question_answer1) Which of the following physical quantity unit is not a fundamental unit?
A) Length done clear
B) Mass done clear
C) Magnetic field done clear
D) Current done clear
View Answer play_arrowquestion_answer2) The dimensional formula of electric potential is
A) \[M{{L}^{2}}{{T}^{-3}}{{A}^{-1}}\] done clear
B) \[{{M}^{-1}}{{L}^{2}}{{T}^{-2}}A\] done clear
C) \[{{M}^{-1}}{{L}^{2}}{{T}^{-2}}{{A}^{-1}}\] done clear
D) \[M{{L}^{2}}{{L}^{2}}{{T}^{-2}}A\] done clear
View Answer play_arrowquestion_answer3) The motion of a particle in straight line is an example of
A) constant velocity motion done clear
B) uniformly accelerated motion done clear
C) non-uniformly accelerated motion done clear
D) zero velocity motion done clear
View Answer play_arrowquestion_answer4) The velocity vector of the motion described by the position vector of a particle, \[r=2t\,\,\hat{i}+{{t}^{2}}\hat{j}\]is given by
A) \[V=2i+2t\,\hat{j}\] done clear
B) \[V=2t\,\,\hat{i}+2t\,\hat{j}\] done clear
C) \[V=t\,\,\hat{i}+{{t}^{2}}\,\hat{j}\] done clear
D) \[V=2\,\,\hat{i}+{{t}^{2}}\,\hat{j}\] done clear
View Answer play_arrowquestion_answer5) The velocity-time graph of particle comes out to be a non-linear curve. The motion is
A) uniform velocity motion done clear
B) uniformly accelerated motion done clear
C) non-uniform accelerated motion done clear
D) nothing can be said about the motion done clear
View Answer play_arrowquestion_answer6) A projectile is thrown with initial velocity \[{{\upsilon }_{0}}\] and angle \[{{30}^{o}}\] with the horizontal. If it remains in the air for \[1\text{ }s,\] what was its initial velocity?
A) \[19.6\text{ }m/s\] done clear
B) \[9.8\text{ }m/s\] done clear
C) \[4.9\text{ }m/s\] done clear
D) \[1\text{ }m/s\] done clear
View Answer play_arrowquestion_answer7) Newton's second law of motion is
A) \[F=dp/dt\] done clear
B) \[F=mv\] done clear
C) \[~F=m{{v}^{2}}\] done clear
D) \[~F={{m}^{2}}v\] done clear
View Answer play_arrowquestion_answer8) The centripetal force is given by the expression
A) \[\frac{M{{V}^{2}}}{R}\] done clear
B) \[\frac{{{M}^{2}}V}{R}\] done clear
C) \[\frac{Mv}{{{R}^{2}}}\] done clear
D) \[\frac{Mv}{R}\] done clear
View Answer play_arrowquestion_answer9) Uniform circular motion is an example of
A) constant speed motion done clear
B) constant velocity motion done clear
C) non-accelerated motion done clear
D) zero accelerated motion done clear
View Answer play_arrowquestion_answer10) The scalar product of two vectors \[A=2\hat{i}+2\hat{j}-\hat{k}\] and \[B=-\hat{j}+\hat{k},\] is given by
A) \[A.B=3\] done clear
B) \[A.B=4\] done clear
C) \[A.B=-4\] done clear
D) \[A.B=-3\] done clear
View Answer play_arrowquestion_answer11) The linear momentum is conserved in
A) elastic collisions done clear
B) inelastic collisions done clear
C) Both 1 and 2 done clear
D) Neither 1 nor 2 done clear
View Answer play_arrowquestion_answer12) The power (P) of an engine lifting a mass of \[100\text{ }kg\]up to a height of \[10\text{ }m\]in \[1\text{ }min\]is
A) \[P=163.3\,\,W\] done clear
B) \[P=9800\text{ }W\] done clear
C) \[P=10000\text{ }W\] done clear
D) \[P=5000\,\,W\] done clear
View Answer play_arrowquestion_answer13) The conservation of angular momentum demands that
A) the external force on the system must be zero done clear
B) the external torque on the system must be zero done clear
C) both the external force as well as the external torque must be zero done clear
D) neither of them must be zero done clear
View Answer play_arrowquestion_answer14) The moment of inertia (J) and the angular momentum (L) are related by the expression
A) \[I=L\omega \] done clear
B) \[L=I\omega \] done clear
C) \[L={{I}^{2}}\omega \] done clear
D) \[\omega =LI\] where (0 is the angular velocity. done clear
View Answer play_arrowquestion_answer15) The moment of inertia (J) of a sphere of radius R and mass M is given by
A) \[I=M{{R}^{2}}\] done clear
B) \[I=(1/2)M{{R}^{2}}\] done clear
C) \[I=(4/3)M{{R}^{2}}\] done clear
D) \[I=(2/5)M{{R}^{2}}\] done clear
View Answer play_arrowquestion_answer16) The universal law of gravitation is the force law known also as the
A) triangular law done clear
B) square law done clear
C) inverse square law done clear
D) parallelogram law done clear
View Answer play_arrowquestion_answer17) The value of acceleration due to gravity at the surface of earth
A) is maximum at the poles done clear
B) is maximum at the equator done clear
C) remains constant everywhere on the surface of the earth done clear
D) is maximum at the international timeline done clear
View Answer play_arrowquestion_answer18) The escape velocity of a particle from the surface of the earth is given by
A) \[{{(g/R)}^{1/2}}\] done clear
B) \[{{(2\,gR)}^{1/2}}\] done clear
C) \[{{(3\,\,gR)}^{1/2}}\] done clear
D) \[{{(\,gR/2)}^{2}}\] done clear
View Answer play_arrowquestion_answer19) The Young's modulus of a rope of \[10\text{ }m\] length and having diameter of \[2\text{ }cm\]is \[200\times {{10}^{11}}\,dyne/c{{m}^{2}}\]. If the elongation produced in the rope is \[1\text{ }cm,\] the force applied on the rope is
A) \[6.28\times {{10}^{5}}\,\,N\] done clear
B) \[6.28\times {{10}^{4}}\,\,N\] done clear
C) \[6.28\times {{10}^{4}}\text{ }dyne\] done clear
D) \[6.28\times {{10}^{5}}\text{ }dyne\] done clear
View Answer play_arrowquestion_answer20) "The pressure exerted at any point in an enclosed fluid is transmitted equally in all directions". This is known as
A) Archimedes 'principle done clear
B) Law of floatation done clear
C) Pascal?s law done clear
D) Bernoulli principal done clear
View Answer play_arrowquestion_answer21) There are two identical small holes on the opposite sides of a tank containing a liquid. The tank is open at the top. The difference in height between the two holes is h. As the liquid comes out of the two holes, the tank will experience a net horizontal force proportional to
A) \[\sqrt{h}\] done clear
B) \[h\] done clear
C) \[{{h}^{3/2}}\] done clear
D) \[{{h}^{2}}\] done clear
View Answer play_arrowquestion_answer22) The zeroth law of thermodynamics for three systems A, B and C in contact demands that
A) A and B are in thermal equilibrium done clear
B) B and C are in thermal equilibrium done clear
C) A and C are in thermal equilibrium done clear
D) A B and C are in thermal equilibrium done clear
View Answer play_arrowquestion_answer23) The efficiency of a Carnot engine kept at the temperatures of \[{{27}^{o}}C\] and \[{{127}^{o}}C\] is
A) \[20%\] done clear
B) \[25%\] done clear
C) \[30%\] done clear
D) \[40%\] done clear
View Answer play_arrowquestion_answer24) The average pressure of an ideal gas is
A) \[p=(1/3)mnV_{av}^{2}\] done clear
B) \[p=(1/3)mn{{V}_{av}}\] done clear
C) \[p=(1/4)mnV_{av}^{2}\] done clear
D) \[p=(1/3)mn{{V}_{av}}\] where symbols have their usual meanings. done clear
View Answer play_arrowquestion_answer25) According to equipartition law of energy each particle in a system of particles have thermal energy E equal to
A) \[E={{k}_{B}}T\] done clear
B) \[E=(1/2){{k}_{B}}T\] done clear
C) \[E=3\,\,{{k}_{B}}T\] done clear
D) \[E=(3/2)\,\,{{k}_{B}}T\] done clear
View Answer play_arrowquestion_answer26) The velocity of sound in a gas is \[1300\text{ }m/s\]at STP and specific heat at constant pressure is \[6.84\,cal\,{{K}^{-1}}\,mo{{l}^{-1}}\]. The rms velocity at STP is \[(R=1.98\,cal\,\,{{K}^{-1}}\,mo{{l}^{-1}})\]
A) \[1300\text{ }m/s\] done clear
B) \[2600\text{ }m/s\] done clear
C) \[1898\text{ }m/s\] done clear
D) \[650\text{ }m/s\] done clear
View Answer play_arrowquestion_answer27) The time period of a simple pendulum of length \[9.8\text{ }m\]is
A) \[0.159\,\,s\] done clear
B) \[3.14\,\,s\] done clear
C) \[6.5\,\,s\] done clear
D) \[6.28\text{ }s\] done clear
View Answer play_arrowquestion_answer28) The displacement, velocity and acceleration in a simple harmonic motion are related as the
A) displacement, velocity and acceleration all act in the same direction done clear
B) displacement and velocity act in the same direction but acceleration in the opposite direction done clear
C) Velocity and acceleration are parallel and both are perpendicular to the displacement done clear
D) displacement and acceleration are antiparallel and both perpendicular to the velocity done clear
View Answer play_arrowquestion_answer29) The beats are the examples of
A) simple harmonic motion done clear
B) interference of two or more waves having same amplitude but slightly different frequencies in the same direction done clear
C) interference of two or more waves having different amplitude but same frequencies in the same direction done clear
D) interference of two or more waves having same amplitude out slightly different frequencies in the perpendicular direction done clear
View Answer play_arrowquestion_answer30) The fundamental frequency of an open pipe of length \[1\text{ }m,\] if the speed of sound in air is \[340\text{ }m/s\]is
A) \[340\text{ }Hz\] done clear
B) \[170\text{ }Hz\] done clear
C) \[680\text{ }Hz\] done clear
D) \[85\text{ }Hz\] done clear
View Answer play_arrowquestion_answer31) A whistle with frequency \[1020\text{ }Hz\]is blown at a station. A man travelling in train moving towards the station at \[30\text{ }m/s\]hears the sound of the whistle. If the speed of sound is \[340\text{ }m/s,\] the apparent frequency heard by him is
A) \[1020\text{ }Hz\] done clear
B) \[1110\text{ }Hz\] done clear
C) \[2040\text{ }Hz\] done clear
D) \[610\text{ }Hz\] done clear
View Answer play_arrowquestion_answer32) An electric charge does not have which of hte following properties?
A) Total charge conservation done clear
B) Quantization of charge done clear
C) Two type of charge done clear
D) Circular line of force done clear
View Answer play_arrowquestion_answer33) The net electric force on a charge of \[+3\mu C\] at the mid-point on the line joining two charges of magnitude \[+2\mu C\] and \[-2\mu C\] separated by the distance of \[6mm,\]is
A) \[6000\,N\] done clear
B) \[500\,N\] done clear
C) \[60\,N\] done clear
D) zero done clear
View Answer play_arrowquestion_answer34) A hollow sphere of radius \[0.1\text{ }m\] has a charge of \[5\times {{10}^{-8}}C.\]. The potential at a distance of \[5\text{ }cm\]from the centre of the sphere is \[=\left( \frac{1}{4\pi {{\varepsilon }_{0}}}=9\times {{10}^{9}}\,\,N{{m}^{2}}\,\,{{C}^{-2}} \right)\]
A) \[4000\,V\] done clear
B) \[4500\,V\] done clear
C) \[5000\,V\] done clear
D) \[6000\,V\] done clear
View Answer play_arrowquestion_answer35) A parallel plate capacitor of capacitance 5 microfarad is charged to \[120\text{ }V\]and then connected to another uncharged capacitor. If the potential falls to \[40\text{ }V,\] and capacitance of the second capacitor is
A) 5 microfarad done clear
B) 10 microfarad done clear
C) 15 microfarad done clear
D) 20 microfarad done clear
View Answer play_arrowquestion_answer36) Two identical capacitors are first connected in series and then in parallel. The ratio of equivalent capacitance is
A) \[1:1\] done clear
B) \[1:2\] done clear
C) \[1:3\] done clear
D) \[1:4\] done clear
View Answer play_arrowquestion_answer37) An electron revolves in a circle at the rate of 1019 rounds per second. The equivalent current is \[(e=1.6\times {{10}^{-19}}C)\]
A) \[1.0\,\,A\] done clear
B) \[1.6\,\,A\] done clear
C) \[2.0\text{ }A\] done clear
D) \[2.6\text{ }A~\] done clear
View Answer play_arrowquestion_answer38) A silver wire of radius \[0.1\text{ }cm\]carries a current of\[2A\]. If the charge density in silver is \[5.86\times {{10}^{28}}{{m}^{-3}},\] the drift velocity is
A) \[0.2\times {{10}^{-3}}m/s\] done clear
B) \[0.4\times {{10}^{-4}}\text{ }m/s\] done clear
C) \[0.68\times {{10}^{-4}}\text{ }m/s\] done clear
D) \[7\times {{10}^{-4}}\text{ }m/s\] done clear
View Answer play_arrowquestion_answer39) A \[1\,m\] long wire of diameter of \[0.31\text{ }mm\] has a resistance of \[4.2\Omega \]. If it is replaced by another wire of same material of length \[1.5\text{ }m\]and diameter \[0.155\text{ }mm,\] the resistance of wire is
A) \[25.2\text{ }\Omega \] done clear
B) \[0.6\text{ }\Omega \] done clear
C) \[26.7\text{ }\Omega \] done clear
D) \[\text{0}\text{.8 }\Omega \] done clear
View Answer play_arrowquestion_answer40) 24 cells of emf \[1.5\text{ }V\]each having internal resistance of \[1\text{ }ohm\]are connected to an external resistance of\[1.5\text{ }ohms\]. To get maximum current
A) all cells are connected in series combination done clear
B) all cells are connected in parallel combination done clear
C) 4 cells in each row are connected in series and6 such rows are connected in parallel done clear
D) 6 cells in each row are connected in series and 4 such rows are connected in parallel done clear
View Answer play_arrowquestion_answer41) The temperature coefficient of the resistance of a wire is\[0.00125\text{ }per{{\text{ }}^{o}}C\]. At \[300\text{ K}\]its resistance is \[1\Omega \]. The resistance of wire will be \[2\,\,\Omega ,\] at
A) \[1154\,\,K\] done clear
B) \[1100\,\,K\] done clear
C) \[1400\text{ }K\] done clear
D) \[1127\,\,K\] done clear
View Answer play_arrowquestion_answer42) A long straight wire is carrying a current of\[12\text{ }A\]334. The magnetic field at a distance of \[8\text{ }cm\]is \[({{\mu }_{0}}=4\pi \times {{10}^{-7}}\,\,N/{{A}^{2}})\]
A) \[2\times {{10}^{-4}}Wb/{{m}^{2}}\] done clear
B) \[3\times {{10}^{-5}}\text{ }Wb/{{m}^{2}}\] done clear
C) \[4\times {{10}^{-4}}Wb/{{m}^{2}}\] done clear
D) \[4\times {{10}^{-5}}\text{ }Wb/{{m}^{2}}\] done clear
View Answer play_arrowquestion_answer43) The magnetic field at a point on the axis of a long solenoid having 5 turns per cm length when a current of \[0.8\,A\]flows through it is
A) \[5.024\times {{10}^{-8}}\text{ }Wb/{{m}^{2}}\] done clear
B) \[6.024\times {{10}^{-8}}\text{ }Wb/{{m}^{2}}\] done clear
C) \[7.024\times {{10}^{-8}}\text{ }Wb/{{m}^{2}}\] done clear
D) \[8.024\times {{10}^{-8}}\text{ }Wb/{{m}^{2}}\] done clear
View Answer play_arrowquestion_answer44) Two straight wires each \[10\text{ }cm\]long are parallel to one another and separated by\[2\text{ }cm\]. When the current flowing in them is \[30\text{ }A\]and \[40\text{ }A\]respectively, the force experienced by either of the wires is
A) \[1.2\times {{10}^{-3}}N\] done clear
B) \[12\times {{10}^{-3}}N\] done clear
C) \[11.2\times {{10}^{-3}}\text{ }N\] done clear
D) \[10.2\times {{10}^{-3}}\text{ }N\] done clear
View Answer play_arrowquestion_answer45) The horizontal and vertical components of earth's magnetic field at a place are \[0.3\text{ }G\] and\[0.52\text{ }G\]. The earth's magnetic field and the angle of dip are
A) \[0.3\text{ }G\]and \[\delta ={{30}^{o}}\] done clear
B) \[0.4\text{ }G\]and \[\delta ={{40}^{o}}\] done clear
C) \[0.5\text{ }G\]and \[\delta ={{50}^{o}}\] done clear
D) \[0.6\text{ }G\]and \[\delta ={{60}^{o}}\] done clear
View Answer play_arrowquestion_answer46) A bar magnet of pole strength \[10\text{ }Am\]is cut into two equal parts breadthwise. The pole strength of each magnet is
A) \[5\text{ }Am\] done clear
B) \[~10\text{ }Am\] done clear
C) \[15\text{ }Am\] done clear
D) \[20\text{ }Am\] done clear
View Answer play_arrowquestion_answer47) A conductor of length \[5\text{ }cm\]is moved parallel to itself with a speed of \[2\text{ }m/s,\] perpendicular to a uniform magnetic field of\[{{10}^{-3}}\text{ }Wb/{{m}^{3}}\]. The induced e.m.f. generated is
A) \[2\times {{10}^{-3}}V\] done clear
B) \[1\times {{10}^{-3}}V\] done clear
C) \[1\times {{10}^{-4}}V\] done clear
D) \[2\times {{10}^{-4}}V\] done clear
View Answer play_arrowquestion_answer48) The induced emf in a coil of \[10\text{ }H\]inductance in which current varies from \[9\text{ }A\]to \[4\text{ }A\]in \[0.2\,\,s\] is
A) \[200\,\,V\] done clear
B) \[250\,\,V\] done clear
C) \[300\,\,V\] done clear
D) \[350\,\,V\] done clear
View Answer play_arrowquestion_answer49) The alternating current in a circuit is given by \[I=50\,\,\sin \,\,314t\]. The peak value and frequency of the current are
A) \[{{I}_{0}}=25\,\,A\]and \[f=100\,\,Hz\] done clear
B) \[{{I}_{0}}=50\,\,Hz\] and \[f=50\,Hz\] done clear
C) \[{{I}_{0}}=50A\] and \[f=100\,\,Hz\] done clear
D) \[{{\text{I}}_{0}}=25A\]and \[f=50\,\,Hz\] done clear
View Answer play_arrowquestion_answer50) A 5\[50\text{ }Hz\] AC signal is applied in a circuit of inductance of \[(1/\pi )H\] and resistance \[2100\,\Omega \]The impedance offered by the circuit is
A) \[1500\text{ }\Omega \] done clear
B) \[1700\,\,\Omega \] done clear
C) \[2102\,\Omega \] done clear
D) \[2500\,\,\Omega \] done clear
View Answer play_arrowquestion_answer51) If the alternating current \[I={{I}_{1}}\,\,\cos \,\,\,\omega t+{{I}_{2}}\,\,\sin \,\,\omega t\](of then the rms current is given by
A) \[\frac{{{I}_{1}}+{{I}_{2}}}{\sqrt{2}}\] done clear
B) \[\frac{|{{I}_{1}}+{{I}_{2}}|}{\sqrt{2}}\] done clear
C) \[\sqrt{\left( \frac{I_{1}^{2}+I_{2}^{2}}{2} \right)}\] done clear
D) \[\sqrt{\frac{I_{1}^{2}+I_{2}^{2}}{\sqrt{2}}}\] done clear
View Answer play_arrowquestion_answer52) The transverse nature of electromagnetic waves is proved by which of the following?
A) Interference phenomena done clear
B) Diffraction phenomena done clear
C) Dispersion phenomena done clear
D) Polarization phenomena done clear
View Answer play_arrowquestion_answer53) Which component of electromagnetic spectrum have maximum wavelength?
A) Radio waves done clear
B) Visible spectrum done clear
C) Gamma rays done clear
D) X-rays done clear
View Answer play_arrowquestion_answer54) An object is 8 cm high. It is desired to form a real image \[4\text{ }cm\]high at \[60\text{ }cm\]from the mirror. The type of mirror needed with the focal length is
A) convex mirror with focal length \[f=40\text{ }cm\] done clear
B) convex mirror with focal length \[f=20\text{ }cm\] done clear
C) concave mirror with focal length \[f=-40\text{ }cm\] done clear
D) concave mirror with focal length \[f=-20\text{ }cm\] done clear
View Answer play_arrowquestion_answer55) When an object is placed \[40\text{ }cm\]from a diverging lens, its virtual image is formed \[20\text{ }cm\]from the lens. The focal length and power of lens are
A) \[F=-20cm,\,P=-5\,D\] done clear
B) \[F=-40cm,\,P=-5\,D\] done clear
C) \[F=-40cm,\,P=-2.5\,D\] done clear
D) \[F=-20\,cm,\,P=-2.5\,D\] done clear
View Answer play_arrowquestion_answer56) A magnifying glass of focal length \[5\text{ }cm\]is used to view an object by a person whose smallest distance of distinct vision is\[25\text{ }cm\]. If he holds the glass close to eye, the magnification is
A) \[5\] done clear
B) \[6\] done clear
C) \[2.5\] done clear
D) \[3\] done clear
View Answer play_arrowquestion_answer57) A person has a minimum distance of distinct vision as\[50\text{ }cm\]. The power of lenses required to read a book at a distance of \[25\text{ }cm\]is
A) \[3\,\,D\] done clear
B) \[1\,\,D\] done clear
C) \[2\,\,D\] done clear
D) \[4\,\,D\] done clear
View Answer play_arrowquestion_answer58) If two slits in Young's experiment are \[0.4\text{ }mm\]apart and fringe width on a screen \[200\text{ }cm\]away is \[2\text{ }mm\]the wavelength of light illuminating the slits is
A) \[500\text{ }nm\] done clear
B) \[600\text{ }nm\] done clear
C) \[400\text{ }nm\] done clear
D) \[300\text{ }nm\] done clear
View Answer play_arrowquestion_answer59) Electric field strength due to a diple at a point on the axial line of dipole is
A) from positive charge to negative charge done clear
B) from negative charge to positive charge done clear
C) along the equatorial line done clear
D) at an angle to axial line done clear
View Answer play_arrowquestion_answer60) The distance of moon form the earth is \[3.8\times {{10}^{5}}\text{ }km\]. Supposing that the eye is most sensitive to the light of wavelength \[550\text{ }nm,\] the separation of two points on the moon that can be resolved by a \[500\text{ }cm\]telescope is
A) \[50\,\,m\] done clear
B) \[55\,\,m\] done clear
C) \[51\text{ }m\] done clear
D) \[60\,\,m\] done clear
View Answer play_arrowquestion_answer61) Unpolarized light falls on two polarizing sheets placed one on top of other. If the intensity of transmitted light is one fourth of the incident light, the angle between them is
A) \[{{35}^{o}}\] done clear
B) \[{{40}^{o}}\] done clear
C) \[{{45}^{o}}\] done clear
D) \[{{50}^{o}}\] done clear
E) Not available done clear
View Answer play_arrowquestion_answer62) The Brewster's law is given by the expression
A) \[\mu =\frac{\sin \,i}{\sin \,r}\] done clear
B) \[\mu =\tan \,{{\theta }^{o}}\] done clear
C) \[\mu =\cos \theta \] done clear
D) \[\mu =sin\theta \] done clear
View Answer play_arrowquestion_answer63) Einstein's photoelectric equation is
A) \[{{E}_{\max }}=hv-\phi \] done clear
B) \[E=m{{c}^{2}}\] done clear
C) \[{{E}^{2}}={{p}^{2}}{{c}^{2}}+m_{0}^{2}{{c}^{4}}\] done clear
D) \[E=\left( \frac{1}{2} \right)m{{v}^{2}}\] done clear
View Answer play_arrowquestion_answer64) The Davission-Germer experiment is the direct evidence of
A) particle nature of electrons done clear
B) wave nature of electrons done clear
C) wave nature of light done clear
D) particle nature of light done clear
View Answer play_arrowquestion_answer65) The Rutherford scattering experiment porves that an atom consists of
A) a sphere of positive charge in which electrons are embedded like seeds of water-melon done clear
B) a sphere of negative charge in which protons are embedded like seeds of water-melon done clear
C) a sphere of electron cloud in which the positive charge in placed at the centre of the sphere done clear
D) a sphere of neutral charge done clear
View Answer play_arrowquestion_answer66) According to Bohr model of hydrogen atom, only those orbits are permissible which satisfy the condition
A) \[mv=nh\] done clear
B) \[\frac{m{{v}^{2}}}{r}=n\left( \frac{h}{2\pi } \right)\] done clear
C) \[mvr=n\left( \frac{h}{2\pi } \right)\] done clear
D) \[mv{{r}^{2}}=n\left( \frac{h}{2\pi } \right)\] done clear
View Answer play_arrowquestion_answer67) The radioactive decay of thorium \[(A=232,\,\,Z=90)\] releases six alpha and four beta particles. The atomic number and mass number of the final product is
A) \[Z=80,\,\,A=207\] done clear
B) \[Z=82,\,\,A=208\] done clear
C) \[Z=92,\,\,A=209\] done clear
D) \[Z=90,\,\,A=207\] done clear
View Answer play_arrowquestion_answer68) Polonium has a half-life of \[140\] days. If we take \[20\,\,g\]of polonium initially then the amount of it that remains after 280 days is
A) \[2.5\,\,g\] done clear
B) \[5\,\,g\] done clear
C) \[10\text{ }g\] done clear
D) \[15\text{ }g\] done clear
View Answer play_arrowquestion_answer69) Based on the band theory of conductors, insulators and semi-conductors, the forbidden gap is smallest in
A) conductors done clear
B) insulators done clear
C) semi-conductors done clear
D) All of these done clear
View Answer play_arrowquestion_answer70) Based on the I-V characteristics of the diode, we can classify diode as
A) bi-directional device done clear
B) ohmic device done clear
C) non-ohmic device done clear
D) passive element done clear
View Answer play_arrowquestion_answer71) The Boolean expression for the XOR gate is
A) \[Y=A+B\] done clear
B) \[Y=A.B\] done clear
C) \[Y=AB=BA\] done clear
D) \[Y=A\oplus B\] done clear
View Answer play_arrowquestion_answer72) Which of the following logic gates are also known as the Universal gates?
A) AND, OR. NOT gate done clear
B) XOR, XNOR gate done clear
C) NAND, NOR gate done clear
D) All logic gates done clear
View Answer play_arrowquestion_answer73) The length of antenna (L) required to propagate a signal of wavelength \[\lambda \] is given as
A) \[L=\frac{\lambda }{2}\] done clear
B) \[L=2\lambda \] done clear
C) \[L=\frac{\lambda }{3}\] done clear
D) \[L=\frac{\lambda }{4}\] done clear
View Answer play_arrowquestion_answer74) The modulation is the process in which the
A) modulating signal is sent by antenna in the air done clear
B) carrier signal is sent by the antenna in the air done clear
C) modulated signal formed by the mixing of modulating signal with the carrier signal is sent by the antenna done clear
D) modulated signal formed by the mixing of modulating signal with the carrier signal is received by a receiver antenna done clear
View Answer play_arrowquestion_answer75) The demodulator or detector circuit consists of a
A) resistor done clear
B) transistor done clear
C) diode done clear
D) capacitor done clear
View Answer play_arrowquestion_answer76) Which of the following would contain the same number of atoms as 20 g of calcium? [At. masses:\[Ca=40,Mg=24,C=12\]]
A) 24 g of magnesium done clear
B) 12 got carbon done clear
C) 24 got carbon done clear
D) 12 g of magnesium done clear
View Answer play_arrowquestion_answer77) 100 mL of \[\text{N}{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\]is mixed with 100 mL of \[\text{1 M NaOH}\]solution. The resulting solution will be
A) highly acidic done clear
B) neutral done clear
C) highly basic done clear
D) slightly acidic done clear
View Answer play_arrowquestion_answer78) The bond order of\[\text{N}_{\text{2}}^{\text{+}}\]on the basis of molecular orbital theory is [Atomic number of\[\text{N}\,\text{=}\,\text{7}\]]
A) 3 done clear
B) 2.5 done clear
C) 2 done clear
D) 1.5 done clear
View Answer play_arrowquestion_answer79) What is the total number of electrons that can have the values \[n=2,l=1,s=1/2\]in the electronic configuration\[1{{s}^{2}}2{{s}^{2}}2{{p}^{3}}\]
A) 1 done clear
B) 3 done clear
C) 5 done clear
D) 7 done clear
View Answer play_arrowquestion_answer80) Calculate the wavelength associated with an electron moving with a velocity of \[{{10}^{6}}\,m/s\](mass of electron \[=9.1\times {{10}^{-31}}\,kg,\]\[h=6.6\times {{10}^{-34}}\,kg\,{{m}^{2}}\,{{s}^{-1}}\])
A) \[6.2\times {{10}^{-8}}\,m\] done clear
B) \[7.25\times {{10}^{-8}}\,m\] done clear
C) \[6.25\,\overset{\text{o}}{\mathop{\text{A}}}\,\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer81) Which of the following pairs is not correctly matched?
A) Hund's rule In orbitals of equivalent energy electron spins remain unpaired if possible done clear
B) Pauli's exclusion No two electrons can principle have all the four quantum numbers identical done clear
C) Zeeman effect The effect of magnetic field on the atomatic spectra done clear
D) Uncertainty It is impossible to principle determine the position of an electron done clear
View Answer play_arrowquestion_answer82) The orbital diagram in which Aufbau principle is violated is
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer83) The \[{{[\text{OH}]}^{-}}\]in a solution is \[1\,\text{mol}\,{{\text{L}}^{-1}}.\] The pH of the solution is
A) 1 done clear
B) 0 done clear
C) 14 done clear
D) \[{{10}^{-14}}\] done clear
View Answer play_arrowquestion_answer84) The solubility of \[\text{Fe(OH}{{\text{)}}_{\text{3}}}\]is \[x\,\text{mol}\,{{\text{L}}^{-1}}.\]Its\[{{K}_{sp}}\] would be
A) \[9{{x}^{3}}\] done clear
B) \[3{{x}^{3}}\] done clear
C) \[27{{x}^{4}}\] done clear
D) \[9{{x}^{4}}\] done clear
View Answer play_arrowquestion_answer85) In which of the following reactions, increase in pressure will favour the forward reaction?
A) \[PC{{l}_{5}}(g)\rightleftharpoons PC{{l}_{3}}(g)+C{{l}_{2}}(g)\] done clear
B) \[2NO(g)+{{O}_{2}}(g)\rightleftharpoons 2N{{O}_{2}}(g)\] done clear
C) \[C(s)+{{H}_{2}}O(g)\rightleftharpoons CO(g)+{{H}_{2}}(g)\] done clear
D) \[2HI(g)\rightleftharpoons {{H}_{2}}(g)+{{I}_{2}}(g)\] done clear
View Answer play_arrowquestion_answer86) Which of the following is a Lewis acid?
A) \[BF_{4}^{-}\] done clear
B) \[O{{H}^{-}}\] done clear
C) \[AlC{{l}_{3}}\] done clear
D) \[RN{{H}_{2}}\] done clear
View Answer play_arrowquestion_answer87) According to collision theory of chemical reactions rates of the reaction increase with increase in the temperature of a reaction because of
A) increase in the velocity of the reacting molecules done clear
B) increase in the number of collisions done clear
C) increase in the number of molecules having the activation energy (threshold energy) done clear
D) None of the above done clear
View Answer play_arrowquestion_answer88) Consider the reaction, \[2{{N}_{2}}O{{}_{5}}(g)\xrightarrow{{}}4N{{O}_{2}}(g)+{{O}_{2}}(g)\] The rate law for this reaction is rate\[=k[{{N}_{2}}{{O}_{5}}].\] Which of the following statements is true regarding the above reaction?
A) Its order is 1 and molecularity is 1 done clear
B) Its order is 1 and molecularity is 2 done clear
C) Its order is 2 and molecularity is 2 done clear
D) Its order is 2 and molecularity is 1 done clear
View Answer play_arrowquestion_answer89) A catalyst is a substance which
A) increases the rate of forward reaction in reversible reaction done clear
B) increases the rate of both forward and backward reaction in a reversible reaction done clear
C) does not influence a reversible reaction done clear
D) increases the rate of backward reaction in a reversible reaction. done clear
View Answer play_arrowquestion_answer90) Which of the following solutions will have the highest boiling point?
A) 1 M glucose solution done clear
B) 1 M sodium nitrate solution done clear
C) 1 M barium chloride solution done clear
D) 1 M aluminium chloride solution done clear
View Answer play_arrowquestion_answer91) Which of the following is a colligative property?
A) Lowering of vapour pressure done clear
B) Osmotic pressure done clear
C) Boiling point done clear
D) Change in entropy done clear
View Answer play_arrowquestion_answer92) van't Hoff factor for \[\text{Ca(N}{{\text{O}}_{\text{3}}}{{\text{)}}_{\text{2}}}\]is
A) 1 done clear
B) 2 done clear
C) 3 done clear
D) 4 done clear
View Answer play_arrowquestion_answer93) What will be the freezing point of 1% solution of glucose in water, given that molal depression constant for water is \[1.84\,\text{K}\,\text{mo}{{\text{l}}^{-}}\]
A) 272.898 K done clear
B) \[~0.102{{\,}^{o}}C\] done clear
C) 273 K done clear
D) \[108{{\,}^{o}}C\] done clear
View Answer play_arrowquestion_answer94) If\[\Delta H\]and\[\Delta S\]are positive for a reaction, the reaction will be spontaneous only when
A) \[T\Delta S=\Delta H\] done clear
B) \[T\Delta S>\Delta H\] done clear
C) \[T\Delta S<\Delta H\] done clear
D) \[T\Delta S\]is negative done clear
View Answer play_arrowquestion_answer95) Calculate the enthalpy change for the reaction, \[{{C}_{2}}{{H}_{4}}(g)+{{H}_{2}}(g)\xrightarrow{{}}{{C}_{2}}{{H}_{6}}(g)\] using the data given below \[{{C}_{2}}{{H}_{4}}(g)+3{{O}_{2}}(g)\xrightarrow{{}}2C{{O}_{2}}(g)+2{{H}_{2}}O(l)\] \[\Delta H=-1415\,kJ\] \[{{C}_{2}}{{H}_{6}}(g)+\frac{7}{2}{{O}_{2}}(g)\xrightarrow{{}}2C{{O}_{2}}(g)+3{{H}_{2}}O\] \[\Delta H=-1566\,kJ\] \[{{H}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)\xrightarrow{{}}{{H}_{2}}O(l);\Delta H=-286\,kJ\]
A) \[-437\,kJ\] done clear
B) \[135\,kJ\] done clear
C) \[-135\,kJ\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer96) In thermodynamics, a quantity whose value simply depends upon the initial and final state of the system is called
A) a thermodynamic quantity done clear
B) a state function done clear
C) an adiabatic quantity done clear
D) a path function done clear
View Answer play_arrowquestion_answer97) All naturally occurring processes proceed spontaneously in a direction which leads to
A) increase in enthalpy of system done clear
B) decrease in entropy of system done clear
C) decrease in free energy of system done clear
D) increase in free energy of system done clear
View Answer play_arrowquestion_answer98) When an electrolytic solution conducts electricity, the current is carried by
A) the electrons done clear
B) cations and anions done clear
C) neutral molecules done clear
D) the atoms of the electrolyte done clear
View Answer play_arrowquestion_answer99) An electrochemical cell has two half cell reactions as, \[{{A}^{2+}}+2{{e}^{-}}\xrightarrow{{}}A;\] \[E_{{{A}^{2+}}/A}^{o}=0.34\,V\] \[X\xrightarrow{{}}{{X}^{2+}}+2{{e}^{-}};\] \[E_{{{x}^{2}}/x}^{0}=-2.37\,V\] The cell voltage will be
A) \[2.71\,V\] done clear
B) \[2.03\,V\] done clear
C) \[-2.71\,V\] done clear
D) \[-2.03\,V\] done clear
View Answer play_arrowquestion_answer100) In the electrolysis of dilute ?[2804 using platinum electrode
A) \[{{\text{H}}_{\text{2}}}\]is liberated at cathode done clear
B) \[{{\text{O}}_{\text{2}}}\]is produced at cathode done clear
C) \[\text{C}{{\text{l}}_{\text{2}}}\] is obtained at cathode done clear
D) \[\text{N}{{\text{H}}_{\text{3}}}\] is produced at anode done clear
View Answer play_arrowquestion_answer101) When a solution of sodium hydroxide is added to acetic acid solution, the conductivity of the resulting solution will
A) increase done clear
B) remain unchanged done clear
C) decrease done clear
D) become zero done clear
View Answer play_arrowquestion_answer102) The behaviour of a real gas approaches ideal behaviour at
A) low temperature, low pressure done clear
B) high temperature, high pressure done clear
C) low temperature, high pressure done clear
D) high temperature, low pressure done clear
View Answer play_arrowquestion_answer103) Which of the following is not the postulate of the kinetic theory of gases?
A) Gas molecules are in a permanent state of random motion done clear
B) Pressure of gas is due to molecular impacts on the walls done clear
C) The molecules are perfectly elastic done clear
D) The molecular collisions are elastic done clear
View Answer play_arrowquestion_answer104) When a cation leaves its normal position in the crystal and moves to some interstitial space, the defect in the crystal is known as
A) Schottky defect done clear
B) F-centre done clear
C) Frenkel defect done clear
D) non-stoichiometric defect done clear
View Answer play_arrowquestion_answer105) Fog is a colloidal system of
A) gas in liquid done clear
B) liquid in gas done clear
C) gas in gas done clear
D) gas in solid done clear
View Answer play_arrowquestion_answer106) The purification of a colloidal solution could be done by
A) sedimentation done clear
B) ultrafiltration done clear
C) filtration done clear
D) precipitation done clear
View Answer play_arrowquestion_answer107) Bakelite is a product of the reaction between
A) formaldehyde and NaOH . done clear
B) aniline and urea done clear
C) phenol and methanol done clear
D) phenol and chloroform done clear
View Answer play_arrowquestion_answer108) How does electron affinity change when we move from left to right in a period in the Periodic Table?
A) It increases done clear
B) It decreases done clear
C) It remains unchanged done clear
D) It first increases and then decreases done clear
View Answer play_arrowquestion_answer109) Which of the following statements is not correct?
A) lonisation energy increases on going down a group in the Periodic Table done clear
B) Among alkaline earth metals, reducing character increases down the group done clear
C) Fluorine is the most electronegative element done clear
D) Metallic character increases on going down a group in the Periodic Table done clear
View Answer play_arrowquestion_answer110) Which of the following species has a trigonal planar shape?
A) \[_{.}^{.}CH_{3}^{-}\] done clear
B) \[CH_{3}^{+}\] done clear
C) \[BF_{4}^{-}\] done clear
D) \[Si{{H}_{4}}\] done clear
View Answer play_arrowquestion_answer111) Which of the following will have maximum dipole moment?
A) \[N{{F}_{3}}\] done clear
B) \[N{{H}_{3}}\] done clear
C) \[C{{H}_{4}}\] done clear
D) \[PC{{l}_{3}}\] done clear
View Answer play_arrowquestion_answer112) Which of the following forces is the strongest?
A) Hydrogen bonding done clear
B) Dipole-dipole forces done clear
C) van der Waals' forces done clear
D) Coordinate bonding done clear
View Answer play_arrowquestion_answer113) Which of the following statements is correct?
A) \[s{{p}^{3}}-\] hybrid orbitals have equal s and p character done clear
B) The bond angle decreases with the decrease of s character of a hybridized orbital done clear
C) Resonance decreases the stability of a molecule done clear
D) Resonance is due to delocalization of sigma electrons done clear
View Answer play_arrowquestion_answer114) Which of the following is the correct order of increasing oxidising character of oxoacids of chlorine?
A) \[HCl{{O}_{3}}<HCl{{O}_{4}}<HCl{{O}_{2}}<HClO\] done clear
B) \[~HCl{{O}_{4}}<HCl{{O}_{3}}<HCl{{O}_{2}}<HClO\] done clear
C) \[~HClO<HCl{{O}_{4}}<HCl{{O}_{3}}<HCl{{O}_{2}}\] done clear
D) \[HClO<HCl{{O}_{2}}<HCl{{O}_{3}}<HCl{{O}_{4}}\] done clear
View Answer play_arrowquestion_answer115) Which of the following oxides of group 16 has the highest boiling point?
A) \[{{H}_{2}}O\] done clear
B) \[{{H}_{2}}S\] done clear
C) \[{{H}_{2}}Se\] done clear
D) \[{{H}_{2}}Te\] done clear
View Answer play_arrowquestion_answer116) The +1 oxidation state of thallium is more stable than its +3 oxidation state because of
A) its atomic size done clear
B) its ionization potential done clear
C) inert pair effect done clear
D) diagonal relationship done clear
View Answer play_arrowquestion_answer117) Which of the following statements is false regarding alkali metals?
A) Alkali metals are soft and can be cut with the help of knife done clear
B) Alkali metals do not occur in free state in nature done clear
C) Alkali metals are highly electropositive elements done clear
D) Alkali metal hydrides are covalent in character done clear
View Answer play_arrowquestion_answer118) Among the following outermost configurations of transition metals, which shows the highest oxidation state?
A) \[~3{{d}^{3}}4{{s}^{2}}\] done clear
B) \[~3{{d}^{5}}\text{ }4{{s}^{1}}\] done clear
C) \[3{{d}^{5}}\text{ }4{{s}^{2}}\] done clear
D) \[3{{d}^{2}}\text{ }4{{s}^{2}}\] done clear
View Answer play_arrowquestion_answer119) The tendency of transition metals to form stable complexes is due to their
A) low ionization energies done clear
B) variable oxidation states done clear
C) strong electropositive nature done clear
D) high charge/size ratio and vacant d orbitals done clear
View Answer play_arrowquestion_answer120) The transition metal ions are generally paramagnetic in nature because
A) they have coloured salts done clear
B) they have one or more unpaired cf-electrons done clear
C) they have one or more paired s-electrons done clear
D) they are reducing agents done clear
View Answer play_arrowquestion_answer121) The most common oxidation state of lanthanides is
A) \[+\,4\] done clear
B) \[+\text{ }3\] done clear
C) \[+\,6\] done clear
D) \[+\,2\] done clear
View Answer play_arrowquestion_answer122) Specify the coordination number of cobalt in \[[Co(CN)({{H}_{2}}O){{(en)}^{2}}]{{~}^{2+}}\]
A) 6 done clear
B) 4 done clear
C) 0 done clear
D) 3 done clear
View Answer play_arrowquestion_answer123) Which of the following complexes is square planar and diamagnetic?
A) \[{{[NiC{{l}_{4}}]}^{2-}}\] done clear
B) \[{{[NI{{(CN)}_{4}}]}^{2-}}\] done clear
C) \[{{[Cr{{(N{{H}_{3}})}_{6}}]}^{3+}}\] done clear
D) \[{{[CuC{{l}_{4}}]}^{2-}}\] done clear
View Answer play_arrowquestion_answer124) Which type of isomerism is exhibited by\[[Pt{{(N{{H}_{3}})}_{2}}C{{l}_{2}}]?\]
A) Coordination isomerism done clear
B) Linkage isomerism done clear
C) Optical isomerism done clear
D) Geometrical isomerism done clear
View Answer play_arrowquestion_answer125) Ethylene diamine tetraacetate ion is a
A) unidentate ligand done clear
B) bidentate ligand done clear
C) pentadentate ligand done clear
D) hexadentate ligand done clear
View Answer play_arrowquestion_answer126) Which of the following is an ore of zinc?
A) Galena done clear
B) Pyrolusite done clear
C) Sphaterite done clear
D) Magnetite done clear
View Answer play_arrowquestion_answer127) The impurities associated with the ore after mining are collectively called
A) flux done clear
B) slag done clear
C) minerals done clear
D) gangue done clear
View Answer play_arrowquestion_answer128) During extraction of iron, the iron obtained at the bottom of blast furnace is known as
A) steel done clear
B) wrought iron done clear
C) cast iron done clear
D) None of these done clear
View Answer play_arrowquestion_answer129) Select the molecule which has only one \[\pi -\]bond
A) \[CH\equiv CH\] done clear
B) \[C{{H}_{2}}=CH-CHO\] done clear
C) \[C{{H}_{3}}-CH=C{{H}_{2}}\] done clear
D) \[C{{H}_{3}}-CH=CH-COOH\] done clear
View Answer play_arrowquestion_answer130) Which of the following groups is ortho and para directing?
A) \[-COCl\] done clear
B) \[-CHO\] done clear
C) \[-OH\] done clear
D) \[-COC{{H}_{3}}\] done clear
View Answer play_arrowquestion_answer131) Amongst the given cations, the most stable carbonium ion is
A) \[{{\,}^{+}}C{{H}_{3}}\] done clear
B) \[{{(C{{H}_{3}})}_{3}}{{C}^{+}}\] done clear
C) \[C{{H}_{3}}C{{H}_{2}}\] done clear
D) \[{{(C{{H}_{3}})}_{2}}\overset{+}{\mathop{C}}\,H\] done clear
View Answer play_arrowquestion_answer132) The hybridization of carbon atoms in C?C single bond of\[HC=C-CH=C{{H}_{2}}\] is
A) \[s{{p}^{3}}-s{{p}^{2}}\] done clear
B) \[s{{p}^{2}}-s{{p}^{3}}\] done clear
C) \[sp-s{{p}^{2}}\] done clear
D) \[s{{p}^{3}}-s{{p}^{3}}\] done clear
View Answer play_arrowquestion_answer133) The number of optical isomers of the compound\[C{{H}_{3}}CHBrCHBrCOOH\]is
A) 0 done clear
B) 1 done clear
C) 3 done clear
D) 4 done clear
View Answer play_arrowquestion_answer134) Electrolysis of an aqueous solution of sodium ethanoate gives
A) methane done clear
B) ethane done clear
C) butane done clear
D) methyl ethanoate done clear
View Answer play_arrowquestion_answer135) Which of the following compounds will exhibit cis-trans (geometrical) isomerism?
A) 2-butene done clear
B) 2-butyne done clear
C) 2-butanol done clear
D) 1-butanol done clear
View Answer play_arrowquestion_answer136) The reaction given below is an example of which of the following? \[2C{{H}_{3}}Br+2Na\xrightarrow{\text{dry}\,\text{ether}}{{C}_{2}}{{H}_{6}}+2NaBr\]
A) Reimer-Tiemann reaction done clear
B) Wurtz reaction done clear
C) Hoffman bromamide reaction done clear
D) Aldol condensation done clear
View Answer play_arrowquestion_answer137) Chlorobenzene can be prepared by reacting aniline with
A) hydrochloric acid in the presence of nitrous acid done clear
B) cuprous chloride in the presence of aluminium chloride done clear
C) chlorine in the presence of aluminium chloride done clear
D) nitrous acid followed by heating with cuprous chloride done clear
View Answer play_arrowquestion_answer138) Phenol on treatment with cone. \[\text{HN}{{\text{O}}_{\text{3}}}\]gives
A) o-nitrophenol done clear
B) p-nitrophenol done clear
C) o-and p-nitrophenol done clear
D) 2, 4, 6-trinitrophenol done clear
View Answer play_arrowquestion_answer139) Which of the following compounds will be formed when methoxy benzene is reacted with HBr?
A) Phenol and bromomethane done clear
B) Methanol and bromobenzene done clear
C) Phenol and methanol done clear
D) Bromobenzene and bromomethane done clear
View Answer play_arrowquestion_answer140) When ethanol and\[{{\text{I}}_{\text{2}}}\]are heated in the presence of\[\text{N}{{\text{a}}_{\text{2}}}\text{C}{{\text{O}}_{\text{3}}}\text{,}\]the yellow crystals obtained are of
A) \[{{C}_{2}}{{H}_{5}}l\] done clear
B) \[C{{H}_{3}}l\] done clear
C) \[CH{{l}_{3}}\] done clear
D) \[C{{H}_{2}}{{l}_{2}}\] done clear
View Answer play_arrowquestion_answer141) Identify B in the following series of reaction \[C{{H}_{3}}CHO\xrightarrow{C{{H}_{3}}MgX}A\xrightarrow{HOH}B\]
A) 2-propanol done clear
B) 1-propanol done clear
C) ethanol done clear
D) None of these done clear
View Answer play_arrowquestion_answer142) Which of the following compounds has maximum acidic character?
A) Dichloroacetic acid done clear
B) Acetic acid done clear
C) Trichloroacetic ucid done clear
D) Triflouoroacetic acid done clear
View Answer play_arrowquestion_answer143) Among the following, the least reactive aldehyde is
A) \[HCHO\] done clear
B) \[{{C}_{6}}{{H}_{5}}CHO\] done clear
C) \[C{{H}_{3}}CHO\] done clear
D) \[{{C}_{2}}{{H}_{5}}CHO\] done clear
View Answer play_arrowquestion_answer144) Propanal on reaction with lithium aluminium hydride gives
A) 1-propanol done clear
B) 2-propanol done clear
C) ethanol done clear
D) butanol done clear
View Answer play_arrowquestion_answer145) Idenitfy Z in the following sequence \[C{{H}_{3}}C{{H}_{2}}I\xrightarrow{KCN}X\xrightarrow{{{H}_{3}}{{O}^{+}}/{{H}_{2}}O}Y\] \[\xrightarrow[\Delta ]{{{H}_{3}}{{O}^{+}}/{{H}_{2}}O}Z\]
A) \[C{{H}_{3}}COCl\] done clear
B) \[C{{H}_{3}}CON{{H}_{2}}\] done clear
C) \[C{{H}_{3}}COOH\] done clear
D) \[C{{H}_{3}}C{{H}_{2}}COOH\] done clear
View Answer play_arrowquestion_answer146) Treatment of aniline with bromine water produces
A) 2,4,6-tribromoaniline done clear
B) a mixture of ortho and para bromoaniline done clear
C) bromobenzene done clear
D) N-bromoaniline done clear
View Answer play_arrowquestion_answer147) \[{{C}_{6}}{{H}_{5}}COCl\xrightarrow{N{{H}_{3}}}X\xrightarrow{{{P}_{2}}{{O}_{5}}}Y\xrightarrow[{{H}_{2}}]{Ni}Z\] The end product in the above sequence of reactions is
A) benzole acid done clear
B) aniline done clear
C) benzyl amine done clear
D) benzonitrile done clear
View Answer play_arrowquestion_answer148) Which of the following is least reactive to nitration?
A) Benzene done clear
B) Nitrobenzene done clear
C) Chlorobenzene done clear
D) Aniline done clear
View Answer play_arrowquestion_answer149) Nucleic acids are polymers of
A) nucleotides done clear
B) nucleosides done clear
C) nuclei of heavy metals done clear
D) proteins done clear
View Answer play_arrowquestion_answer150) Which of the following enzymes helps in digestion of proteins?
A) Invertase done clear
B) Trypsin done clear
C) Tryosinase done clear
D) Urease done clear
View Answer play_arrowquestion_answer151) The value of\[\cos \left( \frac{3\pi }{2}+x \right)\,\cos \,(2\pi +x)\left\{ \cot \left( \frac{3\pi }{2}-x \right)+\cot \,(2\pi +x) \right\}\]is
A) \[0\] done clear
B) \[1\] done clear
C) \[cos\text{ }x\] done clear
D) \[sin\text{ }x\] done clear
View Answer play_arrowquestion_answer152) If \[\sin B=3\sin (2A+B),\] then \[2\tan A+\tan (A+B)\] is equal to
A) \[0\] done clear
B) \[-2\] done clear
C) \[1\] done clear
D) \[1\] done clear
View Answer play_arrowquestion_answer153) If \[\theta =\frac{\pi }{{{2}^{n}}+1},\] then the value of \[{{2}^{n}}\cos \theta \,\cos \,2\theta \,\cos \,{{2}^{2}}\theta .....\cos {{2}^{n-1}}\theta \] is
A) \[\sin \theta \] done clear
B) \[\frac{\pi }{2}\] done clear
C) \[0\] done clear
D) \[1\] done clear
View Answer play_arrowquestion_answer154) Using the principal values, the value of \[{{\sin }^{-1}}\left\{ \sin \frac{5\pi }{6} \right\}+{{\tan }^{-1}}\left\{ \tan \frac{\pi }{6} \right\}\]is equal to
A) \[\frac{\pi }{6}\] done clear
B) \[\frac{2\pi }{3}\] done clear
C) \[\frac{\pi }{3}\] done clear
D) \[\frac{5\pi }{6}\] done clear
View Answer play_arrowquestion_answer155) Find the value of \[{{\cos }^{-1}}\left( \frac{4}{5} \right)+{{\tan }^{-1}}\left( \frac{3}{5} \right)\].
A) \[{{\tan }^{-1}}\left( \frac{7}{10} \right)\] done clear
B) \[{{\tan }^{-1}}\left( \frac{27}{11} \right)\] done clear
C) \[{{\sin }^{-1}}\left( \frac{7}{5} \right)\] done clear
D) \[{{\tan }^{-1}}\left( \frac{1}{5} \right)\] done clear
View Answer play_arrowquestion_answer156) If \[X+Y=\left[ \begin{matrix} 7 & 0 \\ 2 & 5 \\ \end{matrix} \right]\] and \[X-Y=\left[ \begin{matrix} 3 & 0 \\ 0 & 3 \\ \end{matrix} \right]\], then X is equal to
A) \[\left[ \begin{matrix} 5 & 0 \\ 0 & 4 \\ \end{matrix} \right]\] done clear
B) \[\left[ \begin{matrix} 7 & 0 \\ 1 & 5 \\ \end{matrix} \right]\] done clear
C) \[\left[ \begin{matrix} 5 & 0 \\ 1 & 4 \\ \end{matrix} \right]\] done clear
D) \[\left[ \begin{matrix} 7 & 1 \\ 0 & 4 \\ \end{matrix} \right]\] done clear
View Answer play_arrowquestion_answer157) If \[\left| \begin{matrix} x+7 & 5 \\ x+-3 & 3 \\ \end{matrix} \right|=26,\] then x is equal to
A) \[1\] done clear
B) \[3\] done clear
C) \[5\] done clear
D) \[7\] done clear
View Answer play_arrowquestion_answer158) The value of \[\left| \begin{matrix} {{a}^{2}} & 2ab & {{b}^{2}} \\ {{b}^{2}} & {{a}^{2}} & 2ab \\ 2ab & {{b}^{2}} & {{a}^{2}} \\ \end{matrix} \right|\] is
A) \[{{({{a}^{2}}+{{b}^{2}})}^{3}}\] done clear
B) \[{{({{a}^{3}}+{{b}^{3}})}^{2}}\] done clear
C) \[{{({{a}^{4}}+{{b}^{4}})}^{2}}\] done clear
D) \[{{({{a}^{2}}+{{b}^{2}})}^{4}}\] done clear
View Answer play_arrowquestion_answer159) If \[A=\left[ \begin{matrix} 3 & -4 \\ 1 & -1 \\ \end{matrix} \right],\] then \[(A-A')\] is equal to (where, A 'is transpose of matrix A)
A) null matrix done clear
B) identity matrix done clear
C) symmetric done clear
D) skew-symmetric done clear
View Answer play_arrowquestion_answer160) If \[{{A}^{-1}}=\left[ \begin{matrix} 5 & -2 \\ -7 & 3 \\ \end{matrix} \right]\] and \[{{B}^{-1}}=\frac{1}{2}\left[ \begin{matrix} 9 & -7 \\ -8 & 6 \\ \end{matrix} \right],\] then \[{{(AB)}^{-1}}\] is equal to
A) \[\left[ \begin{matrix} 47 & -39/2 \\ -41 & 17 \\ \end{matrix} \right]\] done clear
B) \[\left[ \begin{matrix} 94 & -82 \\ -39 & 34 \\ \end{matrix} \right]\] done clear
C) \[\left[ \begin{matrix} -47 & 46 \\ 39/2 & -17 \\ \end{matrix} \right]\] done clear
D) \[\left[ \begin{matrix} -47 & 39/2 \\ 46 & -17 \\ \end{matrix} \right]\] done clear
View Answer play_arrowquestion_answer161) The value of \[\underset{x\to 1}{\mathop{\lim }}\,\frac{x-1}{{{\log }_{e}}x}\] is
A) \[1\] done clear
B) \[0\] done clear
C) Not defined done clear
D) \[-1\] done clear
View Answer play_arrowquestion_answer162) \[\underset{x\to 0}{\mathop{\lim }}\,\,{{\left\{ \tan \left( \frac{\pi }{4}+x \right) \right\}}^{1/x}}\]is equal to
A) \[e\] done clear
B) \[{{e}^{2}}\] done clear
C) \[1/e\] done clear
D) \[1/{{e}^{2}}\] done clear
View Answer play_arrowquestion_answer163) The value of \[\underset{n\to \infty }{\mathop{\lim }}\,\,\,\left\{ \frac{1+2+3+....+n}{n+2}-\frac{n}{2} \right\}\] is
A) \[\frac{1}{2}\] done clear
B) \[1\] done clear
C) \[-1\] done clear
D) \[-\frac{1}{2}\] done clear
View Answer play_arrowquestion_answer164) If \[y=1+\frac{x}{1!}+\frac{{{x}^{2}}}{2!}+\frac{{{x}^{3}}}{3!}.....,\]then \[\frac{dy}{dx}\] is equal to
A) \[{{e}^{x}}\] done clear
B) \[\sin \,x\] done clear
C) \[y\] done clear
D) \[x\] done clear
View Answer play_arrowquestion_answer165) The value of \[\frac{d}{dx}({{x}^{n}}\,{{\log }_{a}}\,x{{e}^{x}})\] is
A) \[{{e}^{x}}\,{{\log }_{a}}\,x+\frac{{{x}^{n-1}}}{{{\log }_{e}}\,a}\] done clear
B) \[{{e}^{x}}{{x}^{n-1}}\,\left\{ x{{\log }_{a}}\,x+\frac{1}{{{\log }_{e}}\,a}+n\,{{\log }_{a}}x \right\}\] done clear
C) \[n{{x}^{n-1}}\,{{\log }_{a}}\,x{{e}^{x}}\] done clear
D) \[{{x}^{n}}\,{{\log }_{a}}x.{{e}^{x}}\] done clear
View Answer play_arrowquestion_answer166) The interval in which the function \[f(x)=\sin x-\cos x,\,\,\,\,0\le x\le 2\pi \] is strictly decreasing, is
A) \[0<x<\frac{3\pi }{4}\] done clear
B) \[\frac{7\pi }{4}<x<2\pi \] done clear
C) \[\frac{3\pi }{4}<x<\frac{7\pi }{4}\] done clear
D) \[0<x<\frac{7\pi }{4}\] done clear
View Answer play_arrowquestion_answer167) The slope of normal to the curve \[y={{x}^{3}}+2x+6\] which is parallel to line \[x+14y+4=0\] is
A) \[-\frac{1}{3}\] done clear
B) \[-\frac{1}{14}\] done clear
C) \[-4\] done clear
D) \[-\frac{1}{2}\] done clear
View Answer play_arrowquestion_answer168) The approximate value of \[{{(0.009)}^{1/3}}\] is
A) \[0.2\] done clear
B) \[0.2083\] done clear
C) \[0.0032\] done clear
D) \[0.0083\] done clear
View Answer play_arrowquestion_answer169) If \[\left\{ \begin{matrix} \frac{(1-\cos \,4x)}{{{x}^{2}}}, & if & x<0 \\ a, & if & x=0, \\ \frac{\sqrt{x}}{\sqrt{(16+\sqrt{x})}-4}, & if & x>0 \\ \end{matrix} \right.\]then \[f(x)\] is continuous at \[x=0,\] for a
A) \[4\] done clear
B) \[\sqrt{32}\] done clear
C) \[8\] done clear
D) \[16\] done clear
View Answer play_arrowquestion_answer170) The value of \[\int_{0}^{\pi /2}{\frac{dx}{1+\tan x}}\] is
A) \[\frac{\pi }{2}\] done clear
B) \[0\] done clear
C) \[\frac{\pi }{4}\] done clear
D) \[\frac{\pi }{8}\] done clear
View Answer play_arrowquestion_answer171) Evaluate \[\int{\frac{3x-2}{(x+3){{(x+1)}^{2}}}}\,dx.\]
A) \[\frac{11}{4}\log \,[|x+1|\,|x+3|]+\frac{5}{2(x+1)}+C\] done clear
B) \[\frac{11}{4}\log \,\left| \frac{x+3}{x+1} \right|+\frac{1}{x+1}+C\] done clear
C) \[\frac{11}{4}\log \,|x+2|+\frac{5}{2}(x+3)+\frac{1}{x+1}+C\] done clear
D) \[\frac{11}{4}\log \,\left| \frac{x+1}{x+3} \right|+\frac{5}{2(x+1)}+C\] done clear
View Answer play_arrowquestion_answer172) The general solution of the linear differential equation \[\frac{dy}{dx}+\sec \,x.\,y=\tan x\] \[\left( 0\le x\le \frac{\pi }{2} \right)\]is
A) \[y=-x\,{{(\sec x+\tan x)}^{-1}}+\frac{C}{\sec x+\tan x}+1\] done clear
B) \[y=x+\frac{C}{\sec x+\tan x}+\frac{1}{\tan x}\] done clear
C) \[y=\frac{x+1}{\sec x+\tan x}+C\] done clear
D) \[y=x+\sec x-\tan \,x+C\] done clear
View Answer play_arrowquestion_answer173) On solving the differential equation \[{{x}^{2}}y\,dx-({{x}^{3}}+{{y}^{2}})dy=0,\]the value of \[\log \,y\] is
A) \[\frac{{{x}^{3}}}{3{{y}^{3}}}+C\] done clear
B) \[\frac{{{x}^{2}}}{{{y}^{2}}}+C\] done clear
C) \[\frac{{{x}^{2}}}{3{{y}^{3}}}+C\] done clear
D) \[\frac{{{x}^{3}}}{{{x}^{3}}+{{y}^{3}}}+C\] done clear
View Answer play_arrowquestion_answer174) The value of \[\int{\frac{2+\sin x}{1+\cos x}}\,{{e}^{x/2}}dx\] is
A) \[2.{{e}^{x/2}}\,\tan \frac{x}{2}+C\] done clear
B) \[{{e}^{x/2}}\,\tan \,x+C\] done clear
C) \[\frac{1}{2}{{e}^{x/2}}\,\sin x+C\] done clear
D) \[\frac{1}{2}\,\,{{e}^{x/2}}\,\sin \frac{x}{2}+C\] done clear
View Answer play_arrowquestion_answer175) On evaluation, the value of \[\int_{0}^{4}{f(x)\,\,dx,}\]where \[f(x)=\left\{ \begin{matrix} |x-2|+2, & x\le 2 \\ {{x}^{2}}-2, & x>2 \\ \end{matrix} \right.\] is
A) \[\frac{56}{3}\] done clear
B) \[\frac{60}{3}\] done clear
C) \[\frac{66}{3}\] done clear
D) \[\frac{62}{3}\] done clear
View Answer play_arrowquestion_answer176) The particular solution of the differential equation \[\frac{dy}{dx}+y\,\cot \,x=2x+{{x}^{2}}\,\cot \,x,\]such that \[y(\pi /2)=0\] is
A) \[y=\frac{{{\pi }^{2}}}{4\,\cos \,x},(x\ne 0)\] done clear
B) \[y={{x}^{2}}-\frac{\pi }{2}\tan x\] done clear
C) \[y=\frac{2x}{\sin x}+\frac{1}{{{x}^{2}}},(x\ne 0)\] done clear
D) \[y={{x}^{2}}-\frac{{{\pi }^{2}}}{4\sin x}(\sin x\ne 0)\] done clear
View Answer play_arrowquestion_answer177) The differential equation corresponding to the equation\[{{y}^{2}}=a(b-{{x}^{2}})\] where a, b are constants is
A) \[{{y}^{2}}\frac{{{d}^{2}}y}{d{{x}^{2}}}=a\left( b-\frac{dy}{dx}+x \right)\] done clear
B) \[xy\frac{{{d}^{2}}y}{d{{x}^{2}}}+x{{\left( \frac{dy}{dx} \right)}^{2}}-y\frac{dy}{dx}=0\] done clear
C) \[y{{\left( \frac{dy}{dx} \right)}^{2}}-x\frac{dy}{dx}+1=0\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer178) The area bounded by the circle \[{{x}^{2}}+{{y}^{2}}=16\] and the line \[y=x\]in the first quadrant is
A) \[4\pi \,\,\,sq\,units\] done clear
B) \[8\pi \,\,\,sq\,units\] done clear
C) \[2\pi \,\,\,sq\,units\] done clear
D) \[\pi \,\,\,sq\,units\] done clear
View Answer play_arrowquestion_answer179) The focal distance of the point \[(x,y)\] from the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1,\,\,\,\,a>b\] is
A) \[a\pm \sqrt{1-\frac{{{b}^{2}}}{{{a}^{2}}}}y\] done clear
B) \[b\pm \sqrt{1-\frac{{{a}^{2}}}{{{b}^{2}}}}y\] done clear
C) \[a\pm \sqrt{1-\frac{{{b}^{2}}}{{{a}^{2}}}}\,x\] done clear
D) \[b\pm \sqrt{1-\frac{{{a}^{2}}}{{{b}^{2}}}}\,x\] done clear
View Answer play_arrowquestion_answer180) The lines \[3x+y-14=0\] \[\lambda x-2y=0\] \[3x-8y+4=0\] are concurrent. Then, the value of \[\lambda \] is
A) \[1\] done clear
B) \[2\] done clear
C) \[3\] done clear
D) \[4\] done clear
View Answer play_arrowquestion_answer181) The equation of a straight line which cuts off intercept on X-axis which is twice that on y-axis and is at a unit distance from . origin is given by
A) \[x+y=0\] done clear
B) \[x+2y\pm \sqrt{2}=0\] done clear
C) \[x+2y\pm \sqrt{5}=0\] done clear
D) \[x+\sqrt{5}y\pm 2=0\] done clear
View Answer play_arrowquestion_answer182) The equation of a straight line upon which the length of the perpendicular from the origin is 5 and slope of this perpendicular is \[3/4\] is
A) \[2x+5y\pm 16=0\] done clear
B) \[4x+3y\pm 25=0\] done clear
C) \[4x+3y\pm 5=0\] done clear
D) \[2x+5y\pm 4=0\] done clear
View Answer play_arrowquestion_answer183) The radius of the circle \[{{(x\,\cos \theta +y\sin \theta -a)}^{2}}+(x\,\sin \theta -y\cos \theta )={{k}^{2}}\] is
A) \[{{a}^{2}}+{{b}^{2}}-{{k}^{2}}\] done clear
B) \[a\,sin\,\theta -b\,\cos \,\theta \] done clear
C) \[{{a}^{2}}+{{b}^{2}}\] done clear
D) \[k\] done clear
View Answer play_arrowquestion_answer184) The locus of a point which moves in a plane such that its distance from a fixed point in the plane is always equal to its distance from a fixed straight line in the same plane represents
A) a circle done clear
B) a parabola done clear
C) a hyperbola done clear
D) an ellipse done clear
View Answer play_arrowquestion_answer185) The eccentricity of the ellipse \[25{{x}^{2}}+9{{y}^{2}}-150x-90y+225=0\]is
A) \[\frac{4}{5}\] done clear
B) \[\frac{3}{5}\] done clear
C) \[\frac{4}{15}\] done clear
D) \[\frac{9}{5}\] done clear
View Answer play_arrowquestion_answer186) The mean deviation from the median is
A) equal to that measured from another value done clear
B) maximum, if all observations are positive done clear
C) greater than that measured from any other value done clear
D) less than measured from any other value done clear
View Answer play_arrowquestion_answer187) The variance of the data
\[x:1\] | \[a\] | \[{{a}^{2}}\] | ?.. | \[{{a}^{n}}\] |
\[f{{:}^{n}}{{C}_{0}}\] | \[^{n}{{C}_{1}}\] | \[^{n}{{C}_{2}}\] | ?.. | \[^{n}{{C}_{n}}\] |
A) \[{{\left( \frac{1+{{a}^{2}}}{2} \right)}^{n}}-{{\left( \frac{1+a}{2} \right)}^{2n}}\] done clear
B) \[{{\left( \frac{1+{{a}^{2}}}{2} \right)}^{2n}}-{{\left( \frac{1+a}{2} \right)}^{n}}\] done clear
C) \[{{\left( \frac{1+a}{2} \right)}^{2n}}-{{\left( \frac{1+{{a}^{2n}}}{2} \right)}^{n}}\] done clear
D) \[{{\left( \frac{1+a}{2} \right)}^{n}}-{{\left( \frac{1+{{a}^{2n}}}{2} \right)}^{n}}\] done clear
View Answer play_arrowquestion_answer188) An analysis of the weekly wages paid to workers in two firms A and B, belonging to the same industry gives the following results
Firm A | Firm B | |
Number of wage earners | \[586\] | \[648\] |
Average of weekly wages | Rs. \[52.5\] | Rs. \[47.5\] |
Variance of the distribution of wages | \[100\] | \[121\] |
A) \[A,\,B\] done clear
B) \[B,\,A\] done clear
C) \[B,\,B\] done clear
D) \[A,\,A\] done clear
View Answer play_arrowquestion_answer189) If the standard deviation of a variable X is \[\sigma ,\] then the standard deviation of variable \[\frac{aX+b}{c}\]is
A) \[a\sigma \] done clear
B) \[\frac{a}{c}\sigma \] done clear
C) \[\left| \frac{a}{c} \right|\sigma \] done clear
D) \[\frac{a\sigma +b}{c}\] done clear
View Answer play_arrowquestion_answer190) A bag contains 50 tickets numbered 1, 2, 3, ...,50 of which five are drawn at random and arranged in ascending order of magnitude \[({{x}_{1}}<{{x}_{2}}<{{x}_{3}}<{{x}_{4}}<{{x}_{5}}),\] then the probability that \[{{x}_{3}}=30\] is
A) \[\frac{^{29}{{C}_{2}}{{\times }^{20}}{{C}_{2}}}{^{50}{{C}_{5}}}\] done clear
B) \[\frac{^{30}{{C}_{1}}{{\times }^{29}}{{C}_{1}}}{^{50}{{C}_{5}}}\] done clear
C) \[\frac{^{5}{{C}_{1}}{{\times }^{50}}{{C}_{2}}}{^{50}{{C}_{5}}}\] done clear
D) \[\frac{^{50}{{C}_{2}}{{\times }^{29}}{{C}_{1}}}{^{50}{{C}_{5}}}\] done clear
View Answer play_arrowquestion_answer191) If S is the sample space and \[P(A)=\frac{1}{3}\,P(B)\]and \[S=A\cup B,\] where A and B are two mutually exclusive events, then \[P(A)\] is equal to
A) \[\frac{1}{4}\] done clear
B) \[\frac{1}{2}\] done clear
C) \[\frac{3}{4}\] done clear
D) \[\frac{3}{8}\] done clear
View Answer play_arrowquestion_answer192) Five persons entered the lift cabin on the ground floor of an eight floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first, then the probability of all 5 persons leaving at different floors is
A) \[\frac{^{7}{{P}_{5}}}{{{7}^{5}}}\] done clear
B) \[\frac{{{7}^{5}}}{^{7}{{P}_{5}}}\] done clear
C) \[\frac{6}{^{6}{{P}_{5}}}\] done clear
D) \[\frac{^{5}{{P}_{5}}}{{{5}^{5}}}\] done clear
View Answer play_arrowquestion_answer193) In a three dimensional space the equation \[{{x}^{2}}-5x+6=0\]represents
A) points done clear
B) planes done clear
C) curves done clear
D) None of these done clear
View Answer play_arrowquestion_answer194) If \[(3,\,4,-1)\] and \[(-1,\,2,3)\] be end points of the diameter of a sphere, then the radius of the sphere is
A) \[2\] done clear
B) \[3\] done clear
C) \[6\] done clear
D) \[7\] done clear
View Answer play_arrowquestion_answer195) If the position vector a of a point \[(12,\,\,n)\] is such that \[|a|=13,\] then the value of \[\pi \] is
A) \[\pm \,\,3\] done clear
B) \[\pm \,\,4\] done clear
C) \[\pm \,\,5\] done clear
D) \[\pm \,\,6\] done clear
View Answer play_arrowquestion_answer196) The following lines are \[r=(\hat{i}+\hat{j})+\lambda (\hat{i}+2\hat{j}-\hat{k}),\] and \[r=(\hat{i}+\hat{j})+\mu (-\hat{i}+\hat{j}-2\hat{k})\]
A) collinear done clear
B) skew-lines done clear
C) coplanar lines done clear
D) parallel lines done clear
View Answer play_arrowquestion_answer197) The position vector of a point R which divides the line joining \[P(6,\,3,-2)\]and \[Q(3,1,-4)\]Q(3,1, - 4) in the ratio \[2:1\] externally is
A) \[\hat{i}+3\hat{j}-2\hat{k}\] done clear
B) \[3\hat{i}-\hat{k}\] done clear
C) \[-\hat{j}-6\hat{k}\] done clear
D) \[2\hat{i}-\hat{j}\] done clear
View Answer play_arrowquestion_answer198) If \[a=\hat{i}+2\hat{j}-3\hat{k}\] and \[b=2\hat{i}+4\hat{j}+9\hat{k},\] then the unit vector parallel to \[a+b\] is
A) \[\frac{1}{6}\,5\hat{i}-\hat{k}\] done clear
B) \[\frac{1}{\sqrt{35}}(5\hat{i}+3\hat{j}-\hat{k})\] done clear
C) \[\frac{1}{5}(3\hat{j}-5\hat{k})\] done clear
D) \[3\hat{i}+6\hat{j}-6\hat{k}\] done clear
E) None of these done clear
View Answer play_arrowquestion_answer199) The angle between the lines \[\frac{x-5}{-3}=\frac{y+3}{-4}=\frac{z-7}{0},\,\frac{x}{1}=\frac{y-1}{-2}=\frac{z-6}{2}\]is
A) \[\frac{\pi }{3}\] done clear
B) \[{{\tan }^{-1}}\left( \frac{1}{5} \right)\] done clear
C) \[{{\cos }^{-1}}\left( \frac{1}{3} \right)\] done clear
D) \[\frac{\pi }{2}\] done clear
View Answer play_arrowquestion_answer200) If \[|a|=2,\,\,|b|=5\] and \[|a\times b|=8,\] then \[a\,.\,b\] is equal to
A) \[3\] done clear
B) \[4\] done clear
C) \[5\] done clear
D) \[6\] done clear
View Answer play_arrowquestion_answer201) Suppose \[{{A}_{1}},{{A}_{2}}.....,{{A}_{30}}\]are thirty sets each with five elements and \[{{B}_{1}},{{B}_{2}}.....,{{B}_{n}}\] are 'n' sets each with three elements. Let \[\underset{i=1}{\mathop{\overset{30}{\mathop{\cup }}\,}}\,\,\,{{A}_{i}}=\underset{j=1}{\mathop{\overset{n}{\mathop{\cup }}\,}}\,\,\,\,{{B}_{j}}=S.\] Assume that each element of S belongs to exactly 10 of \[{{A}_{i}}s\] and exactly 9 of \[{{B}_{j}}s,\]then the value of x is
A) \[90\] done clear
B) \[15\] done clear
C) \[9\] done clear
D) 45 done clear
View Answer play_arrowquestion_answer202) A survey shows that 63% of the Americans like cheese whereas 76% like apples. If x% of the Americans like both cheese and apples, then the value of x is
A) \[39\le x\le 63\] done clear
B) \[63\] done clear
C) \[39\] done clear
D) \[139\ge x\] done clear
View Answer play_arrowquestion_answer203) The cartesian product \[A\times A\] has 9 elements among which are found \[(-1,0)\] and \[(0,1),\] then set A is equal to
A) \[\{1,\,\,0\}\] done clear
B) \[\{1,\,\,-1,\,\,\,0\}\] done clear
C) \[\{\,0,\,\,-1\}\] done clear
D) \[\{1,\,\,-1\}\] done clear
View Answer play_arrowquestion_answer204) If \[S=\{(a,\,b):b=|a-1|,a\in Z\] and \[|a|<3\},\] where Z denotes the set of integers. Then, the range set of S is
A) \[\{1,\,2,\,3\}\] done clear
B) \[\{-1,\,2,\,3,\,1\}\] done clear
C) \[\{0,\,1,\,2,\,3,\,4\}\] done clear
D) \[\{-\,1,-\,2,-\,3,-\,4\}\] done clear
View Answer play_arrowquestion_answer205) Pisa relation from \[\{11,\,12,\,13\}\]to \[\{8,\,10,\,12\}\] defined by \[y=x-3\]. Then, \[{{R}^{-1}}\] is
A) \[\{(8,\,11),\,(10,13)\}\] done clear
B) \[\{(11,\,8),\,(13,10)\}\] done clear
C) \[\{(10,\,13),\,(8,11),\,(12,\,10)\}\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer206) The quotient of the identity function by the reciprocal function is given by
A) \[{{x}^{2}}\,\forall \,\,x\,\in \,R\] (set of real numbers) done clear
B) \[\frac{1}{{{x}^{2}}}\,\,\forall \,\,x\in R-\{0\}\] done clear
C) \[{{x}^{2}}\,\,\forall \,\,x\in R-\{0\}\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer207) Which of the following is not a function?
A) \[\{(x,y):\,x,\,y\,\in R,{{x}^{2}}=y\}\] done clear
B) \[\{(x,y):\,x,\,y\,\in R,{{y}^{2}}=x\}\] done clear
C) \[\{(x,y):\,x,\,y\,\in R,x={{y}^{3}}\}\] done clear
D) \[\{(x,y):\,x,\,y\,\in R,y={{x}^{3}}\}\] done clear
View Answer play_arrowquestion_answer208) If \[(1+i)\,(2i+1)\,(1+3i)....(1+ni)=x+iy,\] then \[2.5.10....(1+{{n}^{2}})\] is equal to
A) \[1\] done clear
B) \[i\] done clear
C) \[{{x}^{2}}+{{y}^{2}}\] done clear
D) \[1+{{n}^{2}}\] done clear
View Answer play_arrowquestion_answer209) The value of \[|{{z}_{1}}|=|{{z}_{2}}|=...=|{{z}_{n}}|=1,\] then \[|{{z}_{1}}+{{z}_{2}}+{{z}_{3}}+....+{{z}_{n}}|\] is (where, \[{{z}_{1}}\] is complex number with \[i=1\] to n)
A) \[\left| \frac{1}{{{z}_{1}}+{{z}_{2}}+{{z}_{3}}+....+{{z}_{n}}} \right|\] done clear
B) \[\left| \frac{1}{{{z}_{1}}}+\frac{1}{{{z}_{2}}}+\frac{1}{{{z}_{3}}}+...+\frac{1}{{{z}_{n}}} \right|\] done clear
C) \[\left| \frac{1}{{{z}_{1}}{{z}_{2}}}+\frac{1}{{{z}_{3}}{{z}_{4}}}+....+\frac{1}{{{z}_{n-1}}{{z}_{n}}} \right|\] done clear
D) \[1\] done clear
View Answer play_arrowquestion_answer210) The non-zero solutions of the equation \[{{z}^{2}}+|z|=0,\] where z is a complex number, are
A) \[\pm \,\,1\] done clear
B) \[\pm \,\,i\] done clear
C) \[1\pm \,\,i\] done clear
D) \[\pm \,\,1\pm i\] done clear
View Answer play_arrowquestion_answer211) Which of the following shaded regions represents the solution set of in equation \[|x-y|\ge 1\]
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer212) The values of x for which \[-11\le 4x-3\le 13\]is
A) \[-4\le x\le 5\] done clear
B) \[-2\le x\le 4\] done clear
C) \[-8\le x\le 16\] done clear
D) \[-11\le x\le 10\] done clear
View Answer play_arrowquestion_answer213) The solution set of the following linear in equations \[x-2y\ge 0;\,\,\,2x-y\le -2;\,\,x\ge 0,y\ge 0\]is given by
A) \[[1,\,\,2]\] done clear
B) Null set done clear
C) \[x\ge 1\] done clear
D) Set of real numbers done clear
View Answer play_arrowquestion_answer214) For the given LPP (Linear Programming Problem) max \[z=5x+3y\] \[2x+y\le 12\] \[3x+2y\le 20\] \[x\ge 0,\,y\ge 0\] the optimal solution set is
A) \[(0,\,\,0)\] done clear
B) \[(6,\,\,0)\] done clear
C) \[(4,\,\,4)\] done clear
D) \[(0,\,\,10)\] done clear
View Answer play_arrowquestion_answer215) A dietician wishes to mix together two kinds of food X and Y in such a way that the mixture contains atleast 10 units of vitamin A, 12 units of vitamin B and 8 units of vitamin C. The vitamin content of 1 kg food is given below
Food | Vitamin A | Vitamin B | Vitamin C |
x | 1 | 2 | 3 |
y | 2 | 2 | 1 |
A) \[Rs.\,100\] done clear
B) \[Rs.\,98\] done clear
C) \[Rs.\,116\] done clear
D) \[Rs.\,112\] done clear
View Answer play_arrowquestion_answer216) Which of the following is a purely imaginary term of the sequence \[8-6i,\] \[7-4i,\,6-2i,...\]?
A) 9th term done clear
B) 2nd term done clear
C) 4th term done clear
D) 8 term done clear
View Answer play_arrowquestion_answer217) If \[{{S}_{n}}\] denotes the sum of first n terms of AP \[<{{a}_{n}}>,\]such that \[\frac{{{S}_{m}}}{{{S}_{n}}}=\frac{{{m}^{2}}}{{{n}^{2}}},\] then \[\frac{{{a}_{m}}}{{{a}_{n}}}\] is equal to
A) \[\frac{2m+1}{2n+1}\] done clear
B) \[\frac{2m-1}{2n-1}\] done clear
C) \[\frac{m-1}{n-1}\] done clear
D) \[\frac{m+1}{n+1}\] done clear
View Answer play_arrowquestion_answer218) The sum of all possible products of the first n natural numbers taken two by two is
A) \[\frac{n(n+1)}{2}\] done clear
B) \[\frac{n(n+1)(n+2)}{6}\] done clear
C) \[\frac{n({{n}^{2}}-1)(3n+2)}{12}\] done clear
D) \[2{{n}^{3}}+3{{n}^{2}}-1\] done clear
View Answer play_arrowquestion_answer219) How many four digit numbers are there with distinct digits?
A) \[5040\] done clear
B) \[4536\] done clear
C) \[30240\] done clear
D) \[5274\] done clear
View Answer play_arrowquestion_answer220) If \[^{n}{{C}_{r}}{{+}^{n}}{{C}_{r+1}}{{=}^{n+1}}{{C}_{x}},\]then x is equal to
A) \[r\] done clear
B) \[r-1\] done clear
C) \[n\] done clear
D) \[r+1\] done clear
View Answer play_arrowquestion_answer221) The coefficient of the term independent of x in the expansion \[\left( \frac{x+1}{{{x}^{2/3}}-{{x}^{1/3}}+1}-\frac{x-1}{x-{{x}^{1/2}}} \right)\]is
A) \[8064\] done clear
B) \[210\] done clear
C) \[-546\] done clear
D) \[5040\] done clear
View Answer play_arrowquestion_answer222) There are 12 points in a plane. The number of straight lines joining any two of them, when 3 of them are collinear, is
A) \[60\] done clear
B) \[63\] done clear
C) \[64\] done clear
D) \[65\] done clear
View Answer play_arrowquestion_answer223) Which of the following is the correct principle of Mathematical induction?
A) Let \[P(n)\] be a statement such that n be any integer and \[P(1)\] is true. Also. \[P(m)\] is true for m, any natural number, then \[P(n)\] is true for all integers n done clear
B) Let \[P(n)\] be a statement involving natural number n such that \[P(1)\] is true and\[P(m)\] is true whenever \[P(n)\] is true for every \[n\ge m,\]then \[P(n)\] is true for all \[n\in N\] (set of natural numbers) done clear
C) Let\[P(n)\] be a statement where \[n\in N\]such that\[P(1)\] is true and \[P(n),\,P(n+1)\]also holds, then \[P(n)\] is true \[\forall n\in N\] done clear
D) Let \[P(n)\] be a statement involving the natural number n, such trial P(1) is true and s\[P(m+1)\] is true for all \[n\le m\]Then, \[P(n)\] is true for all \[n\in N\] done clear
View Answer play_arrowquestion_answer224) If \[x>0\]and \[{{\cot }^{-1}}\,(x+2)=\frac{\pi }{12},\] then the value of x is
A) \[2\sqrt{3}\] done clear
B) \[\sqrt{3}\] done clear
C) \[\frac{1}{\sqrt{3}}\] done clear
D) \[\sqrt{3}-1\] done clear
View Answer play_arrowquestion_answer225) If \[\cot \,\theta (1+\sin \theta )=4m\] and \[\cot \theta (1-\sin \theta )=4n,\] then \[{{({{m}^{2}}-{{n}^{2}})}^{2}}\]is equal to
A) \[mn\] done clear
B) \[\tan \theta \] done clear
C) \[1\] done clear
D) \[\frac{m+n}{4}\] done clear
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