
  done clear
  B)
   increase to 0.75 ml
  done clear
  C)
   decrease to 0.75 ml
  done clear
  D)
   increase to 1.50 ml
  done clear
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• question_answer41) The surface tension of soap bubbles is 0.03 N/m (both surfaces). The excess pressure inside a soap bubbles of diameter 30 mm is
  A)
   2 Pa             
  done clear
  B)
   8 Pa
  done clear
  C)
   16 Pa            
  done clear
  D)
   10 Pa
  done clear
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• question_answer42) When the displacement is half the amplitude in SHM, then ratio of kinetic energy to the total energy is
  A)
   3/4               
  done clear
  B)
   zero
  done clear
  C)
   1/2                
  done clear
  D)
   1/4
  done clear
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• question_answer43) The length of a sonometer wire AB is 110 cm. At what distance the two bridge are placed so that the wire is divided into such three parts. Basic frequencies of which are in the ratio of 1 : 2 : 3.
  A)
   60 cm and 30 cm
  done clear
  B)
   60 cm and 90 cm
  done clear
  C)
   20 cm and 40 cm
  done clear
  D)
   40 cm and 60 cm
  done clear
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• question_answer44) Two particles of equal mass [m] go round a circle of radius R under the action of their neutral gravitational attraction. The speed of each particle is
  A)
   \[v=\frac{1}{2R\sqrt{Gm}}\]
  done clear
  B)
   \[v=\sqrt{\frac{4Gm}{R}}\]
  done clear
  C)
   \[v=\sqrt{\frac{Gm}{2R}}\]
  done clear
  D)
   \[v=\frac{1}{2}\sqrt{\frac{Gm}{R}}\]
  done clear
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• question_answer45) ABC is a triangular plate of uniform thickness. The sides are in the ratio shown in the figure.\[{{I}_{AB}},{{I}_{BC}},\] \[{{I}_{CA}}\] are moments of inertia of the plate about AB. BC, CA respectively. Which one of the following relation is correct?                      
  A)
  \[{{I}_{BC}}>{{I}_{AB}}\]
  done clear
  B)
  \[{{I}_{CA}}\]is maximum              
  done clear
  C)
   \[{{I}_{AB}}>{{I}_{BC}}\]
  done clear
  D)
   \[{{I}_{AB}}+\text{ }{{I}_{BC}}={{I}_{CA}}\]
  done clear
  View Answer play_arrow

• question_answer46) The angle of prism is\[30{}^\circ \]. A ray passes through the prism and suffers a deviation of\[30{}^\circ \]. If the angle of incidence is\[60{}^\circ ,\]then angle of emergence is
  A)
   \[0{}^\circ \]               
  done clear
  B)
   \[30{}^\circ \]
  done clear
  C)
   \[60{}^\circ \]               
  done clear
  D)
   \[90{}^\circ \]
  done clear
  View Answer play_arrow

• question_answer47) The acceleration of a particle is increasing linearly with time t as bt. The particle starts from the origin with an initial velocity\[{{v}_{0}}\]. The distance travelled by the particle in time t will be
  A)
   \[{{v}_{0}}t+\frac{1}{3}b{{t}^{2}}\]
  done clear
  B)
   \[{{v}_{0}}t-\frac{1}{3}b{{t}^{2}}\]
  done clear
  C)
   \[{{v}_{0}}t+\frac{1}{6}b{{t}^{3}}\]
  done clear
  D)
   \[{{v}_{0}}t+\frac{1}{2}b{{t}^{3}}\]
  done clear
  View Answer play_arrow

• question_answer48) A flywheel is rotating at the rate of 120 revolution per minute. The angular acceleration of the flywheel will be
  A)
   \[4\pi \,rad/{{s}^{2}}\]
  done clear
  B)
   \[4{{\pi }^{2}}\,rad/{{s}^{2}}\]
  done clear
  C)
   \[2\pi \,rad/{{s}^{2}}\]
  done clear
  D)
   \[\pi /2\,\,rad/{{s}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer49) A force \[(2\,\widehat{i}\,-\,2\,\widehat{j}\,+\,3\,\widehat{j}+4\widehat{k})N\] is applied at a point. Whose is the place at position vector is\[r\to =(3\widehat{i}\,-\,2\widehat{j}+3\widehat{k}).\]. The torque about the origin point will be
  A)
   \[-6\,\widehat{i}\,+6\widehat{j}-12\,\widehat{k}\]
  done clear
  B)
   \[-17\,\widehat{i}\,+6\widehat{j}-13\,\widehat{k}\]
  done clear
  C)
   \[6\,\widehat{i}\,+6\widehat{j}-12\,\widehat{k}\]  
  done clear
  D)
   \[\widehat{i}\,-6\widehat{j}-5\,\widehat{k}\]
  done clear
  View Answer play_arrow

• question_answer50) The relative energy of two atoms of a molecule is expressed by the following expression. \[U(x)=\left( \frac{a}{{{x}^{12}}} \right)-\left( \frac{b}{{{x}^{6}}} \right)\] Here \[\alpha \] and b are positive constants and\[x\]is the distance between these atoms. If atom is at a state of permanent equilibrium, then
  A)
   \[x={{\left( \frac{2a}{b} \right)}^{1/6}}\]
  done clear
  B)
   \[x={{\left( \frac{a}{2b} \right)}^{1/6}}\]
  done clear
  C)
   \[x=0\]
  done clear
  D)
   \[x={{\left( \frac{11a}{b} \right)}^{1/6}}\]
  done clear
  View Answer play_arrow

• question_answer51) Chloroform is obtained by the partial reduction of
  A)
   \[CC{{l}_{4}}\]          
  done clear
  B)
   \[C{{H}_{4}}\]
  done clear
  C)
   \[CHC{{l}_{3}}\]         
  done clear
  D)
   \[C{{H}_{3}}OH\]
  done clear
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• question_answer52) Which of the following statements is true for enzymes?

  I. Enzymes do not have nucleophilic groups.

  II. Enzymes are specific in joining with chiral molecules and catalyse their reaction.

  III. Enzyme catalysis the chemical reactions by decreasing the activation energy.

  IV. Pepsin is a proteolytic enzyme.

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

• question_answer53) Identify the correct statement.
  A)
   Plaster of Paris is obtained by the partial oxidation of gypsum.
  done clear
  B)
   The percentage of plaster of calcium in gypsum is less than plaster of Paris.
  done clear
  C)
   Gypsum is obtained by the plaster of Paris on heating.
  done clear
  D)
   Plaster of Paris is obtained by the addition of water in gypsum.
  done clear
  View Answer play_arrow

• question_answer54) The electronic configuration of a element is\[1{{s}^{2}},2{{s}^{2}},2{{p}^{6}},3{{s}^{2}},3{{p}^{3}}\]. What is the atomic number of element which is below exactly this element in the Periodic Table?
  A)
   49              
  done clear
  B)
   31
  done clear
  C)
   34              
  done clear
  D)
   33
  done clear
  View Answer play_arrow

• question_answer55) Sodium is prepared by the electrolysis of molten mixture of 40% \[NaCl\] and 60% \[CaC{{l}_{2}}\] because
  A)
  \[C{{a}^{2+}}\]can reduce the\[NaCl\]into Na.
  done clear
  B)
  \[CaC{{l}_{2}}\]helps in electrical conduction.
  done clear
  C)
   this mixture has less melting point than \[NaCl\].
  done clear
  D)
  \[C{{a}^{2+}}\]can displace Na from\[NaCl\].
  done clear
  View Answer play_arrow

• question_answer56) Ideal gas which obeys the molecular kinetic theory of gases can be liquified. If
  A)
   it cannot be liquified at any pressure and temperature.
  done clear
  B)
   its pressure is greater than\[{{p}_{c}}\]at less temperature from\[{{T}_{c}}\].
  done clear
  C)
   its temperature is greater than critical temperature \[{{T}_{c}}\].
  done clear
  D)
   its pressure is greater than critical pressure.
  done clear
  View Answer play_arrow

• question_answer57) The correct order of\[O-O\]bond length in \[{{O}_{2}},{{H}_{2}}{{O}_{2}}\]and\[{{O}_{3}}\].
  A)
   \[{{H}_{2}}{{O}_{2}}>{{O}_{3}}>{{O}_{2}}\]
  done clear
  B)
   \[{{O}_{2}}>{{O}_{3}}>{{H}_{2}}{{O}_{2}}\]
  done clear
  C)
   \[{{O}_{2}}>{{H}_{2}}{{O}_{2}}>{{O}_{3}}\]
  done clear
  D)
   \[{{O}_{3}}>{{H}_{2}}{{O}_{2}}>{{O}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer58) The oxidation of glucose in living cell is a important reaction. What are number of ATP molecules which are produced by one molecule of glucose in cells?
  A)
   28              
  done clear
  B)
   38
  done clear
  C)
   12              
  done clear
  D)
   18
  done clear
  View Answer play_arrow

• question_answer59) Which of the following compound exists in optically active forms?
  A)
   \[C{{H}_{3}}-\underset{\begin{smallmatrix}  | \\  C{{H}_{3}} \end{smallmatrix}}{\mathop{CH}}\,-C{{H}_{2}}OH\]
  done clear
  B)
   \[C{{H}_{3}}-C{{H}_{2}}-C{{H}_{2}}OH\]
  done clear
  C)
   \[C{{H}_{3}}C{{H}_{2}}-\underset{\begin{smallmatrix}  | \\  OH \end{smallmatrix}}{\mathop{CH}}\,-C{{H}_{3}}\]
  done clear
  D)
   \[C{{H}_{3}}{{(C{{H}_{2}})}_{3}}-C{{H}_{2}}OH\]
  done clear
  View Answer play_arrow

• question_answer60) On moving downward in Be group, the solubility of sulphates in water is :\[Be>Mg>\] \[Ca>Sr>Ba\]. It is due to
  A)
   increase in melting points
  done clear
  B)
   decreasing lattice energy
  done clear
  C)
   increasing molecular weight
  done clear
  D)
   more solvation energy for small ions like \[B{{e}^{2+}}\].
  done clear
  View Answer play_arrow

• question_answer61) A chemical reaction is catalysed by catalyst X. Hence, X
  A)
   increases the activation energy of reaction.
  done clear
  B)
   does not effect the equilibrium constant of reaction.
  done clear
  C)
   decreases the velocity constant of reaction.
  done clear
  D)
   decreases the enthalpy of reaction.
  done clear
  View Answer play_arrow

• question_answer62) What will be the number of neutrons in atom after the emission of one\[\alpha -\]particle and one \[\beta -\]particle from atom\[_{92}^{238}X\]?
  A)
   144             
  done clear
  B)
   143
  done clear
  C)
   142             
  done clear
  D)
   146
  done clear
  View Answer play_arrow

• question_answer63) The formation of bakelite takes place between the reaction of
  A)
   phenol and formaldehyde                                 
  done clear
  B)
   ethylene glycol and dimethyl terephthalate
  done clear
  C)
   urea and formaldehyde
  done clear
  D)
   tetramethylene glycol and hexa methylene diisocynate
  done clear
  View Answer play_arrow

• question_answer64) Aluminium (III) chloride forms a dimer because
  A)
   the ionisation energy of aluminium is high.
  done clear
  B)
   it cannot form trimer.
  done clear
  C)
   high coordination number can obtain by aluminium.
  done clear
  D)
   aluminium belongs to third group.
  done clear
  View Answer play_arrow

• question_answer65) The solubility of\[AgCl\]will be minimum in which of the following?
  A)
   \[0.01\text{ }M\text{ }NaCl\]     
  done clear
  B)
   \[0.01\text{ }M\,CaC{{l}_{2}}\]
  done clear
  C)
   pure water      
  done clear
  D)
   \[0.001\text{ }M\text{ }AgN{{O}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer66) The radius of hydrogen atom is\[0.53\overset{o}{\mathop{\text{A}}}\,\]in the ground state. The radius of\[L{{i}^{2+}}\]ion\[(Z=3)\] in this state is
  A)
   \[0.17\overset{o}{\mathop{\text{A}}}\,\]           
  done clear
  B)
   \[1.06\overset{o}{\mathop{\text{A}}}\,\]
  done clear
  C)
   \[0.53\overset{o}{\mathop{\text{A}}}\,\]            
  done clear
  D)
   \[0.265\overset{o}{\mathop{\text{A}}}\,\]
  done clear
  View Answer play_arrow

• question_answer67) Mercury is the only metal which is liquid at \[0{}^\circ C\]because
  A)
   high vapour pressure
  done clear
  B)
   high ionisation energy and weak metallic bond
  done clear
  C)
   low ionisation potential
  done clear
  D)
   high atomic weight
  done clear
  View Answer play_arrow

• question_answer68) The pH does not change on the addition of some amount of acid or base in the blood, because blood
  A)
   becomes coagulate easily
  done clear
  B)
   has serum protein which acts as buffer
  done clear
  C)
   is liquid of body
  done clear
  D)
   has iron in the form a part of molecule
  done clear
  View Answer play_arrow

• question_answer69) When 3, 3-dimethyl-2-butanol is heated with \[{{H}_{2}}S{{O}_{4}}\]then the major product is
  A)
   3, 3-dimethyl-l-butene
  done clear
  B)
   2, 3-dimethyl-2-butene
  done clear
  C)
   2, 3-dimethyl-l-butene
  done clear
  D)
   cis and trans isomers of product [b].
  done clear
  View Answer play_arrow

• question_answer70) In\[{{K}_{3}}Cr{{({{C}_{2}}{{O}_{4}})}_{3}}\]the coordination number and oxidation state of Cr are respectively
  A)
   6 and +3        
  done clear
  B)
   3 and zero
  done clear
  C)
   4 and+2        
  done clear
  D)
   3 and +3
  done clear
  View Answer play_arrow

• question_answer71) If a metal piece is heated from one end then after sometime the other end becomes hot. It is due to
  A)
   resistance of metal
  done clear
  B)
   small change in the energy of atoms
  done clear
  C)
   movement of energy full electron in other part of metal
  done clear
  D)
   movement of atoms in metal
  done clear
  View Answer play_arrow

• question_answer72) The half-life of\[{{C}^{14}}\]radioactive is 5760 yr. After how much time will 200 mg\[{{C}^{14}}\]sample be reduced to 25 mg?
  A)
   23040 yr         
  done clear
  B)
   17280yr
  done clear
  C)
   11520 yr        
  done clear
  D)
   5760 yr
  done clear
  View Answer play_arrow

• question_answer73) When benzene diazonium chloride solution is boilded it yields
  A)
   benzene         
  done clear
  B)
   phenol
  done clear
  C)
   aniline          
  done clear
  D)
   chlorobenzene
  done clear
  View Answer play_arrow

• question_answer74) Acetone reacts with chloroform in the presence of\[NaOH\]to give
  A)
   chloral           
  done clear
  B)
   chloretone
  done clear
  C)
   acetyl chloride   
  done clear
  D)
   ethyl chloride
  done clear
  View Answer play_arrow

• question_answer75) What will be the uncertainty in position (correct at 0.001%) of a electron which is moving with\[3.0\times {{10}^{4}}\]cm/s. Velocity, (mass of electron\[=9.1\times {{10}^{-28}},\text{ }A=6.626\times {{10}^{-22}}\] erg/s) Use the uncertainty principle of\[h/4\pi \]
  A)
   3.84 cm          
  done clear
  B)
   1.92 cm
  done clear
  C)
   7.68 cm         
  done clear
  D)
   5.76 cm
  done clear
  View Answer play_arrow

• question_answer76) In\[TiF_{6}^{2-},CoF_{6}^{3-},C{{u}_{2}}C{{l}_{2}}\]and\[NiCl_{4}^{2-}\]the colourless species is (Atomic number Ti = 22, Co = 27, Cu = 29, Ni = 28)
  A)
   \[TiF_{6}^{2-}\]and\[C{{u}_{2}}C{{l}_{2}}\]
  done clear
  B)
   \[C{{u}_{2}}C{{l}_{2}}\]and\[NiCl_{4}^{2-}\]
  done clear
  C)
   \[TiF_{6}^{2-}\]and\[CoF_{6}^{3-}\]
  done clear
  D)
   \[CoF_{6}^{3-}\]and\[NiCl_{4}^{2-}\]
  done clear
  View Answer play_arrow

• question_answer77) A ozone layer is present approximately 20 km above from earth. Which of the following statement is correct for ozone and ozone layer?
  A)
   The change of ozone into oxygen is a endothermic reaction.
  done clear
  B)
   Ozone layer is harmful for us because it stops the rays which are useful for photosynthesis.
  done clear
  C)
   Ozone layer is useful to us because ozone absorbs the ultra-violet rays of sun.
  done clear
  D)
   Ozone is a trimolecular linear molecule.
  done clear
  View Answer play_arrow

• question_answer78) For a spontaneous reaction
  A)
   \[\Delta S\]should be negative
  done clear
  B)
   \[(\Delta H-T.\Delta S)\]should be negative
  done clear
  C)
   \[(\Delta H+T.\Delta S)\]should be negative
  done clear
  D)
   \[\Delta H\]should be negative
  done clear
  View Answer play_arrow

• question_answer79) The electronic configuration of valence shell of nitrogen molecule in ground state is \[(\sigma 2{{s}^{2}}),({{\sigma }^{*}}2{{s}^{2}}),(\pi 2{{p}^{4}}),(\sigma 2{{p}^{2}})\]. Hence, the bond order in nitrogen molecule is
  A)
   3                                                      
  done clear
  B)
   0
  done clear
  C)
   1                
  done clear
  D)
   2
  done clear
  View Answer play_arrow

• question_answer80) A chiral centre produces in the reaction \[C{{H}_{3}}CHO+HCN\xrightarrow[{}]{{}}C{{H}_{3}}CH(OH)CN\] The product will be
  A)
   meso compound  
  done clear
  B)
   racemic mixture
  done clear
  C)
   Leavorotatory    
  done clear
  D)
   dextrorotatory
  done clear
  View Answer play_arrow

• question_answer81) If the general formula of a metal carbonyl is \[M{{(CO)}_{x}}.\](where M = metal,\[x=4\]) then metal is bonded with
  A)
  \[C\equiv O\]triple bond
  done clear
  B)
   carbon and oxygen
  done clear
  C)
   carbon          
  done clear
  D)
   oxygen
  done clear
  View Answer play_arrow

• question_answer82) According to Raoult's law, the relative lowering in vapour pressure of a solution is equal to
  A)
   moles of solute
  done clear
  B)
   mole fraction of solvent
  done clear
  C)
   moles of solvent
  done clear
  D)
   mole fraction of solute
  done clear
  View Answer play_arrow

• question_answer83) In ideal condition, the number of moles of oxygen in 1 L air which has 21% oxygen according to volume
  A)
   2.10 mol        
  done clear
  B)
   0.0093 mol
  done clear
  C)
   0.186 mol       
  done clear
  D)
   0.210 mol
  done clear
  View Answer play_arrow

• question_answer84) The increasing acidity order of phenol, p-methyl   phenol,   m-nitrophenol   and p-nitrophenol is
  A)
   phenol, p-methyl phenol, p-nitrophenol, m-nitrophenol
  done clear
  B)
   p-methyl phenol, phenol, m-nitrophenol, p-nitrophenol
  done clear
  C)
   p-methylphenol, m-nitrophenol, phenol, p-nitrophenol
  done clear
  D)
   m-nitrophenol, p-nitrophenol, phenol, p-methylphenol
  done clear
  View Answer play_arrow

• question_answer85) Alkene\[R-CH=C{{H}_{2}}\]reacts with\[{{B}_{2}}{{H}_{6}}\]to give a product. The oxidation of product by alkaline hydrogen peroxide to form
  A)
   \[R-\underset{\begin{smallmatrix}  || \\  O \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{3}}\]
  done clear
  B)
   \[R-\underset{\begin{smallmatrix}  | \\  OH \end{smallmatrix}}{\mathop{C}}\,-\underset{\begin{smallmatrix}  | \\  OH \end{smallmatrix}}{\mathop{C{{H}_{2}}}}\,\]
  done clear
  C)
   \[R-C{{H}_{2}}-CHO\]
  done clear
  D)
   \[R-C{{H}_{2}}-C{{H}_{2}}-OH\]
  done clear
  View Answer play_arrow

• question_answer86) The molecule of\[BC{{l}_{3}}\]is planar while the molecule of\[NC{{l}_{3}}\]is pyramidal because
  A)
  \[N-Cl\] bond is more covalent than\[B-Cl\] bond
  done clear
  B)
   the atom of nitrogen is smaller than boron
  done clear
  C)
  \[B-Cl\]bond is more polar than\[N-Cl\]bond
  done clear
  D)
   in\[BC{{l}_{3}}\]unpaired electron pair is not present while in\[NC{{l}_{3}}\]a unpaired electron pair is present.
  done clear
  View Answer play_arrow

• question_answer87) The concentration unit will independent from temperature
  A)
   weight volume percentage
  done clear
  B)
   molarity
  done clear
  C)
   normality
  done clear
  D)
   molality
  done clear
  View Answer play_arrow

• question_answer88) Which of the following compounds have more than one hybridization for carbon? I. \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}C{{H}_{3}}\] II. \[C{{H}_{3}}-CH=CH-C{{H}_{3}}\] III. \[C{{H}_{2}}=CH-CH=C{{H}_{2}}\] IV. \[H-C\equiv C-H\]
  A)
   II.                 
  done clear
  B)
   III and IV
  done clear
  C)
   I and IV          
  done clear
  D)
   II and III
  done clear
  View Answer play_arrow

• question_answer89) The general reactivity order of carbonyl compounds   for   nucleophilic   addition reactions is
  A)
   \[{{H}_{2}}C=O>{{R}_{2}}C=0>A{{r}_{2}}C=O>RCHO\] \[>ArCHO\]
  done clear
  B)
   \[{{H}_{2}}C=O>RCHO>ArCHO>{{R}_{2}}C=O\] \[>A{{r}_{2}}C=O\]
  done clear
  C)
   \[ArCHO>A{{r}_{2}}C=O>RCHO>{{R}_{2}}C=O\] \[>{{H}_{2}}C=O\]
  done clear
  D)
   \[A{{r}_{2}}C=O>{{R}_{2}}C=O>ArCHO>RCHO\] \[>{{H}_{2}}C=O\]
  done clear
  View Answer play_arrow

• question_answer90) Oxidation of toluene with\[Cr{{O}_{3}}\]in the presence of\[{{(C{{H}_{3}}CO)}_{2}}O\]forms product A which reacts with aqueous\[NaOH\]to give
  A)
   2, 4-diacetyl toluene
  done clear
  B)
   \[{{C}_{6}}{{H}_{5}}COONa\]
  done clear
  C)
   \[{{({{C}_{6}}{{H}_{5}}CO)}_{2}}O\]
  done clear
  D)
   \[{{C}_{6}}{{H}_{5}}CHO\]
  done clear
  View Answer play_arrow

• question_answer91) The IUPAC name of the following compound is \[C{{H}_{3}}-CH=CHC{{H}_{2}}-\underset{\begin{smallmatrix}  | \\  N{{H}_{2}} \end{smallmatrix}}{\mathop{CH}}\,-C{{H}_{2}}COOH\]
  A)
   5-amino-2-heptenoic acid
  done clear
  B)
   p-amino-5-heptenoic acid
  done clear
  C)
   5-amino-hex-2-ene carboxylic acid
  done clear
  D)
   3-amino-5-heptenoic acid
  done clear
  View Answer play_arrow

• question_answer92) pH of 10 M\[HCl\]solution is
  A)
   1               
  done clear
  B)
   0
  done clear
  C)
   2               
  done clear
  D)
   less than zero
  done clear
  View Answer play_arrow

• question_answer93) The number of geometrical isomers of \[[Pt{{(N{{H}_{3}})}_{2}}C{{l}_{2}}]\]are
  A)
   3               
  done clear
  B)
   4
  done clear
  C)
   2               
  done clear
  D)
   1
  done clear
  View Answer play_arrow

• question_answer94) Which of the following oxide cannot act as reductant?
  A)
   \[Cl{{O}_{2}}\]
  done clear
  B)
   \[S{{O}_{2}}\]
  done clear
  C)
   \[NO\]
  done clear
  D)
   \[O_{2}^{2-}\]
  done clear
  View Answer play_arrow

• question_answer95) Which of the following molecule/ion is paramagnetic?
  A)
   \[C{{N}^{-}}\]           
  done clear
  B)
   \[CO\]
  done clear
  C)
   \[NO\]            
  done clear
  D)
   \[O_{2}^{2-}\]
  done clear
  View Answer play_arrow

• question_answer96) Maximum explosive is
  A)
   \[NC{{l}_{3}}\]            
  done clear
  B)
   \[PC{{l}_{3}}\]
  done clear
  C)
   \[AsC{{l}_{3}}\]           
  done clear
  D)
   All of these
  done clear
  View Answer play_arrow

• question_answer97) The purest form of iron is
  A)
   white cast iron   
  done clear
  B)
   grey cast iron
  done clear
  C)
   wrought iron     
  done clear
  D)
   steel
  done clear
  View Answer play_arrow

• question_answer98) The solubiulity of\[AgCl\]is\[1.8\times {{10}^{-3}}\]g/L at\[25{}^\circ C\]The solubility product of\[AgCl\]will (Ag = 108, \[Cl=35.5\])
  A)
   \[1.57\times {{10}^{-10}}\]     
  done clear
  B)
   \[1\times {{10}^{-10}}\]
  done clear
  C)
   \[3.24\times {{10}^{-6}}\]      
  done clear
  D)
   \[1\times {{10}^{-6}}\]
  done clear
  View Answer play_arrow

• question_answer99) Reaction\[{{(C{{H}_{3}})}_{2}}CO\xrightarrow[{}]{Na/{{C}_{2}}{{H}_{5}}OH}{{(C{{H}_{3}})}_{2}}CHOH\]is called
  A)
   Rosenmund reduction
  done clear
  B)
   Bubo-Blanc reduction
  done clear
  C)
   Sabatier and Senderens reduction
  done clear
  D)
   Clemmensen reduction
  done clear
  View Answer play_arrow

• question_answer100) Ethyl amine reacts with nitrous acid to give
  A)
   ethyl nitrite      
  done clear
  B)
   ethyl alcohol
  done clear
  C)
   nitro ethane      
  done clear
  D)
   acetic acid
  done clear
  View Answer play_arrow

• question_answer101) The solution of equation \[{{9}^{x}}-{{2}^{x+\frac{1}{2}}}={{2}^{x+\frac{3}{2}}}-{{3}^{2x-1}}\]is
  A)
   \[{{\log }_{e}}\left( \frac{9}{\sqrt{8}} \right)\]
  done clear
  B)
   \[{{\log }_{9}}\left( \frac{9}{\sqrt{8}} \right)\]
  done clear
  C)
   \[{{\log }_{(9/2)}}\left( \frac{9}{\sqrt{8}} \right)\]
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer102) If the roots of the equation\[a{{x}^{2}}+bx+c=0\]are real and it is of the form\[\frac{\alpha }{\alpha -1}\]and \[\frac{\alpha +1}{\alpha },\]then the value of\[{{(a+b+c)}^{2}}\]is
  A)
   \[{{b}^{2}}-4ac\]
  done clear
  B)
   \[2{{b}^{2}}-ac\]
  done clear
  C)
   \[{{b}^{2}}-ac\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer103) \[{{(3\sqrt{3}+5)}^{7}}=P+F,\]where P is an integer number and F is a proper fraction, then the value of\[F.(P+F)\]is
  A)
   \[{{2}^{6}}\]              
  done clear
  B)
   \[{{2}^{7}}\]
  done clear
  C)
   \[{{3}^{6}}\]              
  done clear
  D)
   \[{{3}^{7}}\]
  done clear
  View Answer play_arrow

• question_answer104) If\[2\left[ \frac{1}{2n+1}+\frac{1}{3{{(2n+1)}^{3}}}+\frac{1}{5{{(2n+1)}^{5}}}+... \right]\]\[=\log \left( \frac{n+1}{n} \right),\]then the value of n for which equation will satisfied, is
  A)
   for \[-1<n<0\]     
  done clear
  B)
   for\[n>-1\]or\[n<0\]
  done clear
  C)
   for all\[n\ne 0,-1\]    
  done clear
  D)
   for no value of n
  done clear
  View Answer play_arrow

• question_answer105) The value of \[\left| \begin{matrix} 1 & \omega  & {{\omega }^{2}}  \\    \omega  & {{\omega }^{2}} & 1  \\    {{\omega }^{2}} & 1 & \omega   \\ \end{matrix} \right|\]is
  A)
   0                   
  done clear
  B)
   1
  done clear
  C)
   \[\infty \]                   
  done clear
  D)
   \[\omega \]
  done clear
  View Answer play_arrow

• question_answer106) If\[\Delta =\left| \begin{matrix} 1 & \sin \theta  & 1  \\ -\sin \theta  & 1 & \sin \theta   \\    -1 & -\sin \theta  & 1  \\ \end{matrix} \right|,\]then A lies in the inteverval
  A)
   [1, 4]               
  done clear
  B)
   [2, 4]
  done clear
  C)
   [3, 4]               
  done clear
  D)
   [4,\[\infty \]]
  done clear
  View Answer play_arrow

• question_answer107) If\[x\]is a positive integer, then the value of \[\Delta =\left| \begin{matrix}    x! & (x+1)! & (x+2)!\grave{\ }  \\    (x+1)! & (x+2)! & (x+3)!  \\    (x+2)! & (x+3)! & (x+4)!  \\ \end{matrix} \right|\]is
  A)
   \[2.x!(x+1)!(x+2)!\]
  done clear
  B)
   \[2.(x+1)!(x+2)!(x+3)!\]
  done clear
  C)
   \[2x!(x+3)!\]
  done clear
  D)
   \[2x!(x+1)!\]
  done clear
  View Answer play_arrow

• question_answer108) The domain of the function \[f(x)=\sqrt{\frac{(x+1)(x-3)}{(x-2)}}\]is
  A)
   \[(-1,2)\cup [3,\infty )\]
  done clear
  B)
   \[[-1,2)\cup [3,\infty )\]
  done clear
  C)
   \[]-\infty ,-1]\cup [3,\infty [\] 
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer109) If\[f(x)=\frac{\sin x}{x},\]then the value of\[\underset{x\to \infty }{\mathop{\lim }}\,f(x)\]is
  A)
   \[-1\]              
  done clear
  B)
   0
  done clear
  C)
   1               
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer110) If\[y={{\left( 1+\frac{1}{x} \right)}^{x}},\]then the value of\[\frac{dy}{dx}\]is
  A)
   \[{{\left( 1+\frac{1}{x} \right)}^{x}}\left[ \log \left( 1+\frac{1}{x} \right)-\frac{1}{1+x} \right]\]
  done clear
  B)
   \[{{\left( 1+\frac{1}{x} \right)}^{x}}\left[ \log \left( 1+\frac{1}{x} \right) \right]\]
  done clear
  C)
   \[{{\left( 1+\frac{1}{x} \right)}^{x}}\left[ \log (x+1)-\frac{x}{x+1} \right]\]
  done clear
  D)
   \[{{\left( 1+\frac{1}{x} \right)}^{x}}\left[ \log \left( 1+\frac{1}{x} \right)+\frac{x}{1+x} \right]\]
  done clear
  View Answer play_arrow

• question_answer111) If\[{{y}^{1/m}}+{{y}^{-1/m}}=2x,\]then the value of \[({{x}^{2}}-1){{y}_{2}}+x{{y}_{1}},\]is
  A)
   \[{{m}^{2}}y\]
  done clear
  B)
   \[-{{m}^{2}}y\]
  done clear
  C)
   \[\pm {{m}^{2}}y\]           
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer112) If the sides of the \[\Delta \]ABC are changed by a very small quantity such that the radius of circumcircle is remains unchanged, then the value of\[\frac{da}{\cos A}+\frac{db}{\cos B}+\frac{dc}{\cos C}\]is
  A)
   0                
  done clear
  B)
   2R
  done clear
  C)
   6R               
  done clear
  D)
   8R
  done clear
  View Answer play_arrow

• question_answer113) The value of\[{{\int{\sqrt{x}e}}^{\sqrt{x}}}dx\]is
  A)
   \[2\sqrt{x}-{{e}^{\sqrt{x}}}-4\sqrt{x}{{e}^{\sqrt{x}}}+c\]
  done clear
  B)
   \[(2x-4\sqrt{x}+4){{e}^{\sqrt{x}}}+c\]
  done clear
  C)
   \[(1+4\sqrt{x}){{e}^{\sqrt{x}}}+c\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer114) The value of\[\int_{-\pi }^{\pi }{{{(\cos px-\sin qx)}^{2}}}dx,\]where p and q are integers, is
  A)
   \[-\pi \]               
  done clear
  B)
   0
  done clear
  C)
   \[\pi \]                
  done clear
  D)
   \[2\pi \]
  done clear
  View Answer play_arrow

• question_answer115) \[\int_{0}^{\pi /2}{\frac{dx}{1+{{\tan }^{3}}x}}\]is equal to
  A)
   \[0\]
  done clear
  B)
   \[1\]
  done clear
  C)
   \[\frac{\pi }{4}\]
  done clear
  D)
   \[\frac{\pi }{2}\]
  done clear
  View Answer play_arrow

• question_answer116) The differential equation of the family of curve\[y={{e}^{x}}(Acosx+B\sin x),\] where A and B are arbitrary constant, is
  A)
   \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-2\frac{dy}{dx}+2y=0\]
  done clear
  B)
   \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+2\frac{dy}{dx}-2y=0\]
  done clear
  C)
   \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+{{\left( \frac{dy}{dx} \right)}^{2}}+y=0\]
  done clear
  D)
   \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-7\frac{dy}{dx}+2y=0\]
  done clear
  View Answer play_arrow

• question_answer117) If\[z=cos\theta +i\text{ }sin\theta ,\]then the value of \[\frac{{{z}^{2n}}-1}{{{z}^{2n}}+1}\]is
  A)
   \[\tan n\theta \]          
  done clear
  B)
   \[\cot n\theta \]
  done clear
  C)
   \[i\tan n\theta \]         
  done clear
  D)
   \[i\cot n\theta \]
  done clear
  View Answer play_arrow

• question_answer118) If\[A+B+C=\frac{3\pi }{2},\]then\[cos\text{ }2A+cos\text{ }2B+cos\text{ }2C\]is equal to
  A)
   \[1-4cos\text{ }A\text{ }cos\text{ }Bcos\text{ }C\]
  done clear
  B)
   \[1+2\text{ }cos\text{ }A\text{ }cos\text{ }Bcos\text{ }C\]
  done clear
  C)
   \[1-4\sin Asin\,BsinC\]
  done clear
  D)
   \[4\text{ }sin\text{ }A\text{ }sin\text{ }B\text{ }sin\text{ }C\]
  done clear
  View Answer play_arrow

• question_answer119) In a\[\Delta ABC,{{r}_{1}},{{r}_{2}},{{r}_{3}}\]are in harmonic series, then a, b, c are in
  A)
   AP             
  done clear
  B)
   GP
  done clear
  C)
   HP             
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer120) For\[{{(1+i)}^{2n}}={{(1-i)}^{2n}},\]minimum positive value of n is
  A)
   4                
  done clear
  B)
   8
  done clear
  C)
   2                
  done clear
  D)
   12
  done clear
  View Answer play_arrow

• question_answer121) A tree is broken by wind, its upper part touches the ground at a point 10 m from the foot of the tree and makes an angle of\[45{}^\circ \]with the ground. The total length of tree is
  A)
   \[10(1+\sqrt{2})m\]
  done clear
  B)
   \[10\left( 1+\frac{\sqrt{3}}{2} \right)m\]
  done clear
  C)
   15 m             
  done clear
  D)
   20 m
  done clear
  View Answer play_arrow

• question_answer122) For the different values of p and q, the line \[(p+2q)x+(p-3q)y=p-q\]passes through the fixed point
  A)
   \[\left( \frac{3}{2},\frac{5}{2} \right)\]
  done clear
  B)
   \[\left( \frac{2}{5},\frac{2}{5} \right)\]
  done clear
  C)
   \[\left( \frac{3}{5},\frac{3}{5} \right)\]           
  done clear
  D)
   \[\left( \frac{2}{5},\frac{3}{5} \right)\]
  done clear
  View Answer play_arrow

• question_answer123) The circle \[{{x}^{2}}+{{y}^{2}}-6x-10y+p=0\]neither touches the axes nor intersect. If point (1, 4) lies inside the circle, then
  A)
   \[0<p<29\]        
  done clear
  B)
   \[25<p<35\]
  done clear
  C)
   \[25<p<29\]       
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer124) If the length of major axis of an ellipse is three times the length of its minor axis, then its eccentricity is
  A)
   \[\frac{1}{\sqrt{3}}\]
  done clear
  B)
   \[\frac{2\sqrt{2}}{3}\]
  done clear
  C)
   \[\frac{1}{\sqrt{2}}\]
  done clear
  D)
   \[\frac{1}{3}\]
  done clear
  View Answer play_arrow

• question_answer125) A sphere whose centre is\[(2,3,-4),\]touches the plane\[2x+6y-3z+15=0,\]then equation of the sphere is
  A)
   \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-4x-6y+8z-20=0\]
  done clear
  B)
   \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+4x-6y-8z-20=0\]
  done clear
  C)
   \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-4x-6y-8z+20=0\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer126) If\[{{4}^{{{\log }_{3}}\sqrt{3}}}+{{9}^{{{\log }_{2}}{{2}^{2}}}}={{10}^{{{\log }_{x}}83}}(x\in R),\]then the value of\[x\]is
  A)
   4                 
  done clear
  B)
   9
  done clear
  C)
   10                
  done clear
  D)
   11
  done clear
  View Answer play_arrow

• question_answer127) If the sum of first n natural number is\[\frac{1}{5}\]times the sum of their squares, then the value of n is
  A)
   5               
  done clear
  B)
   6
  done clear
  C)
   7               
  done clear
  D)
   8
  done clear
  View Answer play_arrow

• question_answer128) \[lo{{g}_{3}}2,\text{ }lo{{g}_{6}}2,\text{ }lo{{g}_{12}}2\]are in
  A)
   AP             
  done clear
  B)
   GP
  done clear
  C)
   HP             
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer129) For\[{{x}^{12}}-{{x}^{9}}+{{x}^{4}}-x+1>0,\]the greatest interval is
  A)
   \[0<x<1\]        
  done clear
  B)
   \[-4<x\le 0\]
  done clear
  C)
   \[0<x<\infty \]         
  done clear
  D)
   \[-10<x<10\]
  done clear
  View Answer play_arrow

• question_answer130) 100 tickets are numbered 1 to 100. One ticket is selected randomly. The probability that the number appearing on a selected ticket be a perfect square, is
  A)
   \[\frac{1}{5}\]
  done clear
  B)
   \[\frac{2}{5}\]
  done clear
  C)
   \[\frac{1}{10}\]               
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer131) The value of\[\underset{x\to 0}{\mathop{\lim }}\,{{\left\{ \tan \left( \frac{\pi }{4}+x \right) \right\}}^{1/x}}\]is
  A)
   1               
  done clear
  B)
   \[-1\]
  done clear
  C)
   \[{{e}^{2}}\]              
  done clear
  D)
   e
  done clear
  View Answer play_arrow

• question_answer132) If\[f(x)=\int_{-1}^{x}{|t|dt},x\ge -1,\]then
  A)
   for\[x+1>0,f\]and\[f'\]are continuous
  done clear
  B)
   for\[x+1>0,f\]is continuous but f is not continuous
  done clear
  C)
   at\[x=0,f\]and f are not continuous
  done clear
  D)
   at\[x=0,f\]is continuous but\[f'\]is not continuous
  done clear
  View Answer play_arrow

• question_answer133) If\[a<0\]and function\[({{e}^{ax}}+{{e}^{-ax}})\]is monotonic decreasing, then
  A)
   \[x>0\]            
  done clear
  B)
   \[x<0\]
  done clear
  C)
   \[x>1\]            
  done clear
  D)
   \[x<1\]
  done clear
  View Answer play_arrow

• question_answer134) Let\[f(x)=\int_{1}^{x}{\frac{\cos t}{t}dt,x<1},\]then the value of\[f(x)\]at \[x=n\pi +\frac{\pi }{2}\]is
  A)
   minimum, when n = 1, 3, 5, ...
  done clear
  B)
   minimum, when n = 0, 2, 4, ...
  done clear
  C)
   maximum, when n = 1, 3, 5,...
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer135) The value of\[\int{\frac{{{e}^{x}}(1+\sin x)}{1+\cos x}}dx\]is
  A)
   \[{{e}^{x}}\tan \frac{x}{2}+c\]      
  done clear
  B)
   \[{{e}^{x}}\cot x+c\]
  done clear
  C)
   \[\log \tan x+c\]      
  done clear
  D)
   \[sin\text{ }log\text{ }x+c\]
  done clear
  View Answer play_arrow

• question_answer136) The value of\[\int_{0}^{\pi /2}{\frac{\phi (x)}{\phi (x)+\phi \left( \frac{\pi }{2}-x \right)}}dx\] is
  A)
   \[\frac{\pi }{4}\]
  done clear
  B)
   \[\frac{\pi }{2}\]
  done clear
  C)
   \[\pi \]
  done clear
  D)
   \[\frac{3\pi }{2}\]
  done clear
  View Answer play_arrow

• question_answer137) If\[\int_{1}^{b}{(b-4x)dx}\ge 6-5b\]and\[b>1,\]then the value of\[b\]is
  A)
   1             
  done clear
  B)
   3
  done clear
  C)
   2                   
  done clear
  D)
   4
  done clear
  View Answer play_arrow

• question_answer138) If\[\alpha \]and\[\beta \]are two complex numbers and\[|P|=1,\]then the value of\[\left| \frac{\beta -\alpha }{1-\overline{\alpha }\beta } \right|\]is
  A)
   0               
  done clear
  B)
   1
  done clear
  C)
   1               
  done clear
  D)
   2
  done clear
  View Answer play_arrow

• question_answer139) If\[5\cos 2\theta +2{{\cos }^{2}}\frac{\theta }{2}+1=0,-\pi <\theta <\pi ,\]then the value of\[\theta \]is
  A)
   \[\frac{\pi }{3}\]
  done clear
  B)
   \[\frac{\pi }{3},{{\cos }^{-1}}\left( \frac{3}{5} \right)\]
  done clear
  C)
   \[{{\cos }^{-1}}\left( \frac{3}{5} \right)\]
  done clear
  D)
   \[\frac{\pi }{3},\pi -{{\cos }^{-1}}\left( \frac{3}{5} \right)\]
  done clear
  View Answer play_arrow

• question_answer140) Line\[3x+4y-24=0\]intersect the\[x-\]axis at point A and y-axis at point B, then incentre of \[\Delta \]AOB, where 0 is the origin, is
  A)
   (1, 2)             
  done clear
  B)
   (2, 2)
  done clear
  C)
   (2, 12)            
  done clear
  D)
   (12, 12)
  done clear
  View Answer play_arrow

• question_answer141) The equation of a tangent to a circle whose centre is\[(2,-1),\]is\[3x+y=0,\]which passes through origin. Then, second equation of tangent which also passes through the origin, is
  A)
   \[3x-y=0\]       
  done clear
  B)
   \[x+3y=0\]
  done clear
  C)
   \[x-3y=0\]       
  done clear
  D)
   \[3x+y=0\]
  done clear
  View Answer play_arrow

• question_answer142) If\[\frac{\log x}{b-c}=\frac{\log y}{c-a}=\frac{\log z}{a-b},\]then the value of\[x\]is
  A)
   \[abc\]              
  done clear
  B)
   \[xyz\]
  done clear
  C)
   \[a\]        
  done clear
  D)
   \[\frac{1}{a}\]
  done clear
  View Answer play_arrow

• question_answer143) If \[|x-2|+|x-3|=7,\]then the value of\[x\]is
  A)
   \[-1\]
  done clear
  B)
   6
  done clear
  C)
   \[-1\]or 6
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer144) If\[{{S}_{n}}\]is the sum of n terms of an AP and \[{{S}_{2n}}=3{{S}_{n}},\]then the value of \[\frac{{{S}_{3n}}}{{{S}_{n}}}\]is
  A)
   4                 
  done clear
  B)
   6
  done clear
  C)
   8                 
  done clear
  D)
   10
  done clear
  View Answer play_arrow

• question_answer145) If\[x,\text{ }y,\text{ }z\]are in GP and\[logx-log2y,\]\[log\text{ }2y-\] \[log\text{ }3z\]and\[log\text{ }3z-log\text{ }x\]are in AP, then\[x,\text{ }y,\text{ }z\]are the sides of a/an
  A)
   equilateral triangle
  done clear
  B)
   acute angled triangle
  done clear
  C)
   obtuse angled triangle
  done clear
  D)
   right angled triangle
  done clear
  View Answer play_arrow

• question_answer146) If \[^{{{a}^{2}}-a}{{C}_{2}}{{=}^{{{a}^{2}}-a}}{{C}_{4}},\] then the value of q is
  A)
   2                   
  done clear
  B)
   3
  done clear
  C)
   4                   
  done clear
  D)
   7
  done clear
  View Answer play_arrow

• question_answer147) The value of\[\left| \begin{matrix}    1 & 1 & 1  \\    ^{m}{{C}_{1}} & ^{m+1}{{C}_{1}} & ^{m+2}{{C}_{1}}  \\    ^{m}{{C}_{2}} & ^{m+1}{{C}_{2}} & ^{m+2}{{C}_{2}}  \\ \end{matrix} \right|\]is
  A)
   0             
  done clear
  B)
   1
  done clear
  C)
   \[m(m+1)\]      
  done clear
  D)
   \[m(m-1)\]
  done clear
  View Answer play_arrow

• question_answer148) Function\[f(x)=1+\alpha x,\alpha \ne 0\]is equal to its reciprocal, then the value of\[\alpha \]is
  A)
   \[-2\]               
  done clear
  B)
   \[-1\]
  done clear
  C)
   \[1\]                
  done clear
  D)
   2
  done clear
  View Answer play_arrow

• question_answer149) At\[x=1,\]function\[f(x)=\left\{ \begin{matrix}    {{x}^{3}}-1, & 1\le x<\infty   \\    x-1, & -\infty <x<1  \\ \end{matrix} \right.\]is
  A)
   continuous and differentiable
  done clear
  B)
   continuous but not differentiable
  done clear
  C)
   differentiable and not continuous
  done clear
  D)
   not continuous and not differentiable
  done clear
  View Answer play_arrow

• question_answer150) If\[y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+.......,}}}\]then the value of\[\frac{dy}{dx}\]is
  A)
   \[\frac{\cos x}{2y-1}\]
  done clear
  B)
   \[\frac{2y-1}{\cos x}\]
  done clear
  C)
   \[\frac{\cos y}{2x-1}\]
  done clear
  D)
   \[\frac{2x-1}{\cos y}\]
  done clear
  View Answer play_arrow