Solved papers for CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2007

done CEE Kerala Engineering Solved Paper-2007

  • question_answer1) A train is moving at\[30\text{ }m{{s}^{-1}}\]in still air. The frequency of the locomotive whistle is 500 Hz and the speed of sound is\[345\text{ }m{{s}^{-1}}\]. The apparent wavelength of sound in front of and behind the locomotive are respectively

    A) 0.80 m, 0.63 m

    B) 0.63 m, 0.80 m

    C) 0.50 m, 0.85 m

    D) 0.63 m, 0.75 m

    E) 0.50m, 0.75m

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  • question_answer2) An open organ pipe is closed suddenly with the result that the second overtone of the closed pipe is found to be higher in frequency by 100 than the first overtone of the original pipe. Then the fundamental frequency of the open pipe is

    A) \[200{{s}^{-1}}\]

    B) \[100{{s}^{-1}}\]

    C) \[300{{s}^{-1}}\]

    D) \[250{{s}^{-1}}\]

    E) \[150{{s}^{-1}}\]

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  • question_answer3) A transverse wave is described by the equation\[y={{y}_{0}}\sin 2\pi \left( ft-\frac{x}{\lambda } \right).\]The maximum particle velocity is equal to four times the wave velocity, if

    A) \[\lambda =\frac{\pi {{y}_{0}}}{4}\]

    B) \[\lambda =\frac{\pi {{y}_{0}}}{2}\]

    C) \[\lambda =\pi {{y}_{0}}\]

    D) \[\lambda =2\pi {{y}_{0}}\]

    E) \[\lambda =\frac{2\pi {{y}_{0}}}{3}\]

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  • question_answer4) Charges\[+2q,+q\]and\[+q\]are placed at the comers A, B and C of an equilateral triangle ABC. If E is the electric field at the circumcentre O of the triangle, due to the charge\[+q\], then the magnitude and direction of the resultant electric field at O is

    A) E along AO

    B) 2 E along AO

    C) E along BO

    D) E along CO

    E) zero

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  • question_answer5) N identical drops of mercury are charged simultaneously to 10 V. When combined to form one large drop, the potential is found to be 40 V, the value of N is

    A) 4

    B) 6

    C) 8

    D) 10

    E) 12

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  • question_answer6) The work done in moving an alpha particle between two points having potential difference 25 V is

    A) \[8\times {{10}^{-18}}J\]

    B) \[8\times {{10}^{-19}}J\]

    C) \[8\times {{10}^{-20}}J\]

    D) \[8\times {{10}^{-16}}J\]

    E) \[4\times {{10}^{-18}}J\]

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  • question_answer7) The electrostatic potential energy between proton and electron separated by a distance \[1\overset{\text{o}}{\mathop{\text{A}}}\,\] is

    A)  13.6 eV               

    B) 27.2 eV

    C)  14.4 eV               

    D) 1.44eV

    E) 28.8 eV

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  • question_answer8) The plates of a parallel plat capacitor with air as medium are separated by a distance of 8 mm. A medium of dielectric constant 2 and thickness 4 mm having the same area is introduced between the plates. For the capacitance to remain the same, the distance between the plates is

    A) 8 mm

    B) 6 mm

    C) 4 mm

    D) 12 mm

    E) 10 mm

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  • question_answer9) The resistance of a wire at room temperature \[30{}^\circ C\]is found to be\[10\,\Omega \]. Now to increase the resistance by 10%, the temperature of the wire must be [The temperature coefficient of resistance of the material of the wire is\[0.002/{}^\circ C\]]

    A) \[36{}^\circ C\]

    B) \[83{}^\circ C\]

    C) \[63{}^\circ C\]

    D) \[33{}^\circ C\]

    E) \[66{}^\circ C\]

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  • question_answer10) In a closed circuit, the current I (in ampere) at an instant of time t (in second) is given by\[I=4-0.08t\]. The number of electrons flowing in 50 s through the cross-section of the conductor is

    A) \[1.25\times {{10}^{19}}\]

    B) \[6.25\times {{10}^{20}}\]

    C) \[5.25\times {{10}^{19}}\]

    D) \[2.55\times {{10}^{20}}\]

    E) \[4.25\times {{10}^{20}}\]

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  • question_answer11) If\[{{R}_{1}}\]and\[{{R}_{2}}\]be the resistances of the filaments of 200 W and 100 W electric bulbs operating at 220 V, then\[\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)\]is

    A) 1

    B) 2

    C) 0.5

    D) 4

    E) 0.25

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  • question_answer12) A potentiometer wire, 10 m long, has a resistance of\[40\,\Omega \]. It is connected in series with a resistance box and a 2 V storage cell. If the potential gradient along the wire is (0.1 mV/cm), the resistance unplugged in the box is

    A) \[260\,\Omega \]

    B) \[760\,\Omega \]

    C) \[960\,\Omega \]

    D) \[1060\,\Omega \]

    E) \[1160\,\Omega \]

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  • question_answer13) When a current I flows through a wire, the drift velocity of the electrons is v. When current 21 flows through another wire of the same material having double the length and double the area of cross-section, the drift velocity of the electrons will be

    A) \[\frac{v}{8}\]

    B) \[\frac{v}{4}\]

    C) \[\frac{v}{2}\]

    D) \[v\]

    E) \[2v\]

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  • question_answer14) A uniform electric field and a uniform magnetic field exist in a region in the same direction. An electron is projected with a velocity pointed in the same direction. Then the electron will

    A) be deflected to the left without increase in speed

    B) be deflected to the right without increase in speed

    C) not be deflected but its speed will decrease

    D) not be deflected but its speed will increase

    E) be deflected to the right with increase in speed

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  • question_answer15) A galvanometer of resistance \[20\Omega \] shows a deflection of 10 divisions when a current of 1 mA is passed through it. If a shunt of\[4\,\Omega \] is connected and there are 50 divisions on the scale, the range of the galvanometer is

    A) 1 A

    B) 3 A

    C) 10 mA

    D) 30 A

    E) 30 mA

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  • question_answer16) A conducting rod of 1 m length and 1 kg mass is suspended by two vertical wires through its ends. An external magnetic field of 2 T is applied normal to the rod. Now the current to be passed through the rod so as to make the tension in the wires zero is [Take\[g=10\text{ }m{{s}^{-2}}\]]

    A) 0.5 A

    B) 15 A

    C) 5 A

    D) 1.5 A

    E) 2.5 A

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  • question_answer17) A circular coil of 5 turns and of 10 cm mean diameter is connected to a voltage source. If the resistance of the coil is \[10\,\Omega \]the voltage of the source so as to nullify the horizontal component of earths magnetic field of 30 A turn\[{{m}^{-1}}\]at the centre of the coil should be

    A) 6 V, plane of the coil normal to magnetic meridian

    B) 2 V, plane of the coil normal to magnetic meridian

    C) 6 V, plane of the coil along the magnetic meridian

    D) 2 V, plane of the coil along the magnetic meridian

    E) 4V, plane of the coil normal to magnetic meridian

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  • question_answer18) A paramagnetic substance of susceptibility \[3\times {{10}^{-4}}\]is placed in a magnetic field of\[4\times {{10}^{-4}}A{{m}^{-1}}\]. Then the intensity of .magnetization in the units of\[A{{m}^{-1}}\]is

    A) \[1.33\times {{10}^{8}}\]

    B) \[0.75\times {{10}^{-8}}\]

    C) \[12\times {{10}^{-8}}\]

    D) \[14\times {{10}^{-8}}\]

    E) \[1.2\times {{10}^{-8}}\]

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  • question_answer19) A square coil of side 25 cm having 1000 turns is rotated with a uniform speed in a magnetic field about an axis perpendicular to the direction of the field. At an instant t, the emf induced in the coil is\[e=200\text{ }sin\text{ }100\text{ }\pi t\]. The magnetic induction is

    A) \[0.50\text{ }T\]

    B) \[0.02\text{ }T\]

    C) \[{{10}^{-3}}T\]

    D) \[0.1\text{ }T\]

    E) \[0.01\text{ }T\]

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  • question_answer20) A transformer has an efficiency of 80%. It is connected to a power input of 5 kW at 200 V. If the secondary voltage is 250 V, the primary and secondary currents are respectively

    A) 25 A, 20 A

    B) 20 A, 16 A

    C) 25 A, 16 A

    D) 40 A, 25 A

    E) 40 A, 16 A

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  • question_answer21) When a DC voltage of 200 V is applied to a coil of self-inductance\[\left( \frac{2\sqrt{3}}{\pi } \right)H,\] a current of 1 A flows through it. But by replacing DC source with AC source of 200 V, the current in the coil is reduced to 0.5 A. Then the frequency of AC supply is

    A) 100 Hz

    B) 75 Hz

    C) 60 Hz

    D) 30 Hz

    E) 50 Hz

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  • question_answer22) In a L-R circuit, the value of L is\[\left( \frac{0.4}{\pi } \right)H,\]and the value of R is \[30\Omega \]. If in the circuit, an alternating emf of 200 V at 50 cycles/s is connected, the impedance of the circuit and current will be

    A) \[11.4\Omega ,17.5A\]

    B) \[30.7\Omega ,6.5A\]

    C) \[40.4\,\Omega ,\,5\,A\]

    D) \[50\text{ }\Omega ,\text{ }4\text{ }A\]

    E) \[35\text{ }\Omega ,6.5\text{ }A\]

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  • question_answer23) The dielectric constant of air is 1.006. The speed of electromagnetic wave travelling in air is\[a\times {{10}^{8}}m{{s}^{-1}},\]where a is about

    A) 3

    B) 3.88

    C) 2.5

    D) 3.2

    E) 2.8

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  • question_answer24) A. The wavelength of microwaves is greater than that of UV-rays. B. The wavelength of IR rays is lesser than that of UV-rays. C. The wavelength of microwaves is lesser than that of IR rays D. Gamma rays have shortest wavelength in the electromagnetic spectrum. Of the above statements

    A) A and B are true

    B) B and C are true

    C) C and D are true

    D) A and Care true

    E) A and D are true

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  • question_answer25) Magnification at least distance of distinct vision of a simple microscope having its focal length 5 cm is

    A) 2

    B) 4

    C) 5

    D) 6

    E) 7

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  • question_answer26) The position of final image formed by the given lens combination from the third lens will be at a distance of [\[{{f}_{1}}=+10\text{ }cm,\]\[{{f}_{2}}=-10cm,\]\[{{f}_{3}}=+30\text{ }cm\]]

    A) 15 cm

    B) infinity

    C) 45cm

    D) 30cm

    E) 35 cm

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  • question_answer27) A slit of width a is illuminated by red light of wavelength \[6500\overset{\text{o}}{\mathop{\text{A}}}\,\]. If the first minimum falls at\[\theta =30{}^\circ ,\] the value of a is

    A)  \[6.5\times {{10}^{-4}}mm\]

    B) \[1.3\,\,micron\]

    C)  \[3250\,\overset{\text{o}}{\mathop{\text{A}}}\,\]

    D)  \[2.6\times {{10}^{-4}}cm\]

    E)  \[1.3\times {{10}^{-4}}m\]

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  • question_answer28) Two beams of light of intensity\[{{I}_{1}}\]and\[{{I}_{2}}\] interfere to give an interference pattern. If the ratio of maximum intensity to that of minimum intensity is\[\frac{25}{9}\], then\[\frac{{{I}_{1}}}{{{I}_{2}}}\]is

    A) \[\frac{5}{3}\]

    B) \[4\]

    C) \[\frac{81}{625}\]

    D) \[16\]

    E) \[\frac{1}{2}\]

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  • question_answer29) If the polarizing angle of a piece of glass for green light is\[54.74{}^\circ ,\]then the angle of minimum deviation for an equilateral prism made of same glass is [Given: \[tan\text{ }54.74{}^\circ =1.414\]]

    A) \[45{}^\circ \]

    B) \[54.74{}^\circ \]

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

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

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

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  • question_answer30) When a monochromatic point source of light is at a distance 0.2 m from a photoelectric cell, the saturation current and cut-off voltage are 12.0 mA and 0.5 V. If the same source is placed 0.4 m away from the photoelectric cell, then the saturation current and the stopping potential respectively are

    A) 4 mA and 1 V

    B) 12mA and IV

    C) 3mA and IV

    D) 12mA and 0.5V

    E) 3mA and 0.5V

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  • question_answer31) Consider the nuclear reaction \[{{X}^{200}}\to {{A}^{110}}+{{B}^{80}}\] binding energy per nucleon for\[X,\text{ }A\]and B are 7.4 MeV, 8.2 MeV and 8.1 MeV respectively, then the energy released in the reaction is

    A) 70 MeV

    B) 200 MeV

    C) 190 MeV

    D) 10 MeV

    E) 1480 MeV

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  • question_answer32) The natural boron of atomic weight 10.81 is found to have two isotopes \[{{B}^{10}}\] and \[{{B}^{11}}\]. The ratio of abundance of isotopes in natural boron should be

    A) \[11:10\]

    B) \[81:19\]

    C) \[10:11\]

    D) \[15:16\]

    E) \[19:81\]

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  • question_answer33) Radium has a half-life of 5 yr. The probability of decay of a radium nucleus in 10 yr is

    A) 50%

    B) 75%

    C) 100%

    D) 60%

    E) 25%

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  • question_answer34) When the forward bias voltage of a diode is changed from 0.6 V to 0.7 V, the current changes from 5 mA to 15 mA. Then its forward bias resistance is

    A) \[0.01\,\Omega \]

    B) \[0.1\,\,\Omega \]

    C) \[10\,\,\Omega \]

    D) \[100\,\,\Omega \]

    E) \[0.2\,\,\Omega \]

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  • question_answer35) In common emitter amplifier, the current gain is 62. The collector resistance and input resistance are \[5\,k\,\Omega \]and\[500\,\Omega \]respectively. If the input voltage is 0.01 V, the output voltage is

    A) 0.62V

    B) 6.2V

    C) 62 V

    D) 620 V

    E) 0.01 V

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  • question_answer36) The current gain of a transistor in common base mode is 0.995. The current gain of the same transistor in common emitter mode is

    A) 197

    B) 201

    C) 198

    D) 202

    E) 199

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  • question_answer37) The real time variation of input signals A and B are as shown below. If the inputs are fed into NAND gate, then select the output signal from the following.






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  • question_answer38) The time variations of signals are given as in A, B and C. Point out the true statement from the following.

    A) A, B and C are analogue signals

    B) A and B are analogue, but C is digital signal

    C) A and C digital, but B is analogue signal

    D) A and C are analogue but B is digital signal

    E) A, B and C are digital signals

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  • question_answer39) The optical fibres have an inner core of refractive index\[{{n}_{1}}\]and a cladding of refractive index\[{{n}_{2}},\]such that

    A) \[{{n}_{1}}={{n}_{2}}\]

    B) \[{{n}_{1}}\le {{n}_{2}}\]

    C) \[{{n}_{1}}<{{n}_{2}}\]

    D) \[{{n}_{1}}>{{n}_{2}}\]

    E) \[{{n}_{1}}\ge {{n}_{2}}\]

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  • question_answer40) A photodetector used to detect the wavelength of 1700 nm, has energy gap of about

    A) 0:073 eV

    B) 1:2 eV

    C) 7.3 eV

    D) 1.16 eV

    E) 0.73eV

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  • question_answer41) The energy gap between conduction band and the valence band is of the order of 0.7 eV. Then it is

    A) an insulator

    B) a conductor

    C) a semiconductor

    D) an alloy

    E) a superconductor

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  • question_answer42) The physical quantity angular momentum has the same dimensions as that of

    A) work

    B) force

    C) momentum

    D) torque

    E) Plancks constant

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  • question_answer43) The values of two resistors are\[{{R}_{1}}=(6\pm 0.3)k\Omega \]and\[{{R}_{2}}=(10\pm 0.2)k\Omega \]. The percentage error in the equivalent resistance when they are connected in parallel is

    A) 5.125%

    B) 2%

    C) 3.125%

    D) 7%

    E) 10.125%

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  • question_answer44) Two trains are moving with equal speed in opposite directions along two parallel railway tracks. If the wind is blowing with speed u along the track so that the relative velocities of the trains with respect to the wind are in the ratio\[1:2,\] then the speed of each train must be

    A) \[3u\]

    B) \[2u\]

    C) \[5u\]

    D) \[4u\]

    E) \[u\]

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  • question_answer45) Two balls are dropped to the ground from different heights. One ball is dropped 2 s after the other but they both strike the ground at the same time. If the first ball takes 5 s to reach the ground, then the difference in initial heights is\[(g=10m{{s}^{-2}})\]

    A) 20m

    B) 80m

    C) 170m

    D) 40m

    E) 160m

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  • question_answer46) A ball is thrown vertically upwards with a velocity of\[25\text{ }m{{s}^{-1}}\] from the top of a tower of height 30 m. How long will it travel before it hits ground?

    A) 6s

    B) 5s

    C) 4s

    D) 12s

    E) 10s

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  • question_answer47) A ball is projected from the ground at a speed of\[10\text{ }m{{s}^{-1}}\]making an angle of\[30{}^\circ \]with the horizontal. Another ball is simultaneously released from a point on the vertical line along the maximum height of the projectile. The initial height of the second ball is \[(g=10m{{s}^{-2}})\]

    A) 6.25m

    B) 2.5m

    C) 3.75m

    D) 5m

    E) 1.25m

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  • question_answer48) The sum of the magnitudes of two forces acting at a point is 18 N and the magnitude of their resultant is 12N. If the resultant is at \[{{90}^{{}^\circ }}\]with the smaller force, the magnitude of the forces in N are

    A) 6, 12

    B) 11, 7

    C) 5, 13

    D) 14, 4

    E) 10, 8

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  • question_answer49) The position of a particle is given by \[\overrightarrow{r}=\hat{i}+2\hat{j}-\hat{k}\]and its linear momentum is given by\[\overrightarrow{P}=3\hat{i}+4\hat{j}-2\hat{k}\]. Then its angular momentum, about the origin is perpendicular to

    A) \[yz-\]plane

    B) \[z-\]axis

    C) \[y-\]axis

    D) \[x-\]axis

    E) \[xz-\]plane

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  • question_answer50) A mass of 6 kg is suspended by a rope of length 2 m from a ceiling. A force of 50 N in the horizontal direction is applied at the mid-point of the rope. The angle made by the rope with the vertical, in equilibrium is

    A) \[50{}^\circ \]

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

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

    D) \[40{}^\circ \]

    E) \[5.5{}^\circ \]

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  • question_answer51) A shell at rest at the origin explodes into three fragments of masses 1kg, 2 kg and m kg. The 1kg and 2 kg pieces fly off with speeds of\[5\text{ }m{{s}^{-1}}\] along x-axis and\[6\text{ }m{{s}^{-1}}\]along y-axis respectively. If the m kg piece flies off with a speed of\[6.5\text{ }m{{s}^{-1}},\]the total mass of the shell must be

    A) 4kg

    B) 5kg

    C) 3.5 kg

    D) 4.5 kg

    E) 5.5kg

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  • question_answer52) If the road is unbanked and the coefficient of friction between the road and the tyres is 0.8, then the maximum speed with which an automobile can move around a curve of 84.5 m radius without slipping \[(g=10\text{ }m{{s}^{-2}})\]is

    A) \[26\text{ }m{{s}^{-1}}\]

    B) \[67.6m{{s}^{-1}}\]

    C) \[13m{{s}^{-1}}\]

    D) \[36.7m{{s}^{-1}}\]

    E) \[8.2\text{ }m{{s}^{-1}}\]

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  • question_answer53) A rod AB of mass 10 kg and length 4 m rests on a horizontal floor with end A fixed so as to rotate it in vertical plane about perpendicular axis passing through A. If the work done on the rod is 100 J, the height to which the end B be raised vertically above the floor is

    A) 1.5m

    B) 2.0m

    C) 1.0m

    D) 2.5m

    E) 3.0m

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  • question_answer54) A particle is released from a height 5. At certain height its kinetic energy is three times its potential energy. The height and speed of the particle at that instant are respectively

    A) \[\frac{S}{4},\frac{3gS}{2}\]

    B) \[\frac{S}{4},\frac{\sqrt{3gS}}{2}\]

    C) \[\frac{S}{2},\frac{\sqrt{3gS}}{2}\]

    D) \[\frac{S}{2},\frac{\sqrt{3gS}}{2}\]

    E) \[\frac{S}{3},\frac{\sqrt{3gS}}{2}\]

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  • question_answer55) An electric pump is used to fill an overhead tank of capacity \[9\,{{m}^{3}}\] kept at a height of 10 m above the ground. If the pump takes 5 min to fill the tank by consuming 10 kW power the efficiency of the pump should be (Take \[g=10\text{ }m{{s}^{-2}}\])

    A) 60%

    B) 40%

    C) 20%

    D) 30%

    E) 50%

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  • question_answer56) A sphere of mass m and radius r rolls on a horizontal plane without slipping with the speed u. Now, if it rolls up vertically, the maximum height it would attain will be

    A) \[\frac{3{{u}^{2}}}{4g}\]

    B) \[\frac{5{{u}^{2}}}{2g}\]

    C) \[\frac{7{{u}^{2}}}{10g}\]

    D) \[\frac{{{u}^{2}}}{2g}\]

    E) \[\frac{11{{u}^{2}}}{9g}\]

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  • question_answer57) A simple pendulum is released from A as shown. If m and I represent the mass of the bob and length of the pendulum, the gain in kinetic energy at B is

    A) \[\frac{mgl}{2}\]

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

    C) \[\frac{\sqrt{3}}{2}mgl\]

    D) \[\frac{2}{\sqrt{3}}mgl\]

    E) \[mgl\]

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  • question_answer58) If the earth were to contract such that its radius becomes one quarter, without change in its mass, the duration of one full day would be

    A) 3h

    B) 1.5 h

    C) 6h

    D) 4h

    E) 2h

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  • question_answer59) A satellite is launched in a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 1.01R. The period of second satellite is longer than the first one (approximately) by

    A) 1.5%

    B) 0.5%

    C) 3%

    D) 1%

    E) 2%

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  • question_answer60) The change in potential energy when a body of mass m is raised to a height nR from earths surface is (R = radius of the earth)

    A) \[mgR=\frac{n}{(n-1)}\]

    B) \[mgR\]

    C) \[mgR=\frac{n}{(n+1)}\]

    D) \[mgR=\frac{{{n}^{2}}}{({{n}^{2}}+1)}\]

    E) \[\frac{mgR}{n}\]

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  • question_answer61) The escape velocity of a body on the surface of earth is 11.2 km/s. If the mass of the earth is doubled and its radius halved, the escape velocity becomes

    A) 5.6 km/s

    B) 11.2 km/s

    C) 22.4 km/s

    D) 44.8 km/s

    E) 67.2 km/s

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  • question_answer62) A tank of height H is fully filled with water. If the water rushing from a hole made in the tank below the free surface, strikes the floor at maximum horizontal distance, then the depth of the hole from the free surface must be

    A) \[\left( \frac{3}{4} \right)H\]

    B) \[\left( \frac{2}{3} \right)H\]

    C) \[\left( \frac{1}{4} \right)H\]

    D) \[\left( \frac{1}{2} \right)H\]

    E) \[\left( \frac{1}{3} \right)H\]

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  • question_answer63) The length of a rubber cord is\[{{l}_{1}}\]metre when the tension is 4 N and\[{{l}_{2}}\]metre when the tension is 6 N. The length when the tension is 9 N, is

    A) \[(2.5{{l}_{2}}-1.5{{l}_{1}})m\]

    B) \[(6{{l}_{2}}-1.5{{l}_{1}})m\]

    C) \[(3{{l}_{2}}-2{{l}_{1}})m\]

    D) \[(3.5{{l}_{2}}-2.5{{l}_{1}})m\]

    E) \[(2.5{{l}_{2}}+1.5{{l}_{1}})m\]

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  • question_answer64) A wire of natural length\[l,\]Youngs modulus Y and area of cross-section A is extended by\[x\]. Then the energy stored in the wire is given by

    A) \[\frac{1}{2}\frac{YA}{l}{{x}^{2}}\]

    B) \[\frac{1}{3}\frac{YA}{l}{{x}^{2}}\]

    C) \[\frac{1}{2}\frac{Yl}{A}{{x}^{2}}\]

    D) \[\frac{1}{2}\frac{YA}{{{l}^{2}}}{{x}^{2}}\]

    E) \[\frac{1}{2}\frac{A}{Yl}{{x}^{2}}\]

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  • question_answer65) A piece of solid weighs 120 g in air, 80 g in water and 60 g in a liquid. The relative density of the solid and that of the liquid are respectively

    A) \[3,\text{ }2\]

    B) \[2,\frac{3}{4}\]

    C) \[\frac{3}{2},2\]

    D) \[4,\text{ }3\]

    E) \[3,\frac{3}{2}\]

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  • question_answer66) A closed gas cylinder is divided into two parts by a piston held tight. The pressure and volume of gas in two parts respectively are (P, 5V) and (10P, V). If now the piston is left free and the system undergoes isothermal process, then the volume of the gas in two parts respectively are

    A) 2V, 4V

    B) 3V, 3V

    C) 5V, V

    D) 4V, 2V

    E) 2.5V, 3.5V

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  • question_answer67) A Carnot engine with sinks temperature at \[17{}^\circ C\] has 50% efficiency. By how much should its source temperature be changed to increase its efficiency to 60%?

    A) 225 K

    B) \[128{}^\circ C\]

    C) 580 K

    D) 145 K

    E) \[145{}^\circ C\]

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  • question_answer68) Two moles of oxygen is mixed with eight moles of helium. The effective specific heat of the mixture at constant volume is

    A) 1.3R

    B) 1.4R

    C) 1.7 R

    D) 1.97R

    E) 1.2R

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  • question_answer69) On heating, the temperature at which water has minimum volume is

    A) \[0{}^\circ C\]

    B) \[4{}^\circ C\]

    C) \[4K\]

    D) \[100{}^\circ C\]

    E) \[-273{}^\circ C\]

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  • question_answer70) In damped oscillations, the amplitude of oscillations is reduced to one-third of its initial value\[{{a}_{0}}\]at the end of 100 oscillations. When the oscillator completes 200 oscillations, its amplitude must be

    A) \[\frac{{{a}_{0}}}{2}\]

    B) \[\frac{{{a}_{0}}}{6}\]

    C) \[\frac{{{a}_{0}}}{12}\]

    D) \[\frac{{{a}_{0}}}{4}\]

    E) \[\frac{{{a}_{0}}}{9}\]

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  • question_answer71) A particle executes simple harmonic motion with a time period of 16 s. At time\[t=2\text{ }s,\]the particle crosses the mean position while at \[t=4s,\]its velocity is\[4\text{ }m{{s}^{-1}}\]. The amplitude of motion in metre is

    A) \[\sqrt{2}\pi \]

    B) \[16\sqrt{2}\pi \]

    C) \[24\sqrt{2}\pi \]

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

    E) \[\frac{32\sqrt{2}}{\pi }\]

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  • question_answer72) For a simple pendulum, the graph between\[{{T}^{2}}\]L is

    A) a straight line passing through the origin

    B) parabola

    C) circle

    D) ellipse

    E) hyperbola

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  • question_answer73) The relative lowering of vapour pressure of a dilute aqueous solution containing nonvolatile solute is 0.0125. The molality of the solution is about

    A) 0.70

    B) 0.50

    C) 0.90

    D) 0.80

    E) 0.60

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  • question_answer74) If the elevation in boiling point of a solution of 10 g of solute (mol. wt. = 100) in 100 g of water is\[\Delta {{T}_{b}},\]the ebullioscopic constant of water is

    A) 10

    B) \[100\,{{T}_{b}}\]

    C) \[\Delta {{T}_{b}},\]

    D) \[\frac{\Delta \,{{T}_{b}}}{10}\]

    E) \[10\,{{T}_{b}}\]

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  • question_answer75) An alloy of Pb-Ag weighing 1.08 g was dissolved in dilute \[HN{{O}_{3}}\] and the volume made to 100 mL. A silver electrode was dipped in the solution and the emf of the cell set up \[Pt(s),{{H}_{2}}(g)|{{H}^{+}}(1\,M)||A{{g}^{+}}(aq)|Ag(s)\] was 0.62V. If\[E_{cell}^{o}=0.80\,V\]is the percentage of Ag in the alloy? \[[At\text{ }25{}^\circ C,\text{ }RT/F=0.06]\]

    A) 25

    B) 2.50

    C) 10

    D) 1

    E) 50

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  • question_answer76) The standard oxidation potentials of Zn, Cu, Ag and Ni electrodes are\[+0.76,-0.34,-0.80\]and +0.25 V respectively. Which of the following reaction will provide maximum voltage?

    A) \[Cu+2A{{g}^{+}}(aq)\to C{{u}^{2+}}(aq)+2Ag\]

    B) \[Zn+2A{{g}^{+}}(aq)\to Z{{n}^{2+}}(aq)+2Ag\]

    C) \[{{H}_{2}}+N{{i}^{2+}}(aq)\to 2{{H}^{+}}(aq)+Ni\]

    D) \[Zn+C{{u}^{2+}}(aq)\to Z{{n}^{2+}}(aq)+Cu\]

    E) \[Zn+2{{H}^{+}}(aq)\to Z{{n}^{2+}}(aq)+{{H}_{2}}\]

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  • question_answer77) The activation energy of exothermic reaction \[A\to B\] is\[80\text{ }kJ\text{ }mo{{l}^{-1}}\]. The heat of reaction is\[200\text{ }kJ\text{ }mo{{l}^{-1}}\]. The activation energy for the reaction\[B\to A\]\[(in\text{ }kJ\text{ }mo{{l}^{-1}})\]will be

    A) 80

    B) 120

    C) 40

    D) 200

    E) 280

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  • question_answer78) At 500 K, the half-life period of a gaseous reaction at an initial pressure of 80 kPa is 350 s. When the pressure is 40 kPa, the half-life period is 175 s. The order of the reaction is

    A) zero

    B) one

    C) two

    D) three

    E) half

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  • question_answer79) The efficiency of enzyme catalysis is due to its capacity to

    A) form a strong enzyme-substrate complex

    B) change the shape of the substrate

    C) lower the activation energy of the reaction

    D) form a colloidal solution in water

    E) decrease the bond energies in substrate molecules

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  • question_answer80) On adding one mL of solution of\[10%\text{ }NaCl\]to 10 mL of gold sol in the presence of 0.25 g of starch, the coagulation is just prevented. The gold number of starch is

    A) 0.25

    B) 0.025

    C) 2.5

    D) 25

    E) 250

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  • question_answer81) Which of the following statements is not correct?

    A) The complexes\[{{[NiC{{l}_{4}}]}^{2-}}\]and\[{{[Ni{{(CN)}_{4}}]}^{2-}}\] differ in the state of hybridization of nickel

    B) The complexes\[{{[NiC{{l}_{4}}]}^{2-}}\]and\[{{[Ni{{(CN)}_{4}}]}^{2-}}\] differ in the magnetic properties

    C) The complexes\[{{[NiC{{l}_{4}}]}^{2-}}\]and\[{{[Ni{{(CN)}_{4}}]}^{2-}}\] differ in geometry

    D) The complexes\[{{[NiC{{l}_{4}}]}^{2-}}\]and\[{{[Ni{{(CN)}_{4}}]}^{2-}}\]differ in primary valencies of nickel

    E) Nickel ion has the same secondary valency in the complexes\[{{[NiC{{l}_{4}}]}^{2-}}\]and\[{{[Ni{{(CN)}_{4}}]}^{2-}}\]

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  • question_answer82) Both\[C{{o}^{3+}}\]and\[P{{t}^{4+}}\]have a coordination number of six. Which of the following pairs of complexes will show approximately the same electrical conductance for their 0.001M aqueous solutions?

    A) \[CoC{{l}_{3}}.4N{{H}_{3}}\,and\,PtC{{l}_{4}}.4N{{H}_{3}}\]

    B) \[CoC{{l}_{3}}.3N{{H}_{3}}\,and\,PtC{{l}_{4}}.5N{{H}_{3}}\]

    C) \[CoC{{l}_{3}}.6N{{H}_{3}}\,and\,PtC{{l}_{4}}.5N{{H}_{3}}\]

    D) \[CoC{{l}_{3}}.6N{{H}_{3}}\,and\,PtC{{l}_{4}}.3N{{H}_{3}}\]

    E) \[CoC{{l}_{3}}.5N{{H}_{3}}\,and\,PtC{{l}_{4}}.6N{{H}_{3}}\]

    View Answer play_arrow
  • question_answer83) Compare List-I and List-II and choose the correct matching codes from the choices given.

    List-I List-II
    A. Glycerol (i) Sublimation
    B. o-nitrophenol (ii) Beilsteins test
    C. Anthracene (iii) Victor-Meyers method
    D. Halogens distillation (iv) Steam
    E. Molecular weight (v) Vacuum distillation
    (vi) Eudiometry

    A) A-(v), B-(iv), C-(i), D-(ii), E-(iii)

    B) A-(iv), B-(v), C-(i), D-(vi), E-(ii)

    C) A-(vi), B-(iv), C-(i), D-(m), E-(ii)

    D) A-(v), B-(iv), C-(vi), D-(ii), E-(iii)

    E) A-(iv), B-(vi), C-(ii), D-(iii), E-(v)

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  • question_answer84) An aromatic hydrocarbon with empirical formula\[{{C}_{5}}{{H}_{4}}\]on treatment with concentrated \[{{H}_{2}}S{{O}_{4}}\]gave a monosulphonic acid. 0.104 g of the acid required 10 mL of\[\frac{N}{20}NaOH\]for complete neutralization. The molecular formula of hydrocarbon is

    A) \[{{C}_{5}}{{H}_{4}}\]

    B) \[{{C}_{10}}{{H}_{8}}\]

    C) \[{{C}_{15}}{{H}_{12}}\]

    D) \[{{C}_{20}}{{H}_{16}}\]

    E) \[{{C}_{15}}{{H}_{20}}\]

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  • question_answer85) Under which one of the following conditions, does the reaction, \[CH\equiv CH+C{{H}_{3}}OH\xrightarrow[{}]{?}C{{H}_{3}}O-CH=C{{H}_{2}}\]take place?

    A) \[N{{H}_{4}}OH/80{}^\circ C\]

    B) cone. \[{{H}_{2}}S{{O}_{4}}/160{}^\circ C\]

    C) Anhydrous \[ZnC{{l}_{2}}/150{}^\circ C\]

    D) Dilute \[HCl/THF,\,80{}^\circ C\]

    E) \[C{{H}_{3}}OK/160-200{}^\circ C\]

    View Answer play_arrow
  • question_answer86) Identify the product/s in the following reaction. \[3C{{H}_{3}}CH=C{{H}_{2}}\xrightarrow[{}]{B{{H}_{3}}}X\xrightarrow[{}]{{{H}_{2}}{{O}_{2}}/O{{H}^{-}}}\] \[product/s+{{H}_{3}}B{{O}_{3}}\]

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

    B) \[C{{H}_{3}}CHOHC{{H}_{3}}\]

    C) \[C{{H}_{3}}C{{H}_{2}}CHO\]

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

    E) \[C{{H}_{3}}CHO+C{{H}_{3}}OH\]

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  • question_answer87) Pick out the wrong statement.

    A) Toluene shows resonance

    B) is non-aromatic

    C) The hybrid state of carbon in carbonyl group is\[S{{p}^{2}}\]

    D) The hyperconjugative effect is known as no bond resonance

    E) Dipole moment of vinyl chloride is less than that of methyl chloride

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  • question_answer88) Which of the following is not true of carbanions?

    A) The carbon carrying the charge has eight valence electrons

    B) They are formed by heterolytic fission

    C) They are paramagnetic

    D) The carbon carrying the charge is\[S{{p}^{3}}\]hybridized

    E) They have pyramidal structure

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  • question_answer89) The number of isomers for the compound with the molecular formula\[{{C}_{2}}BrClFI\]is

    A) 3

    B) 4

    C) 5

    D) 6

    E) 7

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  • question_answer90) Which among the following statements is correct with respect to the optical isomers?

    A) Enantiomers are non-superimposable mirror images

    B) Diastereomers are superimposable mirror images

    C) Enantiomers are superimposable mirror images

    D) Meso forms have no plane of symmetry

    E) Enantiomers have plane of symmetry

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  • question_answer91) The\[{{S}_{N}}1\]reactivity of the following halides will be in the order

    (ii) \[{{({{C}_{6}}{{H}_{5}})}_{2}}CHBr\]
    (iii) \[{{({{C}_{6}}{{H}_{5}})}_{2}}C(C{{H}_{3}})Br\]
    (iv) \[{{(C{{H}_{3}})}_{2}}CHBr\]
    (v) \[{{C}_{2}}{{H}_{5}}Br\]

    A) (v)>(iv)>(i)>(ii)>(iii)

    B) (ii)>(i)>(iii)>(v)>(iv)

    C) (i)>(iii)>(v)>(ii)>(iv)

    D) (v)>(i)>(ii)>(iv)>(iii)

    E) (iii)>(ii)>(i)>(iv)>(v)

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  • question_answer92) Which of the following does not answer iodoform test?

    A) n-butyl alcohol

    B) sec-butyl alcohol

    C) acetophenone

    D) acetaldehyde

    E) ethylmethyl ketone

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  • question_answer93) Crown ethers are named as X-crown-Y. In the following crown ether, X and Y are respectively

    A) 6 and 12

    B) 18 and 6

    C) 24 and 6

    D) 6 and 24

    E) 6 and 18

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  • question_answer94) The most suitable reagent for the conversion of primary alcohol into aldehyde with the same number of carbon is

    A) acidified\[{{K}_{2}}C{{r}_{2}}{{O}_{7}}\]

    B) acidified \[KMn{{O}_{4}}\]

    C) alkaline \[KMn{{O}_{4}}\]

    D) pyridinium chlorochromate

    E) \[Cr{{O}_{3}}\]

    View Answer play_arrow
  • question_answer95) The strongest base among the following is

    A) \[{{C}_{6}}{{H}_{5}}N{{H}_{2}}\]

    B) \[{{({{C}_{2}}{{H}_{5}})}_{2}}NH\]

    C) \[{{(C{{H}_{3}})}_{3}}N\]

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

    E) \[{{({{C}_{6}}{{H}_{5}})}_{3}}N{{H}^{+}}C{{l}^{-}}\]

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  • question_answer96) Which one of the following compounds will dissolve in an alkali solution after it has undergone reaction with Hinsberg reagent?

    A) \[C{{H}_{3}}N{{H}_{2}}\]

    B) \[{{(C{{H}_{3}})}_{3}}N\]

    C) \[{{({{C}_{2}}{{H}_{5}})}_{2}}NH\]

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

    E) \[{{({{C}_{6}}{{H}_{5}})}_{3}}N{{H}^{+}}C{{l}^{-}}\]

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  • question_answer97) Which of the following hexoses will form the same osazone when treated with excess phenyl hydrazine?

    A) D-glucose, D-fructose and D-galactose

    B) D-glucose, D-fructose and D-mannose

    C) D-glucose, D-mannose and D-galactose

    D) D-fructose, D-mannose and D-galactose

    E) D-glucose, D-galactose and D-talose

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  • question_answer98) Match List-I with List-II and select the correct answer using the codes given below

    List - I List - II
    1. Buna-N A. Phthalic acid and ethylene glycol
    2. Nylon-6,6 B. Terephthalic acid and ethylene glycol
    3. Dacron C. Hexamethylene diamine and adipic acid
    4. Glyptal plastic D. Isobutylene and isoprene
    E. Acrylonitrile and butadiene

    A) 1-B, 2-A, 3-D, 4-E

    B) 1-C, 2-D, 3-A, 4-B

    C) 1-D, 2-C, 3-B, 4-A

    D) 1-E, 2-C, 3-A, 4-B

    E) 1-E, 2-C, 3-B, 4-A

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  • question_answer99) The photochemical smog can be suppressed by

    A) nitrogen oxides

    B) hydrocarbons

    C) radical traps

    D) formaldehyde

    E) peroxy acetyl nitrate

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  • question_answer100) Pick out the statement which is not true.

    A) Tetrazine is harmful edible colour

    B) Alitame is an artificial sweetner

    C) BHT is an antioxidant

    D) Sodium alkyl sulphate is a cationic detergent

    E) The performance of a rocket propellant is measured in terms of specific impulse

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  • question_answer101) The radius of the first Bohr orbit of hydrogen atom is \[0.529\overset{\text{o}}{\mathop{\text{A}}}\,\]. The radius of the third orbit of\[{{H}^{+}}\]will be

    A) \[8.46\overset{\text{o}}{\mathop{\text{A}}}\,\]

    B) \[0.705\overset{\text{o}}{\mathop{\text{A}}}\,\]

    C) \[1.59\overset{\text{o}}{\mathop{\text{A}}}\,\]

    D) \[4.29\overset{\text{o}}{\mathop{\text{A}}}\,\]

    E) \[2.38\overset{\text{o}}{\mathop{\text{A}}}\,\]

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  • question_answer102) Which diagram best represents the appearance of the line spectrum of atomic hydrogen in the visible region?






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  • question_answer103) Which of the following is paramagnetic with bond order 0.5?

    A) \[{{F}_{2}}\]

    B) \[H_{2}^{+}\]

    C) \[{{N}_{2}}\]

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

    E) \[{{B}_{2}}\]

    View Answer play_arrow
  • question_answer104) Match List-I with List-II and choose the correct matching codes from the choices given.

    List - I List - II
    A. \[PC{{l}_{5}}\] 1. Linear
    B. \[I{{F}_{7}}\] 2. Pyramidal
    C. \[{{H}_{3}}{{O}^{+}}\] 3. Trigonal bipyramidal
    D. \[Cl{{O}_{2}}\] 4. Tetrahedral
    E. \[NH_{4}^{+}\] 5. Pentagonal bipyramidal
    6. Angular

    A) A-3, B-5, C-2, D-1, E-4

    B) A-3, B-5, C-4, D-1, E-2

    C) A-3, B-5, C-6, D-1, E-2

    D) A-3, B-5, C-2, D-6, E-4

    E) A-3, B-5, C-2, D-4, E-1

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  • question_answer105) Which one of the following volume (V)- temperature (T) plots represents the behaviour of one mole of an ideal gas at one atmospheric pressure?






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  • question_answer106) The cubic unit cell of Al (molar mass 27 g \[mo{{l}^{-1}}\]) has an edge length of 405 pm. Its density is\[2.7\text{ }g\text{ }c{{m}^{-3}}\]. The cubic unit cell is

    A) face centred

    B) body centred

    C) primitive

    D) edge centred

    E) simple

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  • question_answer107) The hardness of water sample containing 0.002 mole of magnesium sulphate dissolved in a litre of water is expressed as

    A) 20ppm

    B) 200 ppm

    C) 2000 ppm

    D) 120 ppm

    E) 240 ppm

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  • question_answer108) In which one of the following pairs the radius of the second species is greater than that of the first?

    A) \[Na,Mg\]

    B) \[{{O}^{2-}},{{N}^{3-}}\]

    C) \[L{{i}^{+}},B{{e}^{2+}}\]

    D) \[B{{a}^{2+}},S{{r}^{2+}}\]

    E) \[Al,Be\]

    View Answer play_arrow
  • question_answer109) The carbonate that will not decompose on heating is

    A) \[N{{a}_{2}}C{{O}_{3}}\]

    B) \[CaC{{O}_{3}}\]

    C) \[BaC{{O}_{3}}\]

    D) \[SrC{{O}_{3}}\]

    E) \[L{{i}_{2}}C{{O}_{3}}\]

    View Answer play_arrow
  • question_answer110) Match List-I with List-II. Choose the correct matching codes from the choices given.

    List - I (Hydride) List - II (Type of hydride)
    A. \[B{{e}_{2}}{{H}_{2}}\] 1. Complex
    B. \[As{{H}_{3}}\] 2. Lewis acid
    C. \[{{B}_{2}}{{H}_{6}}\] 3. Interstitial
    D. \[La{{H}_{3}}\] 4. Covalent
    E. \[LiAl{{H}_{4}}\] 5. Intermediate
    6. Ionic

    A) A-6, B-2, C-4, D-5, E-1

    B) A-6, B-2, C-4, D-3, E-1

    C) A-6, B-4, C-2, D-3, E-5

    D) A-6, B-4, C-2, D-3, E-1

    E) A-5, B-4, C-2, D-3, E-1

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  • question_answer111) Which among the following statements are correct?

    (i) Carbon monoxide is neutral whereas\[S{{O}_{3}}\]is acidic
    (ii) Potassium oxide is basic whereas nitrous oxide is acidic
    (iii) Aluminium and zinc oxides are amphoteric
    (iv) Sulphur trioxide is acidic whereas phosphorus pentoxide is basic
    (v) Carbon dioxide is neutral whereas sulphur dioxide is amphoteric

    A) (ii) and (iii)

    B) (i) and (iv)

    C) (i) and (iii)

    D) (ii) and (iv)

    E) (iii) and (v)

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  • question_answer112) Among the following, the pair in which the two species are not isostructural is

    A) \[IO_{3}^{-}\]and\[Xe{{O}_{3}}\]

    B) \[PF_{6}^{-}\]and\[S{{F}_{6}}\]

    C) \[BH_{4}^{-}\]and \[NH_{4}^{+}\]

    D) \[CO_{3}^{2-}\]and\[NO_{2}^{-}\]

    E) \[Si{{F}_{4}}\]and \[S{{F}_{4}}\]

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  • question_answer113) Which of the following ions has a magnetic moment of 5.93 BM? (At. No. :\[V=23,Cr=24,Mn=25,Fe=26\])

    A) \[M{{n}^{2+}}\]

    B) \[F{{e}^{2+}}\]

    C) \[C{{r}^{2+}}\]

    D) \[{{V}^{3+}}\]

    E) \[C{{r}^{3+}}\]

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  • question_answer114) When hydrogen peroxide is added to acidified potassium dichromate, a blue colour is produced due to formation of

    A) \[Cr{{O}_{3}}\]

    B) \[C{{r}_{2}}{{O}_{3}}\]

    C) \[Cr{{O}_{5}}\]

    D) \[CrO_{4}^{2-}\]

    E) \[C{{r}_{2}}O_{7}^{2-}\]

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  • question_answer115) The radioactive isotope of caesium\[-137\]of weight 8g was collected on 1st February, 2006 and kept in a sealed tube. On 1st July 2006 it was found that only 0.25 g of it remained. The half-life period of the isotope is

    A) 37.5 day

    B) 30 day

    C) 25 day

    D) 50 day

    E) 60 day

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  • question_answer116) Which of the following make up an isotonic triad?

    A) \[_{32}^{78}Ge,_{33}^{77}As,,_{31}^{74}Ga\]

    B) \[_{18}^{40}Ar,_{19}^{40}K,_{20}^{40}Ca\]

    C) \[_{92}^{233}U,_{90}^{232}Th,_{94}^{239}Pu\]

    D) \[_{6}^{13}C,_{2}^{12}C,_{7}^{14}N\]

    E) \[_{6}^{14}C,_{8}^{16}C,_{7}^{15}N\]

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  • question_answer117) The age of a specimen t is related to the daughter/parent ratio of number of atoms (D / P) by the equation (\[\lambda =\]decay constant)

    A) \[t=\frac{1}{\lambda }\,\ln \,\left\{ \frac{D}{p} \right\}\]

    B) \[t=\frac{1}{\lambda }\,\ln \,\left\{ 1+\frac{p}{D} \right\}\]

    C) \[t=\frac{1}{\lambda }\,\ln \,\left\{ 2+\frac{p}{D} \right\}\]

    D) \[t=\frac{1}{\lambda }\,\ln \,\left\{ 1+\frac{D}{p} \right\}\]

    E) \[t=\frac{1}{\lambda }\,\ln \,\left\{ 2+\frac{D}{p} \right\}\]

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  • question_answer118) Which one of the following set of units represents the smallest and largest amount of energy respectively?

    A) J and erg

    B) erg and\[cal\]

    C) \[cal\]and eV

    D) lit-atm and J

    E) eV and lit-atm

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  • question_answer119) The equlibrium constant for the reaction \[2N{{O}_{2}}(g)2NO(g)+{{O}_{2}}(g)\]is\[2\times {{10}^{-6}}\]at\[185{}^\circ C\]. Then the equilibrium constant for the reaction,\[4NO(g)+2{{O}_{2}}(g)\]\[4N{{O}_{2}}(g)\]at the same temperature would be

    A) \[2.5\times {{10}^{-5}}\]

    B) \[4\times {{10}^{-12}}\]

    C) \[2.5\times {{11}^{11}}\]

    D) \[2\times {{10}^{6}}\]

    E) \[5\times {{10}^{5}}\]

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  • question_answer120) The pH of a neutral water is 6.5. Then the temperature of water

    A) is\[25{}^\circ C\]

    B) is more than\[25{}^\circ C\]

    C) is less than\[25{}^\circ C\]

    D) can be more or less than\[25{}^\circ C\]

    E) Cannot be predicted

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  • question_answer121) On the set N of all natural numbers define the relation R by aRb if and only if the GCD of a and b is 2, then R is

    A) reflexive, but not symmetric

    B) symmetric only

    C) reflexive and transitive

    D) reflexive, symmetric and transitive

    E) not reflexive, not symmetric and not transitive

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  • question_answer122) Let Z denote the set of all integers and\[A=\{(a,b):{{a}^{2}}+3{{b}^{2}}=28,a,b\in z\}\]and\[B=\{(a,b):a>b,a,b\in z\}\]. Then the number of elements in\[A\cap B\]is

    A) 2

    B) 3

    C) 4

    D) 5

    E) 6

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  • question_answer123) If\[f(x)=2{{x}^{2}}+bx+c\]and\[f(0)=3\]and \[f(2)=1,\]then\[f(1)\]is equal to

    A) 1

    B) 2

    C) 0

    D) 1/2

    E) \[-2\]

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  • question_answer124) The domain of the real valued function \[f(x)=\sqrt{1-2x}+2{{\sin }^{-1}}\left( \frac{3x-1}{2} \right)\]is

    A) \[\left[ -\frac{1}{3},1 \right]\]

    B) \[\left[ \frac{1}{2},1 \right]\]

    C) \[\left[ -\frac{1}{2},\frac{1}{3} \right]\]

    D) \[\left[ -1,\frac{1}{3} \right]\]

    E) \[\left[ -\frac{1}{3},\frac{1}{2} \right]\]

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  • question_answer125) The period of the function\[f(x)={{a}^{\{\tan (\pi x)+x-[x]\}}},\]where\[a>0,[\,\,.\,\,]\]denotes the greatest integer function and\[x\]is a real number, is

    A) \[\pi \]

    B) \[\pi /2\]

    C) \[\pi /4\]

    D) \[2\pi \]

    E) 1

    View Answer play_arrow
  • question_answer126) If\[\omega \]is a complex cube root of unity, then the value of\[\sin \left\{ ({{\omega }^{10}}+{{\omega }^{23}})\pi -\frac{\pi }{6} \right\}\]is

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

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

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

    D) \[-\frac{\sqrt{3}}{2}\]

    E) \[\frac{1}{2}\]

    View Answer play_arrow
  • question_answer127) Let\[z=\frac{11-3!}{1+i}.\]If a is a real number such that \[z-i\alpha \]is real, then the value of\[\alpha \]is

    A) 4

    B) \[-\,4\]

    C) 7

    D) \[-\text{ }7\]

    E) 3

    View Answer play_arrow
  • question_answer128) Let\[{{z}_{1}}\]and\[{{z}_{2}}\]be the roots of the equation \[{{z}^{2}}+pz+q=0\]where p, q are real. The points represented by\[{{z}_{1}},{{z}_{2}}\]and the origin form an equilateral triangle, if

    A) \[{{p}^{2}}=3q\]

    B) \[{{p}^{2}}>3q\]

    C) \[{{p}^{2}}<3q\]

    D) \[{{p}^{2}}=2q\]

    E) \[p=3q\]

    View Answer play_arrow
  • question_answer129) If\[\alpha ,\beta ,\gamma \]are the cube roots of a negative number p, then for any three real numbers,\[x,y,z\] the value of \[\frac{x\alpha +y\beta +z\gamma }{x\beta +y\gamma +z\alpha }\] is

    A) \[\frac{1-i\sqrt{3}}{2}\]

    B) \[\frac{-1-i\sqrt{3}}{2}\]

    C) \[(x+y+z)i\]

    D) \[pi\]

    E) \[\frac{x+y+z}{2}pi\]

    View Answer play_arrow
  • question_answer130) The magnitude and amplitude of \[\frac{(1+i\sqrt{3})(2+2i)}{(\sqrt{3}-i)}\]are respectively

    A) \[2,\frac{3\pi }{4}\]

    B) \[4,\frac{3\pi }{4}\]

    C) \[2\sqrt{2},\frac{\pi }{4}\]

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

    E) \[2\sqrt{2},\frac{3\pi }{4}\]

    View Answer play_arrow
  • question_answer131) If\[1+{{x}^{2}}=\sqrt{3}x,\]then\[\sum\limits_{n=1}^{24}{{{\left( {{x}^{n}}-\frac{1}{{{x}^{n}}} \right)}^{2}}}\]is equal to

    A) 0

    B) 48

    C) \[-24\]

    D) 24

    E) \[-48\]

    View Answer play_arrow
  • question_answer132) If \[\alpha \] and \[\beta \] are the roots of the equation\[a{{x}^{2}}+\] \[bx+c=0,\text{ }\alpha \beta =3\] and a, b, c are in AP, then \[\alpha +\beta \]is equal to

    A) \[-4\]

    B) 1

    C) 4

    D) \[-\,2\]

    E) 2

    View Answer play_arrow
  • question_answer133) If one root of the equation\[{{x}^{2}}+px+12=0\]is 4, while the equation\[{{x}^{2}}+px+q=0\]has equal roots, then the value of q is

    A) \[4\]

    B) \[12\]

    C) \[3\]

    D) \[\frac{29}{4}\]

    E) \[\frac{49}{4}\]

    View Answer play_arrow
  • question_answer134) Given\[tan\text{ }A\]and\[tan\text{ B}\]are the roots of\[{{x}^{2}}-ax+b=0\]. The value of\[{{\sin }^{2}}(A+B)\]is

    A) \[\frac{{{a}^{2}}}{{{a}^{2}}+{{(1-b)}^{2}}}\]

    B) \[\frac{{{a}^{2}}}{{{a}^{2}}+{{b}^{2}}}\]

    C) \[\frac{{{a}^{2}}}{{{(a+b)}^{2}}}\]

    D) \[\frac{{{b}^{2}}}{{{a}^{2}}+{{(1-b)}^{2}}}\]

    E) \[\frac{{{a}^{2}}}{{{b}^{2}}+{{(1-a)}^{2}}}\]

    View Answer play_arrow
  • question_answer135) The number of roots of the equation \[|x|={{x}^{2}}+x-4\]is

    A) 4

    B) 3

    C) 1

    D) 0

    E) 2

    View Answer play_arrow
  • question_answer136) The first term of an infinite GP is 1 and each term is twice the sum of the succeeding terms, then the sum of the series is

    A) \[2\]

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

    C) \[\frac{7}{2}\]

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

    E) \[\frac{9}{2}\]

    View Answer play_arrow
  • question_answer137) If\[\frac{a}{b+c},\frac{b}{c+a},\frac{c}{a+b}\]are in AP, then

    A) a, b, c are in AP

    B) c, a, b are hi AP

    C) \[{{a}^{2}},\text{ }{{b}^{2}},\text{ }{{c}^{2}}\]are in AP

    D) a, b, care in GP

    E) \[{{c}^{2}},\text{ }{{a}^{2}},\text{ }{{b}^{2}}\]are in AP

    View Answer play_arrow
  • question_answer138) If an infinite geometric series the first term is a and common ratio is r. If the sum of the series is 4 and the second term is 3/4 then (a, r) is

    A) (4/7, 3/7)

    B) (2, 3/8)

    C) (3/2, 1/2)

    D) (3, 1/4)

    E) (4, 3/4)

    View Answer play_arrow
  • question_answer139) The sets\[{{S}_{1}},{{S}_{2}},{{S}_{3}},....\]are given by \[{{S}_{1}}=\left\{ \frac{2}{1} \right\},\] \[{{S}_{2}}=\left\{ \frac{3}{2},\frac{5}{2} \right\},{{S}_{3}}=\left\{ \frac{4}{3},\frac{7}{3},\frac{10}{3} \right\},\] \[{{S}_{4}}=\left\{ \frac{5}{4},\frac{9}{4},\frac{13}{4},\frac{17}{4} \right\},....\] Then the sum of the numbers in the set\[{{S}_{25}}\]is

    A) 320

    B) 322

    C) 324

    D) 325

    E) 326

    View Answer play_arrow
  • question_answer140) If\[{{H}_{1}},{{H}_{2}}\]are two harmonic means between two positive numbers a and\[b(a\ne b),A\]and G are the arithmetic and geometric means between a and b, then\[\frac{{{H}_{2}}+{{H}_{1}}}{{{H}_{2}}{{H}_{1}}}\]is

    A) \[\frac{A}{G}\]

    B) \[\frac{2A}{G}\]

    C) \[\frac{A}{2{{G}^{2}}}\]

    D) \[\frac{A}{{{G}^{2}}}\]

    E) \[\frac{2A}{{{G}^{2}}}\]

    View Answer play_arrow
  • question_answer141) If\[{{\log }_{\sqrt{3}}}5=a\]and\[{{\log }_{\sqrt{3}}}2=b,\]then \[{{\log }_{\sqrt{3}}}300\]is equal to

    A) \[2(a+b)\]

    B) \[2(a+b+1)\]

    C) \[2(a+b+2)\]

    D) \[a+b+4\]

    E) \[a+b+1\]

    View Answer play_arrow
  • question_answer142) If a, b, c are distinct positive numbers each being different from 1 such that \[({{\log }_{b}}a.{{\log }_{c}}a-{{\log }_{a}}a)\] \[+({{\log }_{a}}b.{{\log }_{c}}b-{{\log }_{b}}b)\] \[+({{\log }_{a}}c.{{\log }_{b}}c-{{\log }_{c}}c)=0,\]then \[abc\] is

    A) \[0\]

    B) \[e\]

    C) \[1\]

    D) \[2\]

    E) \[3\]

    View Answer play_arrow
  • question_answer143) If\[\alpha \]and\[\beta \]are the roots of the equation \[{{x}^{2}}+px+q=0\]and if the sum \[(\alpha +\beta )x-\frac{{{\alpha }^{2}}+{{\beta }^{2}}}{2}+{{x}^{2}}+\frac{{{\alpha }^{2}}+{{\beta }^{3}}}{3}{{x}^{3}}\] \[-\frac{{{\alpha }^{4}}+{{\beta }^{4}}}{4}{{x}^{4}}+.....\] exists, then it is equal to

    A) \[\log ({{x}^{2}}+px+q)\]

    B) \[\log ({{x}^{2}}-px+q)\]

    C) \[\log (1+px+q{{x}^{2}})\]

    D) \[\log (1-px+q{{x}^{2}})\]

    E) \[\log ({{x}^{2}}+qx+p)\]

    View Answer play_arrow
  • question_answer144) If\[m{{=}^{n}}{{C}_{2}},\]then\[^{m}{{C}_{2}}\]is equal to

    A) \[{{3}^{n}}{{C}_{4}}\]

    B) \[^{n+1}{{C}_{4}}\]

    C) \[{{3}^{n+1}}{{C}_{4}}\]

    D) \[{{3}^{n+1}}{{C}_{3}}\]

    E) \[{{3}^{n+1}}{{C}_{2}}\]

    View Answer play_arrow
  • question_answer145) The number of permutations of the letters of the word CONSEQUENCE- in which all the three Es are together, is

    A) \[9!3!\]

    B) \[\frac{9!}{2!}\]

    C) \[\frac{9!}{2!2!3!}\]

    D) \[\frac{9!}{2!3!}\]

    E) \[\frac{9!}{2!2!}\]

    View Answer play_arrow
  • question_answer146) If \[{{(1+x-3{{x}^{2}})}^{10}}=1+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+....\]\[+{{a}_{20}}{{x}^{20}},\]then\[{{a}_{2}}+{{a}_{4}}+{{a}_{6}}+....+{{a}_{20}}\]is equal to

    A) \[\frac{{{3}^{10}}+1}{2}\]

    B) \[\frac{{{3}^{9}}+1}{2}\]

    C) \[\frac{{{3}^{10}}-1}{2}\]

    D) \[\frac{{{3}^{9}}-1}{2}\]

    E) \[{{2}^{19}}-1\]

    View Answer play_arrow
  • question_answer147) The value of\[\left( \frac{^{50}{{C}_{0}}}{1}+\frac{^{50}{{C}_{2}}}{3}+\frac{^{50}{{C}_{4}}}{5}+.... \right.\]\[\left. +\frac{^{50}{{C}_{50}}}{51} \right)\]is

    A) \[\frac{{{2}^{50}}}{51}\]

    B) \[\frac{{{2}^{50}}-1}{51}\]

    C) \[\frac{{{2}^{50}}-1}{50}\]

    D) \[\frac{{{2}^{51}}-1}{51}\]

    E) \[\frac{{{2}^{51}}-1}{50}\]

    View Answer play_arrow
  • question_answer148) In the expansion of\[{{(1+x+{{x}^{2}}+{{x}^{3}})}^{6}},\]the coefficient of\[{{x}^{14}}\]is

    A) 130

    B) 120

    C) 128

    D) 125

    E) 115

    View Answer play_arrow
  • question_answer149) If\[n=5,\]then \[{{{{(}^{n}}{{C}_{0}})}^{2}}+{{{{(}^{n}}{{C}_{1}})}^{2}}+{{{{(}^{n}}{{C}_{2}})}^{2}}+.....\] \[+{{{{(}^{n}}{{C}_{5}})}^{2}}\]is equal to

    A) 250

    B) 254

    C) 245

    D) 252

    E) 258

    View Answer play_arrow
  • question_answer150) If\[l,m\]and\[n\]are real numbers such that\[{{l}^{2}}+{{m}^{2}}\] \[+{{n}^{2}}=0,\] then \[\left| \begin{matrix} 1+{{l}^{2}} & lm & \ln \\ lm & 1+{{m}^{2}} & mn \\ \ln & mn & 1+{{n}^{2}} \\ \end{matrix} \right|\]is equal to

    A) 0

    B) 1

    C) \[l+m+n+2\]

    D) \[2(Z+m+n)+3\]

    E) \[lmn-1\]

    View Answer play_arrow
  • question_answer151) If\[f(x)={{x}^{2}}+4x-5\] and\[A=\left[ \begin{matrix} 1 & 2 \\ 4 & -3 \\ \end{matrix} \right],\]then \[f(A)\]is equal to

    A) \[\left[ \begin{matrix} 0 & -4 \\ 8 & 8 \\ \end{matrix} \right]\]

    B) \[\left[ \begin{matrix} 2 & 1 \\ 2 & 0 \\ \end{matrix} \right]\]

    C) \[\left[ \begin{matrix} 1 & 1 \\ 1 & 0 \\ \end{matrix} \right]\]

    D) \[\left[ \begin{matrix} 8 & 4 \\ 8 & 0 \\ \end{matrix} \right]\]

    E) \[\left[ \begin{matrix} 1 & 0 \\ 1 & 2 \\ \end{matrix} \right]\]

    View Answer play_arrow
  • question_answer152) \[\left| \begin{matrix} \alpha & -\beta & 0 \\ 0 & \alpha & \beta \\ \beta & 0 & \alpha \\ \end{matrix} \right|=0,\]then

    A) \[\frac{\alpha }{\beta }\]is one of the cube roots of unity

    B) \[\alpha \]is one of the cube roots of unity

    C) \[\beta \]is one of the cube roots of unity

    D) \[\alpha \beta \]is one of the cube roots of unity

    E) none of the above

    View Answer play_arrow
  • question_answer153) The coefficient of\[x\]in \[f(x)=\left| \begin{matrix} x & 1+\sin x & \cos x \\ 1 & \log (1+x) & 2 \\ {{x}^{2}} & 1+{{x}^{2}} & 0 \\ \end{matrix} \right|,-1<x\le 1,\]is

    A) 1

    B) \[-2\]

    C) \[-1\]

    D) 0

    E) 2

    View Answer play_arrow
  • question_answer154) If\[\left| \begin{matrix} x & 3 & 6 \\ 3 & 6 & x \\ 6 & x & 3 \\ \end{matrix} \right|=\left| \begin{matrix} 2 & x & 7 \\ x & 7 & 2 \\ 7 & 2 & x \\ \end{matrix} \right|=\left| \begin{matrix} 4 & 5 & x \\ 5 & x & 4 \\ x & 4 & 5 \\ \end{matrix} \right|=0,\] then\[x\]is equal to

    A) 9

    B) \[-9\]

    C) 0

    D) \[-1\]

    E) 1

    View Answer play_arrow
  • question_answer155) If\[\omega \]be the complex cube root of unity and matrix\[H=\left[ \begin{matrix} \omega & 0 \\ 0 & \omega \\ \end{matrix} \right],\]then\[{{H}^{70}}\]is equal to

    A) 0

    B) \[-H\]

    C) 2

    D) \[{{H}^{2}}\]

    E) 1

    View Answer play_arrow
  • question_answer156) Number of integral solutions of\[\frac{x+2}{{{x}^{2}}+1}>\frac{1}{2}\]is

    A) 0

    B) 1

    C) 2

    D) 3

    E) 4

    View Answer play_arrow
  • question_answer157) If r is a real number such that\[|r|<1\]and if \[a=5(1-r),\]then

    A) \[0<a<5\]

    B) \[-5<a<5\]

    C) \[0<a<10\]

    D) \[0\le a<10\]

    E) \[-10<a<10\]

    View Answer play_arrow
  • question_answer158) If\[p:4\]is an even prime number,\[q:6\]is a divisor of 12 and r : the HCF of 4 and 6 is 2, then which one of the following is true?

    A) \[(p\wedge q)\]

    B) \[(p\vee q)\wedge \tilde{\ }r\]

    C) \[\tilde{\ }(q\wedge r)\vee p\]

    D) \[\tilde{\ }p\vee (q\wedge r)\]

    E) \[p\to (q\wedge r)\]

    View Answer play_arrow
  • question_answer159) Which of the following is not true for any two statements p and q?

    A) \[\tilde{\ }[p\vee (\tilde{\ }q)]\equiv (\tilde{\ }p)\wedge q\]

    B) \[(p\vee q)\vee (\tilde{\ }q)\]is a tautology

    C) \[(p\wedge q)\wedge (\tilde{\ }q)\]is contradiction

    D) \[\tilde{\ }[p\wedge (\tilde{\ }p)]\]is a tautology

    E) \[\tilde{\ }(p\vee q)\equiv (\tilde{\ }p)\vee (\tilde{\ }q)\]

    View Answer play_arrow
  • question_answer160) The output of the circuit is

    A) \[({{x}_{2}}+{{x}_{3}}).[({{x}_{1}}.{{x}_{2}}).x_{3}^{}]\]

    B) \[({{x}_{2}}+x_{3}^{}).[({{x}_{1}}.\,{{x}_{2}})\,.\,x_{3}^{}]\]

    C) \[({{x}_{2}}+{{x}_{3}})+[({{x}_{1}}.\,{{x}_{2}})\,.\,x_{3}^{}]\]

    D) \[({{x}_{2}}.{{x}_{3}})+[({{x}_{1}}.\,{{x}_{2}})\,.\,x_{3}^{}]\]

    E) \[({{x}_{1}}+{{x}_{3}})+[({{x}_{1}}.\,{{x}_{2}})\,.\,x_{3}^{}]\]

    View Answer play_arrow
  • question_answer161) If\[A+B+C=7\pi \]then \[\tan \left( \frac{A}{2} \right)\tan \left( \frac{B}{2} \right)+\tan \left( \frac{B}{2} \right)\tan \left( \frac{C}{2} \right)\]\[+\tan \left( \frac{C}{2} \right)\tan \left( \frac{A}{2} \right)\]is equal to

    A) \[\pi /6\]

    B) 3

    C) \[2\]

    D) 1

    E) \[-1\]

    View Answer play_arrow
  • question_answer162) If\[\sin 4A-\cos 2A=\cos 4A-\sin 2A,\]\[\left( 0<A<\frac{\pi }{4} \right)\]then the value of tan 4A is

    A) \[1\]

    B) \[\frac{1}{\sqrt{3}}\]

    C) \[\sqrt{3}\]

    D) \[\frac{\sqrt{3}-1}{\sqrt{3}+1}\]

    E) \[\frac{\sqrt{3}+1}{\sqrt{3}-1}\]

    View Answer play_arrow
  • question_answer163) \[{{\tan }^{-1}}\frac{m}{n}-{{\tan }^{-1}}\frac{m-n}{m+n}\]is equal to

    A) \[{{\tan }^{-1}}\frac{n}{m}\]

    B) \[{{\tan }^{-1}}\frac{m+n}{m-n}\]

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

    D) \[{{\tan }^{-1}}\left( \frac{1}{2} \right)\]

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

    View Answer play_arrow
  • question_answer164) In a\[\Delta ABC,\]if\[(\sqrt{3}-1)a=2b,A=3B,\]then C is

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

    B) \[120{}^\circ \]

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

    D) \[45{}^\circ \]

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

    View Answer play_arrow
  • question_answer165) If\[{{\sec }^{-1}}\sqrt{1+{{x}^{2}}}+\cos e{{c}^{-1}}\frac{\sqrt{1+{{y}^{2}}}}{y}+{{\cot }^{-1}}\frac{1}{z}=\pi ,\]then\[x+y+z\]is equal to

    A) \[xyz\]

    B) \[2xyz\]

    C) \[xy{{z}^{2}}\]

    D) \[{{x}^{2}}yz\]

    E) \[3xyz\]

    View Answer play_arrow
  • question_answer166) If sec a and cosec a are the roots of the equation\[{{x}^{2}}-px+q=0,\]then

    A) \[{{p}^{2}}=p+2q\]

    B) \[{{q}^{2}}=p+2q\]

    C) \[{{p}^{2}}=q(p+2)\]

    D) \[{{q}^{2}}=p(p+2)\]

    E) \[{{p}^{2}}=q(q-2)\]

    View Answer play_arrow
  • question_answer167) If\[x{{\sin }^{3}}\theta +y{{\cos }^{3}}\theta =\sin \theta \cos \theta \]and \[x\sin \theta =y\cos \theta ,\]then\[{{x}^{2}}+{{y}^{2}}\]is

    A) 2

    B) 0

    C) 3

    D) 4

    E) 1

    View Answer play_arrow
  • question_answer168) In a\[\Delta ABC\].if \[\tan \frac{A}{2}=\frac{5}{6},\tan \frac{C}{2}=\frac{2}{5},\] then

    A) a, c, b are in AP

    B) a, b, c are in GP

    C) b, a, c are in AP

    D) a, b, c are in AP

    E) a, c, b are in GP

    View Answer play_arrow
  • question_answer169) If the angles of a triangle are in the ratio\[4:1:1,\]then the ratio of the longest side to the perimeter is

    A) \[\sqrt{3}:2+\sqrt{3}\]

    B) \[1:6\]

    C) \[1:2+\sqrt{3}\]

    D) \[2:3\]

    E) \[\sqrt{2}:2+\sqrt{3}\]

    View Answer play_arrow
  • question_answer170) In a triangle ABC,\[(b+c)(bc)\cos A+(a+c)\] \[(ac)\cos B+(a+b)(ab)\cos C\]is

    A) \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}\]

    B) \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}\]

    C) \[(a+b+c)({{a}^{2}}+{{b}^{2}}+{{c}^{2}})\]

    D) \[(a+b+c)(ab+bc+ca)\]

    E) \[abc\]

    View Answer play_arrow
  • question_answer171) If in\[\Delta ABC,\sin \frac{A}{2}\sin \frac{C}{2}=\sin \frac{B}{2}\]and\[2s\]is the perimeter of the triangle, then\[s\]is

    A) 2b

    B) b

    C) 3b

    D) 4b

    E) 3b/2

    View Answer play_arrow
  • question_answer172) ABC is a right angled triangle wit\[\angle B=90{}^\circ ,\] \[a=6\text{ }cm\]. If the radius of the circumcircle is 5 cm, then the area of\[\Delta ABC\]is

    A) \[25c{{m}^{2}}\]

    B) \[30c{{m}^{2}}\]

    C) \[36c{{m}^{2}}\]

    D) \[24c{{m}^{2}}\]

    E) \[48c{{m}^{2}}\]

    View Answer play_arrow
  • question_answer173) The vertices A, B, C of a triangle are (2, 1), (5, 2) and (3, 4) respectively. Then the circumcentre is

    A) \[\left( \frac{13}{4},\frac{-9}{4} \right)\]

    B) \[\left( \frac{-13}{4},\frac{9}{4} \right)\]

    C) \[\left( \frac{-13}{4},\frac{-9}{4} \right)\]

    D) \[\left( \frac{13}{4},\frac{9}{4} \right)\]

    E) \[\left( \frac{13}{2},\frac{9}{4} \right)\]

    View Answer play_arrow
  • question_answer174) The \[x-\]axis,\[y-\]axis and a line passing through the point A (6, 0) form a triangle ABC. If\[\angle A=30{}^\circ ,\]then the area of the triangle, in sq unit is

    A) \[6\sqrt{3}\]

    B) \[12\sqrt{3}\]

    C) \[4\sqrt{3}\]

    D) \[8\sqrt{3}\]

    E) \[2\sqrt{3}\]

    View Answer play_arrow
  • question_answer175) The midpoint of the line joining the points \[(-10,\text{ }8)\]and\[(-6,12)\]divides the line joining the points\[(4,-2)\]and\[(-2,4)\]in the ratio

    A) \[1:2\]internally

    B) \[1:2\]externally

    C) \[2:1\]internally

    D) \[2:1\]externally

    E) \[2:3\]externally

    View Answer play_arrow
  • question_answer176) The equation of the lines through the point\[(3,2)\]which makes an angle of\[45{}^\circ \]with the line\[x-2y=3\]are

    A) \[3x-y=7\]and \[x+3y=9\]

    B) \[x-3y=7\text{ }and\text{ }3x+y=9\]

    C) \[x-y=3\,and\,x+y=2\]

    D) \[2x+y=7\text{ }and\text{ }x-2y=9\]

    E) \[2x-y=7\text{ }and\text{ }x+2y=9\]

    View Answer play_arrow
  • question_answer177) The straight line\[3x+4y-5=0\]and \[4x=3y+15\]intersect at the point P. On these lines the points Q and R are chosen so that PQ = PR. The slopes of the lines QR passing through (1, 2) are

    A) \[-7,1/7\]

    B) \[7,1/7\]

    C) \[7,-1/7\]

    D) \[3,-1/3\]

    E) \[-3,1/3\]

    View Answer play_arrow
  • question_answer178) The equation of the line which is such that the portion of line segment intercepted between the coordinate axes is bisected at\[(4,-3),\]is

    A) \[3x+4y=24\]

    B) \[3x-4y=12\]

    C) \[3x-4y=24\]

    D) \[4x-3y=24\]

    E) \[4x-3y=12\]

    View Answer play_arrow
  • question_answer179) The acute angle between the lines joining the origin to the points of intersection of the line\[\sqrt{3}x+y=2\]and the circle is\[{{x}^{2}}+{{y}^{2}}=4,\]is

    A) \[\pi /2\]

    B) \[\pi /3\]

    C) \[\pi /4\]

    D) \[\pi /6\]

    E) \[\pi /12\]

    View Answer play_arrow
  • question_answer180) If the circle \[{{x}^{2}}+{{y}^{2}}+4x+22y+c=0\]bisects the circumference of the circle\[{{x}^{2}}+{{y}^{2}}-2x+\]\[8y-d=0,\] then\[c+d\]is equal to

    A) 30

    B) 50

    C) 40

    D) 56

    E) 52

    View Answer play_arrow
  • question_answer181) Two diameters of the circle\[3{{x}^{2}}+3{{y}^{2}}-6x\]\[-18y-7=0\]are along the lines\[3x+y=q\] and\[x-3y={{c}_{2}}\].Then the value of\[{{c}_{1}}{{c}_{2}}\]is

    A) \[-\,48\]

    B) 80

    C) \[-\,72\]

    D) 54

    E) 24

    View Answer play_arrow
  • question_answer182) The area of an equilateral triangle that can be inscribed in\[{{x}^{2}}+{{y}^{2}}-4x-6y-12=0,\]is

    A) \[\frac{25\sqrt{3}}{4}\,sq\] unit

    B) \[\frac{35\sqrt{3}}{4}sq\,\] unit

    C) \[\frac{55\sqrt{3}}{4}sq\] unit

    D) \[\frac{75\sqrt{3}}{4}sq\] unit

    E) \[\frac{25}{4}sq\] unit

    View Answer play_arrow
  • question_answer183) Length of the tangents from the point\[(1,2)\]to the circles\[{{x}^{2}}+{{y}^{2}}+x+y-4=0\]and\[3{{x}^{2}}+\] \[3{{y}^{2}}-x-y-k=0\]are in the ratio\[4:3,\] then k is equal to

    A) 37/2

    B) 4/37

    C) 21

    D) 7

    E) 39/4

    View Answer play_arrow
  • question_answer184) The parametric representation of a point on the ellipse whose foci are (3, 0) and\[(-1,\text{ }0)\] and eccentricity 2/3 is

    A) \[(1+3\text{ }cos\text{ }\theta ,\text{ }\sqrt{3}sin\theta )\]

    B) \[(1+3\text{ }cos\theta ,\text{ }5\text{ }sin\theta )\]

    C) \[(1+3\text{ }cos\theta ,1+\sqrt{5}sin\theta )\]

    D) \[(1+3\text{ }cos\theta ,1+5\text{ }sin\theta )\]

    E) \[(1+3cos\theta ,\sqrt{5}sin\theta )\]

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  • question_answer185) The eccentricity of the conic \[\frac{{{(x+2)}^{2}}}{7}+{{(y-1)}^{2}}=14\]

    A) \[\sqrt{\frac{7}{8}}\]

    B) \[\sqrt{\frac{6}{17}}\]

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

    D) \[\sqrt{\frac{6}{11}}\]

    E) \[\sqrt{\frac{6}{7}}\]

    View Answer play_arrow
  • question_answer186) If for the ellipse\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1,\]\[y-\]axis is the minor axis and the length of the latus rectum is one half of the length of its minor axis, then its eccentricity is

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

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

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

    D) \[\frac{3}{4}\]

    E) \[\frac{3}{5}\]

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  • question_answer187) If the ellipse\[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\]and the hyperbola \[\frac{{{x}^{2}}}{100}-\frac{4{{y}^{2}}}{225}=1\]have the same directrices, then the value of\[{{b}^{2}}\]is

    A) 9

    B) 144

    C) 12

    D) 4

    E) 25

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  • question_answer188) The position vectors of the points A and B with respect to O are\[2\hat{i}+2\hat{j}+\hat{k}\]and\[2\hat{i}+4\hat{j}+4\hat{k}\]. The length of the internal bisector of\[\angle BOA\]of\[\Delta AQB\]is

    A) \[\frac{\sqrt{136}}{9}\]

    B) \[\frac{\sqrt{136}}{3}\]

    C) \[\frac{20}{3}\]

    D) \[\sqrt{\frac{217}{9}}\]

    E) \[\frac{25}{3}\]

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  • question_answer189) Given\[(\overrightarrow{a}\times \overrightarrow{b})\times (\overrightarrow{c}\times \overrightarrow{d})=5\overrightarrow{c}\times 6\overrightarrow{d},\]then the value of\[(\overrightarrow{a}.\overrightarrow{b})\times (\overrightarrow{a}+\overrightarrow{c}+2\overrightarrow{d})\]is

    A) 7

    B) 16

    C) \[-1\]

    D) 4

    E) \[-17\]

    View Answer play_arrow
  • question_answer190) Let a, b and c be non-zero vectors such that\[(\overrightarrow{a}.\overrightarrow{b})\times \overrightarrow{c}=\frac{-1}{4}|\overrightarrow{b}||\overrightarrow{c}|\overrightarrow{a}.\]. If\[\theta \]is the acute angle between the vectors \[\vec{b}\] and \[\vec{c}\], then the angle between\[\overrightarrow{a}\]and\[\overrightarrow{c}\]is equal to

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

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

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

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

    E) \[\frac{\pi }{6}\]

    View Answer play_arrow
  • question_answer191) A vector of magnitude 12 unit perpendicular to the plane containing the vectors \[4\hat{i}+6\hat{j}-\hat{k}\] and\[3\hat{i}+8\hat{j}+\hat{k}\]is

    A) \[-8\hat{i}+4\hat{j}+8\hat{k}\]

    B) \[8\hat{i}+4\hat{j}+8\hat{k}\]

    C) \[8\hat{i}-4\hat{j}+8\hat{k}\]

    D) \[8\hat{i}-4\hat{j}-8\hat{k}\]

    E) \[4i-8\hat{j}-8\hat{k}\]

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  • question_answer192) Forces of magnitudes 3 and 4 unit acting along\[6\hat{i}+2\hat{j}+3\hat{k}\]and\[3\hat{i}-2\hat{j}+6\hat{k}\]respectively act on a particle and displace it from (2, 2, -1) to (4, 3, 1). The work done is

    A) 124/7

    B) 120/7

    C) 125/7

    D) 121/7

    E) 123/7

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  • question_answer193) If ABCD be a parallelogram and M be the point of intersection of the diagonals. If O is any point, then\[\overset{\to }{\mathop{OA}}\,+\overset{\to }{\mathop{OB}}\,+\overset{\to }{\mathop{OC}}\,+\overset{\to }{\mathop{OD}}\,\]is

    A) \[3\overset{\to }{\mathop{OM}}\,\]

    B) \[4\overset{\to }{\mathop{OM}}\,\]

    C) \[\overset{\to }{\mathop{OM}}\,\]

    D) \[2\overset{\to }{\mathop{OM}}\,\]

    E) \[\frac{1}{2}\overset{\to }{\mathop{OM}}\,\]

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  • question_answer194) If D, E and F are the mid points of the sides \[\overset{\to }{\mathop{BC}}\,,\text{ }\overset{\to }{\mathop{CA}}\,\] and\[\overset{\to }{\mathop{AB}}\,\]respectively of the triangle ABC and G is the centroid of the triangle, then \[\overset{\to }{\mathop{GD}}\,+\overset{\to }{\mathop{GE}}\,+\overset{\to }{\mathop{GF}}\,\]is

    A) \[\overset{\to }{\mathop{O}}\,\]

    B) \[2\overset{\to }{\mathop{AB}}\,\]

    C) \[2\overset{\to }{\mathop{GE}}\,\]

    D) \[2\overset{\to }{\mathop{GC}}\,\]

    E) \[\overset{\to }{\mathop{GA}}\,+\overset{\to }{\mathop{GB}}\,\]

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  • question_answer195) The shortest distance from the point\[(1,2,-1)\] to the surface of the sphere\[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=54\]is

    A) \[3\sqrt{6}\]

    B) \[2\sqrt{6}\]

    C) \[\sqrt{6}\]

    D) \[2\]

    E) \[4\]

    View Answer play_arrow
  • question_answer196) If from a point P (a, b, c) perpendiculars PA, PB are drawn to yz and zx planes, then the equation of the plane OAB is

    A) \[bcx+cay+abz=0\]

    B) \[bcx+cay-abz=0\]

    C) \[bcx-cay+abz=0\]

    D) \[-bcx+cay+abz=0\]

    E) \[ax+by+cz=0\]

    View Answer play_arrow
  • question_answer197) If\[P(x,y,z)\]is a point on the line segment joining Q (2, 2, 4) and R (3, 5, 6) such that projections of\[\overrightarrow{OP}\]on the axes are\[\frac{13}{5},\frac{19}{5},\frac{26}{5}\]respectively, then P divides QR in the ratio

    A) 1 : 2

    B) 3 : 2

    C) 2 : 3

    D) 1 : 3

    E) 3 : 1

    View Answer play_arrow
  • question_answer198) The equation to the plane through the points (2, 3, 1) and\[(4,-\text{ }5,3)\]parallel to\[x-\]axis is

    A) \[x+y+4z=7\]

    B) \[x+4z=7\]

    C) \[y-4z=7\]

    D) \[y+4z=-7\]

    E) \[y+4z=7\]

    View Answer play_arrow
  • question_answer199) The angle between\[\overrightarrow{r}=(1+2\mu )\hat{i}+(2+\mu )\hat{j}+(2\mu -1)\hat{k}\]and the plane\[3x-2y+6z=0\](where u is a scalar) is

    A) \[{{\sin }^{-1}}\left( \frac{15}{21} \right)\]

    B) \[{{\cos }^{-1}}\left( \frac{16}{21} \right)\]

    C) \[{{\sin }^{-1}}\left( \frac{16}{21} \right)\]

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

    E) \[{{\cos }^{-1}}\left( \frac{\sqrt{3}}{2} \right)\]

    View Answer play_arrow
  • question_answer200) The length of the shortest distance between the two lines \[r=(-3\hat{i}+6\hat{j})+s(-4\hat{i}+3\hat{j}+2\hat{k})\]and\[\overrightarrow{r}=(-2\hat{i}+7\hat{k})+t(-4\hat{i}+\hat{j}+\hat{k})\]is

    A) 7 unit

    B) 13 unit

    C) 8 unit

    D) 9 unit

    E) 11 unit

    View Answer play_arrow
  • question_answer201) The perpendicular distance of the point (6, 5, 8) from y-axis is

    A) 5 unit

    B) 6 unit

    C) 8 unit

    D) 9 unit

    E) 10 unit

    View Answer play_arrow
  • question_answer202) The equation of the plane passing through the origin and containing the line \[\frac{x-1}{5}=\frac{y-2}{4}=\frac{z-3}{5}\]is

    A) \[x+5y-3z=0\]

    B) \[x-5y+3z=0\]

    C) \[x-5y-3z=0\]

    D) \[3x-10y+5z=0\]

    E) \[x+5y+3z=0\]

    View Answer play_arrow
  • question_answer203) The standard deviation of the numbers 31, 32, 33, ..., 46, 47 is

    A) \[\sqrt{\frac{17}{12}}\]

    B) \[\sqrt{\frac{{{47}^{2}}-1}{12}}\]

    C) \[2\sqrt{6}\]

    D) \[4\sqrt{3}\]

    E) \[\frac{5}{12}\]

    View Answer play_arrow
  • question_answer204) A random variable X takes values 0, 1, 2, 3,... with probability\[p(X=x)=k(x+1){{\left( \frac{1}{5} \right)}^{x}}\] where k is constant, then\[P\{X=0)\]is

    A) 7/25

    B) 18/25

    C) 13/25

    D) 19/25

    E) 16/25

    View Answer play_arrow
  • question_answer205) Out of 15 persons 10 can speak Hindi and 8 can speak English. If two persons are chosen at random, then the probability that one person speaks Hindi only and the other speaks both Hindi and English is

    A) 3/5

    B) 7/12

    C) 1/5

    D) 2/5

    E) 2/3

    View Answer play_arrow
  • question_answer206) A random variable X has the following probability distribution

    \[X={{x}_{1}}\] 1 2 3 4
    \[P(X={{x}_{1}})\] 0.1 0.2 0.3 0.4
    The mean and the standard deviation are respectively

    A) 3 and 2

    B) 3 and 1

    C) 3 and\[\sqrt{3}\]

    D) 2 and 1

    E) 3 and \[\sqrt{2}\]

    View Answer play_arrow
  • question_answer207) If\[g(x)=\int_{0}^{x}{{{\cos }^{4}}}tdt,\]then\[g(x+\pi )\]is equal to

    A) \[g(x)+g(\pi )\]

    B) \[g(x)-g(\pi )\]

    C) \[g(x).g(\pi )\]

    D) \[\frac{g(x)}{g(\pi )}\]

    E) \[\frac{g(\pi )}{g(x)}\]

    View Answer play_arrow
  • question_answer208) If\[\underset{x\to 1}{\mathop{\lim }}\,\frac{a{{x}^{2}}+bx+c}{{{(x-1)}^{2}}}=2,\]then (a, b, c) is

    A) \[(2,-4,\text{ }2)\]

    B) (2, 4, 2)

    C) \[(2,4,-2)\]

    D) \[(2,-4,-2)\]

    E) \[(-2,4,2)\]

    View Answer play_arrow
  • question_answer209) Let\[[x]\]denote the greatest integer\[\le x\]. If\[f(x)=[x]\]and\[g(x)=|x|,\]then the value of \[f\left( g\left( \frac{8}{5} \right) \right)-g\left( f\left( -\frac{8}{5} \right) \right)\]is

    A) 2

    B) \[-2\]

    C) 1

    D) 0

    E) \[-1\]

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  • question_answer210) If\[f(x)=\frac{{{\log }_{e}}(1+{{x}^{2}}\tan x)}{\sin {{x}^{3}}},x\ne 0\]is to be continuous at\[x=0,\]then\[f(0)\]must be defined as

    A) 1

    B) 0

    C) 1/2

    D) \[-1\]

    E) 2

    View Answer play_arrow
  • question_answer211) The derivative of\[f(tan\text{ }x)\]w.r.t.\[g(sec\text{ }x)\]at \[x=\pi /4\]where\[f(1)=2\]and\[g(\sqrt{2})=4\]is

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

    B) \[\sqrt{2}\]

    C) \[1\]

    D) \[2\]

    E) \[\frac{1}{2}\]

    View Answer play_arrow
  • question_answer212) lf\[\sec \left( \frac{x-y}{x+y} \right)=a,\]then\[\frac{dy}{dx}\]is

    A) \[\frac{y}{x}\]

    B) \[-\frac{y}{x}\]

    C) \[\frac{x}{y}\]

    D) \[-\frac{x}{y}\]

    E) \[\frac{x-y}{x+y}\]

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  • question_answer213) If\[x=\frac{2at}{1+{{t}^{3}}}\]and\[y=\frac{2a{{t}^{2}}}{{{(1+{{t}^{3}})}^{2}}}\]then\[\frac{dy}{dx}\]is

    A) \[ax\]

    B) \[{{a}^{2}}{{x}^{2}}\]

    C) \[\frac{x}{a}\]

    D) \[\frac{x}{2a}\]

    E) x\[2a\]

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  • question_answer214) If\[\cos \frac{x}{2}.\cos \frac{x}{{{2}^{2}}}...\cos \frac{x}{{{2}^{n}}}=\frac{\sin x}{{{2}^{n}}\sin \frac{x}{{{2}^{n}}}},\]then \[\frac{1}{2}\tan \frac{x}{2}+\frac{1}{{{2}^{2}}}\tan \frac{x}{{{2}^{2}}}+......+\frac{1}{{{2}^{n}}}\tan \frac{x}{{{2}^{n}}}\]is

    A) \[\cot x-\cot \frac{x}{{{2}^{n}}}\]

    B) \[\frac{1}{{{2}^{n}}}\cot \left( \frac{x}{{{2}^{n}}} \right)-\cot x\]

    C) \[\frac{1}{{{2}^{n}}}\tan \left( \frac{x}{{{2}^{n}}} \right)-\tan x\]

    D) \[\frac{1}{2}\cot x-\frac{1}{{{2}^{n}}}\cot \left( \frac{x}{{{2}^{n}}} \right)\]

    E) \[\cot \left( \frac{x}{{{2}^{n}}} \right)-\cot x\]

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  • question_answer215) If\[y=\underset{n\to \infty }{\mathop{\lim }}\,(1+x)(1+{{x}^{2}})(1+{{x}^{4}})\]\[...(1+{{x}^{2n}}\text{ })\]and\[{{x}^{2}}<1,\]then y is equal to

    A) 1

    B) \[\frac{1}{1-x}\]

    C) \[\frac{1}{1+x}\]

    D) \[\frac{-1}{{{(1-x)}^{2}}}\]

    E) \[\frac{1}{{{(1-x)}^{2}}}\]

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  • question_answer216) . If\[f(x)={{\log }_{{{x}^{3}}}}({{\log }_{e}}{{x}^{2}}),\]then\[f(x)\]at\[x=e\]is

    A) \[\frac{1}{3e}(1-{{\log }_{e}}2)\]

    B) \[\frac{1}{3e}(1+{{\log }_{e}}2)\]

    C) \[\frac{1}{3e}(-1+{{\log }_{e}}2)\]

    D) \[-\frac{1}{3e}(1+{{\log }_{e}}2)\]

    E) \[\frac{1}{3e}({{\log }_{e}}2)\]

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  • question_answer217) If\[f(x)=(x-2)(x-4)(x-6)....(x-2n),\] then\[f(2)\]is

    A) \[{{(-1)}^{n}}{{2}^{n-1}}(n-1)!\]

    B) \[{{(-2)}^{n-1}}{{2}^{n}}(n-1)!\]

    C) \[{{(-2)}^{n}}n!\]

    D) \[{{(-1)}^{n-1}}{{2}^{n}}(n-1)!\]

    E) \[{{2}^{n-1}}(n-1)!\]

    View Answer play_arrow
  • question_answer218) If\[\theta \]is semi vertical angle of a cone of maximum volume and given slant height, then \[tan\theta \]is equal to

    A) 2

    B) 1

    C) \[\sqrt{2}\]

    D) \[\sqrt{3}\]

    E) \[\sqrt{3}+\sqrt{2}\]

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  • question_answer219) A man of 2 m height walks at a uniform speed of 6 km/h away from a lamp post of 6 m height. The rate at which the length of his shadow increases is

    A) 2 km/h

    B) 1 km/h

    C) 3 km/h

    D) 6 km/h

    E) 3/2 km/h

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  • question_answer220) If\[y=4x-5\]is a tangent to the curve\[{{y}^{2}}=p{{x}^{3}}+q\]at (2, 3), then

    A) \[p=2,q=-7\]

    B) \[p=-2,q=7\]

    C) \[p=-2,q=-7\]

    D) \[p=2,q=7\]

    E) \[p=0,q=7\]

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  • question_answer221) A missile is fired from the ground level rises\[x\]metres vertically upwards in t seconds where\[x=100t-\frac{25}{2}{{t}^{2}}.\]The maximum height reached is

    A) 200m

    B) 125m

    C) 160m

    D) 190m

    E) 300m

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  • question_answer222) If the curves\[{{x}^{2}}=9A(9-y)\]and\[{{x}^{2}}=A(y+1)\]intersect orthogonally, then the value of A is

    A) 3

    B) 4

    C) 5

    D) 7

    E) 9

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  • question_answer223) If\[f(x)=3{{x}^{4}}+4{{x}^{3}}-12{{x}^{2}}+12,\] then\[f(x)\]is

    A) increasing in\[(-\infty ,-2)\]and in (0, 1)

    B) increasing in\[(-2,0)\] and in\[(1,\infty )\]

    C) decreasing in\[(-2,\text{ }0)\]and in (0, 1)

    D) decreasing in\[(-\infty ,-2)\] and in\[(1,\text{ }\infty )\]

    E) increasing in\[(-2,\text{ }0)\]and in (0,1)

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  • question_answer224) If the distance s covered by a particle in time t is proportional to the cube root of its velocity, then the acceleration is

    A) a constant

    B) \[\propto {{s}^{3}}\]

    C) \[\propto \frac{1}{{{s}^{3}}}\]

    D) \[\propto {{s}^{5}}\]

    E) \[\propto \frac{1}{{{s}^{5}}}\]

    View Answer play_arrow
  • question_answer225) \[\int{({{\sin }^{6}}x+{{\cos }^{6}}x+3{{\sin }^{2}}x{{\cos }^{2}}x)}dx\]is equal to

    A) \[x+c\]

    B) \[\frac{3}{2}\sin 2x+c\]

    C) \[-\frac{3}{2}\cos 2x+c\]

    D) \[\frac{1}{3}\sin 3x-\cos 3x+c\]

    E) \[\frac{1}{3}\sin 3x+\cos 3x+c\]

    View Answer play_arrow
  • question_answer226) \[\int{\frac{{{4}^{x+1}}-{{7}^{x-1}}}{{{28}^{x}}}}dx\]is equal to

    A) \[\frac{1}{7{{\log }_{e}}4}{{4}^{-x}}-\frac{4}{{{\log }_{e}}7}{{7}^{-x}}+c\]

    B) \[\frac{1}{7{{\log }_{e}}4}{{4}^{-x}}+\frac{4}{{{\log }_{e}}7}{{7}^{-x}}++c\]

    C) \[\frac{{{4}^{-x}}}{{{\log }_{e}}7}-\frac{{{7}^{-x}}}{{{\log }_{e}}4}+c\]

    D) \[\frac{{{4}^{-x}}}{{{\log }_{e}}4}-\frac{{{7}^{-x}}}{{{\log }_{e}}7}+c\]

    E) \[\frac{1}{28}{{\log }_{e}}{{4}^{-x}}+\frac{1}{7}{{\log }_{e}}{{7}^{-x}}+c\]

    View Answer play_arrow
  • question_answer227) The value of\[\int{{{e}^{{{\tan }^{-1}}x}}\frac{(1+x+{{x}^{2}})}{1+{{x}^{2}}}}dx\]is

    A) \[{{\tan }^{-1}}x+c\]

    B) \[{{e}^{{{\tan }^{-1}}x}}+2x+c\]

    C) \[{{e}^{{{\tan }^{-1}}x}}+c\]

    D) \[{{e}^{{{\tan }^{-1}}x}}-x+c\]

    E) \[x{{e}^{{{\tan }^{-1}}x}}+c\]

    View Answer play_arrow
  • question_answer228) The value of\[\int{\frac{{{e}^{5{{\log }_{e}}x}}-{{e}^{4{{\log }_{e}}x}}}{{{e}^{3{{\log }_{e}}x}}-{{e}^{2{{\log }_{e}}x}}}}dx\]is

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

    B) \[\frac{{{x}^{2}}}{2}+c\]

    C) \[\frac{{{x}^{3}}}{3}+c\]

    D) \[\frac{x}{2}+c\]

    E) \[e\]

    View Answer play_arrow
  • question_answer229) If\[f(x)=\frac{{{\sin }^{-1}}x}{\sqrt{1-{{x}^{2}}}}\]and\[g(x)={{e}^{{{\sin }^{-1}}x}},\]then \[\int{f(x)g(x)}dx\]is equal to

    A) \[{{e}^{{{\sin }^{-1}}x}}({{\sin }^{-1}}x-1)+c\]

    B) \[{{e}^{{{\sin }^{-1}}x}}+c\]

    C) \[{{e}^{{{({{\sin }^{-1}}x)}^{2}}}}+c\]

    D) \[{{e}^{2{{\sin }^{-1}}x}}+c\]

    E) \[{{e}^{{{\sin }^{-1}}x}}{{\sin }^{-1}}x+c\]

    View Answer play_arrow
  • question_answer230) The value of\[\int{\frac{{{x}^{2}}+1}{{{x}^{4}}-{{x}^{2}}+1}}dx\]is

    A) \[{{\tan }^{-1}}(2{{x}^{2}}-1)+c\]

    B) \[{{\tan }^{-1}}\frac{{{x}^{2}}+1}{x}+c\]

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

    D) \[{{\tan }^{-1}}{{x}^{2}}+c\]

    E) \[{{\tan }^{-1}}\left( \frac{{{x}^{2}}-1}{x} \right)+c\]

    View Answer play_arrow
  • question_answer231) \[\int{\cos \left\{ 2{{\tan }^{-1}}\sqrt{\frac{1-x}{1+x}} \right\}}dx\]is equal to

    A) \[\frac{1}{8}({{x}^{2}}-1)+c\]

    B) \[\frac{{{x}^{4}}}{4}+c\]

    C) \[\frac{x}{2}+c\]

    D) \[\frac{x}{4}+c\]

    E) \[\frac{{{x}^{2}}}{2}+c\]

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  • question_answer232) The area bounded by the parabola\[{{y}^{2}}=8x\]and its latusrectum in sq unit is

    A) 16/3 sq unit

    B) 32/3 sq unit

    C) 8/3 sq unit

    D) 64/3 sq unit

    E) 4/3 sq unit

    View Answer play_arrow
  • question_answer233) \[\int_{\pi /6}^{\pi /3}{\frac{1}{1+{{\tan }^{3}}x}dx}\] is

    A) \[\pi /12\]

    B) \[\pi /4\]

    C) \[\pi /3\]

    D) \[\pi /6\]

    E) \[\pi /2\]

    View Answer play_arrow
  • question_answer234) \[\int_{-1}^{1}{\frac{17{{x}^{5}}-{{x}^{4}}+29{{x}^{3}}-31x+1}{{{x}^{2}}+1}}dx\]is

    A) 4/5

    B) 5/4

    C) 4/3

    D) 3/4

    E) 2/3

    View Answer play_arrow
  • question_answer235) If\[{{I}_{n}}=\int_{0}^{\pi /4}{{{\tan }^{n}}x},\]then\[\frac{1}{{{I}_{3}}+{{I}_{5}}}\]is

    A) 1/4

    B) 1/2

    C) 1/8

    D) 4

    E) 6

    View Answer play_arrow
  • question_answer236) If\[\int_{0}^{\pi /2}{{{\sin }^{6}}x}dx=\frac{5\pi }{32},\]then the value of\[\int_{-\pi }^{\pi }{({{\sin }^{6}}x+{{\cos }^{6}}x)}dx\]is

    A) \[5\pi /8\]

    B) \[5\pi /16\]

    C) \[5\pi /2\]

    D) \[5\pi /4\]

    E) \[5\pi /32\]

    View Answer play_arrow
  • question_answer237) The solution of the differential equation \[\frac{dy}{dx}=\frac{y}{x}+\frac{\phi \left( \frac{y}{x} \right)}{\phi \left( \frac{y}{x} \right)}\]is

    A) \[x\phi \left( \frac{y}{x} \right)=k\]

    B) \[\phi \left( \frac{y}{x} \right)=kx\]

    C) \[y\phi \left( \frac{y}{x} \right)=k\]

    D) \[\phi \left( \frac{y}{x} \right)=ky\]

    E) \[\phi \left( \frac{y}{x} \right)=k{{e}^{y/x}}\]

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  • question_answer238) If the integrating factor of the differential equation\[\frac{dy}{dx}+p(x)t=Q(x)\]then\[P(x)\]is

    A) \[x\]

    B) \[{{x}^{2}}/2\]

    C) \[1/x\]

    D) \[1/{{x}^{2}}\]

    E) \[1/2x\]

    View Answer play_arrow
  • question_answer239) If\[{{c}_{1}},{{c}_{2}},{{c}_{3}},{{c}_{4}},{{c}_{5}}\]and\[{{c}_{6}}\]are constants, then the order of the differential equation whose general solution is given by \[y={{c}_{1}}cos\]\[(x+{{c}_{2}})+{{c}_{3}}\sin (x+{{c}_{4}})+{{c}_{5}}{{e}^{x}}+{{c}_{6}}\]

    A) 6

    B) 5

    C) 4

    D) 3

    E) 2

    View Answer play_arrow
  • question_answer240) \[y=2{{e}^{2x}}-{{e}^{-x}}\]is a solution of the differential equation

    A) \[{{y}_{2}}+{{y}_{1}}+2y=0\]

    B) \[{{y}_{2}}-{{y}_{1}}+2y=0\]

    C) \[{{y}_{2}}+{{y}_{1}}=0\]

    D) \[{{y}_{2}}-{{y}_{1}}-2y=0\]

    E) \[{{y}_{2}}-2{{y}_{1}}-y=0\]

    View Answer play_arrow


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