# Solved papers for CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2009

### done CEE Kerala Engineering Solved Paper-2009

• question_answer1) The percentage errors in the measurement of length and time period of a simple pendulum are 1% and 2% respectively. Then the maximum error in the measurement of acceleration due to gravity is

A) 8%

B) 3%

C) 4%

D) 6%

E) 5%

• question_answer2) Dimensional formula of Stefans constant is

A) $[M{{T}^{-3}}{{K}^{-4}}]$

B) $[ML{{T}^{-2}}{{K}^{-4}}]$

C) $[M{{L}^{2}}{{T}^{-2}}]$

D) $[M{{T}^{-2}}{{L}^{0}}]$

E) $[M{{T}^{-4}}{{L}^{0}}]$

• question_answer3) A body is falling freely under gravity. The distances covered by the body in first, second and third minute of its motion are in the ratio

A) $1:4:9$

B) $1:2:3$

C) $1:3:5$

D) $1:5:6$

E) $1:5:13$

• question_answer4) A bullet fired into a fixed wooden block loses half of its velocity after penetrating 40 cm. It comes to rest after penetrating a further distance of

A) $\frac{22}{3}cm$

B) $\frac{40}{3}cm$

C) $\frac{20}{3}cm$

D) $\frac{22}{5}cm$

E) $\frac{26}{5}cm$

• question_answer5) A ball A is thrown up vertically with a speed u and at the same instant another ball B is released from a height h. At time t, the speed of A relative to B is

A) $u$

B) $2u$

C) $u-gt$

D) $\sqrt{({{u}^{2}}-gt)}$

E) $gt$

• question_answer6) A bullet is to be fired with a speed of 2000 $m{{s}^{-1}}$to hit a target 200 m away on a level ground. If$g=10\text{ }m{{s}^{-2}},$the gun should be aimed

A) directly at the target

B) 5 cm below the target

C) 5 cm above the target

D) 2 cm above the target

E) 2 cm below the target

• question_answer7) The resultant of two vectors$\overrightarrow{P}$and$\overrightarrow{Q}$is$\overrightarrow{R}$. If the magnitude of$\overrightarrow{Q}$is doubled, the new resultant becomes perpendicular to$\overrightarrow{P}$. Then the magnitude of$\overrightarrow{R}$is

A) $P+Q$

B) $Q$

C) $P$

D) $\frac{P+Q}{2}$

E) $P-Q$

• question_answer8) A motor car is moving with a speed of$20\text{ }m{{s}^{-1}}$ on a circular track of radius 100 m. If its speed is increasing at the rate of$3m{{s}^{-1}},$ its resultant acceleration is

A) $3\,m{{s}^{-2}}$

B) $5\,m{{s}^{-2}}$

C) $2.5\,m{{s}^{-2}}$

D) $3.5\,m{{s}^{-2}}$

E) $4\,m{{s}^{-2}}$

• question_answer9) A stationary body of mass 3 kg explodes into three equal pieces. Two of the pieces fly off in two mutually perpendicular directions, one with a velocity of$3\hat{i}\,m{{s}^{-1}}$and the other with a velocity of$4\hat{j}\,m{{s}^{-1}}$. If the explosion occurs in${{10}^{-4}}s,$the average force acting on the third piece in newton is

A) $(3\hat{i}+4\hat{j})\times {{10}^{-4}}$

B) $(3\hat{i}-4\hat{j})\times {{10}^{-4}}$

C) $(3\hat{i}+4\hat{j})\times {{10}^{4}}$

D) $-(3\hat{i}+4\hat{j})\times {{10}^{4}}$

E) $(4\hat{i}-3\hat{j})\times {{10}^{4}}$

• question_answer10) A mass of 1 kg is just able to slide down the slope of an inclined rough surface when the angle of inclination is${{60}^{o}}$. The minimum force necessary to pull the mass up the inclined plane$(g=10m{{s}^{-2}})$is

A) 14.14 N

B) 17.32 N

C) 10 N

D) 16.66 N

E) 0.866 N

• question_answer11) A block of mass m is resting on a smooth horizontal surface. One end of a uniform rope of mass$\left( \frac{m}{3} \right)$is fixed to the block, which is pulled in the horizontal direction by applying force F at the other end. The tension in the middle of the rope is

A) $\frac{8}{7}F$

B) $\frac{1}{7}F$

C) $\frac{1}{8}F$

D) $\frac{1}{5}F$

E) $\frac{7}{8}F$

• question_answer12) A particle is acted upon by a force F which varies with position$x$as shown in figure. If the particle at$x=0$has kinetic energy of $25J,$ then the kinetic energy of the particle at $x=16\text{ }m$is

A) $45\text{ }J$

B) $30\text{ }J$

C) $70\text{ }J$

D) $135\text{ }J$

E) $20\text{ }J$

• question_answer13) Two springs P and Q of force constants${{k}_{p}}$and${{k}_{Q}}$ $\left( {{k}_{Q}}=\frac{{{k}_{p}}}{2} \right)$are stretched by applying forces of equal magnitude. If the energy stored in Q is E, then the energy stored in P is

A) $E$

B) $2E$

C) $\frac{E}{8}$

D) $\frac{E}{4}$

E) $\frac{E}{2}$

• question_answer14) A rod of mass m and length (is made to stand at an angle of${{60}^{o}}$with the vertical. Potential energy of the rod in this position is

A) $mgl$

B) $\frac{mgl}{2}$

C) $\frac{mgl}{3}$

D) $\frac{mgl}{4}$

E) $\frac{mgl}{\sqrt{2}}$

• question_answer15) From a circular ring of mass M and radius R, an arc corresponding to a${{90}^{o}}$sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is k times$M{{R}^{2}}$. Then the value of k is

A) $\frac{3}{4}$

B) $\frac{7}{8}$

C) $\frac{1}{4}$

D) $1$

E) $\frac{1}{8}$

• question_answer16) A system consists of 3 particles each of mass m located at points (1, 1), (2, 2) and (3, 3). The coordinates of the centre of mass are

A) (6, 6)

B) (3, 3)

C) (1, 1)

D) (2, 2)

E) (5, 5)

• question_answer17) A wheel of moment of inertia$2.5\text{ }kg-{{m}^{2}}$has an initial angular velocity of$40\text{ }rad\text{ }{{s}^{-1}}$. A constant torque of 10 Nm acts on the wheel. The time during which the wheel is accelerated to$60\text{ }rad\text{ }{{s}^{-1}}$ is

A) 4s

B) 6s

C) 5s

D) 2.5s

E) 4.5s

• question_answer18) The ratio of radii of earth to another planet is$\frac{2}{3}$and the ratio of their mean densities is$\frac{4}{5}$. If an astronaut can jump to1 a maximum height of 1.5m on the earth, with the same effort, the maximum height he can jump on the planet is

A) 1 m

B) 0.8 m

C) 0.5m

D) 1.25m

E) 2m

• question_answer19) If an object of mass m is taken from the surface of earth (radius R) to a height 2R, then the work done is

A) $2mgR$

B) $mgR$

C) $\frac{2}{3}mgR$

D) $\frac{3}{2}mgR$

E) $\frac{1}{3}mgR$

• question_answer20) At what depth below the surface of the earth, the value of g is the same as that at a height of 5 km?

A) 1.25 km

B) 2.5 km

C) 5 km

D) 7.5 km

E) 10km

• question_answer21) A small spherical ball falling through a viscous medium of negligible density has terminal velocity v. Another ball of the same mass but of radius twice that of the earlier falling through the same viscous medium will have terminal velocity

A) $v$

B) $v/4$

C) $1:4$

D) $1:64$

E) $30:1$

• question_answer22) The excess pressure inside a spherical drop of water is four times that of another drop. Then their respective mass ratio is

A) $1:16$

B) $8:1$

C) $1:4$

D) $1:64$

E) $32:1$

• question_answer23) In a capillary rise experiment, the water level rises to a height of 5 cm. If the same capillary tube is placed in water such that only 3 cm of the tube projects outside the water level, then

A) water will begin to overflow through the capillary

B) angle of contact decreases

C) angle of contact increases

D) the meniscus completely vanishes

E) water will rise to a level less than 3 cm

• question_answer24) The Youngs modulus of the material of a wire is$2\times {{10}^{10}}N{{m}^{-2}}$.If the elongation strain is 1%, then the energy stored in the wire per unit: volume in$J{{m}^{-3}}$is

A) ${{10}^{6}}$

B) ${{10}^{8}}$

C) $2\times {{10}^{6}}$

D) $2\times {{10}^{8}}$

E) $0.5\times {{10}^{6}}$

• question_answer25) The change in internal energy of a given mass of gas, when its volume changes from V to 2V at constant pressure p is($\frac{{{C}_{P}}}{{{C}_{V}}}=\gamma ,$universal gas constant =R)

A) $\frac{pV}{\gamma }$

B) $\frac{pV}{(2\gamma -1)}$

C) $\frac{pV}{2(\gamma -1)}$

D) $\frac{R}{(\gamma -1)}$

E) $\frac{pV}{(\gamma -1)}$

• question_answer26) In a Carnot engine, the temperature of reservoir is${{927}^{o}}C$and that of sink is${{27}^{o}}C$. If the work done by the engine when it transfers heat from reservoir to sink is$12.6\times {{10}^{,}}^{6}J,$the quantity of heat absorbed by the engine from the reservoir is

A) $16.8\times {{10}^{6}}J$

B) $4\times {{10}^{6}}J$

C) $7.6\times {{10}^{6}}J$

D) $4.25\times {{10}^{6}}J$

E) $20.8\times {{10}^{6}}J$

• question_answer27) In the given$p-V$diagram, I is the initial state and F is the final state. The gas goes from$I$to F by (i) $IAF$ (ii) $IBF$ (iii) $ICF$ The heat absorbed by gas is

A) the same in all three processes

B) the same in (i) and (ii)

C) greater in (i) than in (ii)

D) the same in (i) and (iii)

E) greater in (iii) than in (i)

• question_answer28) Hot water cools from$60{}^\circ C$to$50{}^\circ C$in the first 10 min and to$42{}^\circ C$in the next 10 min. The temperature of the surroundings is

A) $10{}^\circ C$

B) $5{}^\circ C$

C) $15{}^\circ C$

D) $20{}^\circ C$

E) $22{}^\circ C$

• question_answer29) In a sinusoidal wave, the time required for a particular point to move from maximum displacement to zero displacement is 0.14 s. The frequency of the wave is

A) 0.42 Hz

B) 2.75 Hz

C) 1.79 Hz

D) 0.56 Hz

E) 3.5 Hz

• question_answer30) An electric motor of mass 40. kg is mounted on four vertical springs each having a spring constant of$4000\text{ }N{{m}^{-1}}$. The period with which the motor vibrates vertically is

A) 0.314s

B) 3.14s

C) 0.628s

D) 0.157s

E) 0.078s

• question_answer31) Two simple harmonic motions are represented by${{y}_{1}}=4\sin (4\pi t+\pi /2)$and${{y}_{2}}=3\cos (4\pi t)$. The resultant amplitude is

A) 7

B) 1

C) 5

D) $2+\sqrt{3}$

E) $2-\sqrt{3}$

• question_answer32) An observer is approaching a stationary source with a velocity$\frac{1}{4}$th of the velocity of sound. Then the ratio of the apparent frequency to actual frequency of source is

A) $4:5$

B) $5:4$

C) $2:3$

D) $3:2$

E) $2:5$

• question_answer33) When a wave travels in a medium, the particle displacement is given by the equation$y=a\sin 2\pi (bt-cx)$where a, b and c are constants. The maximum particle velocity will be twice the wave velocity, if

A) $c=\frac{1}{\pi a}$

B) $c=\pi a$

C) $b=ac$

D) $b=\frac{1}{ac}$

E) $a=bc$

• question_answer34) A progressive wave$y=A\sin (kx-\omega t)$is reflected by a rigid wall at$x=0$. Then the reflected wave can be represented by

A) $y=A\sin (kx+\omega t)$

B) $y=A\cos (kx+\omega t)$

C) $y=-A\sin (kx-\omega t)$

D) $y=-A\sin (kx+\omega t)$

E) $y=A\cos (kx-\omega t)$

• question_answer35) Which one of the following graphs represents the variation of electric field with distance r from the centre of a charged spherical conductor of radius R?

A)

B)

C)

D)

E)

• question_answer36) Two conducting spheres A and B of radius a and b respectively are at the same potential. The ratio of the surface charge densities of A and B is

A) $\frac{b}{a}$

B) $\frac{a}{b}$

C) $\frac{{{a}^{2}}}{{{b}^{2}}}$

D) $\frac{{{b}^{2}}}{{{a}^{2}}}$

E) $\frac{(a+b)}{(ab)}$

• question_answer37) Three charges 2 q,-q,-q are located at the vertices of an equilateral triangle. At the circumcentre of the triangle

A) the field is zero but potential is non-zero

B) potential is zero and the field is infinity

C) both the field and potential are zero

D) both the field and potential are non-zero

E) the field is non-zero but potential is zero

• question_answer38) A particle of mass m carrying charge q is kept at rest in a uniform electric field E and then released. The kinetic energy gained by the particle, when it moves through a distance y is.

A) $\frac{1}{2}qE{{y}^{2}}$

B) $qEy$

C) $qE{{y}^{2}}$

D) $q{{E}^{2}}y$

E) ${{q}^{2}}Ey$

• question_answer39) C, V, U and Q are capacitance, potential difference, energy stored and charge of a parallel plate capacitor respectively. The quantities that, increase when a dielectric slab is introduced between the plates without disconnecting the battery are

A) V and C

B) V and U

C) U and Q

D) V and Q

E) U but not Q

• question_answer40) A heater of 220 V heats a volume of water in 5 min. The same heater when connected to 110 V heats the same volume of water in (minute)

A) 5

B) 20

C) 10

D) 2.5

E) 1.25

• question_answer41) Two copper wires have their masses in the ratio$2:3$and the lengths in the ratio$3:4$. The ratio of their resistance is

A) $4:9$

B) $27:32$

C) $16:9$

D) $27:128$

E) $1:2$

• question_answer42) Two different conductors have same resistance at${{0}^{o}}C$. It is found that the resistance of the first conductor at${{t}_{1}}^{o}C$is equal to the resistance of the second conductor at${{t}_{2}}^{o}C$. The ratio of the temperature coefficients of resistance of the conductors,$\frac{{{\alpha }_{1}}}{{{\alpha }_{2}}}$is

A) $\frac{{{t}_{1}}}{{{t}_{2}}}$

B) $\frac{{{t}_{2}}-{{t}_{1}}}{{{t}_{2}}}$

C) $\frac{{{t}_{2}}-{{t}_{1}}}{{{t}_{1}}}$

D) $\frac{{{t}_{2}}}{{{t}_{1}}}$

E) $\frac{{{t}_{2}}}{{{t}_{2}}-{{t}_{1}}}$

• question_answer43) In the given circuit diagram the current through the battery and the charge on the capacitor respectively in steady state are

A) 1A and$3\mu C$

B) 17 A and $0\mu C$

C) $\frac{6}{7}A$ and$\frac{12}{7}\mu C$

D) 6 A and$0\mu C$

E) $11A$ and$3\mu C$

• question_answer44) A potentiometer wire of length 10 m and resistance$20\,\Omega$is connected in series with a 15 V battery and an external resistance$40\,\Omega$. A secondary cell of emf? in the secondary circuit is balanced by 240 cm long potentiometer wire. The emf E of the cell is

A) 2.4 V

B) 1.2 V

C) 2.0 V

D) 3 V

E) 6 V

• question_answer45) A current I enters a circular coil of radius R branches into two parts and then recombines as shown in the circuit diagram. The resultant magnetic field at the centre of the coil is

A) zero

B) $\frac{{{\mu }_{0}}I}{2R}$

C) $\frac{3}{4}\left( \frac{{{\mu }_{0}}I}{2R} \right)$

D) $\frac{1}{4}\left( \frac{{{\mu }_{0}}I}{2R} \right)$

E) $\frac{1}{2}\left( \frac{{{\mu }_{0}}I}{2R} \right)$

• question_answer46) The resistance of a galvanometer is$50\,\Omega$. and it shows full scale deflection for a current of 1 mA. To convert it into a voltmeter to measure 1 V and as well as 10 V (Refer circuit diagram) the resistances${{R}_{1}}$and${{R}_{2}}$respectively are

A) $950\,\Omega$and $9150\,\Omega$

B) $900\,\Omega$and$9950\,\Omega$

C) $900\,\Omega$and$9900\,\Omega$

D) $950\,\Omega$and $9000\,\Omega$

E) $950\,\Omega$and$9950\,\Omega$

• question_answer47) Two long parallel wires carry currents${{i}_{1}}$and${{i}_{2}}$such that${{i}_{1}}>{{i}_{2}}$. When the currents are in the same direction, the magnetic field at a point midway between the wires is$6\times {{10}^{-6}}T$. If the direction of${{i}_{2}}$is reversed, the field becomes$3\times {{10}^{-5}}T.$The ratio$\frac{{{i}_{1}}}{{{i}_{2}}}$is

A) $\frac{1}{2}$

B) 2

C) $\frac{2}{3}$

D) $\frac{3}{2}$

E) $\frac{1}{5}$

• question_answer48) A coil of 100 turns and area$2\times {{10}^{-2}}{{m}^{2}},$pivoted about a vertical diameter in a uniform magnetic field carries a current of 5A. When the coil is held with its plane in North-South direction, it experiences a torque of 0.3 Nm. When the plane is in East-West direction the torque is 0.4 Nm. The value of magnetic induction is (Neglect earths magnetic field)

A) 0.2 T

B) 0.3 T

C) 0.4 AT

D) 0.1T

E) 0.05 T

• question_answer49) The angle of dip at a place is${{37}^{o}}$and the vertical component of the earths magnetic field is$6\times {{10}^{-5}}T.$The earths magnetic field at this place is$(tan\text{ }{{37}^{o}}=3/4)$

A) $7\times {{10}^{-5}}T$

B) $6\times {{10}^{-5}}T$

C) $5\times {{10}^{-5}}T$

D) ${{10}^{-4}}T$

E) $4\times {{10}^{-5}}\,T$

• question_answer50) The impedance of a$R-C$circuit is${{Z}_{1}}$for frequency$f$and${{Z}_{2}}$for frequency$2f$. Then, ${{Z}_{1}}/{{Z}_{2}}$is

A) between 1 and 2

B) 2

C) 2 between$\frac{1}{2}$and 1

D) $\frac{1}{2}$

E) 4

• question_answer51) In an L-C-R series AC circuit the voltage across L, C and R is 10 V each. If the inductor is short circuited, the voltage across the capacitor would become on

A) $10\,V$

B) $\frac{20}{\sqrt{2}}\,V$

C) $20\sqrt{2}\,V$

D) $\frac{10}{\sqrt{2}}\,V$

E) $20\,V$

• question_answer52) A transformer of efficiency 90% draws an input power of 4 kW. An electrical appliance connected across the secondary draws a current of 6 A. The impedance of the device is

A) $60\,\Omega$

B) $50\,\Omega$

C) $80\,\Omega$

D) $100\,\Omega$

E) $120\,\Omega$

• question_answer53) The inductance of a coil in which a current of 0.1 A increasing at the rate of$0.5\text{ }A{{s}^{-1}}$represents a power flow of$\frac{1}{2}W,$is

A) 2H

B) 8H

C) 20 H

D) 10 H

E) 5H

• question_answer54) A point source of electromagnetic radiation has an average power output of 1500 W. The maximum value of electric field at a distance of 3 m from this source in$V{{m}^{-1}}$is

A) 500

B) 100

C) $\frac{500}{3}$

D) $\frac{250}{3}$

E) $10\sqrt{5}$

• question_answer55) The refractive index and the permeability of a medium are respectively 1.5 and$5\times {{10}^{-7}}H{{M}^{-1}}$. The relative permittivity of the medium is nearly

A) 25

B) 15

C) 81

D) 10

E) 6

• question_answer56) A square wire of side 1 cm is placed perpendicular to the principal axis of a concave mirror of focal length 15 cm at a distance of 20 cm. The area enclosed by the image of the wire is

A) $4c{{m}^{2}}$

B) $6c{{m}^{2}}$

C) $2c{{m}^{2}}$

D) $8c{{m}^{2}}$

E) $9c{{m}^{2}}$

• question_answer57) A thin prism P of refracting angle${{3}^{o}}$and refractive index 1.5 is combined with another thin prism Q of refractive index 1.6 to produce dispersion without deviation. Then the angle of prism Q is

A) ${{3}^{o}}$

B) ${{4}^{o}}$

C) ${{3.5}^{o}}$

D) ${{2.5}^{o}}$

E) ${{5}^{o}}$

• question_answer58) Light of wavelength $6000\,\overset{\text{o}}{\mathop{\text{A}}}\,$ falls on a single slit of width 0.1 mm. The second minimum will be formed for the angle of diffraction of

• question_answer59) In a double slit experiment, the screen is placed at a distance of 1.25 m from the slits. When the apparatus is immersed in water$({{\mu }_{w}}=4/3)$, the angular width of a fringe is found to be${{0.2}^{o}}$. When the experiment is performed in air with same set up, the angular width of the fringe is

A) ${{0.4}^{o}}$

B) ${{0.27}^{o}}$

C) ${{0.35}^{o}}$

D) ${{0.15}^{o}}$

E) ${{0.22}^{o}}$

• question_answer60) Two plano-concave lenses (1 and 2) of) glass of refractive index 1.5 have radii of curvature 25 cm and 20 cm. They are placed in contact with their curved surfaces towards each other and the space between them is filled with liquid of refractive index$\frac{4}{3}$. Then the combination is

A) convex of focal length 70 cm

B) concave of focal length 70 cm

C) concave of focal length 66.6 cm

D) convex of focal length 66.6 cm

E) concave of focal length 72.5 cm

• question_answer61) When a metallic surface is illuminated by a light of wavelength$\lambda ,$the stopping potential for the photoelectric current is 3 V. When the same surface is illuminated by light of wavelength$2\lambda ,$the stopping potential is 1 V, the threshold wavelength for this surface is

A) $4\lambda$

B) $3.5\lambda$

C) $3\lambda$

D) $2.75\lambda$

E) $2.5\lambda$

• question_answer62) The temperature at which protons in proton gas would have enough energy to overcome Coulomb barrier of$4.14\times {{10}^{-14}}J$is (Boltzmann constant$=1.38\,\times {{10}^{-23}}\,J{{K}^{-1}}$)

A) $2\times {{10}^{9}}K$

B) ${{10}^{9}}K$

C) $6\times {{10}^{9}}K$

D) $3\times {{10}^{9}}K$

E) $4.5\times {{10}^{9}}K$

• question_answer63) The activity of a radioactive element decreases to one-third of the original activity ${{A}_{0}}$in a period of 69 yr. After a further lapes of 9 yr, its activity will

A) ${{A}_{0}}$

B) $\frac{2}{3}{{A}_{0}}$

C) $\frac{{{A}_{0}}}{9}$

D) $\frac{{{A}_{0}}}{6}$

E) $\frac{{{A}_{0}}}{18}$

• question_answer64) Two nucleons are at a separation of 1 fermi The net force between them is${{F}_{1}}$if both are neutrons${{F}_{2}}$if both are protons and${{F}_{3}}$if one is proton and the other is a neutron. Then

A) ${{F}_{1}}>{{F}_{2}}>{{F}_{3}}$

B) ${{F}_{1}}={{F}_{3}}>{{F}_{2}}$

C) ${{F}_{2}}>{{F}_{1}}>{{F}_{3}}$

D) ${{F}_{1}}={{F}_{2}}>{{F}_{3}}$

E) ${{F}_{3}}={{F}_{2}}>{{F}_{1}}$

• question_answer65) The truth table for the following logic circuit is

A) $\left| \begin{matrix} A & B & Y \\ 0 & 0 & 0 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ \end{matrix} \right|$

B) $\left| \begin{matrix} A & B & Y \\ 0 & 0 & 0 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 1 \\ \end{matrix} \right|$

C) $\left| \begin{matrix} A & B & Y \\ 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ \end{matrix} \right|$

D) $\left| \begin{matrix} A & B & Y \\ 0 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 0 \\ 1 & 1 & 1 \\ \end{matrix} \right|$

E) $\left| \begin{matrix} A & B & Y \\ 0 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ \end{matrix} \right|$

• question_answer66) In the operation of n-p-n transistor compared to that of a triode, the p base acts as

A) emitter

B) cathode

C) grid

D) plate

E) collector

• question_answer67) In the diagram, the input AC is across the terminals A and C. The output across B and D is

A) same as the input

B) half wave rectified

C) zero

D) full wave rectified

• question_answer68) In the following circuit, the current flowing through$1\,k\Omega$resistor is

A) 0 mA

B) 5mA

C) 10mA

D) 15mA

E) 20mA

• question_answer69) Electromagnetic waves of frequencies higher than$9\sqrt{2}$MHz are found to be reflected by the ionosphere on a particular day at a place. The maximum electron density in the ionosphere is

A) $\sqrt{5}\times {{10}^{12}}{{m}^{-3}}$

B) $\sqrt{2}\times {{10}^{12}}{{m}^{-3}}$

C) $2\times {{10}^{12}}{{m}^{-3}}$

D) $5\times {{10}^{12}}{{m}^{-3}}$

E) $3\times {{10}^{12}}{{m}^{-3}}$

• question_answer70) Which one of the following statements is wrong ?

A) Radio waves in the frequency range 30 MHz to 60 MHz are called sky waves

B) Radio horizon of the transmitting antenna for space wave is${{d}_{T}}=\sqrt{(2R{{h}_{T}})}$ (R = radius of earth,${{h}_{T}}=$height of transmitting antenna)

C) Within the skip distance neither the ground waves nor the sky waves are received

D) The principle of fibre optical communication is total internal reflection

E) Fibre optical communication is free from electrical disturbances

• question_answer71) A diode AM detector with the output circuit consisting of$R=1\text{ k}\Omega$and$C=1\text{ }\mu \text{F}$would be more suitable for detecting a carrier signal of

A) 0.1 kHz

B) 0.5 kHz

C) 1 kHz

D) 0.75 kHz

E) 10 kHz

• question_answer72) In optical communication system operating at 1200 nm, only 2% of the source frequency is available for TV transmission having a bandwidth of 5 MHz. The number of TV channels that can be transmitted is

A) 2 million

B) 10 million

C) 0.1 million

D) 1 million

E) 0.5 million

• question_answer73) The electrons, identified by quantum numbers $n$and$l,$

 (I) $n=3;\text{ }l=2$ (II)$n=5;\text{ }l=0$ (III) $n=4;\text{ }l=1$ (IV) $n=4;\text{ }l=2$ (V) $n=4;\text{ }l=0$
can be placed in order of increasing energy, as

A) $I<V<III<IV<II$

B) $I<V<III<II<IV$

C) $V<I<III<II<IV$

D) $V<I<II<IIII<IV$

E) $V<I<IV<III<II$

• question_answer74) The number of photons emitted per second by a 60 W source of monochromatic light of wavelength 663 nm is $(h=6.63\times {{10}^{-34}}Js)$

A) $4\times {{10}^{-20}}$

B) $1.5\times {{10}^{20}}$

C) $3\times {{10}^{-20}}$

D) $2\times {{10}^{20}}$

E) $1\times {{10}^{-20}}$

• question_answer75) Among the following species, identify the pair having same bond order$C{{N}^{-}},O_{2}^{-},N{{O}^{+}},C{{N}^{+}}$

A) $C{{N}^{-}}$and$O_{2}^{-}$

B) $O_{2}^{-}$and$N{{O}^{+}}$

C) $C{{N}^{-}}$and $N{{O}^{+}}$

D) $C{{N}^{-}}$and $C{{N}^{+}}$

E) $N{{O}^{+}}$and$C{{N}^{+}}$

• question_answer76) Hydration of different ions in aqueous solution is an example of

A) ion-induced dipole interaction

B) dipole-dipole interaction

C) dipole-induced dipole interaction

D) attractive dispersion forces between atoms

E) ion-dipole interaction

• question_answer77) When a sample of gas is compressed at constant temperature from 15 atm to 60 atm, its volume changes from$76\,c{{m}^{3}}\text{ }to\text{ }20.50\text{ }{{m}^{3}}$. Which of the following statements are possible explanations of this behaviour?

 1. The gas behaves non-ideally 2. The gas dimerises 3. The gas is adsorbed into the vessel walls

A) 1, 2 and 3

B) 1 and 2 only

C) 2 and 3 only

D) 1 only

E) 3 only

• question_answer78) The vapour pressure of two liquids X and Y are 80 and 60 Torr respectively. The total vapour pressure of the ideal solution obtained by mixing 3 moles of X and 2 moles of Y would be

A) 68 Torr

B) 140 Torr

C) 48 Torr

D) 72 Torr

E) 54 Torr

• question_answer79) Which one of the following pairs of substances will not produce hydrogen when reacted together?

A) Copper and cone. nitric acid

B) Ethanol and metallic sodium

C) Magnesium and steam

D) Phenol and metallic sodium

E) Sodium hydride and water

• question_answer80) Hydride Gap is referred to which region of the Periodic Table?

A) Groups 3, 4 and 5

B) Groups 5, 6 and 7

C) Groups 4, 5 and 6

D) Groups 7, 8 and 9

E) Groups 6, 7 and 8

• question_answer81) Which of the following pairs of substances would give same gaseous product on reaction with water?

A) Na and$N{{a}_{2}}{{O}_{2}}$

B) $Ca$and$Ca{{H}_{2}}$

C) Ca and CaO

D) Ba and$Ba{{O}_{2}}$

E) Ca and$Ca{{C}_{2}}$

• question_answer82) The elements present in the core of earth are collectively known as

A) lithophiles

B) nucleophiles

C) chalcophiles

D) siderophiles

E) atmophiles

• question_answer83) The shape of$Xe{{F}_{4}}$molecule and hybridisation of xenon in it are

A) tetrahedral and $s{{p}^{3}}$

B) square planar and$ds{{p}^{2}}$

C) square planar and $s{{p}^{3}}{{d}^{2}}$

D) octahedral and $s{{p}^{3}}{{d}^{2}}$

E) octahedral and ${{d}^{2}}s{{p}^{3}}$

• question_answer84) Concentrated sulphuric acid can be reduced by

A) $NaCl$

B) $NaF$

C) $NaOH$

D) $NaN{{O}_{3}}$

E) $NaBr$

• question_answer85) A compound in which a metal ion ${{M}^{x+}}(Z=25)$has a spin only magnetic moment of$\sqrt{24}$BM. The number of unpaired electrons in the compound and the oxidation state of the metal ion are respectively

A) 4 and 2

B) 5 and 3

C) 3 and 2

D) 4 and 3

E) 3 and 1

• question_answer86) To an aqueous solution containing anions a few drops of acidified$KMn{{O}_{4}}$are added. Which one of the following anions, if present will not decolourise the$KMn{{O}_{4}}$solution?

A) ${{I}^{-}}$

B) $CO_{3}^{2-}$

C) ${{S}^{2-}}$

D) $NO_{2-}^{{}}$

E) $C{{l}^{-}}$

• question_answer87) Lead is the final product formed by a series of changes in which the rate determining stage is the radioactive decay of uranium$-238$with a half-life of$4.5\times {{10}^{9}}yr$. What would be the age of a rock sample originally lead free in which the molar proportion of uranium to lead is now 1 : 3?

A) $1.5\times {{10}^{9}}yr$

B) $2.25\times {{10}^{9}}yr$

C) $4.5\times {{10}^{8}}yr$

D) $9.0\times {{10}^{9}}yr$

E) $13.5\times {{10}^{9}}yr$

• question_answer88) Energy released when one atom of uranium undergoes nuclear fission according to the following reaction is (atomic mass of U= 235.060; n= 1.009; Ba = 143.881 and Kr= 89.947) about $_{92}{{U}^{235}}{{+}_{0}}{{n}^{1}}{{\to }_{56}}B{{a}^{144}}{{+}_{36}}K{{r}^{90}}+{{2}_{0}}{{n}^{1}}$

A) 235 MeV

B) 208 MeV

C) 931.5 MeV

D) $5.33\times {{10}^{23}}MeV$

E) 20.8 MeV

• question_answer89) When 0.2 g of 1-butanol was burnt in a suitable apparatus, the heat evolved was sufficient to raise the temperature of 200 g water by$5{}^\circ C$. The enthalpy of combustion of 1-butanol in kcal$mo{{l}^{-1}}$will be

A) + 37

B) + 370

C) $-370$

D) $-740$

E) $-14.8$

• question_answer90) Given that $dE=TdS-pdV$ and$H=E+pV$. Which one of the following relations is true?

A) $dH=TdS+Vdp$

B) $dH=SdT+Vdp$

C) $dH=-SdT+Vdp$

D) $dH=dE+pdV$

E) $dH=dE-TdS$

• question_answer91) When 200 mL of aqueous solution of$HCl$ (pH = 2) is mixed with 300 mL of an aqueous solution of NaOH (pH = 12), the pH of the resulting mixture is

A) 10

B) 2.7

C) 4.0

D) 11.3

E) 2

• question_answer92) At a certain temperature, the dissociation constants of formic acid and acetic acid are $1.8\times {{10}^{-4}}$and$1.8\times {{10}^{-5}}$respectively. The concentration of acetic acid solution in which the hydrogen ion has the same concentration as in 0.001 M formic acid solution is equal to

A) 0.01 M

B) 0.001 M

C) 0.1 M

D) 0.0001 M

E) 0.1010 M

• question_answer93) An 1% solution of$KCl$(I),$NaCl$(II),$BaC{{l}_{2}}$(III) and urea (IV) have their osmotic pressure at thesame temperature in the ascending order (molar masses of$NaCl,KCl,BaC{{l}_{2}}$and urea are respectively 58.5, 74.5, 208.4 and 60 g. $mo{{l}^{-1}})$.Assume 100% ionization of the electrolytes at this temperature

A) $I<III<II<\text{ }IV$

B) $III<I<II<IV$

C) $I<\text{ }II<III<IV$

D) $I<\text{ }III<IV<II$

E) $III<IV<I<II$

• question_answer94) The difference between the boiling point and freezing point of an aqueous solution containing sucrose (molecular wt = 342 g$mo{{l}^{-1}}$) in 100 g of water is$105.0{}^\circ C$. If${{k}_{f}}$and${{k}_{b}}$of water are 1.86 and$0.51\text{ }K\text{ }kg\text{ }mo{{l}^{-1}}$ espectively, the weight of sucrose in the solution is about

A) 34.2 g

B) 342 g

C) 7.2 g

D) 72 g

E) 68.4 g

• question_answer95) In the following reaction, ${{M}^{x+}}+MnO_{4}^{-}\xrightarrow{{}}MO_{3}^{-}+M{{n}^{2+}}+\frac{1}{2}{{O}_{2}},$ If one mole of$MnO_{4}^{-}$oxidizes 2.5 moles of${{M}^{x+}},$then the value of$x$is

A) 5

B) 3

C) 2

D) 1

E) 4

• question_answer96) In acid medium Zn reduces nitrate ion to$NH_{4}^{+}$ ion according to the reaction$Zn+NO_{3}^{-}\to Z{{n}^{2+}}$$+NH_{4}^{+}+{{H}_{2}}O$(unbalanced) How many moles of$HCl$are required to reduce half a mole of$NaN{{O}_{3}}$ completely? Assume the availability of sufficient$Zn$

A) 5

B) 4

C) 3

D) 2

E) 1

• question_answer97) The activation energies of two reactions are ${{E}_{1}}$and${{E}_{2}}({{E}_{1}}>{{E}_{2}})$If the temperature of the system is increased from${{T}_{1}}$to${{T}_{2}},$he rate constant of the reactions changes from${{k}_{1}}$to $k{{}_{1}}$ in the first reaction and ${{k}_{2}}$ to $k{{}_{2}}$ in the second reaction. Predict which of the following expression is correct?

A) $\frac{k_{1}^{}}{{{k}_{1}}}=\frac{k_{2}^{}}{{{k}_{2}}}$

B) $\frac{k_{1}^{}}{{{k}_{1}}}>\frac{k_{2}^{}}{{{k}_{2}}}$

C) $\frac{k_{1}^{}}{{{k}_{1}}}<\frac{k_{2}^{}}{{{k}_{2}}}$

D) $\frac{k_{1}^{}}{{{k}_{1}}}=\frac{k_{2}^{}}{{{k}_{2}}}=1$

E) $\frac{k_{1}^{}}{{{k}_{1}}}=\frac{k_{2}^{}}{{{k}_{2}}}=0$

• question_answer98) A reaction was observed for 15 days and the percentage of the reactant remaining after the days indicated was recorded in the following table

 Time (days) % Reactant remaining 0 100 2 50 4 39 6 25 8 21 10 18 12 15 14 12.5 15 10
Which one of the following best describes the order and the half-life of the reaction?

A)

 Reaction order Half-life (days) First 2

B)

 Reaction order Half-life (days) First 6

C)

 Reaction order Half-life (days) Second 2

D)

 Reaction order Half-life (days) Zero 6

E)

 Reaction order Half-life (days) Third 2

• question_answer99) The ion that is more effective for the coagulation of$A{{s}_{2}}{{S}_{3}}$sol is

A) $B{{a}^{2+}}$

B) $N{{a}^{+}}$

C) $PO_{4}^{3-}$

D) $SO_{4}^{2-}$

E) $A{{l}^{3+}}$

• question_answer100) Which one of the following impurities present in colloidal solution cannot be remove by electrodialysis?

A) Sodium chloride

B) Potassium sulphate

C) Urea

D) Calcium chloride

E) Magnesium chloride

• question_answer101) Match List-1 and List-11 and choose the correct matching codes.

 List - I List - II (A) ${{[Ni{{(CN)}_{4}}]}^{2-}}$ 1. $T{{i}^{4+}}$ (B) Chlorophyll 2.$s{{p}^{3}};$paramagnetic (C) Ziegler - Natta catalyst 3. non-planar (D) ${{[NiC{{l}_{4}}]}^{2-}}$ 4. $M{{g}^{2+}}$ (E) Deoxyhaemoriobin 5. Planar 6.$ds{{p}^{2}};$ diamagnetic

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

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

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

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

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

• question_answer102) What is the overall formation equilibrium constant for the ion${{[M{{L}_{4}}]}^{2-}}$ion, given that${{\beta }_{4}}$for this complex is$2.5\times {{10}^{13}}$?

A) $2.5\times {{10}^{13}}$

B) $5\times {{10}^{-13}}$

C) $2.5\times {{10}^{-14}}$

D) $4.0\times {{10}^{-13}}$

E) $4.0\times {{10}^{-14}}$

• question_answer103) 0.25 g of an organic compound on Kjeldahls analysis gave enough ammonia to just neutralize $10\text{ }c{{m}^{3}}$of$0.5\text{ }M\text{ }{{H}_{2}}S{{O}_{4}}$. The percentage of nitrogen in the compound is

A) 28

B) 56

C) 14

D) 112

E) 42

• question_answer104) Lassaignes test for the detection of nitrogen fails in

A) ${{H}_{2}}NCONHN{{H}_{2}}-HCl$

B) $N{{H}_{2}}N{{H}_{2}}-HCl$

C) $N{{H}_{2}}CON{{H}_{2}}$

D) ${{C}_{6}}{{H}_{5}}-NH-N{{H}_{2}}.HCl$

E) ${{C}_{6}}{{H}_{5}}CON{{H}_{2}}$

• question_answer105) When tetrahydrafuran is treated with excess $HI,$the product formed is

A) 1, 4-diiodobutane

B) 1, 4-butanediol

C) 2-iodotetrahydrofuran

D) 4-iodo-l-butanol

E) 2, 5-diiodotetrahydrofuran

• question_answer106) Pick out the correct statements from the following and choose the correct answer from the codes given below

 1. Hexa 1, 5 diene is a conjugated diene 2. Prop 1, 2 diene is conjugated diene 3. Hexa 1, 3 diene is a conjugated diene 4. Buta 1, 3 diene is an isolated diene 5. Prop 1, 2 diene is a cumulative diene

A) 1, 2

B) 2, 3

C) 4, 5

D) 2, 5

E) 3, 5

• question_answer107) In which of the following species, all the three types of hybrid carbons are present?

A) $C{{H}_{2}}=C=C{{H}_{2}}$

B) $C{{H}_{3}}CH=CHCH_{2}^{+}$

C) $C{{H}_{3}}C\equiv CCH_{2}^{+}$

D) $C{{H}_{3}}-CH=CH-CH_{2}^{-}$

E) $C{{H}_{2}}=CHCH=C{{H}_{2}}$

• question_answer108) The alkyi halide that undergoes${{S}_{N}}1$reaction more readily is

A) ethyl bromide

B) isopropyi bromide

C) vinyl bromide

D) n-propyi bromide

E) t-butyl bromide

• question_answer109) Select R-isomers from the following

A) I and III

B) II, IV and V

C) I, II and III

D) II and III

E) I, III and V

• question_answer110) The correct IUPAC name of the acid

A) Z-3-ethyl-4-methyl hex-3-en-1-oic acid

B) Z-3-ethyl-4-methyl hexanoic acid

C) Z-3, 4-diethylpent-3-en-1-oic acid

D) Z-3-ethyl-4-methylhex-4-en-1-oic acid

E) E-3-ethyl-4-methylhex-3-en-1-oic acid

• question_answer111) ${{(C{{H}_{3}})}_{3}}CMgCl$on reaction with ${{D}_{2}}O$ produces

A) ${{(C{{H}_{3}})}_{3}}COD$

B) ${{(C{{D}_{3}})}_{3}}CH$

C) ${{(C{{H}_{3}})}_{3}}CD$

D) ${{(C{{D}_{3}})}_{3}}CD$

E) ${{(C{{D}_{3}})}_{3}}COD$

• question_answer112) An alkyi halide (RX) reacts with Na to form 4, 5-diethyloctane. Compound RX is

A) $C{{H}_{3}}{{(C{{H}_{2}})}_{3}}Br$

B) $C{{H}_{3}}{{(C{{H}_{2}})}_{2}}CH(Br)C{{H}_{2}}C{{H}_{3}}$

C) $C{{H}_{3}}{{(C{{H}_{2}})}_{3}}CH(Br)C{{H}_{3}}$

D) $C{{H}_{3}}{{(C{{H}_{2}})}_{5}}Br$

E) $C{{H}_{3}}Br$

• question_answer113) A compound A having the molecular formula ${{C}_{5}}{{H}_{12}}O,$on oxidation give a compound B with molecular formula${{C}_{5}}{{H}_{10}}O.$ Compound B gave a 2, 4-dinitrophenylhydrazine derivative but did not answer haloform test or silver mirror test. The structure of compound A is

A) $C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}C{{H}_{2}}C{{H}_{2}}OH$

B) $C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{CH}}\,C{{H}_{3}}$

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

D) $C{{H}_{3}}C{{H}_{2}}\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{CH}}\,C{{H}_{2}}OH$

E) $C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}}\,-C{{H}_{2}}-OH$

• question_answer114) Which of the following is a better reducing agent for the following reduction? $RCOOH\xrightarrow{{}}RC{{H}_{2}}OH$

A) $SnC{{l}_{2}}/HCl$

B) $NaB{{H}_{4}}/$ether

C) ${{H}_{2}}/Pd$

D) ${{N}_{2}}{{H}_{4}}/{{C}_{2}}{{H}_{5}}ONa$

E) ${{B}_{2}}{{H}_{6}}/{{H}_{3}}{{O}^{+}}$

• question_answer115) Choose the amide which on reduction with $LiAl{{H}_{4}}$yields a secondary amine

A) ethanamide

B) N-methylethanamide

C) N, N-dimethylethanamide

D) phenylmethanamide

E) butanamide

• question_answer116) Arrange the following amines in the decreasing order of their basic strength. Aniline (I), Benzylamine (II), p-toluidine (III)

A) $I>II>III$

B) $III>II>I$

C) $II>I>III$

D) $III>I>II$

E) $II\text{ }>\text{ }III\text{ }>\text{ }I$

• question_answer117) Which one among the following is not an analgesic?

A) Ibuprofen

B) Naproxen

C) Aspirin

D) Valium

E) Diclofenac sodium

• question_answer118) Match the vitamin of column I with deficiency disease given in column II.

 Column - I Column - II 1. Vitamin A A. Scurvy 2. Vitamin ${{B}_{12}}$ B. Hemorrhagic condition 3. Vitamin C C. Sterility 4. Vitamin E D. Xerophthalmia 5. Vitamin K E. Pernicious anaemia

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

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

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

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

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

• question_answer119) Which of the following is a double base propellant?

A) Methyl nitrate and nitromethane

B) Nitroglycerine and nitrocellulose

C) Kerosine and alcohol

D) Acrylic rubber and liquid${{N}_{2}}{{O}_{4}}$

E) Nitromethane and${{H}_{2}}{{O}_{2}}$

A) softener

B) hardener

C) dryer

D) buffering agent

E) antiseptic

• question_answer121) If $\alpha ,\,\beta ,\,\gamma$ are the cube roots of unity, then the value of the determinant$\left| \begin{matrix} {{e}^{\alpha }} & {{e}^{2\alpha }} & ({{e}^{3\alpha }}-1) \\ {{e}^{\beta }} & {{e}^{2\beta }} & ({{e}^{2\beta }}-1) \\ {{e}^{\gamma }} & {{e}^{2\gamma }} & ({{e}^{3\gamma }}-1) \\ \end{matrix} \right|$is equal to

A) $-2$

B) $-1$

C) 0

D) 1

E) 2

• question_answer122) If B is a non-singular matrix and A is a square matrix such that${{B}^{-1}}AB$exists, then det$({{B}^{-1}}AB)$is equal to

A) det$({{A}^{-1}})$

B) det$({{B}^{-1}})$

C) $\det \,(B)$

D) $\det \,(A)$

E) det $(A{{B}^{-1}})$

• question_answer123) If$1,\omega ,{{\omega }^{2}}$are the cube roots of unity and if$\left[ \begin{matrix} 1+\omega & 2\omega \\ -2\omega & -b \\ \end{matrix} \right]+\left[ \begin{matrix} a & -\omega \\ 3\omega & 2 \\ \end{matrix} \right]=\left[ \begin{matrix} 0 & \omega \\ \omega & 1 \\ \end{matrix} \right],$ then${{a}^{2}}+{{b}^{2}}$is equal to

A) $1+{{\omega }^{2}}$

B) ${{\omega }^{2}}-1$

C) $1+\omega$

D) ${{(1+\omega )}^{2}}$

E) ${{\omega }^{2}}$

• question_answer124) If the three linear equations $x+4ay+az=0$ $x+3by+bz=0$ $x+2cy+cz=0$ have a non-trivial solution, where$a\ne 0,b\ne 0,$ $c\ne 0,$then $ab+bc$is equal to

A) $2ac$

B) $-ac$

C) $ac$

D) $-2ac$

E) $a$

• question_answer125) If$A=\left| \begin{matrix} 1 & 0 & 0 \\ x & 1 & 0 \\ x & x & 1 \\ \end{matrix} \right|$and$I=\left| \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{matrix} \right|,$then ${{A}^{3}}-4{{A}^{2}}+3A+I$is equal to

A) $3I$

B) $I$

C) $-I$

D) $-2I$

E) $2I$

• question_answer126) If$A=\left[ \begin{matrix} 1 & 2 \\ 3 & 5 \\ \end{matrix} \right],$then the value of the determinant$|{{A}^{2009}}-5{{A}^{2008}}|$is

A) $-6$

B) $-5$

C) $-4$

D) $4$

E) $6$

• question_answer127) If$x$satisfies the in equations$2x-7<1$ $3x+4<-5,$then. $x-$lies in the interval

A) $(-\infty ,3)$

B) $(-\infty ,2)$

C) $(-\infty ,-3)$

D) $(-\infty ,\infty )$

E) $(3,\infty )$

• question_answer128) The set of all real$x$satisfying the in equal$\frac{3-|x|}{4-|x|}\ge 0$

A) $[-3,3]\cup (-\infty ,-4)\cup (4,\infty )$

B) $(-\infty ,-4)\cup (4,\infty )$

C) $(-\infty ,-3)\cup (4,\infty )$

D) $(-\infty ,-3)\cup (3,\infty )$

E) $[-3,3]\cup (4,\infty )$

• question_answer129) Identify the false statement

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

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

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

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

E) $\tilde{\ }(p\vee q)\equiv (\tilde{\ }p)\vee (\tilde{\ }q)$

• question_answer130) The boolean expression corresponding to the combinational circuit is

A) $({{x}_{1}}+{{x}_{2}}.x_{3}^{}){{x}_{2}}$

B) $({{x}_{1}}.({{x}_{2}}+{{x}_{3}}))+{{x}_{2}}$

C) $({{x}_{1}}.({{x}_{2}}+x_{3}^{}))+{{x}_{2}}$

D) $({{x}_{1}}.({{x}_{2}}+x_{3}^{}))+{{x}_{3}}$

E) $({{x}_{1}}+x_{2}^{}+{{x}_{3}}).{{x}_{2}}$

• question_answer131) In a boolean algebra B with respect to$+$and$x$denotes the negation of$x\in B$. Then

A) $x-x=1$and$x.x=1$

B) $x+x=1$and$x.x=0$

C) $x+x=0$and$x.x=0$

D) $x+x=0$and$x.x=0$

E) $x-x=0$and$x.x=0$

• question_answer132) If${{\cos }^{-1}}\left( \frac{5}{13} \right)-{{\sin }^{-1}}\left( \frac{12}{13} \right)={{\cos }^{-1}}x,$then$x$is equal to

A) $1$

B) $\frac{1}{\sqrt{2}}$

C) $0$

D) $\frac{\sqrt{3}}{2}$

E) $-1$

• question_answer133) The value of$\cos [{{\tan }^{-1}}\{\sin ({{\cot }^{-1}}x)\}]$is

A) $\sqrt{\frac{{{x}^{2}}+1}{{{x}^{2}}-1}}$

B) $\sqrt{\frac{1-{{x}^{2}}}{{{x}^{2}}+2}}$

C) $\sqrt{\frac{1-{{x}^{2}}}{1+{{x}^{2}}}}$

D) $\sqrt{\frac{{{x}^{2}}+1}{{{x}^{2}}+2}}$

E) $\sqrt{\frac{1-{{x}^{2}}}{2-{{x}^{2}}}}$

• question_answer134) If a and b are positive numbers such that$a>b,$then the minimum value of$a\sec \theta -b\tan \theta \left( 0<\theta <\frac{\pi }{2} \right)$is

A) $\frac{1}{\sqrt{{{a}^{2}}-{{b}^{2}}}}$

B) $\frac{1}{\sqrt{{{a}^{2}}+{{b}^{2}}}}$

C) $\sqrt{{{a}^{2}}+{{b}^{2}}}$

D) $\sqrt{{{a}^{2}}-{{b}^{2}}}$

E) ${{a}^{2}}-{{b}^{2}}$

• question_answer135) If$-\frac{\pi }{2}<{{\sin }^{-1}}x<\frac{\pi }{2},$then$\tan ({{\sin }^{-1}}x)$is equal

A) $\frac{x}{1-{{x}^{2}}}$

B) $\frac{x}{1+{{x}^{2}}}$

C) $\frac{x}{\sqrt{1-{{x}^{2}}}}$

D) $\frac{1}{\sqrt{1-{{x}^{2}}}}$

E) $\frac{x}{\sqrt{{{x}^{2}}-1}}$

• question_answer136) If$A+B=45{}^\circ ,$then$(\cot A-1)(\cot B-1)$is equal to

A) $1$

B) $\frac{1}{2}$

C) $-1$

D) $-2$

E) $2$

• question_answer137) The solution of the equation${{[\sin x+\cos x]}^{1+\sin 2x}}=2,-\pi \le x\le \pi$is

A) $\frac{\pi }{2}$

B) $\pi$

C) $\frac{\pi }{4}$

D) $\frac{3\pi }{4}$

E) $\frac{\pi }{3}$

• question_answer138) If$\sin A-\sqrt{6}\cos A=\sqrt{7}\cos A,$then$\cos A+\sqrt{6}\sin A$is equal to

A) $\sqrt{6}\sin A$

B) $-\sqrt{7}\sin A$

C) $\sqrt{6}\cos A$

D) $\sqrt{7}\cos A$

E) $\sqrt{42}\cos A$

• question_answer139) If tan A and tan B are the roots of $ab{{x}^{2}}-{{c}^{2}}x+$$ab=0$ where a, b, c are the sides of the triangle ABC, then the value of $si{{n}^{2}}A+si{{n}^{2}}B+si{{n}^{2}}C\text{ }is$

A) 1

B) 3

C) 4

D) 2

E) 5

• question_answer140) In a triangle ABC, if$a=3,b=4,c=5,$then the distance between its incentre and circumcentre is

A) $\frac{1}{2}$

B) $\frac{\sqrt{3}}{2}$

C) $\frac{3}{2}$

D) $\frac{5}{2}$

E) $\frac{\sqrt{5}}{2}$

• question_answer141) In triangle ABC, the value of $\frac{\cot \frac{A}{2}\cot \frac{B}{2}-1}{\cot \frac{A}{2}\cot \frac{B}{2}}$is

A) $\frac{a}{a+b+c}$

B) $\frac{c}{a+b+c}$

C) $\frac{2a}{a+b+c}$

D) $\frac{2b}{a+b+c}$

E) $\frac{2c}{a+b+c}$

• question_answer142) In a triangle ABC, if$\angle A=60{}^\circ ,a=5,b=4,$then c is a$root{}^\circ$of the equation

A) ${{c}^{2}}-5c-9=0$

B) ${{c}^{2}}-4c-9=0$

C) ${{c}^{2}}-10c+25=0$

D) ${{c}^{2}}-5c-41=0$

E) ${{c}^{2}}-4c-41=0$

• question_answer143) From the top of a tower, the angle of depression of a point on the ground is$60{}^\circ$. If the distance of this point from the tower is$\frac{1}{\sqrt{3}+1}m,$then the height of the tower is

A) $\frac{4\sqrt{3}}{2}m$

B) $\frac{\sqrt{3}+3}{2}m$

C) $\frac{3-\sqrt{3}}{2}m$

D) $\frac{\sqrt{3}}{2}m$

E) $\sqrt{3}+1m$

• question_answer144) The vertices of a family of triangles have integer coordinates. If two of the vertices of all the triangles are (0, 0) and (6, 8), then the least value of areas of the triangles is

A) $1$

B) $\frac{3}{2}$

C) $2$

D) $\frac{5}{2}$

E) $3$

• question_answer145) A line has slope m and $y-$intercept 4. The distance between the origin and the line is equal to

A) $\frac{4}{\sqrt{1-{{m}^{2}}}}$

B) $\frac{4}{\sqrt{{{m}^{2}}-1}}$

C) $\frac{4}{\sqrt{{{m}^{2}}+1}}$

D) $\frac{4m}{\sqrt{1+{{m}^{2}}}}$

E) $\frac{4m}{\sqrt{m-1}}$

• question_answer146) One side of length 3a of a triangle of area${{a}^{2}}$square unit lies on the line$x=a$. Then, one of the lines on which the third vertex lies, is

A) $x=-{{a}^{2}}$

B) $x={{a}^{2}}$

C) $x=-a$

D) $x=\frac{a}{3}$

E) $x=-\frac{a}{3}$

• question_answer147) The distance of the point (1, 2) from the line $x+y+5=0$measured along the line parallel to$3x-y=7$is equal to

A) $4\sqrt{10}$

B) $40$

C) $\sqrt{40}$

D) $10\sqrt{2}$

E) $2\sqrt{20}$

• question_answer148) Area of the triangle formed by the lines$y=2x,$$y=3x$and$y=5$is equal to (in square unit)

A) $\frac{25}{6}$

B) $\frac{25}{12}$

C) $\frac{5}{6}$

D) $\frac{17}{12}$

E) $6$

• question_answer149) Triangle ABC has vertices (0, 0), (11, 60) and (91, 0). If the line$y=kx$cuts the triangle into 2 two triangles of equal area, then k is equal to

A) $\frac{30}{51}$

B) $\frac{4}{7}$

C) $\frac{7}{4}$

D) $\frac{30}{91}$

E) $\frac{27}{37}$

• question_answer150) If the lines$y=3x+1$and$2y=x+3$are equally inclined to the line$y=mx+4,\left( \frac{1}{2}<m<3 \right),$then the values of m are

A) $\frac{1}{7}(1\pm 5\sqrt{3})$

B) $\frac{1}{7}(1\pm 5\sqrt{5})$

C) $\frac{1}{7}(1\pm 5\sqrt{2})$

D) $\frac{1}{7}(1\pm 2\sqrt{5})$

E) $\frac{1}{7}(1\pm 3\sqrt{2})$

• question_answer151) The vertices of a triangle are (3, 0), (3, 3) and (0, 3). Then, the coordinates of the circumcentre are

A) (0, 0)

B) (1, 1)

C) $\left( \frac{5}{2},\frac{5}{2} \right)$

D) (2, 2)

E) $\left( \frac{3}{2},\frac{3}{2} \right)$

• question_answer152) Area of the equilateral triangle inscribed in the circle${{x}^{2}}+{{y}^{2}}-7x+9y+5=0$is

A) $\frac{155}{8}\sqrt{3}\,sq\,unit$

B) $\frac{165}{8}\sqrt{3}\,sq\,unit$

C) $\frac{175}{8}\sqrt{3}\,sq\,unit$

D) $\frac{185}{8}\sqrt{3}\,sq\,unit$

E) $\frac{195}{8}\sqrt{3}\,sq\,unit$

• question_answer153) The equation of one of the diameters of the circle${{x}^{2}}+{{y}^{2}}-6x+2y=0$is

A) $x+y=0$

B) $x-y=0$

C) $3x+y=0$

D) $x+3y=0$

E) $x+2y=0$

• question_answer154) If two chords having lengths${{a}^{2}}-1$and$3(a+1),$where a is a constant of a circle bisect each other, then the radius of the circle is

A) 6

B) $\frac{15}{2}$

C) 8

D) $\frac{19}{2}$

E) 10

• question_answer155) The equation of the parabola whose focus (3, 2) and vertex (1, 2), is

A) ${{x}^{2}}+4x-8y+12=0$

B) ${{x}^{2}}-4x-8y+12=0$

C) ${{y}^{2}}-8x-4y+12=0$

D) ${{y}^{2}}+4y-8x+12=0$

E) ${{y}^{2}}-8x-2y-17=0$

• question_answer156) The sum of the distances of a point$(2,-3)$from the foci of an ellipse$16{{(x-2)}^{2}}+25({{y}^{4}}-$ $3{{)}^{2}}=400$is

A) 8

B) 6

C) 50

D) 32

E) 10

• question_answer157) The equation of one of the tangents to $\frac{{{x}^{2}}}{3}-\frac{{{y}^{2}}}{2}=1$which is parallel to$y=x,$is

A) $x-y+2=0$

B) $x+y-1=0$

C) $x+y-2=0$

D) $x-y+1=0$

E) $x+y+1=0$

• question_answer158) If${{e}_{1}}$is the eccentricity of the ellipse $\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{7}=1$and${{e}_{2}}$is the eccentricity of the hyperbola$\frac{{{x}^{2}}}{9}-\frac{{{y}^{2}}}{7}=1,$then${{e}_{1}}+{{e}_{2}}$is equal to

A) $\frac{16}{7}$

B) $\frac{25}{4}$

C) $\frac{25}{12}$

D) $\frac{16}{9}$

E) $\frac{23}{16}$

• question_answer159) If$\overrightarrow{p}\times \overrightarrow{q}=\overrightarrow{r}$and$\overrightarrow{q}\times \overrightarrow{r}=\overrightarrow{p},$then

A) $r=1,\text{ }p=q$

B) $p=1,\text{ }q=1$

C) $r=2p,\text{ }q=2$

D) $q=1,\text{ }p=r$

E) $q=1,r=1$

• question_answer160) Vectors$\overrightarrow{a}$and$\overrightarrow{b}$are inclined at an angle$\theta =120{}^\circ$.If$|\overrightarrow{a}|=1,|\overrightarrow{b}|=2,$then ${{[(\overrightarrow{a}+3\overrightarrow{b})\times (3\overrightarrow{a}+\overrightarrow{b})]}^{2}}$is equal to

A) 190

B) 275

C) 300

D) 320

E) 192

• question_answer161) If the projection of the vector a on b is$\overrightarrow{a}$on$\overrightarrow{b}$is $|\overrightarrow{a}\times \overrightarrow{b}|$and if$3\overrightarrow{b}=\hat{i}+\hat{j}+\hat{k},$ then the angle between $\vec{a}$ and $\vec{b}$ is

A) $\pi /3$

B) $\pi /2$

C) $\pi /4$

D) $\pi /6$

E) $0$

• question_answer162) If$\overrightarrow{x}=\overrightarrow{a}+\overrightarrow{b},\overrightarrow{y}=\overrightarrow{a}-\overrightarrow{b},|\overrightarrow{a}|=2,|\overrightarrow{b}|=3$and the angle between$\overrightarrow{a}$and$\overrightarrow{b}$is$\frac{\pi }{3}$,then$|\overrightarrow{x}\times \overrightarrow{y}|$is equal to

A) $5\sqrt{3}$

B) 6

C) $4\sqrt{3}$

D) 9

E) $6\sqrt{3}$

• question_answer163) If the position vectors of three consecutive vertices, of a parallelogram are$\hat{i}+\hat{j}+\hat{k},$ $\hat{i}+3\hat{j}+5\hat{k}$ and$7\hat{i}+9\hat{j}+11\hat{k},$ then the coordinates of the fourth vertex are

A) (2, 1, 3)

B) (6, 7, 8)

C) (4, 1, 3)

D) (7, 7, 7)

E) (8, 8, 8)

• question_answer164) The two variable vectors$3x\hat{i}+y\hat{j}-3\hat{k}$and$x\hat{i}-4y\hat{j}+4\hat{k}$are orthogonal to each other, then the locus of$(x,\text{ }y)$is

A) hyperbola

B) circle

C) straight line

D) ellipse

E) parabola

• question_answer165) If$\overrightarrow{a},\text{ }\overrightarrow{b},\text{ }\overrightarrow{c}$ are non-coplanar and $(\overrightarrow{a}+\lambda \overrightarrow{b}).[(\overrightarrow{b}+3\overrightarrow{c})\times (\overrightarrow{c}\times 4\overrightarrow{a})]=0,$ then the value of$\lambda$is equal to

A) $0$

B) $\frac{1}{12}$

C) $\frac{5}{12}$

D) $3$

E) $\frac{7}{12}$

• question_answer166) The angle between the line $\frac{3x-1}{3}=\frac{y+3}{-1}$$=\frac{5-2z}{4}$and the plane$3x-3y-6z=10$is equal to

A) $\frac{\pi }{6}$

B) $\frac{\pi }{4}$

C) $\frac{\pi }{3}$

D) $\frac{\pi }{2}$

E) $\frac{2\pi }{3}$

• question_answer167) The angle between the straight lines$\overrightarrow{r}=(2-3t)\hat{i}+(1+2t)\hat{j}+(2+6t)\hat{k}$and$\overrightarrow{r}=(1+4s)\hat{i}+(2-s)\hat{j}+(8s-1)\hat{k}$is

A) ${{\cos }^{-1}}\left( \frac{\sqrt{41}}{34} \right)$

B) ${{\cos }^{-1}}\left( \frac{21}{34} \right)$

C) ${{\cos }^{-1}}\left( \frac{43}{63} \right)$

D) ${{\cos }^{-1}}\left( \frac{5\sqrt{23}}{41} \right)$

E) ${{\cos }^{-1}}\left( \frac{34}{63} \right)$

• question_answer168) If Q is the image of the point P(2, 3, 4) under the reflection in the plane$x-2y+5z=6,$then the equation of the line PQ is

A) $\frac{x-2}{-1}=\frac{y-3}{2}=\frac{z-4}{5}$

B) $\frac{x-2}{1}=\frac{y-3}{-2}=\frac{z-4}{5}$

C) $\frac{x-2}{-1}=\frac{y-3}{-2}=\frac{z-4}{5}$

D) $\frac{x-2}{1}=\frac{y-3}{2}=\frac{z-4}{5}$

E) None of the above

• question_answer169) The distance of the point of intersection of the line$\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{12}$and me plane $x-y+z=5$from the point$(-1,-5,-10)$is

A) 13

B) 12

C) 11

D) 8

E) 7

• question_answer170) If the direction cosines of a line are$\left( \frac{1}{c},\frac{1}{c},\frac{1}{c} \right),$then

A) $0<c<1$

B) $c>2$

C) $c=\pm \sqrt{2}$

D) $c=\pm \sqrt{3}$

E) $c=\pm 3$

• question_answer171) The vector form of the sphere$2({{x}^{2}}+{{y}^{2}}+{{z}^{2}})-4x+6y+8z-5=0$is

A) $\overrightarrow{r}.[\overrightarrow{r}-(2\hat{i}+\hat{j}+\hat{k})]=\frac{2}{5}$

B) $\overrightarrow{r}.[\overrightarrow{r}-(2\hat{i}-3\hat{j}-4\hat{k})]=\frac{1}{2}$

C) $\overrightarrow{r}.[\overrightarrow{r}-(2\hat{i}+3\hat{j}+4\hat{k})]=\frac{5}{2}$

D) $\overrightarrow{r}.[\overrightarrow{r}+(2\hat{i}-3\hat{j}-4\hat{k})]=\frac{5}{2}$

E) $\overrightarrow{r}.[\overrightarrow{r}-(2\hat{i}-3\hat{j}-4\hat{k})]=\frac{5}{2}$

• question_answer172) If the lines$\frac{1-x}{3}=\frac{y-2}{2\alpha }=\frac{z-3}{2}$and$\frac{x-1}{3\alpha }$$=y-1=\frac{6-z}{5}$are perpendicular, then the value of$\alpha$is

A) $\frac{-10}{7}$

B) $\frac{10}{7}$

C) $\frac{-10}{11}$

D) $\frac{10}{11}$

E) $\frac{10}{9}$

• question_answer173) The distance between the lines$\overrightarrow{r}=(4\hat{i}-7\hat{j}-9\hat{k})+t(3\hat{i}-7\hat{j}+4\hat{k})$and$\overrightarrow{r}=(7\hat{i}-14\hat{j}-5\hat{k})+s(3\hat{i}+7\hat{j}-4\hat{k})$is equal to

A) 1

B) $\frac{1}{2}$

C) $\frac{3}{4}$

D) $17$

E) $0$

• question_answer174) If the variance of 1, 2, 3, 4, 5, ..., 10 is$\frac{99}{12},$then the standard deviation of 3, 6, 9, 12, ...,30 is

A) $\frac{297}{4}$

B) $\frac{3}{2}\sqrt{33}$

C) $\frac{3}{2}\sqrt{99}$

D) $\sqrt{\frac{99}{12}}$

E) $\frac{3\sqrt{3}}{2}$

• question_answer175) The mean of the values 0, 1, 2, 3, ..., n with the corresponding weights$^{n}{{C}_{0}}{{,}^{n}}{{C}_{1}},....{{,}^{n}}{{C}_{n}}$respectively, is

A) $\frac{n+1}{2}$

B) $\frac{n-1}{2}$

C) $\frac{{{2}^{n}}-1}{2}$

D) $\frac{{{2}^{n}}+1}{2}$

E) $\frac{n}{2}$

• question_answer176) A complete cycle of a traffic light takes 60 s. During each cycle the light is green for 25 s, yellow for 5 s and red for 30 s. At a randomly chosen time, the probability that the light will not be green, is

A) $\frac{1}{3}$

B) $\frac{1}{4}$

C) $\frac{4}{12}$

D) $\frac{7}{12}$

E) $\frac{3}{4}$

• question_answer177) If the random variable X takes the values${{x}_{1}},{{x}_{2}},{{x}_{3}},....,{{x}_{10}}$with probabilities$p(X={{x}_{i}})=ki,$then the value of k is equal to

A) $\frac{1}{10}$

B) $\frac{1}{4}$

C) $\frac{1}{55}$

D) $\frac{7}{12}$

E) $\frac{3}{4}$

• question_answer178) Let$\alpha$and$\beta$be the roots of$a{{x}^{2}}+bx+c=0$. Then,$\underset{x\to \alpha }{\mathop{\lim }}\,\frac{1-\cos (a{{x}^{2}}+bx+c)}{{{(x-\alpha )}^{2}}}$is equal to

A) $0$

B) $\frac{1}{2}{{(\alpha -\beta )}^{2}}$

C) $\frac{{{a}^{2}}}{2}{{(\alpha -\beta )}^{2}}$

D) $(\alpha -\beta )$

E) $1$

• question_answer179) The number of discontinuities of the greatest integer function$f(x)=[x],x\in \left( -\frac{7}{2},100 \right)$is equal to

A) 104

B) 100

C) 102

D) 101

E) 103

• question_answer180) If$f(x)=\left\{ \begin{matrix} \frac{3\sin \pi x}{5x} & ,x\ne 0 \\ 2k & ,x=0 \\ \end{matrix} \right.$is continuous at$x=0,$then the value of k is equal to

A) $\frac{3\pi }{10}$

B) $\frac{3\pi }{5}$

C) $\frac{\pi }{10}$

D) $\frac{3\pi }{2}$

E) $\frac{2\pi }{3}$

• question_answer181) If a function$f$satisfies$f\{f(x)\}=x+1$for all real values of x and if$f(0)=\frac{1}{2},$then$f(1)$is equal to

A) $\frac{1}{2}$

B) 1

C) $\frac{3}{2}$

D) 2

E) 0

• question_answer182) If$y={{\log }_{2}}{{\log }_{2}}(x),$then$\frac{dy}{dx}$is equal to

A) $\frac{{{\log }_{2}}e}{{{\log }_{e}}x}$

B) $\frac{{{\log }_{2}}e}{x{{\log }_{x}}2}$

C) $\frac{{{\log }_{2}}x}{{{\log }_{e}}2}$

D) $\frac{{{\log }_{2}}e}{{{\log }_{2}}x}$

E) $\frac{{{\log }_{2}}e}{x{{\log }_{e}}x}$

• question_answer183) If $\frac{d}{dx}\{f(x)\}=\frac{1}{1+{{x}^{2}}},$then$\frac{d}{dx}\{f({{x}^{3}})\}$is equal to

A) $\frac{3x}{1+{{x}^{3}}}$

B) $\frac{3{{x}^{2}}}{1+{{x}^{6}}}$

C) $\frac{-6{{x}^{5}}}{{{(1+{{x}^{6}})}^{2}}}$

D) $\frac{-6{{x}^{5}}}{1+{{x}^{6}}}$

E) ${{\tan }^{-1}}x$

• question_answer184) If$y=\sin [{{\cos }^{-1}}\{\sin ({{\cos }^{-1}}x)\}],$$\frac{dy}{dx}$at$x=\frac{1}{2}$is equal to

A) $0$

B) $-1$

C) $\frac{2}{\sqrt{3}}$

D) $\frac{1}{\sqrt{3}}$

E) 1

• question_answer185) If${{x}^{2}}+{{y}^{2}}=t-\frac{1}{t}$and${{x}^{4}}+{{y}^{4}}={{r}^{2}}+\frac{1}{{{t}^{2}}},$then $\frac{dx}{dy}$is equal to

A) $\frac{1}{{{x}^{2}}{{y}^{3}}}$

B) $\frac{1}{x{{y}^{3}}}$

C) $\frac{1}{{{x}^{2}}{{y}^{2}}}$

D) $\frac{1}{{{x}^{3}}y}$

E) $\frac{-1}{{{x}^{3}}y}$

• question_answer186) If$y={{\sec }^{-1}}[\cos ecx]+\cos e{{c}^{-1}}[\sec x]$ $+{{\sin }^{-1}}[\cos x]+{{\cos }^{-1}}[\sin x],$then$\frac{dy}{dx}$is equal to

A) 0

B) 2

C) $-2$

D) $-\,4$

E) 1

• question_answer187) If$y={{e}^{x}}.{{e}^{{{x}^{2}}}}.{{e}^{{{x}^{3}}}}.....{{e}^{{{x}^{n}}}}....,$for$0<x<1,$then $\frac{dy}{dx}$at$x=\frac{1}{2}$is

A) e

B) 4e

C) 2e

D) 3e

E) 5e

• question_answer188) The derivative of${{\tan }^{-1}}\left( \frac{2x}{1-{{x}^{2}}} \right)$with respect to${{\cos }^{-1}}\sqrt{1-{{x}^{2}}}$is

A) $\frac{\sqrt{1-{{x}^{2}}}}{1+{{x}^{2}}}$

B) $\frac{1}{\sqrt{1-{{x}^{2}}}}$

C) $\frac{2}{\sqrt{1-{{x}^{2}}}(1+{{x}^{2}})}$

D) $\frac{2}{1+{{x}^{2}}}$

E) $\frac{2\sqrt{1-{{x}^{2}}}}{1+{{x}^{2}}}$

• question_answer189) If the curves$\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{12}=1$and${{y}^{3}}=8x$intersect at right angle, then the value of${{a}^{2}}$is equal to

A) 16

B) 12

C) 8

D) 4

E) 2

• question_answer190) If the function $f(x)={{x}^{3}}-12a{{x}^{2}}+36{{a}^{2}}x$ $-4(a>0)$attains its maximum and minimum at$x=p$and$x=g$respectively and if$3p={{q}^{2}},$then a is equal to

A) $\frac{1}{6}$

B) $\frac{1}{36}$

C) $\frac{1}{3}$

D) $18$

E) $6$

• question_answer191) The equation of the tangent to the curve $y=4{{e}^{\frac{x}{4}}}$at the point where the curve crosses $y-$axis is equal to

A) $3x+4y=16$

B) $4x+y=4$

C) $x+y=4$

D) $4x-3y=-12$

E) $x-y=-4$

• question_answer192) The diagonal of a square is changing at the rate of$0.5\text{ }cm{{s}^{-1}}$. Then, the rate of change of area, when the area is$400\text{ }c{{m}^{2}},$is equal to

A) $20\sqrt{2}c{{m}^{2}}/s$

B) $10\sqrt{2}c{{m}^{2}}/s$

C) $\frac{1}{10\sqrt{2}}c{{m}^{2}}/s$

D) $\frac{10}{\sqrt{2}}c{{m}^{2}}/s$

E) $5\sqrt{2}\,c{{m}^{2}}/s$

• question_answer193) The equation of the tangent to the curve ${{x}^{2}}-2xy+{{y}^{2}}+2x+y-6=0$at (2, 2) is

A) $2x+y-6=0$

B) $2y+x-6=0$

C) $x+3y-8=0$

D) $3x+y-8=0$

E) $x+y-4=0$

• question_answer194) The angle between the curves$y={{a}^{x}}$of and $y={{b}^{x}}$is equal to

A) ${{\tan }^{-1}}\left( \left| \frac{a-b}{1+ab} \right| \right)$

B) ${{\tan }^{-1}}\left( \left| \frac{a+b}{1-ab} \right| \right)$

C) ${{\tan }^{-1}}\left( \left| \frac{\log b+\log a}{1+\log a\log b} \right| \right)$

D) ${{\tan }^{-1}}\left( \left| \frac{\log a+\log b}{1-\log a\log b} \right| \right)$

E) ${{\tan }^{-1}}\left( \left| \frac{\log a-\log b}{1+\log a\log b} \right| \right)$

• question_answer195) Let$f(x)={{(x-7)}^{2}}{{(x-2)}^{7}}{{(x-2)}^{7}},x\in [2,7]$. The value of$\theta \in (2,7)$such that$f(\theta )=0$is equal to

A) $\frac{49}{4}$

B) $\frac{53}{9}$

C) $\frac{53}{7}$

D) $\frac{49}{9}$

E) $\frac{45}{7}$

• question_answer196) $\int{(\sqrt[3]{x})}\left( \sqrt[3]{1+\sqrt[3]{{{x}^{4}}}} \right)dx$is equal to

A) ${{\left( 1+{{x}^{\frac{3}{4}}} \right)}^{\frac{5}{6}}}+c$

B) ${{\left( 1+{{x}^{\frac{4}{3}}} \right)}^{\frac{5}{6}}}+c$

C) $\frac{5}{8}{{\left( 1+{{x}^{\frac{4}{3}}} \right)}^{\frac{6}{5}}}+c$

D) $\frac{1}{6}{{\left( 1+{{x}^{\frac{4}{3}}} \right)}^{6}}+c$

E) $\frac{15}{8}{{\left( 1+{{x}^{\frac{4}{3}}} \right)}^{\frac{6}{5}}}+c$

• question_answer197) If$u=-f(\theta )\sin \theta +f(\theta )\cos \theta$and $v=f(\theta )\cos \theta +f(\theta )\sin \theta$,then ${{\int{\left[ {{\left( \frac{du}{d\theta } \right)}^{2}}+{{\left( \frac{dv}{d\theta } \right)}^{2}} \right]}}^{\frac{1}{2}}}d\theta$is equal to

A) $f(\theta )-f(\theta )+c$

B) $f(\theta )+f(\theta )+c$

C) $f(\theta )+f(\theta )+c$

D) $f(\theta )-f(\theta )+c$

E) $f(\theta )+f(\theta )+c$

• question_answer198) $\int{\frac{{{e}^{6{{\log }_{e}}x}}-{{e}^{5{{\log }_{e}}x}}}{{{e}^{4{{\log }_{e}}x}}-{{e}^{3{{\log }_{e}}x}}}}dx$is equal to

A) $\frac{{{x}^{3}}}{3}+c$

B) $\frac{{{x}^{2}}}{2}+c$

C) $\frac{{{x}^{2}}}{3}+c$

D) $\frac{-{{x}^{3}}}{3}+c$

E) $x+c$

• question_answer199) ${{\int{{{e}^{x}}\left( \frac{1-x}{1+{{x}^{2}}} \right)}}^{2}}dx$is equal to

A) ${{e}^{x}}\left( \frac{1-x}{1+{{x}^{2}}} \right)+c$

B) ${{e}^{x}}\left( \frac{1}{1+{{x}^{2}}} \right)+c$

C) ${{e}^{x}}\left( \frac{1+x}{1+{{x}^{2}}} \right)+c$

D) ${{e}^{x}}\left( \frac{1-x}{{{(1+{{x}^{2}})}^{2}}} \right)+c$

E) ${{e}^{x}}\left( \frac{1}{{{(1+{{x}^{2}})}^{2}}} \right)+c$

• question_answer200) $\int{\frac{{{x}^{4}}-1}{{{x}^{2}}{{({{x}^{4}}+{{x}^{2}}1)}^{\frac{1}{2}}}}}dx$is equal to

A) $\sqrt{\frac{{{x}^{4}}+{{x}^{2}}+1}{x}}+c$

B) $\frac{{{x}^{2}}}{\sqrt{{{x}^{4}}+{{x}^{2}}+1}}+c$

C) $x{{({{x}^{4}}+{{x}^{2}}+1)}^{\frac{3}{2}}}+c$

D) $\frac{\sqrt{{{x}^{4}}+{{x}^{2}}+1}}{x}+c$

E) $\sqrt{{{x}^{4}}+{{x}^{2}}+1}+c$

• question_answer201) $\int{\frac{\cos x-\sin x}{1+2\sin x\cos x}}dx$is equal to

A) $-\frac{1}{\cos x-\sin x}+c$

B) $\frac{\cos x+\sin x}{\cos x-\sin x}+c$

C) $-\frac{1}{\sin x+\cos x}+c$

D) $\frac{x}{\sin x+\cos x}+c$

E) $\tan x+\sec x+c$

• question_answer202) $\int{\frac{1}{x}({{\log }_{ex}}e)}dx$is equal to

A) ${{\log }_{e}}(1-{{\log }_{e}}x)+c$

B) ${{\log }_{e}}({{\log }_{e}}ex-1)+c$

C) ${{\log }_{e}}({{\log }_{e}}x-1)+c$

D) ${{\log }_{e}}({{\log }_{e}}x+x)+c$

E) ${{\log }_{e}}(1+{{\log }_{e}}x)+c$

• question_answer203) The value of$\int_{1}^{e}{{{10}^{{{\log }_{e}}x}}}dx$is equal to

A) $10{{\log }_{e}}(10e)$

B) $\frac{10e-1}{{{\log }_{e}}10e}$

C) $\frac{10e}{{{\log }_{e}}10e}$

D) $(10e){{\log }_{e}}(10e)$

E) $3\,sq\,unit$

• question_answer204) The area between the curve$y=1-|x|$and the $x-$axis is equal to

A) $1\,sq\,unit$

B) $\frac{1}{2}sq\,unit$

C) $\frac{1}{3}sq\,unit$

D) $2sq\,unit$

E) $3sq\,unit$

• question_answer205) The value of$\int_{{{e}^{-1}}}^{e}{\frac{dt}{t(1+t)}}$is equal to

A) $0$

B) $\log \left( \frac{e}{1+e} \right)$

C) $\log \left( \frac{1}{1+e} \right)$

D) $\log (1+e)$

E) $1$

• question_answer206) The figure shows a triangle AOB and the parabola$y={{x}^{2}}$. The ratio of the area of the triangle AOB to the area of the region AOB of the parabola$y={{x}^{2}}$is equal to

A) $\frac{3}{5}$

B) $\frac{3}{4}$

C) $\frac{7}{8}$

D) $\frac{5}{6}$

E) $\frac{2}{3}$

• question_answer207) The value of$\int_{-2}^{4}{|x+1|}dx$is equal to

A) 12

B) 14

C) 13

D) 16

E) 15

• question_answer208) The solution of $\cos y\frac{dy}{dx}={{e}^{x+\sin y}}+{{x}^{2}}{{e}^{\sin y}}$is

A) ${{e}^{x}}-{{e}^{-\sin y}}+\frac{{{x}^{3}}}{3}=c$

B) ${{e}^{-x}}-{{e}^{-\sin y}}+\frac{{{x}^{3}}}{3}=c$

C) ${{e}^{x}}+{{e}^{-\sin y}}+\frac{{{x}^{3}}}{3}=c$

D) ${{e}^{x}}-{{e}^{\sin y}}-\frac{{{x}^{3}}}{3}=c$

E) ${{e}^{x}}-{{e}^{\sin y}}+\frac{{{x}^{3}}}{3}=c$

• question_answer209) The order and degree of the differential equation ${{\left( 1+{{\left( \frac{dy}{dx} \right)}^{2}} \right)}^{\frac{3}{4}}}={{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{\frac{1}{3}}}$is

A) (2, 4)

B) (2, 3)

C) (6, 4)

D) (6, 9)

E) (2, 12)

• question_answer210) The integrating factor of the differential equation$(y\log y)dx=(\log y-x)dy$is

A) $\frac{1}{\log y}$

B) $\log (\log y)$

C) $1+\log y$

D) $\frac{1}{\log (\log y)}$

E) $\log y$

• question_answer211) The solution of the differential equation $\frac{dy}{dx}=\frac{1}{x+{{y}^{2}}}$is

A) $y=-{{x}^{2}}-2x-2+c{{e}^{x}}$

B) $y={{x}^{2}}+2x+2-c{{e}^{x}}$

C) $x=-{{y}^{2}}-2y+2-c{{e}^{y}}$

D) $x=-{{y}^{2}}-2y-2+c{{e}^{y}}$

E) $x={{y}^{2}}+2y+2-cey$

• question_answer212) The domain of the function $f(x)={{\log }_{2}}({{\log }_{3}}({{\log }_{4}}x))$is

A) $(-\infty ,4)$

B) $(4,\infty )$

C) $(0,4)$

D) $(1,\infty )$

E) $(-\infty ,1)$

• question_answer213) If$f:R\to R$and$g:R\to R$are denned by $f(x)=x-3$and$g(x)={{x}^{2}}+1,$then the values of$x$for which$g\{f(x)\}=10$are

A) $0,-6$

B) $2,-2$

C) $1,-1$

D) 0, 6

E) 0, 2

• question_answer214) Two finite sets A and B have m and n elements respectively. If the total number of subsets of A is 112 more than the total number of subsets of B, then the value of m is

A) 7

B) 9

C) 10

D) 12

E) 13

• question_answer215) If$f(x)$satisfies the relation$2f(x)+f(1-x)={{x}^{2}}$for all real$x,$then$f(x)$is

A) $\frac{{{x}^{2}}+2x-1}{6}$

B) $\frac{{{x}^{2}}+2x-1}{3}$

C) $\frac{{{x}^{2}}+4x-1}{3}$

D) $\frac{{{x}^{2}}-3x+1}{6}$

E) $\frac{{{x}^{2}}+3x-1}{3}$

• question_answer216) The range of the function $f(x)\frac{{{x}^{2}}-x+1}{{{x}^{2}}+x+1}$ where$x\in R,$is

A) $(-\infty ,3]$

B) $(-\infty ,\,\infty )$

C) $[3,\infty )$

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

E) $\left( -\infty ,\frac{1}{3} \right)\cup (3,\infty )$

• question_answer217) If the area of the triangle formed by the points$z,z+iz$and$iz$is 50 sq unit, then$|z|$is equal to

A) 5

B) 8

C) 10

D) 12

E) $5\sqrt{2}$

• question_answer218) The locus of z such that $\arg [(1-2i)z-2+5i]$$=\frac{\pi }{4}$is a

A) line not passing through the origin

B) circle not passing through the origin

C) line passing through the origin

D) circle passing through the origin

E) circle with centre at the origin

• question_answer219) If$z=\sqrt{3}+i,$then the argument of${{z}^{2}}{{e}^{z-i}}$is equal to

A) $\frac{\pi }{2}$

B) $\frac{\pi }{6}$

C) ${{e}^{\pi /6}}$

D) ${{e}^{\pi /3}}$

E) $\frac{\pi }{3}$

• question_answer220) If$\omega \ne 1$and${{\omega }^{3}}=1,$then$\frac{a\omega +b+c{{\omega }^{2}}}{a{{\omega }^{2}}+b\omega +c}+\frac{a{{\omega }^{2}}+b+c\omega }{a+b\omega +c{{\omega }^{2}}}$is equal to

A) 2

B) $\omega$

C) $2\omega$

D) $2{{\omega }^{2}}$

E) $a+b+c$

• question_answer221) The centre of a regular hexagon is at the point$z=i$. If one of its vertices is at$2+i,$then the adjacent vertices of$2+i$are at the points

A) $1\pm 2i$

B) $i+1\pm \sqrt{3}$

C) $2+i(1\pm \sqrt{3})$

D) $1+i(1\pm \sqrt{3})$

E) $1-i(1\pm \sqrt{3})$

• question_answer222) If the roots of the equation$\frac{1}{x+p}+\frac{1}{x+q}=\frac{1}{r},$ $(x\ne -p,x\ne -q,r\ne 0)$are equal in magnitude but opposite in sign, then$p+q$is equal to

A) $r$

B) $2r$

C) ${{r}^{2}}$

D) $\frac{1}{r}$

E) $\frac{2}{r}$

• question_answer223) The solution of the equation ${{(3+2\sqrt{2})}^{{{x}^{2}}-8}}+{{(3+2\sqrt{2})}^{8-{{x}^{2}}}}=6$are

A) $3\pm 2\sqrt{2}$

B) $\pm 1$

C) $\pm 3\sqrt{3},\pm 2\sqrt{2}$

D) $\pm 7,\pm \sqrt{3}$

E) $\pm 3,\pm \sqrt{7}$

• question_answer224) If$2-i$is a root of the equation $a{{x}^{2}}+12x+b=0$(where a and b are real), then the value of ab is equal to

A) 45

B) 15

C) $-15$

D) $-45$

E) 25

• question_answer225) If one root of the equation$l{{x}^{2}}+mx+n=0$is $\frac{9}{2}$ $(l,m$and n are positive integers) and $\frac{m}{4n}=\frac{l}{m},$then$\frac{1}{x}+\frac{1}{y}$is equal to

A) 80

B) 85

C) 90

D) 95

E) 100

• question_answer226) If${{x}^{2}}+4ax+2>0$for all values of$x,$then a lies in the interval

A) $(-2,\text{ }4)$

B) (1, 2)

C) $(-\sqrt{2},\sqrt{2})$

D) $\left( -\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}} \right)$

E) $(-4,\text{ }2)$

• question_answer227) If a, b, c are in GP and$x,y$are arithmetic mean of a, b and b, c respectively, then $\frac{1}{x}+\frac{1}{y}$ is equal to

A) $\frac{2}{b}$

B) $\frac{3}{b}$

C) $\frac{b}{3}$

D) $\frac{b}{2}$

E) $\frac{1}{b}$

• question_answer228) A student read common difference of an AP as$-3$instead of 3 and obtained the sum of first 10 terms as$-30$. Then, the actual sum of first 10 terms is equal to

A) 240

B) 120

C) 300

D) 180

E) 480

• question_answer229) If${{a}_{1}}=1$and${{a}_{n}}=n{{a}_{n-1}}$for all positive integer$n>2,$then${{a}_{5}}$is equal to

A) 125

B) 120

C) 100

D) 24

E) 6

• question_answer230) If${{a}_{1}},{{a}_{2}},.....,{{a}_{n}}$are in AP with common difference$d\ne 0,$then$(\sin d)$$[\sec {{a}_{1}}\sec {{a}_{2}}+$ $\sec {{a}_{2}}\sec {{a}_{3}}+...+\sec {{a}_{n-1}}\sec {{a}_{n}}]$is equal to

A) $\cot {{a}_{n}}-\cot {{a}_{1}}$

B) $\cot {{a}_{1}}-\cot {{a}_{n}}$

C) $\tan {{a}_{n}}-\tan {{a}_{1}}$

D) $\tan {{a}_{n}}-\tan {{a}_{n-1}}$

E) $\tan {{a}_{1}}-\tan {{a}_{n}}$

• question_answer231) The value of$\frac{1}{2!}+\frac{2}{3!}+....+\frac{999}{1000!}$is equal to

A) $\frac{1000!-1}{1000!}$

B) $\frac{1000!+1}{1000!}$

C) $\frac{999!-1}{999!}$

D) $\frac{999!+1}{999!}$

E) $\frac{1000!-999!}{1000!}$

• question_answer232) ${{\log }_{e}}\frac{1+3x}{1-2x}$is equal to

A) $-5x-\frac{5{{x}^{2}}}{2}-\frac{35{{x}^{3}}}{3}-...$

B) $-5x+\frac{5{{x}^{2}}}{2}-\frac{35{{x}^{3}}}{3}+...$

C) $5x-\frac{5{{x}^{2}}}{2}\,+\frac{35{{x}^{3}}}{3}+...$

D) $5x+\frac{5{{x}^{2}}}{2}+\frac{35{{x}^{3}}}{3}-...$

E) $x+\frac{3{{x}^{2}}}{2}+\frac{5{{x}^{3}}}{4}+...$

• question_answer233) The sum of the infinite series$\frac{1}{2}\left( \frac{1}{3}+\frac{1}{4} \right)-\frac{1}{4}\left( \frac{1}{{{3}^{2}}}+\frac{1}{{{4}^{2}}} \right)+\frac{1}{6}\left( \frac{1}{{{3}^{3}}}+\frac{1}{{{4}^{3}}} \right)-....$is equal to

A) $\frac{1}{2}\log 2$

B) $\log \frac{3}{5}$

C) $\log \frac{5}{3}$

D) $\frac{1}{2}\log \frac{5}{3}$

E) $\frac{1}{2}\log \frac{3}{5}$

• question_answer234) The sum of the infinite series$\frac{{{2}^{2}}}{2!}+\frac{{{2}^{4}}}{4!}+\frac{{{2}^{6}}}{6!}+..$is equal to

A) $\frac{{{e}^{2}}+1}{2e}$

B) $\frac{{{e}^{4}}+1}{2{{e}^{2}}}$

C) $\frac{{{({{e}^{2}}-1)}^{2}}}{2{{e}^{2}}}$

D) $\frac{{{({{e}^{2}}+1)}^{2}}}{2{{e}^{2}}}$

E) $\frac{{{({{e}^{2}}-1)}^{2}}}{4{{e}^{2}}}$

• question_answer235) If$|x|<1,$then the coefficient of${{x}^{6}}$in the expansion of${{(1+x+{{x}^{2}})}^{-3}}$is

A) 3

B) 6

C) 9

D) 12

E) 15

• question_answer236) $^{15}{{C}_{0}}{{,}^{5}}{{C}_{5}}{{+}^{15}}{{C}_{1}}{{.}^{5}}{{C}_{4}}{{+}^{15}}{{C}_{2}}{{.}^{5}}{{C}_{3}}{{+}^{15}}{{C}_{3}}{{.}^{5}}{{C}_{2}}$${{+}^{15}}{{C}_{4}}{{.}^{5}}{{C}_{1}}$is equal to

A) ${{2}^{20}}-{{2}^{5}}$

B) $\frac{20!}{5!15!}$

C) $\frac{20!}{5!15!}-1$

D) $\frac{20!}{5!15!}-\frac{15!}{5!10!}$

E) $\frac{15!}{5!10!}$

• question_answer237) If$^{2n+1}{{p}_{n-1}}{{:}^{2n-1}}{{p}_{n}}=3:5,$then the value of$n$is equal to

A) 4

B) 3

C) 2

D) 1

E) 5

• question_answer238) Let$[x]$denote the greatest integer less than or equal to$x$. If$x={{(\sqrt{3}+1)}^{5}},$then M is equal to

A) 75

B) 50

C) 76

D) 51

E) 152

• question_answer239) If$n$is a positive integer, then ${{5}^{2n+2}}-24n-25$is divisible by

A) 574

B) 575

C) 675

D) 674

E) 576

• question_answer240) Let${{T}_{n}}$denote the number of triangles which can be formed by using the vertices of a regular polygon of n sides. If ${{T}_{n+1}}-{{T}_{n}}=28,$then$n$equals

A) 4

B) 5

C) 6

D) 7

E) 8

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