Solved papers for RAJASTHAN ­ PET Rajasthan PET Solved Paper-2006

done Rajasthan PET Solved Paper-2006

  • 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) \[-\left( \frac{4v}{234} \right)\]

    B) \[\left( \frac{v}{234} \right)\]

    C) \[\left( \frac{v}{238} \right)\]

    D) \[\frac{4v}{238}\]

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  • question_answer2) \[_{90}{{X}^{200}}\,\xrightarrow[{}]{{}}{{\,}_{80}}{{Y}^{168}}.\]In this reaction how many \[\alpha \] and \[\beta \]-particles are emitted?

    A) 6, 8

    B) 8, 6

    C) 12, 8

    D) 8, 12

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  • 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) \[25{{s}^{-1}}\]

    B) \[80{{s}^{-1}}\]

    C) \[625{{s}^{-1}}\]

    D) \[20{{s}^{-1}}\]

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  • question_answer4) When hydrogen atom makes a transition from ground state to excited state, then

    A) its kinetic and potential energies decrease.

    B) potential energy increases and kinetic energy decreases

    C) potential energy decreases and kinetic energy increases

    D) its kinetic and potential energies increase

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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

    B) continuous spectrum

    C) characteristic radiation

    D) white radiation

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  • question_answer6) If we consider wavelength of electron and photon are same. They will have same

    A) velocity

    B) energy

    C) momentum

    D) angular momentum

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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

    B) 4 N/C

    C) \[\sqrt{3}\] N/C

    D) 20 N/C

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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\[\Omega \]

    B) 2\[\Omega \]

    C) 4\[\Omega \]

    D) 1\[\Omega \]

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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

    B) 40 J

    C) 4000 J

    D) 400 J

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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

    B) 25.2 V

    C) 2.52 V

    D) 0.252 V

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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

    B) \[i\]oscillates between 1mA and 2mA

    C) \[i=1\text{ }mA\] at all t

    D) at \[t=0,i=2\text{ }mA\]and with time it goes to 1mA

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  • question_answer12) Dimension of RC is

    A) square of time

    B) equal to time

    C) inverse of time

    D) inverse of square of time

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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

    B) 1, 2, 3, 4, 5

    C) 2, 3, 5

    D) 1, 2, 3

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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) \[\frac{{{A}_{1}}+{{A}_{2}}}{2}\]

    B) \[\sqrt{{{A}_{1}}{{A}_{2}}}\]

    C) \[{{\left[ \frac{\sqrt{{{A}_{1}}}\,+\,\sqrt{{{A}_{2}}}}{2} \right]}^{2}}\]

    D) \[{{\left[ \frac{1}{{{A}_{1}}}+\frac{1}{{{A}_{2}}} \right]}^{-1}}\]

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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

    B) 600 K

    C) 400 K

    D) 500 K

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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

    B) 1 : 2

    C) 1 : 8

    D) 1 : 3

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  • question_answer17) Which of the following is used to produce radio waves of constant amplitude

    A) oscillator

    B) FET

    C) Rectifier

    D) Amplifier

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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) \[2\times {{10}^{-4}}m\]

    B) \[6\times {{10}^{-3}}m\]

    C) \[2\times {{10}^{-3}}m\]

    D) \[4\times {{10}^{-4}}m\]

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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) \[{{t}_{1}}<{{t}_{2}}<{{t}_{3}}\]

    B) \[{{t}_{1}}>{{t}_{2}}>{{t}_{3}}\]

    C) \[{{t}_{2}}<{{t}_{1}}<{{t}_{3}}\]

    D) \[{{t}_{1}}>{{t}_{2}}>{{t}_{3}}\]

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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

    B) \[16\times {{10}^{24}}N\]

    C) \[25\times {{10}^{16}}N\]

    D) \[36\times {{10}^{21}}N\]

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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

    B) 3.75 m

    C) 4.00 m

    D) 1.25 m

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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

    B) not depend upon r

    C) be inversely proportional to r

    D) be proportional to\[{{r}^{2}}\]

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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) \[mgH\]

    B) \[\sqrt{2gH}\]

    C) \[2gH\]

    D) zero

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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) \[\rho =\left[ \frac{g}{G} \right]/\left[ \frac{4\pi }{3}R_{e}^{2} \right]\]

    B) \[\rho =\left[ \frac{g}{G} \right]/\left[ \frac{4\pi }{3}R_{e}^{3} \right]\]

    C) \[\rho =\left[ \frac{g}{G} \right]/\left[ \frac{4\pi }{3}R_{e}^{3} \right]\]

    D) \[\rho =\left[ \frac{g}{G} \right]/\left[ \frac{4\pi }{3}R_{e}^{{}} \right]\]

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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

    B) perpendicular to position vector

    C) along the origin

    D) along to opposite of origin

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  • 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\[\left[ L{{T}^{-1}} \right]\]

    B) \[\left[ {{M}^{0}}L{{T}^{-1}} \right]and\left[ {{T}^{-1}} \right]\]

    C) \[\left[ {{M}^{0}}L{{T}^{-1}} \right]and\,\left[ T \right]\]

    D) \[\left[ {{M}^{0}}L{{T}^{0}} \right]and\,\left[ {{T}^{-1}} \right]\]

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  • 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?





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  • 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) \[4({{x}_{1}}+{{x}_{2}})\]

    B) \[({{x}_{1}}{{x}_{2}})\]

    C) \[({{x}_{1}}+{{x}_{2}})\]

    D) \[4({{x}_{2}}{{x}_{1}})\]

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  • 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

    B) 3R/16

    C) 16/3 R

    D) 9R/16

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  • question_answer30) The bond present in conductors are

    A) covalent

    B) metallic

    C) van der Waals

    D) ionic

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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) \[\lambda \sqrt{\frac{m}{M}}\]

    B) \[\frac{\lambda M}{m}\]

    C) \[\frac{\lambda m}{M}\]

    D) \[\lambda \sqrt{\frac{M}{m}}\]

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  • 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) \[-\frac{Q}{2}\]

    B) \[-\frac{Q}{4}\]

    C) \[+\frac{Q}{4}\]

    D) \[+\frac{Q}{2}\]

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  • 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) \[4\times {{10}^{2}}C\]

    B) \[5\times {{10}^{-2}}C\]

    C) \[2\times {{10}^{-2}}C\]

    D) \[4\times {{10}^{-2}}C\]

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  • 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) \[40\,\Omega \]

    B) \[\frac{40}{3}\Omega \]

    C) \[\frac{5}{2}\,\Omega \]

    D) \[100\,\Omega \]

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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) \[{{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{2}}\]

    B) \[\frac{{{R}_{1}}}{{{R}_{2}}}\]

    C) \[{{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{3}}\]

    D) \[{{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{1/2}}\]

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  • 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

    B) zero

    C) 40 W

    D) 20 W

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  • 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

    B) 2

    C) 1/2

    D) 1

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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\[\overset{o}{\mathop{\text{A}}}\,\]

    B) 25\[\overset{o}{\mathop{\text{A}}}\,\]

    C) 2.5\[\overset{o}{\mathop{\text{A}}}\,\]

    D) zero

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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

    B) 0.2 s

    C) 0.4 s

    D) 0.04 s

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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

    B) increase to 0.75 ml

    C) decrease to 0.75 ml

    D) increase to 1.50 ml

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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

    B) 8 Pa

    C) 16 Pa

    D) 10 Pa

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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

    B) zero

    C) 1/2

    D) 1/4

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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

    B) 60 cm and 90 cm

    C) 20 cm and 40 cm

    D) 40 cm and 60 cm

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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) \[v=\frac{1}{2R\sqrt{Gm}}\]

    B) \[v=\sqrt{\frac{4Gm}{R}}\]

    C) \[v=\sqrt{\frac{Gm}{2R}}\]

    D) \[v=\frac{1}{2}\sqrt{\frac{Gm}{R}}\]

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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) \[{{I}_{BC}}>{{I}_{AB}}\]

    B) \[{{I}_{CA}}\]is maximum

    C) \[{{I}_{AB}}>{{I}_{BC}}\]

    D) \[{{I}_{AB}}+\text{ }{{I}_{BC}}={{I}_{CA}}\]

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  • 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) \[0{}^\circ \]

    B) \[30{}^\circ \]

    C) \[60{}^\circ \]

    D) \[90{}^\circ \]

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  • 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) \[{{v}_{0}}t+\frac{1}{3}b{{t}^{2}}\]

    B) \[{{v}_{0}}t-\frac{1}{3}b{{t}^{2}}\]

    C) \[{{v}_{0}}t+\frac{1}{6}b{{t}^{3}}\]

    D) \[{{v}_{0}}t+\frac{1}{2}b{{t}^{3}}\]

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  • question_answer48) A flywheel is rotating at the rate of 120 revolution per minute. The angular acceleration of the flywheel will be

    A) \[4\pi \,rad/{{s}^{2}}\]

    B) \[4{{\pi }^{2}}\,rad/{{s}^{2}}\]

    C) \[2\pi \,rad/{{s}^{2}}\]

    D) \[\pi /2\,\,rad/{{s}^{2}}\]

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  • 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) \[-6\,\widehat{i}\,+6\widehat{j}-12\,\widehat{k}\]

    B) \[-17\,\widehat{i}\,+6\widehat{j}-13\,\widehat{k}\]

    C) \[6\,\widehat{i}\,+6\widehat{j}-12\,\widehat{k}\]

    D) \[\widehat{i}\,-6\widehat{j}-5\,\widehat{k}\]

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  • 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) \[x={{\left( \frac{2a}{b} \right)}^{1/6}}\]

    B) \[x={{\left( \frac{a}{2b} \right)}^{1/6}}\]

    C) \[x=0\]

    D) \[x={{\left( \frac{11a}{b} \right)}^{1/6}}\]

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  • question_answer51) Chloroform is obtained by the partial reduction of

    A) \[CC{{l}_{4}}\]

    B) \[C{{H}_{4}}\]

    C) \[CHC{{l}_{3}}\]

    D) \[C{{H}_{3}}OH\]

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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

    B) I and IV

    C) I and III

    D) II, III and IV

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  • question_answer53) Identify the correct statement.

    A) Plaster of Paris is obtained by the partial oxidation of gypsum.

    B) The percentage of plaster of calcium in gypsum is less than plaster of Paris.

    C) Gypsum is obtained by the plaster of Paris on heating.

    D) Plaster of Paris is obtained by the addition of water in gypsum.

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  • 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

    B) 31

    C) 34

    D) 33

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  • 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.

    B) \[CaC{{l}_{2}}\]helps in electrical conduction.

    C) this mixture has less melting point than \[NaCl\].

    D) \[C{{a}^{2+}}\]can displace Na from\[NaCl\].

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  • 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.

    B) its pressure is greater than\[{{p}_{c}}\]at less temperature from\[{{T}_{c}}\].

    C) its temperature is greater than critical temperature \[{{T}_{c}}\].

    D) its pressure is greater than critical pressure.

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  • question_answer57) The correct order of\[O-O\]bond length in \[{{O}_{2}},{{H}_{2}}{{O}_{2}}\]and\[{{O}_{3}}\].

    A) \[{{H}_{2}}{{O}_{2}}>{{O}_{3}}>{{O}_{2}}\]

    B) \[{{O}_{2}}>{{O}_{3}}>{{H}_{2}}{{O}_{2}}\]

    C) \[{{O}_{2}}>{{H}_{2}}{{O}_{2}}>{{O}_{3}}\]

    D) \[{{O}_{3}}>{{H}_{2}}{{O}_{2}}>{{O}_{2}}\]

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  • 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

    B) 38

    C) 12

    D) 18

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  • question_answer59) Which of the following compound exists in optically active forms?

    A) \[C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{CH}}\,-C{{H}_{2}}OH\]

    B) \[C{{H}_{3}}-C{{H}_{2}}-C{{H}_{2}}OH\]

    C) \[C{{H}_{3}}C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{CH}}\,-C{{H}_{3}}\]

    D) \[C{{H}_{3}}{{(C{{H}_{2}})}_{3}}-C{{H}_{2}}OH\]

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  • 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

    B) decreasing lattice energy

    C) increasing molecular weight

    D) more solvation energy for small ions like \[B{{e}^{2+}}\].

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  • question_answer61) A chemical reaction is catalysed by catalyst X. Hence, X

    A) increases the activation energy of reaction.

    B) does not effect the equilibrium constant of reaction.

    C) decreases the velocity constant of reaction.

    D) decreases the enthalpy of reaction.

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  • 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

    B) 143

    C) 142

    D) 146

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  • question_answer63) The formation of bakelite takes place between the reaction of

    A) phenol and formaldehyde

    B) ethylene glycol and dimethyl terephthalate

    C) urea and formaldehyde

    D) tetramethylene glycol and hexa methylene diisocynate

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  • question_answer64) Aluminium (III) chloride forms a dimer because

    A) the ionisation energy of aluminium is high.

    B) it cannot form trimer.

    C) high coordination number can obtain by aluminium.

    D) aluminium belongs to third group.

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  • question_answer65) The solubility of\[AgCl\]will be minimum in which of the following?

    A) \[0.01\text{ }M\text{ }NaCl\]

    B) \[0.01\text{ }M\,CaC{{l}_{2}}\]

    C) pure water

    D) \[0.001\text{ }M\text{ }AgN{{O}_{3}}\]

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  • 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) \[0.17\overset{o}{\mathop{\text{A}}}\,\]

    B) \[1.06\overset{o}{\mathop{\text{A}}}\,\]

    C) \[0.53\overset{o}{\mathop{\text{A}}}\,\]

    D) \[0.265\overset{o}{\mathop{\text{A}}}\,\]

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  • question_answer67) Mercury is the only metal which is liquid at \[0{}^\circ C\]because

    A) high vapour pressure

    B) high ionisation energy and weak metallic bond

    C) low ionisation potential

    D) high atomic weight

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  • 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

    B) has serum protein which acts as buffer

    C) is liquid of body

    D) has iron in the form a part of molecule

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  • 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

    B) 2, 3-dimethyl-2-butene

    C) 2, 3-dimethyl-l-butene

    D) cis and trans isomers of product [b].

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  • 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

    B) 3 and zero

    C) 4 and+2

    D) 3 and +3

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  • 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

    B) small change in the energy of atoms

    C) movement of energy full electron in other part of metal

    D) movement of atoms in metal

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  • 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

    B) 17280yr

    C) 11520 yr

    D) 5760 yr

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  • question_answer73) When benzene diazonium chloride solution is boilded it yields

    A) benzene

    B) phenol

    C) aniline

    D) chlorobenzene

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  • question_answer74) Acetone reacts with chloroform in the presence of\[NaOH\]to give

    A) chloral

    B) chloretone

    C) acetyl chloride

    D) ethyl chloride

    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

    B) 1.92 cm

    C) 7.68 cm

    D) 5.76 cm

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  • 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\[C{{u}_{2}}C{{l}_{2}}\]

    B) \[C{{u}_{2}}C{{l}_{2}}\]and\[NiCl_{4}^{2-}\]

    C) \[TiF_{6}^{2-}\]and\[CoF_{6}^{3-}\]

    D) \[CoF_{6}^{3-}\]and\[NiCl_{4}^{2-}\]

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  • 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.

    B) Ozone layer is harmful for us because it stops the rays which are useful for photosynthesis.

    C) Ozone layer is useful to us because ozone absorbs the ultra-violet rays of sun.

    D) Ozone is a trimolecular linear molecule.

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  • question_answer78) For a spontaneous reaction

    A) \[\Delta S\]should be negative

    B) \[(\Delta H-T.\Delta S)\]should be negative

    C) \[(\Delta H+T.\Delta S)\]should be negative

    D) \[\Delta H\]should be negative

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  • 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

    B) 0

    C) 1

    D) 2

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  • 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

    B) racemic mixture

    C) Leavorotatory

    D) dextrorotatory

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  • 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

    B) carbon and oxygen

    C) carbon

    D) oxygen

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  • question_answer82) According to Raoult's law, the relative lowering in vapour pressure of a solution is equal to

    A) moles of solute

    B) mole fraction of solvent

    C) moles of solvent

    D) mole fraction of solute

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  • 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

    B) 0.0093 mol

    C) 0.186 mol

    D) 0.210 mol

    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

    B) p-methyl phenol, phenol, m-nitrophenol, p-nitrophenol

    C) p-methylphenol, m-nitrophenol, phenol, p-nitrophenol

    D) m-nitrophenol, p-nitrophenol, phenol, p-methylphenol

    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) \[R-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{3}}\]

    B) \[R-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C{{H}_{2}}}}\,\]

    C) \[R-C{{H}_{2}}-CHO\]

    D) \[R-C{{H}_{2}}-C{{H}_{2}}-OH\]

    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

    B) the atom of nitrogen is smaller than boron

    C) \[B-Cl\]bond is more polar than\[N-Cl\]bond

    D) in\[BC{{l}_{3}}\]unpaired electron pair is not present while in\[NC{{l}_{3}}\]a unpaired electron pair is present.

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  • question_answer87) The concentration unit will independent from temperature

    A) weight volume percentage

    B) molarity

    C) normality

    D) molality

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  • 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.

    B) III and IV

    C) I and IV

    D) II and III

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  • question_answer89) The general reactivity order of carbonyl compounds for nucleophilic addition reactions is

    A) \[{{H}_{2}}C=O>{{R}_{2}}C=0>A{{r}_{2}}C=O>RCHO\] \[>ArCHO\]

    B) \[{{H}_{2}}C=O>RCHO>ArCHO>{{R}_{2}}C=O\] \[>A{{r}_{2}}C=O\]

    C) \[ArCHO>A{{r}_{2}}C=O>RCHO>{{R}_{2}}C=O\] \[>{{H}_{2}}C=O\]

    D) \[A{{r}_{2}}C=O>{{R}_{2}}C=O>ArCHO>RCHO\] \[>{{H}_{2}}C=O\]

    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

    B) \[{{C}_{6}}{{H}_{5}}COONa\]

    C) \[{{({{C}_{6}}{{H}_{5}}CO)}_{2}}O\]

    D) \[{{C}_{6}}{{H}_{5}}CHO\]

    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

    B) p-amino-5-heptenoic acid

    C) 5-amino-hex-2-ene carboxylic acid

    D) 3-amino-5-heptenoic acid

    View Answer play_arrow
  • question_answer92) pH of 10 M\[HCl\]solution is

    A) 1

    B) 0

    C) 2

    D) less than zero

    View Answer play_arrow
  • question_answer93) The number of geometrical isomers of \[[Pt{{(N{{H}_{3}})}_{2}}C{{l}_{2}}]\]are

    A) 3

    B) 4

    C) 2

    D) 1

    View Answer play_arrow
  • question_answer94) Which of the following oxide cannot act as reductant?

    A) \[Cl{{O}_{2}}\]

    B) \[S{{O}_{2}}\]

    C) \[NO\]

    D) \[O_{2}^{2-}\]

    View Answer play_arrow
  • question_answer95) Which of the following molecule/ion is paramagnetic?

    A) \[C{{N}^{-}}\]

    B) \[CO\]

    C) \[NO\]

    D) \[O_{2}^{2-}\]

    View Answer play_arrow
  • question_answer96) Maximum explosive is

    A) \[NC{{l}_{3}}\]

    B) \[PC{{l}_{3}}\]

    C) \[AsC{{l}_{3}}\]

    D) All of these

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  • question_answer97) The purest form of iron is

    A) white cast iron

    B) grey cast iron

    C) wrought iron

    D) steel

    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) \[1.57\times {{10}^{-10}}\]

    B) \[1\times {{10}^{-10}}\]

    C) \[3.24\times {{10}^{-6}}\]

    D) \[1\times {{10}^{-6}}\]

    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

    B) Bubo-Blanc reduction

    C) Sabatier and Senderens reduction

    D) Clemmensen reduction

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  • question_answer100) Ethyl amine reacts with nitrous acid to give

    A) ethyl nitrite

    B) ethyl alcohol

    C) nitro ethane

    D) acetic acid

    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) \[{{\log }_{e}}\left( \frac{9}{\sqrt{8}} \right)\]

    B) \[{{\log }_{9}}\left( \frac{9}{\sqrt{8}} \right)\]

    C) \[{{\log }_{(9/2)}}\left( \frac{9}{\sqrt{8}} \right)\]

    D) None of these

    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) \[{{b}^{2}}-4ac\]

    B) \[2{{b}^{2}}-ac\]

    C) \[{{b}^{2}}-ac\]

    D) None of the above

    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) \[{{2}^{6}}\]

    B) \[{{2}^{7}}\]

    C) \[{{3}^{6}}\]

    D) \[{{3}^{7}}\]

    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 \[-1<n<0\]

    B) for\[n>-1\]or\[n<0\]

    C) for all\[n\ne 0,-1\]

    D) for no value of n

    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

    B) 1

    C) \[\infty \]

    D) \[\omega \]

    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]

    B) [2, 4]

    C) [3, 4]

    D) [4,\[\infty \]]

    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) \[2.x!(x+1)!(x+2)!\]

    B) \[2.(x+1)!(x+2)!(x+3)!\]

    C) \[2x!(x+3)!\]

    D) \[2x!(x+1)!\]

    View Answer play_arrow
  • question_answer108) The domain of the function \[f(x)=\sqrt{\frac{(x+1)(x-3)}{(x-2)}}\]is

    A) \[(-1,2)\cup [3,\infty )\]

    B) \[[-1,2)\cup [3,\infty )\]

    C) \[]-\infty ,-1]\cup [3,\infty [\]

    D) None of these

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  • question_answer109) If\[f(x)=\frac{\sin x}{x},\]then the value of\[\underset{x\to \infty }{\mathop{\lim }}\,f(x)\]is

    A) \[-1\]

    B) 0

    C) 1

    D) None of these

    View Answer play_arrow
  • question_answer110) If\[y={{\left( 1+\frac{1}{x} \right)}^{x}},\]then the value of\[\frac{dy}{dx}\]is

    A) \[{{\left( 1+\frac{1}{x} \right)}^{x}}\left[ \log \left( 1+\frac{1}{x} \right)-\frac{1}{1+x} \right]\]

    B) \[{{\left( 1+\frac{1}{x} \right)}^{x}}\left[ \log \left( 1+\frac{1}{x} \right) \right]\]

    C) \[{{\left( 1+\frac{1}{x} \right)}^{x}}\left[ \log (x+1)-\frac{x}{x+1} \right]\]

    D) \[{{\left( 1+\frac{1}{x} \right)}^{x}}\left[ \log \left( 1+\frac{1}{x} \right)+\frac{x}{1+x} \right]\]

    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) \[{{m}^{2}}y\]

    B) \[-{{m}^{2}}y\]

    C) \[\pm {{m}^{2}}y\]

    D) None of these

    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

    B) 2R

    C) 6R

    D) 8R

    View Answer play_arrow
  • question_answer113) The value of\[{{\int{\sqrt{x}e}}^{\sqrt{x}}}dx\]is

    A) \[2\sqrt{x}-{{e}^{\sqrt{x}}}-4\sqrt{x}{{e}^{\sqrt{x}}}+c\]

    B) \[(2x-4\sqrt{x}+4){{e}^{\sqrt{x}}}+c\]

    C) \[(1+4\sqrt{x}){{e}^{\sqrt{x}}}+c\]

    D) None of the above

    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) \[-\pi \]

    B) 0

    C) \[\pi \]

    D) \[2\pi \]

    View Answer play_arrow
  • question_answer115) \[\int_{0}^{\pi /2}{\frac{dx}{1+{{\tan }^{3}}x}}\]is equal to

    A) \[0\]

    B) \[1\]

    C) \[\frac{\pi }{4}\]

    D) \[\frac{\pi }{2}\]

    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) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-2\frac{dy}{dx}+2y=0\]

    B) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+2\frac{dy}{dx}-2y=0\]

    C) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+{{\left( \frac{dy}{dx} \right)}^{2}}+y=0\]

    D) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-7\frac{dy}{dx}+2y=0\]

    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) \[\tan n\theta \]

    B) \[\cot n\theta \]

    C) \[i\tan n\theta \]

    D) \[i\cot n\theta \]

    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) \[1-4cos\text{ }A\text{ }cos\text{ }Bcos\text{ }C\]

    B) \[1+2\text{ }cos\text{ }A\text{ }cos\text{ }Bcos\text{ }C\]

    C) \[1-4\sin Asin\,BsinC\]

    D) \[4\text{ }sin\text{ }A\text{ }sin\text{ }B\text{ }sin\text{ }C\]

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  • question_answer119) In a\[\Delta ABC,{{r}_{1}},{{r}_{2}},{{r}_{3}}\]are in harmonic series, then a, b, c are in

    A) AP

    B) GP

    C) HP

    D) None of these

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  • question_answer120) For\[{{(1+i)}^{2n}}={{(1-i)}^{2n}},\]minimum positive value of n is

    A) 4

    B) 8

    C) 2

    D) 12

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  • 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) \[10(1+\sqrt{2})m\]

    B) \[10\left( 1+\frac{\sqrt{3}}{2} \right)m\]

    C) 15 m

    D) 20 m

    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) \[\left( \frac{3}{2},\frac{5}{2} \right)\]

    B) \[\left( \frac{2}{5},\frac{2}{5} \right)\]

    C) \[\left( \frac{3}{5},\frac{3}{5} \right)\]

    D) \[\left( \frac{2}{5},\frac{3}{5} \right)\]

    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) \[0<p<29\]

    B) \[25<p<35\]

    C) \[25<p<29\]

    D) None of these

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  • 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) \[\frac{1}{\sqrt{3}}\]

    B) \[\frac{2\sqrt{2}}{3}\]

    C) \[\frac{1}{\sqrt{2}}\]

    D) \[\frac{1}{3}\]

    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) \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-4x-6y+8z-20=0\]

    B) \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+4x-6y-8z-20=0\]

    C) \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-4x-6y-8z+20=0\]

    D) None of the above

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  • 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

    B) 9

    C) 10

    D) 11

    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

    B) 6

    C) 7

    D) 8

    View Answer play_arrow
  • question_answer128) \[lo{{g}_{3}}2,\text{ }lo{{g}_{6}}2,\text{ }lo{{g}_{12}}2\]are in

    A) AP

    B) GP

    C) HP

    D) None of these

    View Answer play_arrow
  • question_answer129) For\[{{x}^{12}}-{{x}^{9}}+{{x}^{4}}-x+1>0,\]the greatest interval is

    A) \[0<x<1\]

    B) \[-4<x\le 0\]

    C) \[0<x<\infty \]

    D) \[-10<x<10\]

    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) \[\frac{1}{5}\]

    B) \[\frac{2}{5}\]

    C) \[\frac{1}{10}\]

    D) None of these

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  • 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

    B) \[-1\]

    C) \[{{e}^{2}}\]

    D) e

    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

    B) for\[x+1>0,f\]is continuous but f is not continuous

    C) at\[x=0,f\]and f are not continuous

    D) at\[x=0,f\]is continuous but\[f'\]is not continuous

    View Answer play_arrow
  • question_answer133) If\[a<0\]and function\[({{e}^{ax}}+{{e}^{-ax}})\]is monotonic decreasing, then

    A) \[x>0\]

    B) \[x<0\]

    C) \[x>1\]

    D) \[x<1\]

    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, ...

    B) minimum, when n = 0, 2, 4, ...

    C) maximum, when n = 1, 3, 5,...

    D) None of the above

    View Answer play_arrow
  • question_answer135) The value of\[\int{\frac{{{e}^{x}}(1+\sin x)}{1+\cos x}}dx\]is

    A) \[{{e}^{x}}\tan \frac{x}{2}+c\]

    B) \[{{e}^{x}}\cot x+c\]

    C) \[\log \tan x+c\]

    D) \[sin\text{ }log\text{ }x+c\]

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  • question_answer136) The value of\[\int_{0}^{\pi /2}{\frac{\phi (x)}{\phi (x)+\phi \left( \frac{\pi }{2}-x \right)}}dx\] is

    A) \[\frac{\pi }{4}\]

    B) \[\frac{\pi }{2}\]

    C) \[\pi \]

    D) \[\frac{3\pi }{2}\]

    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

    B) 3

    C) 2

    D) 4

    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

    B) 1

    C) 1

    D) 2

    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) \[\frac{\pi }{3}\]

    B) \[\frac{\pi }{3},{{\cos }^{-1}}\left( \frac{3}{5} \right)\]

    C) \[{{\cos }^{-1}}\left( \frac{3}{5} \right)\]

    D) \[\frac{\pi }{3},\pi -{{\cos }^{-1}}\left( \frac{3}{5} \right)\]

    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)

    B) (2, 2)

    C) (2, 12)

    D) (12, 12)

    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) \[3x-y=0\]

    B) \[x+3y=0\]

    C) \[x-3y=0\]

    D) \[3x+y=0\]

    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) \[abc\]

    B) \[xyz\]

    C) \[a\]

    D) \[\frac{1}{a}\]

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  • question_answer143) If \[|x-2|+|x-3|=7,\]then the value of\[x\]is

    A) \[-1\]

    B) 6

    C) \[-1\]or 6

    D) None of these

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  • 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

    B) 6

    C) 8

    D) 10

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  • 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

    B) acute angled triangle

    C) obtuse angled triangle

    D) right angled triangle

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  • question_answer146) If \[^{{{a}^{2}}-a}{{C}_{2}}{{=}^{{{a}^{2}}-a}}{{C}_{4}},\] then the value of q is

    A) 2

    B) 3

    C) 4

    D) 7

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  • 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

    B) 1

    C) \[m(m+1)\]

    D) \[m(m-1)\]

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  • question_answer148) Function\[f(x)=1+\alpha x,\alpha \ne 0\]is equal to its reciprocal, then the value of\[\alpha \]is

    A) \[-2\]

    B) \[-1\]

    C) \[1\]

    D) 2

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  • 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

    B) continuous but not differentiable

    C) differentiable and not continuous

    D) not continuous and not differentiable

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  • question_answer150) If\[y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+.......,}}}\]then the value of\[\frac{dy}{dx}\]is

    A) \[\frac{\cos x}{2y-1}\]

    B) \[\frac{2y-1}{\cos x}\]

    C) \[\frac{\cos y}{2x-1}\]

    D) \[\frac{2x-1}{\cos y}\]

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