Solved papers for BCECE Engineering BCECE Engineering Solved Paper-2012

BCECE Engineering Solved Paper-2012 Total Questions - 150

1) The dimensional formula of wave number is

A)

\[[{{M}^{0}}{{L}^{0}}{{T}^{0}}]\]

B)

\[[{{M}^{0}}{{L}^{-1}}{{T}^{0}}]\]

C)

\[[{{M}^{0}}{{L}^{0}}{{T}^{-1}}]\]

D)

       \[[{{M}^{-1}}{{L}^{-1}}{{T}^{0}}]\]

View Answer
2) A body of mass m is moving in a circle of radius r with a constant speed v. If a force \[\frac{m{{v}^{2}}}{r}\] is acting on the body towards the centre, then what will be the work done by this force in moving the body over half the circumference of the circle?

A)

zero

B)

\[\frac{m{{v}^{2}}}{{{r}^{2}}}\]

C)

       \[\frac{m{{v}^{2}}}{r}\times \pi r\]

D)

       \[\frac{\pi {{r}^{2}}}{m{{v}^{2}}}\]

View Answer
3) If under the action of a force \[(4i+j+3k)N,\] a   particle   moves   from   position\[{{r}_{1}}=3i+2j-6k\]        to        position \[{{r}_{2}}=14i+13j+9k,\]then the work done will be

A)

50 J

B)

                       75 J

C)

       100 J

D)

       175 J

View Answer
4) A particle of mass m moving with velocity u makes an elastic one dimensional collision with a stationary particle of mass m. They are in contact for a short time T. Their force of interaction increases from zero to \[{{F}_{0}}\]linearly in time \[\frac{T}{2}\] and decreases linearly to zero in further time \[\frac{T}{2}\] (shown in figure). The magnitude of \[{{F}_{0}}\]is

A)

mu/2 T

B)

mu/T

C)

2mu/T

D)

       None of these

View Answer
5) Two planets revolves around the sun with frequencies \[{{N}_{1}}\]and \[{{N}_{2}}\]revolutions per year. If their average radii (orbital) be \[{{R}_{1}}\] and\[{{R}_{2}}\] respectively, then \[{{R}_{1}}/{{R}_{2}}\]is equal to

A)

\[{{({{N}_{1}}/{{N}_{2}})}^{2/3}}\]

B)

       \[{{({{N}_{1}}/{{N}_{2}})}^{3/2}}\]

C)

\[{{({{N}_{2}}/{{N}_{1}})}^{2/3}}\]

D)

\[{{({{N}_{2}}/{{N}_{1}})}^{3/2}}\]

View Answer
6) To what height water should be filled in a container of height 21 cm, so that it appears as half-filled when viewed from the top \[\left( \text{Take}\,{{\,}_{a}}{{\mu }_{w}}=\frac{4}{3} \right)\]

A)

12 cm

B)

       15 cm

C)

10.5 cm

D)

       7 cm

View Answer
7) A progressive wave is represented as \[y=0.2\cos \pi \left( 0.04t+0.2x-\frac{\pi }{6} \right)\] where distance is expressed in cm and time in second. What will be the minimum distance between two particles having the phase difference of\[\frac{\pi }{2}\]?

A)

4 cm

B)

8 cm

C)

25 cm

D)

       12.5 cm

View Answer
8) When the temperature increases, then the frequency or the sound produced by the organ pipe will

A)

unchanged

B)

       increases

C)

decreases

D)

       Not definite

View Answer
9) The distance between the poles of a horse shoe magnet is 0.1 m and its pole strength is 0.01 A-m. The induction of magnetic field at a point mid way between the poles will be

A)

Zero

B)

       \[2\times {{10}^{-5}}T\]

C)

\[4\times {{10}^{-6}}T\]

D)

       \[8\times {{10}^{-7}}T\]

View Answer
10) Which logic gate is represented by the following combination of logic gates?

A)

OR

B)

       NAND

C)

XOR

D)

       None of these

View Answer
11) For the transistor circuit shown in figure, if \[\beta =100,\]voltage drop across emitter and base is 0.7 V, then the value of \[{{\text{V}}_{\text{CE}}}\]will be

A)

Zero

B)

5 V

C)

10 V

D)

       13 V

View Answer
12) If a uniform solid sphere and a disc of same mass and same radius rolls down on an inclined smooth plane from rest to the same distance, then the ratio of the time taken by them will be

A)

15 : 14

B)

       \[\sqrt{14}:\sqrt{15}\]

C)

14 : 15

D)

       \[{{15}^{2}}:{{14}^{2}}\]

View Answer
13) If a stone is projected from ground with a velocity \[\text{50}\,\text{m}{{\text{s}}^{-1}}\] and at an angle of \[{{30}^{o}},\] it takes 3 s to cross a wall. How far beyond the wall the stone will strike the ground? (Take\[g=10\,m{{s}^{-2}}\])

A)

50.5 m

B)

       91.5 m

C)

86.6 m

D)

       100 m

View Answer
14) For a body starting from rest, what will be the ratio of the distance travelled by the body during the 4th and 3rd second during its journey?

A)

\[\frac{7}{5}\]

B)

       \[\frac{7}{3}\]

C)

\[\frac{5}{7}\]

D)

       \[\frac{3}{7}\]

View Answer
15) If the compressibility of water is \[\sigma \](sigma) per unit atmospheric pressure, then the decrease in volume V due to p, atmospheric pressure will be

A)

\[\sigma V/p\]

B)

\[\sigma pV\]

C)

\[\sigma /pV\]

D)

\[\sigma p/V\]

View Answer
16) A soap film of surface tension \[3\times {{10}^{-2}}N{{m}^{-1}}\] formed in a rectangular frame, can support a straw. If the length of the film is 10 cm, then the mass of the straw that film can support is

A)

0.06 g

B)

       0.6 g

C)

6 g

D)

       60 g

View Answer
17) There are two identical small holes of area of cross section a on the either sides of a tank containing a liquid of density \[\rho \](shown in figure). The difference in height between the holes is h. Tank is resting on a smooth horizontal surface. Horizontal force which will has to be applied on the tank to keep it in equilibrium is

A)

\[\frac{2gh}{\rho a}\]

B)

       \[\frac{\rho gh}{a}\]

C)

\[gh\rho a\]

D)

       \[2\rho agh\]

View Answer
18) Certain amount of an ideal gas of molecular mass M is contained in a closed vessel. If the vessel is moving with a constant velocity v, then the rise in temperature of the gas when the vessel is suddenly stopped will be\[(Take\gamma =\frac{{{C}_{p}}}{{{C}_{V}}})\]

A)

\[\frac{M{{v}^{2}}}{2R(\gamma +1)}\]

B)

       \[\frac{M{{v}^{2}}}{2R(\gamma -1)}\]

C)

\[\frac{M{{v}^{2}}(\gamma -1)}{2R}\]

D)

       \[\frac{M{{v}^{2}}(\gamma +1)}{2R}\]

View Answer
19) Water and turpentine oil (specific heat less than that of water) are both heated to same temperature. Equal amounts of both are then placed in identical calorimeters and then left in air

A)

A and B will represent cooling curves of water and oil respectively

B)

B and A will represent cooling curves of water and oil respectively

C)

their cooling curves will be identical

D)

None of the above

View Answer
20) By suspending a mass of 0.50 kg a spring is stretched by 8.20 m. If a mass of 0.25 kg is suspended, then its period of oscillation will be (Take\[g=10\,m{{s}^{-2}}\])

A)

\[0.137\text{ }s\]

B)

       \[0.328\text{ }s\]

C)

\[0.628s\]

D)

       \[1.000\,s\]

View Answer
21) If the period of revolution of a nearest satellite around a planet of radius R is T then its period of revolution around another planet, having radius 3R and same density will be

A)

T

B)

3 T

C)

\[3\sqrt{3}T\]

D)

9 T

View Answer
22) A body of mass m is suspended from a string of length \[l.\]What is the minimum horizontal velocity that should be given to the body at its lowest position so that it may complete one full revolution in the vertical plane with the point of suspension as the centre of the circle?

A)

\[v=\sqrt{2lg}\]

B)

\[v=\sqrt{3lg}\]

C)

\[v=\sqrt{4lg}\]

D)

       \[v=\sqrt{5lg}\]

View Answer
23) Rest mass energy of an electron is 0.54 MeV. If velocity of the electron is 0.8 C, then its kinetic energy will be

A)

0.36 MeV

B)

       0.41 MeV

C)

0.48 MeV

D)

       1.32 MeV

View Answer
24) Which one of the following graphs represents the graph between the instantaneous concentration (N) of a radioactive element and time (t)?

A)



B)

C)



D)



View Answer
25) In the circuit given below the value of current is

A)

0

B)

\[{{10}^{-2}}A\]

C)

\[{{10}^{2}}A\]

D)

\[{{10}^{-3}}A\]

View Answer
26) In a diode AM detector, the output circuit consists of \[R=1\,k\Omega \]and \[C=10\,pF.\]A carrier signal of 100 k Hz is to be detected. Is it good?

A)

Yes

B)

No

C)

Information is not sufficient

D)

None of the above

View Answer
27) Let a straight wire of length \[l\] carries a current \[i.\]The magnitude of magnetic field produced by the current at point P (as shown in figure) is

A)

\[\frac{{{\mu }_{0}}i}{2\sqrt{2}\pi l}\]

B)

       \[\frac{\sqrt{2}{{\mu }_{0}}i}{8\pi l}\]

C)

\[\frac{{{\mu }_{0}}i}{4\pi l}\]

D)

       \[\frac{\sqrt{2}{{\mu }_{0}}i}{\pi l}\]

View Answer
28) 0.8 J work is done in rotating a magnet by \[\text{6}{{\text{0}}^{\text{o}}}\text{,}\] placed parallel to a uniform magnetic field. How much work is done in rotating it \[\text{3}{{\text{0}}^{\text{o}}}\] further?

A)

\[0.8\times {{10}^{7}}\,\text{erg}\]

B)

       \[0.8\,erg\]

C)

\[8\,J\]

D)

       \[0.4\,J\]

View Answer
29) The magnetic moment produced in a substance of 1 g is\[6\times {{10}^{-7}}\,A-{{m}^{2}}.\] If its density is \[5g\,c{{m}^{-3}},\] then the intensity of magnetization in A/m will be

A)

3.0

B)

       \[3\times {{10}^{-6}}\]

C)

\[8.3\times {{10}^{6}}\]

D)

       \[1.2\times {{10}^{-7}}\]

View Answer
30) In which of the following circuit is the current maximum just after the switch S is closed?

(i) (ii) (iii)

A)

(i)

B)

(ii)

C)

(iii)

D)

                                       Both (ii) and (iii)

View Answer
31) Let ABC is a right angled triangle in which \[AB=3\,cm\]and \[BC=4\,cm\] and \[\angle ABC={{90}^{o}}.\] The three charges +15, +12 and \[-20\] esu are placed on A, B and C respectively. The force acting on B will be

A)

Zero

B)

       25 dyne

C)

30 dyne

D)

                       150 dyne

View Answer
32) Four plates of same area of cross-section are joined as shown in figure. The distance between each plate is d. The equivalent capacity between A and B will be

A)

\[\frac{2{{\varepsilon }_{0}}A}{d}\]

B)

       \[\frac{{{\varepsilon }_{0}}A}{d}\]

C)

\[\frac{3{{\varepsilon }_{0}}A}{d}\]

D)

       \[\frac{3{{\varepsilon }_{0}}A}{2d}\]

View Answer
33) If a voltmeter of resistance \[1000\,\Omega \]is connected across a resistance of \[500\,\Omega \]in the given circuit, then the reading of voltmeter will be

A)

1 V

B)

       2 V

C)

6 V

D)

       4 V

View Answer
34) In the grid circuit of a triode a signal \[E=2\sqrt{2}\cos \omega t\]is applied. If \[\mu =14\]and \[{{r}_{p}}=10\,k\Omega ,\]then rms current flowing through \[{{R}_{L}}=12\,k\Omega \]will be

A)

1.5 mA

B)

       1.27 mA

C)

10 mA

D)

       12.4 mA

View Answer
35) A rigid body of mass m rotates with angular velocity \[\omega \]about an axis at a distance a from the centre of mass C. The radius of gyration about C is K. Then, kinetic energy of rotation of the body about new parallel axis is

A)

\[\frac{1}{2}m{{K}^{2}}{{\omega }^{2}}\]

B)

       \[\frac{1}{2}m{{a}^{2}}{{\omega }^{2}}\]

C)

\[\frac{1}{2}m(a+{{K}^{2}}){{\omega }^{2}}\]

D)

       \[\frac{1}{2}m({{a}^{2}}+{{K}^{2}}){{\omega }^{2}}\]

View Answer
36) The angle of contact between glass and water is \[{{0}^{o}}\] and it rises in a capillary upto 6 cm when its surface tension is 70 dyne/cm. Another liquid of surface tension 140 dyne/cm, angle of contact \[{{60}^{o}}\] and relative density 2 will rise in the same capillary by

A)

3 cm

B)

       16 cm

C)

12 cm

D)

       24 cm

View Answer
37) If the height of a mercury barometer is 75 cm at sea level and 50 cm at the top of a hill and the ratio of density of mercury to that of air is \[{{10}^{4}}\] then the height of the hill is

A)

1.25 km

B)

       2.5 km

C)

250 m

D)

                       750 m

View Answer
38) If the displacement equation of a particle from its mean position is given as \[y=0.2\sin (10\pi t+1.5\pi )\cos (10\pi t+1.5\pi )\] then, the motion of particle is

A)

non-periodic

B)

periodic but not SHM

C)

SHM with period 0.2 s

D)

SHM with period 0.1 s

View Answer
39) Let PQR is a right angled prism with other angles as \[{{60}^{o}}\] and \[{{30}^{o}}.\] PQ has a thin layer of liquid and light falls normally on the face PR as shown in figure. If the refractive index of prism is 1.5, then for total internal reflection, maximum refractive index of liquid will be

A)

1.2

B)

       1.3

C)

1.4

D)

       1.5

View Answer
40) According to corpuscular theory of light, the different colours of light are due to

A)

different size of the corpuscules

B)

different electromagnetic waves

C)

different force of attraction among the corpuscles

D)

None of the above

View Answer
41) An antenna is a device

A)

that converts radio frequency signal into electromagnetic theory

B)

that converts electromagnetic energy into radio frequency signal

C)

that converts guided electromagnetic waves into free space electromagnetic waves and vice-versa

D)

None of the above

View Answer
42) A resistor R, inductor L and a capacitor C are connected in series to an oscillator of frequency v. If the resonant frequency is \[{{v}_{r}},\] then the current lags behind the voltage, when

A)

\[v=0\]

B)

\[v<{{v}_{r}}\]

C)

\[v>{{v}_{r}}\]

D)

\[v={{v}_{r}}\]

View Answer
43) The instantaneous values of current and voltage in an AC circuit are\[i=100\sin \,31\,4\,t\] amp and\[e=200\sin \left( 314t+\frac{\pi }{3} \right)V\] respectively. If the resistance is \[1\Omega ,\] then the reactance of the circuit will be

A)

\[\sqrt{3}\,\Omega \]

B)

       \[100\sqrt{3}\Omega \]

C)

       \[-200\sqrt{3}\Omega \]

D)

       \[-200/\sqrt{3}\Omega \]

View Answer
44) When green light is incident on the surface of a metal, it emits photo electrons but there is no such emission with yellow colour light. Which one of the colour can produce emission of photo electrons?

A)

Red

B)

       Indigo

C)

Orange

D)

       None of these

View Answer
45) If an electron jumps from the 4th orbit to the 2nd orbit of hydrogen atom, then the frequency of emitted radiation in the hertz will be (Take Rydbergs constant,\[R={{10}^{5}}c{{m}^{-1}}\])

A)

\[\frac{3}{4}\times {{10}^{15}}\]

B)

       \[\frac{3}{16}\times {{10}^{15}}\]

C)

\[\frac{3}{16}\times {{10}^{15}}\]

D)

       \[\frac{9}{16}\times {{10}^{15}}\]

View Answer
46) If the ratio of radii of nuclei \[_{\text{13}}^{\text{27}}\text{Al}\]and \[_{\text{52}}^{\text{A}}\text{X}\]is 3 : 5, then the number of neutrons in the nuclei of X will be

A)

13

B)

       52

C)

100

D)

       73

View Answer
47) Number of nuclei of a radioactive substance at time t = 0 are 1000 and 900 at time t = 2 s. What will be the number of nuclei at time\[t=4s\]?

A)

810

B)

800

C)

790

D)

       700

View Answer
48) A bar magnet has coercivity \[4\times {{10}^{3}}\,A{{m}^{-1}}.\] It is desired to demagnetise it by inserting it inside a solenoid 12 cm long and having 60 turns. The current that should be sent through the solenoid is

A)

8 A

B)

10 A

C)

12 A

D)

       14 A

View Answer
49) A potentiometer is an ideal device of measuring potential difference because

A)

it uses a sensitive galvanometer

B)

it is an elaborate arrangement

C)

it has a long wire hence heat developed is quickly radiated

D)

it does not disturb the potential difference it measures

View Answer
50) If the momentum of a body is increased by n times, then its kinetic energy increases

A)

\[n\]times

B)

       \[{{n}^{2}}\]times

C)

\[2n\]times

D)

       \[\sqrt{n}\]times

View Answer
51) When 1 mole gas is heated at constant volume, temperature is raised from 298 K to 308K. Heat supplied to the gas is 500 J. Then which statement is correct?

A)

\[q=W=500J,\Delta U=0\]

B)

\[q=\Delta U=500\,J,\,W=0\]

C)

\[q=W=500\,J,\Delta U=0\]

D)

\[\Delta U=0,q=W=-500\,J\]

View Answer
52) For the reaction, \[2{{N}_{2}}{{O}_{5}}\to 4N{{O}_{2}}+{{O}_{2}}\] rate and rate constant are \[1.02\times {{10}^{-4}}\]and \[3.4\times {{10}^{-5}}{{s}^{-1}}\]     respectively, then concentration of \[{{\text{N}}_{\text{2}}}{{\text{O}}_{\text{5}}}\]at that time will be

A)

\[\text{1}\text{.732}\]

B)

3

C)

\[1.02\times {{10}^{-4}}\]

D)

       \[3.4\times {{10}^{5}}\]

View Answer
53) A human body required the 0.01 M activity of radioactive substance after 24 h. Half-life of radioactive substanu is 6 h. Then injection of maximum activity of radioactive substance that can be injected

A)

0.08

B)

0.04

C)

0.16

D)

       0.32

View Answer
54) Molarity of liquid \[HCl\] if density of solution is 1.17 g/cc

A)

36.5

B)

       18.25

C)

       32.05

D)

       42.10

View Answer
55) Which one of the following is not paramagnetic?

A)

NO

B)

\[N_{2}^{+}\]

C)

       CO

D)

       \[{{O}_{2}}\]

View Answer
56) Among the following ions the \[p\pi -d\pi \] overlap could be present in

A)

\[NO_{2}^{-}\]

B)

       \[NO_{3}^{-}\]

C)

       \[PO_{4}^{3-}\]

D)

       \[CO_{3}^{2-}\]

View Answer
57) A compound formed by elements A and B crystallizes in the cubic structure where A atoms are at the corners of a cube and B atoms are at the face centres. The formula of the compound is

A)

\[{{A}_{2}}{{B}_{2}}\]

B)

       \[A{{B}_{3}}\]

C)

       \[AB\]

D)

       \[{{A}_{3}}B\]

View Answer
58) Assuming fully decomposed, the volume of \[\text{C}{{\text{O}}_{\text{2}}}\]released at STP on heating 9.85 g of \[\text{BaC}{{\text{O}}_{3}}\](atomic mass, Ba = 137) will be

A)

1.12 L

B)

       0.84 L

C)

       2.24 L

D)

       4.06 L

View Answer
59) The correct structure of\[Fe{{(CO)}_{5}}\] is

A)

trigonal bipyramidal

B)

octahedral

C)

tetrahedral

D)

square pyramidal

View Answer
60) Which one of the following forms a colourless solution in aqueous medium? (Atomic number\[Sc=21,\text{ }Ti=22,\]\[\text{ }V=23,Cr=24\])

A)

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

B)

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

C)

       \[T{{i}^{3+}}\]

D)

       \[S{{c}^{3+}}\]

View Answer
61) \[{{\,}_{92}}{{U}^{235}}\]nucleus absorbs a neutron and disintegrate in \[{{\,}_{54}}X{{e}^{139}},{{\,}_{38}}S{{r}^{139}}\] and X so, what will be product X?

A)

3-neutrons

B)

       2-neutrons

C)

       \[\alpha \]-particle

D)

       \[\beta \]-particle

View Answer
62) In hydrogen atom, energy of first excited state is \[-3.4\text{ }eV.\] Then KE of same orbit of hydrogen atom

A)

\[+\text{ }3.4eV\]

B)

       \[+\text{ }6.8\text{ }eV\]

C)

       \[~-\text{ }13.6\text{ }eV\]

D)

       \[+\text{ }13.6\text{ }eV\]

View Answer
63) Reaction, \[Ba{{O}_{2}}(s)BaO(s)+{{O}_{2}}(g);\Delta H =+ve.\] In equilibrium condition, pressure of \[{{O}_{2}}\] depends on

A)

increased mass of \[Ba{{O}_{2}}\]

B)

increased mass of \[BaO\]

C)

increased temperature of equilibrium

D)

increased mass of \[Ba{{O}_{2}}\]and \[BaO\]both

View Answer
64) Solution of \[\text{0}\text{.1 N N}{{\text{H}}_{\text{4}}}\text{OH}\]and \[\text{0}\text{.1 N N}{{\text{H}}_{\text{4}}}\text{Cl}\]has pH 9.25, then find out \[\text{p}{{\text{K}}_{b}}\]of \[\text{N}{{\text{H}}_{\text{4}}}\text{OH}\text{.}\]

A)

9.25

B)

       4.75

C)

3.75

D)

       8.25

View Answer
65) van der Waals real gas, acts as an ideal gas at which condition?

A)

High temperature, low pressure

B)

Low temperature, high pressure

C)

High temperature, high pressure

D)

Low temperature, low pressure

View Answer
66) Unit of entropy is

A)

\[J{{K}^{-1}}mo{{l}^{-1}}\]

B)

\[J\,mo{{l}^{-1}}\]

C)

       \[{{J}^{-1}}{{K}^{-1}}mo{{l}^{-1}}\]

D)

       \[JK\,mo{{l}^{-1}}\]

View Answer
67) \[3A\xrightarrow{{}}B+C\] It would be a zero order reaction when

A)

the rate of reaction is proportional to square of concentration of A

B)

the rate of reaction remains the same at any concentration of A

C)

the rate remains unchanged at any concentration of B and C

D)

the rate of reaction doubles if concentration of B is increased to double

View Answer
68) In electrolysis of \[\text{NaCl}\]when Pt electrode is taken then \[{{\text{H}}_{2}}\]is liberated at cathode while with Hg cathode it forms sodium amalgam because

A)

Hg is more inert than Pt

B)

more voltage is required to reduce \[{{\text{H}}^{\text{+}}}\]at Hg than at Pt

C)

Na is dissolved in Hg while it does not dissolved in Pt

D)

concentration of \[{{\text{H}}^{\text{+}}}\]ions is larger when Pt electrode is taken

View Answer
69) Which of the following statement is true?

A)

Silicon exhibits 4 coordination number in its compounds

B)

Bond energy of \[{{\text{F}}_{2}}\]is less than \[\text{C}{{\text{l}}_{\text{2}}}\]

C)

Mn(III) oxidation state is more stable than Mn(II) in aqueous state

D)

Elements of 15th group shows only +3 and +5 oxidation states

View Answer
70) An atom has electronic configuration \[1{{s}^{2}},\text{ }2{{s}^{2}}2{{p}^{6}},3{{s}^{2}}3{{p}^{6}}3{{d}^{3}},4{{s}^{2}}.\]You will place it in

A)

fifth group

B)

       fifteenth group

C)

                       second group

D)

       third group

View Answer
71) The hypothetical complex chloro diaquatriammine cobalt (III) chloride can be represented as

A)

\[[CoCl{{(N{{H}_{3}})}_{3}}{{({{H}_{2}}O)}_{2}}]C{{l}_{2}}\]

B)

\[[Co{{(N{{H}_{3}})}_{3}}({{H}_{2}}O)C{{l}_{3}}]\]

C)

\[[Co{{(N{{H}_{3}})}_{3}}{{({{H}_{2}}O)}_{2}}Cl]\]

D)

\[[Co{{(N{{H}_{3}})}_{3}}{{({{H}_{2}}O)}_{3}}]C{{l}_{3}}\]

View Answer
72) In the silver plating of copper,\[K[Ag{{(CN)}_{2}}]\] is used instead of\[AgN{{O}_{3}}.\] The reason is

A)

a thin layer of Ag is formed on Cu

B)

more voltage is required

C)

\[A{{g}^{+}}\]ions are completely removed from solution

D)

less availability of \[A{{g}^{+}}\]ions, as Cu cannot displace Ag from \[{{[Ag(C{{N}_{2}})]}^{-}}\]ion

View Answer
73) \[\text{CuS}{{\text{O}}_{\text{4}}}\]when reacts with KCN forms CuCN which is insoluble in water. It is soluble in excess of KCN due to the formation of the following complex

A)

\[{{\text{K}}_{2}}[Cu{{(CN)}_{4}}]\]

B)

       \[{{K}_{3}}[Cu{{(CN)}_{4}}]\]

C)

       \[CuC{{N}_{2}}\]

D)

       \[Cu[K\,Cu{{(CN)}_{4}}]\]

View Answer
74) Zn gives\[{{\text{H}}_{\text{2}}}\] gas with \[{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\]and \[\text{HCl}\]but not with \[\text{HN}{{\text{O}}_{\text{3}}}\]

A)

Zn act as oxidizing agent when react with \[\text{HN}{{\text{O}}_{3}}\]

B)

\[\text{HN}{{\text{O}}_{3}}\]is weaker acid than \[{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\]and \[\text{HCl}\]

C)

in electrochemical series Zn is above hydrogen

D)

\[\text{NO}_{3}^{-}\] is reduced in preference to hydronium ion

View Answer
75) IUPAC name of the following is \[C{{H}_{2}}=CH-C{{H}_{2}}-C{{H}_{2}}-C\equiv CH\]

A)

1, 5-hexenyne

B)

1-hexene-5-yne

C)

l-hexyne-5-ene

D)

       1, 5-hexynene

View Answer
76) Product P in the above reaction is

A)



B)

C)



D)



View Answer
77) n-propyl alcohol and isopropyl alcohol can be chemically distinguished by which reagent?

A)

\[PC{{l}_{5}}\]

B)

Reduction

C)

Oxidation with potassium dichromate

D)

Ozonolysis

View Answer
78) In the following reaction, product P is \[R-\underset{O}{\mathop{\underset{||}{\mathop{C}}\,}}\,-Cl\xrightarrow[Pd-BaS{{O}_{4}}]{{{H}_{2}}}P\]

A)

\[RC{{H}_{2}}OH\]

B)

                       \[RCOOH\]

C)

RCHO

D)

       \[RC{{H}_{3}}\]

View Answer
79) Enzymes are made up of

A)

edible proteins

B)

proteins with specific structure

C)

nitrogen, containing carbohydrates

D)

carbohydrates

View Answer
80) Geometrical isomers differ in

A)

position of functional group

B)

position of atoms

C)

spatial arrangement of atoms

D)

length of carbon chain

View Answer
81) Monomer of \[{{\left[ -\underset{C{{H}_{3}}}{\overset{C{{H}_{3}}}{\mathop{\underset{|}{\overset{|}{\mathop{C}}}\,}}}\,-C{{H}_{2}}- \right]}_{n}}\]is

A)

2-methylpropene

B)

styrene

C)

propylene

D)

ethane

View Answer
82) Which one of the following will have largest number of atoms?

A)

\[\text{1 g Au}\]

B)

       \[\text{1 g Na}\]

C)

       \[\text{1 g Li}\]

D)

       \[\operatorname{l}\,g\,C{{l}_{2}}\]

View Answer
83) The size of isoelectronic species ;\[{{\text{F}}^{-}},Ne,N{{a}^{+}}\] is affected by

A)

nuclear charge (Z)

B)

valence principal quantum number (n)

C)

electron-electron interaction in the outer orbitals

D)

None of the factors because their size is the same

View Answer
84) \[{{\text{U}}^{\text{o}}}\]of combustion of methane is\[-X\,k\,J\,mo{{l}^{-1}}.\] The value of \[\Delta {{ H }^{o}}\] is

A)

\[=\Delta {{U}^{o}}\]

B)

\[>\Delta {{U}^{o}}\]

C)

\[<\Delta {{U}^{o}}\]

D)

\[=0\]

View Answer
85) In the sample of soft drink, the concentration of \[{{\text{H}}^{\text{+}}}\] ion is\[\text{3}\text{.8}\times {{10}^{-3}}M.\]Its pH is

A)

2

B)

       2.42

C)

3

D)

       3.42

View Answer
86) Which one of the following alkali metals gives hydrated salts?

A)

Li

B)

       Na

C)

       K

D)

       Cs

View Answer
87) Boric acid is polymeric due to

A)

its acidic nature

B)

the presence of hydrogen bonds

C)

its monobasic nature

D)

its geometry

View Answer
88) Which one of the following carbocation is most stable?

A)

\[{{(C{{H}_{3}})}_{3}}C\overset{+}{\mathop{C}}\,{{H}_{2}}\]

B)

       \[{{(C{{H}_{3}})}_{3}}\overset{+}{\mathop{C}}\,\]

C)

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

D)

       \[C{{H}_{3}}\overset{+}{\mathop{C}}\,HC{{H}_{2}}C{{H}_{3}}\]

View Answer
89) The best and latest technique for isolation, purification and separation of organic compounds is

A)

crystallization

B)

       distillation

C)

       sublimation

D)

       chromatography

View Answer
90) Which one of the following vitamins is water soluble?

A)

Vitamin B

B)

       Vitamin E

C)

       Vitamin K

D)

       Vitamin A

View Answer
91) Which one of the following on reduction with lithium aluminium hydride yield a secondary amine?

A)

Nitroethane

B)

       Methyl isocyanide

C)

       Acetamide

D)

       Methyl cyanide

View Answer
92) Which one of the following ionic species has the greatest proton affinity to form stable compound?

A)

\[H{{S}^{-}}\]

B)

       \[NH_{2}^{-}\]

C)

       \[{{F}^{-}}\]

D)

       \[{{I}^{-}}\]

View Answer
93) The reaction, \[C{{H}_{3}}-\overset{C{{H}_{3}}}{\mathop{\overset{|}{\mathop{C}}\,}}\,H-C{{H}_{2}}-O-C{{H}_{2}}C{{H}_{3}}\] \[+HI\xrightarrow{\Delta }\]? Which of the following compound will be formed?

A)

\[C{{H}_{3}}-\underset{C{{H}_{3}}}{\mathop{\underset{|}{\mathop{C}}\,}}\,H-C{{H}_{2}}-I+C{{H}_{3}}C{{H}_{2}}OH\]

B)

\[C{{H}_{3}}-\underset{C{{H}_{3}}}{\mathop{\underset{|}{\mathop{C}}\,}}\,H-C{{H}_{3}}+C{{H}_{3}}C{{H}_{2}}OH\]

C)

\[C{{H}_{3}}-\underset{C{{H}_{3}}}{\mathop{\underset{|}{\mathop{C}}\,}}\,H-C{{H}_{2}}OH+C{{H}_{3}}C{{H}_{3}}\]

D)

\[C{{H}_{3}}-\underset{C{{H}_{3}}}{\mathop{\underset{|}{\mathop{C}}\,}}\,H-C{{H}_{2}}OH+C{{H}_{3}}C{{H}_{2}}I\]

View Answer
94) Predict the product C obtained in the following reaction of butyne -1. \[C{{H}_{3}}C{{H}_{2}}-C\equiv CH+HCl\xrightarrow{{}}B\xrightarrow{HI}C\]

A)

\[C{{H}_{3}}-\underset{Cl}{\mathop{\underset{|}{\mathop{C}}\,}}\,H-C{{H}_{2}}-C{{H}_{2}}I\]

B)

\[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}-\underset{Cl}{\overset{I}{\mathop{\underset{|}{\overset{|}{\mathop{C}}}\,}}}\,-H\]

C)

\[C{{H}_{3}}-C{{H}_{2}}\overset{I}{\mathop{\overset{|}{\mathop{C}}\,}}\,H-C{{H}_{2}}Cl\]

D)

\[C{{H}_{3}}C{{H}_{2}}-\underset{Cl}{\overset{I}{\mathop{\underset{|}{\overset{|}{\mathop{C}}}\,}}}\,-C{{H}_{3}}\]

View Answer
95) Sulphide ores of metals are usually concentrated by froth floatation process. Which one of the following sulphide ores offers an exception and is concentrated by chemical leaching?

A)

Argentite

B)

       Galena

C)

       Copper pyrite

D)

       Sphalerite

View Answer
96) The equilibrium constant of the reaction; \[Cu(s)+2A{{g}^{+}}(aq)\xrightarrow{{}}C{{u}^{2+}}(aq)+2Ag(s)\] \[{{E}^{o}}=0.46\,V\]at 298 K

A)

\[2.4\times {{10}^{10}}\]

B)

\[2.0\times {{10}^{10}}\]

C)

\[4.0\times {{10}^{10}}\]

D)

       \[4.0\times {{10}^{15}}\]

View Answer
97) In the preparation of alkene from alcohol using \[\text{A}{{\text{l}}_{\text{2}}}{{\text{O}}_{\text{3}}}\] which is effective factor?

A)

Porosity of \[\text{A}{{\text{l}}_{2}}{{O}_{3}}\]

B)

Temperature

C)

Concentration

D)

Surface area of \[A{{l}_{2}}{{O}_{3}}\]

View Answer
98) Which one of the following is correct?

A)

On reduction any aldehyde gives secondary alcohol

B)

Reaction of vegetable oil with \[{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\] gives glycerine

C)

Alcoholic iodine with NaOH gives iodoform

D)

Sucrose on reaction with NaCI gives invert sugar

View Answer
99) Which one of the following is correct about H-bonding in nucleotide?

A)

\[A-T,G-C\]

B)

\[A-G,T-C\]

C)

\[G-T,A-C\]

D)

\[A-A,T-T\]

View Answer
100) Change in enthalpy for the reaction, \[2{{H}_{2}}{{O}_{2}}(l)\xrightarrow{{}}2{{H}_{2}}O(l)+{{O}_{2}}(g)\] if heat of formation of \[{{H}_{2}}{{O}_{2}}(l)\]and\[{{H}_{2}}O(l)\] are -188 and -286 kJ/mol respectively is

A)

\[-196\text{ }kJ/mol\]

B)

       \[+196\text{ }kJ/mol\]

C)

       \[+948\text{ }kJ/mol\]

D)

       \[-948\text{ }kJ/mol\]

View Answer
101) The complex numbers \[\sin x+i\cos 2x\]and \[\cos x-i\sin 2x\]are conjugate to each other for

A)

\[x=n\pi \]

B)

\[x=\left( n+\frac{1}{2} \right)\pi \]

C)

                       \[x=0\]

D)

       No value of \[x\]

View Answer
102) The sum of the integers from 1 to 100 which are divisible by 3 and 5, is

A)

2317

B)

2632

C)

       315

D)

       2489

View Answer
103) If \[1+\sin x+{{\sin }^{2}}x+\]upto \[\infty \] \[=4+2\sqrt{3},0<x<\pi \]and \[x\ne \frac{\pi }{2},\]then \[x\]is equal to

A)

\[\frac{\pi }{3},\frac{5\pi }{6}\]

B)

\[\frac{2\pi }{3},\frac{\pi }{6}\]

C)

       \[\frac{\pi }{3},\frac{2\pi }{3}\]

D)

       \[\frac{\pi }{6},\frac{\pi }{3}\]

View Answer
104) If \[\alpha +\beta =-2\]and\[{{\alpha }^{2}}+{{\beta }^{3}}=-56,\] then the quadratic equation whose roots are \[\alpha \] and \[\beta \] is

A)

\[{{x}^{2}}+2x-16=0\]

B)

       \[{{x}^{2}}+2x+15=0\]

C)

       \[~{{x}^{2}}+2x-12=0\]

D)

       \[{{x}^{2}}+2x-\text{ }8=0\]

View Answer
105) If one root of equation \[{{x}^{2}}+ax+12=0\]is 4 while the equation \[{{x}^{2}}+ax+b=0\]has equal roots, then the value of b is

A)

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

B)

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

C)

       \[\frac{7}{4}\]

D)

       \[\frac{4}{7}\]

View Answer
106) 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

View Answer
107) The number of ways in which 5 boys and 5 girls can be seated for a photograph, so that no two girls sit next to each other is

A)

\[6!5!\]

B)

       \[{{(5!)}^{2}}\]

C)

       \[\frac{10!}{(5!)}\]

D)

       \[\frac{10!}{{{(5!)}^{2}}}\]

View Answer
108) The coefficient of \[{{x}^{20}}\]in the expansion of \[{{(1+3x+3{{x}^{2}}+{{x}^{3}})}^{20}}\]is

A)

\[{{\,}^{60}}{{C}_{40}}\]

B)

       \[{{\,}^{30}}{{C}_{20}}\]

C)

       \[{{\,}^{15}}{{C}_{2}}\]

D)

       None of these

View Answer
109) If \[A={{[{{a}_{ij}}]}_{2\times 2}},\]where \[{{a}_{ij}}=i+j,\]then A is equal to

A)

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

B)

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

C)

       \[\left[ \begin{matrix}    1 & 2 \\    3 & 4 \\ \end{matrix} \right]\]

D)

       \[\left[ \begin{matrix}    2 & 3 \\    3 & 4 \\ \end{matrix} \right]\]

View Answer
110) If\[C=2\cos \theta ,\] then the value of the determinant\[\Delta =\left| \begin{matrix}    C & 1 & 0 \\    1 & C & 1 \\    6 & 1 & C \\ \end{matrix} \right|\]is

A)

\[\frac{\sin 4\theta }{\sin \theta }\]

B)

       \[\frac{2{{\sin }^{2}}2\theta }{\sin \theta }\]

C)

       \[4{{\cos }^{2}}\theta (2cos\theta -1)\]

D)

       None of the above

View Answer
111) \[\sin \left( 2{{\sin }^{-1}}\sqrt{\frac{63}{65}} \right)\]is equal to

A)

\[\frac{2\sqrt{126}}{65}\]

B)

       \[\frac{4\sqrt{65}}{65}\]

C)

       \[\frac{8\sqrt{63}}{65}\]

D)

       \[\frac{\sqrt{63}}{65}\]

View Answer
112) 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)

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

View Answer
113) The value of \[x\] in \[\left( 0,\frac{\pi }{2} \right)\] satifying the equation \[\sin x\cos x=\frac{1}{4}\]is

A)

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

B)

       \[\frac{\pi }{12}\]

C)

       \[\frac{\pi }{8}\]

D)

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

View Answer
114) The equation \[\sqrt{3}\sin x+\cos x=4\]has

A)

infinitely many solutions

B)

       no solution

C)

       two solutions

D)

       only one solution

View Answer
115) In \[\Delta ABC,2ac\,\sin \frac{A-B+C}{2}\]is equal to

A)

\[{{a}^{2}}+{{b}^{2}}-{{c}^{2}}\]

B)

       \[{{c}^{2}}+{{a}^{2}}-{{b}^{2}}\]

C)

       \[{{b}^{2}}-{{a}^{2}}-{{c}^{2}}\]

D)

       \[{{c}^{2}}-{{a}^{2}}-{{b}^{2}}\]

View Answer
116) From the top of a tower, the angle of depression of a point on the ground is \[\text{6}{{\text{0}}^{\text{o}}}\text{.}\] 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)

       \[\frac{\sqrt{3}}{2}m\]

View Answer
117) If the three points \[(0,1),(0,-1)\]and \[(x,0)\] are vertices of an equilateral triangle, then the value of \[x\] are

A)

\[\sqrt{3},\sqrt{2}\]

B)

       \[\sqrt{3},-\sqrt{3}\]

C)

       \[-\sqrt{5},\sqrt{3}\]

D)

       \[\sqrt{2},-\sqrt{2}\]

View Answer
118) The equation of the straight line passing through the point (4, 3) and making intercepts on the coordinate axes whose sum is -1, is

A)

\[\frac{x}{y}+\frac{y}{3}=-1\]and \[\frac{x}{-2}+\frac{y}{1}=-1\]

B)

       \[\frac{x}{2}-\frac{y}{3}=-1\]and \[\frac{x}{-2}+\frac{y}{1}=-1\]

C)

       \[\frac{x}{2}-\frac{y}{3}=1\]and \[\frac{x}{-2}+\frac{y}{1}=1\]

D)

       \[\frac{x}{y}-\frac{y}{3}=1\]and \[\frac{x}{-2}+\frac{y}{1}=1\]

View Answer
119) The angle between the lines represented by the equation \[2{{x}^{2}}+3xy-5{{y}^{2}}=0\]is

A)

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

B)

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

C)

       \[{{\tan }^{-1}}\left| \frac{12}{5} \right|\]

D)

       \[{{\tan }^{-1}}\left| \frac{7}{3} \right|\]

View Answer
120) The other end of the diameter through the point \[(-1,1)\] on the circle \[{{x}^{2}}+{{y}^{2}}-6x+4y-12y=0\]is

A)

\[(-7,5)\]

B)

       \[(-7,-\text{ }5)\]

C)

       \[(7,-\text{ }5)\]

D)

                       \[(7,\text{ }5)\]

View Answer
121) The number of common tangents to the circles \[{{x}^{2}}+{{y}^{2}}=4\] and \[{{x}^{2}}+{{y}^{2}}-6x-8y+24=0\] is

A)

3

B)

       4

C)

       2

D)

       1

View Answer
122) The distance between the foci of the conic \[7{{x}^{2}}-9y=63\]is equal to

A)

8

B)

       4

C)

       3

D)

       7

View Answer
123) The two parabolas \[{{x}^{2}}=4y\]and \[{{y}^{2}}=4x\]meet in two distinct points. One of these is the origin and the other is

A)

\[(2,2)\]

B)

       \[(4,-4)\]

C)

       \[(4,4)\]

D)

                       \[(-2,2)\]

View Answer
124) The sum of the series \[1+\frac{1}{3}.\frac{1}{4}+\frac{1}{5}.\frac{1}{{{4}^{2}}}+\frac{1}{7}.\frac{1}{{{4}^{3}}}+\,.....\infty \]is

A)

\[{{\log }_{e}}1\]

B)

       \[{{\log }_{e}}2\]

C)

       \[{{\log }_{e}}3\]

D)

       \[{{\log }_{e}}4\]

View Answer
125) The coefficient of \[{{x}^{n}}\]in the series \[1+\frac{a+bx}{1!}+\frac{{{(a+bx)}^{2}}}{2!}+\frac{{{(a+bx)}^{3}}}{3!}...\infty \]

A)

\[\frac{{{(ab)}^{n}}}{n!}\]

B)

       \[{{e}^{b}}.\frac{{{a}^{n}}}{n!}\]

C)

       \[{{e}^{a}}.\frac{{{b}^{n}}}{n!}\]

D)

       \[{{e}^{a+b}}\frac{{{(ab)}^{n}}}{n!}\]

View Answer
126) The angle between the lines whose direction cosines are \[\left( \frac{\sqrt{3}}{4},\frac{1}{4},\frac{\sqrt{3}}{2} \right)\] and \[\left( \frac{\sqrt{3}}{4},\frac{1}{4}-\frac{\sqrt{3}}{2} \right)\]is

A)

\[\pi \]

B)

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

C)

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

D)

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

View Answer
127) A straight line which makes an angle of \[{{60}^{o}}\] with each of \[y\]and \[z-\]axes, this line makes with \[x-\]axis at an angle

A)

\[{{30}^{o}}\]

B)

       \[{{60}^{o}}\]

C)

       \[{{75}^{o}}\]

D)

       \[{{45}^{o}}\]

View Answer
128) If a and b are unit vectors and \[|a+b|=1,\] then \[|a-b|\] is equal to

A)

\[\sqrt{2}\]

B)

       1

C)

       \[\sqrt{5}\]

D)

       \[\sqrt{3}\]

View Answer
129) If ABCDEF is a regular hexagon with AB = a and BC = b, then CE equals

A)

b - a

B)

       -b

C)

       b - 2a

D)

       None of these

View Answer
130) If \[a=i+2j+3k\]and \[b=i\times (a\times i)+j\times (a\times j)+k\times (a\times k)\]the length of b is equal to

A)

\[\sqrt{12}\]

B)

       \[2\sqrt{12}\]

C)

       \[3\sqrt{14}\]

D)

       \[2\sqrt{14}\]

View Answer
131) Range of the function \[f(x)=\frac{x}{1+{{x}^{2}}}\]is

A)

\[(-\infty ,\infty )\]

B)

       \[[-1,1]\]

C)

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

D)

       \[[-\sqrt{2},\sqrt{2}]\]

View Answer
132) The domain of the real function\[f(x)=\frac{1}{\sqrt{4-{{x}^{2}}}}\]is

A)

the set of all real numbers

B)

       the set of all positive real numbers

C)

       \[(-2,2)\]

D)

       \[[-2,2]\]

View Answer
133) \[\underset{x\to \infty }{\mathop{\lim }}\,{{\left( \frac{x+a}{a+b} \right)}^{x+b}}\]is

A)

1

B)

       \[{{e}^{b-a}}\]

C)

       \[{{e}^{a-b}}\]

D)

       \[{{e}^{b}}\]

View Answer
134) The function \[f(x)=|x|+\frac{|x|}{x}\]is

A)

continuous at the origin

B)

       discontinuous at the origin because \[|x|\] is discontinuous there

C)

       discontinuous at the origin because \[\frac{|x|}{x}\] is discontinuous there

D)

       discontinuous at the origin because \[|x|\] and \[\frac{|x|}{x}\]are discontinuous there

View Answer
135) If \[f(x)=\frac{x}{1+|x|}\]for \[x\in R,\]then \[f(0)\]is

A)

0

B)

       1

C)

       2

D)

       does not exist

View Answer
136) If \[y=\sqrt{\frac{1+{{e}^{x}}}{1-{{e}^{x}}}},\]then \[\frac{dy}{dx}\]is

A)

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

B)

       \[\frac{{{e}^{x}}}{(1-{{e}^{x}})\sqrt{1-{{e}^{x}}}}\]

C)

       \[\frac{{{e}^{x}}}{(1-{{e}^{x}})\sqrt{1+{{e}^{2x}}}}\]

D)

       \[\frac{{{e}^{x}}}{(1-{{e}^{x}})\sqrt{1+{{e}^{x}}}}\]

View Answer
137) If\[f(x)=\sin (\log x)\]and \[y=f\left( \frac{2x+3}{3-2x} \right),\]then \[\frac{dy}{dx}\]is

A)

\[\frac{9\cos (\log x)}{x{{(3-2x)}^{2}}}\]

B)

       \[\frac{9\cos \left( \log \frac{2x+3}{3-2x} \right)}{x{{(3-2x)}^{2}}}\]

C)

       \[\frac{9\sin \left( \log \frac{2x+3}{3-2{{x}^{2}}} \right)}{{{(3-2x)}^{2}}}\]

D)

       None of the above

View Answer
138) If \[x={{e}^{t}}\sin \,t,y={{e}^{t}}\cos t,t\]is a parameter, then \[\frac{{{d}^{2y}}}{d{{x}^{2}}}\]at \[(1,1)\]is equal to

A)

\[-\frac{1}{2}\]

B)

       \[-\frac{1}{4}\]

C)

       0

D)

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

View Answer
139) The slope of tangent to the curve \[x={{t}^{2}}+3t-8,y=2{{t}^{2}}-2t-5\]at the point \[(2,-1)\]is

A)

\[\frac{22}{7}\]

B)

       \[\frac{6}{7}\]

C)

       \[-6\]

D)

       None of these

View Answer
140) \[\int_{{}}^{{}}{\frac{1}{x\sqrt{{{x}^{2}}-1}}dx}\]is equal to

A)

\[{{\cos }^{-1}}x+C\]

B)

       \[{{\sec }^{-1}}x+C\]

C)

       \[co{{t}^{-1}}x+C\]

D)

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

View Answer
141) \[\int_{{}}^{{}}{\frac{2x{{\tan }^{-1}}{{x}^{2}}}{1+{{x}^{4}}}}dx\]

A)

\[{{[{{\tan }^{-1}}{{x}^{2}}]}^{2}}+C\]

B)

       \[\frac{1}{2}{{[{{\tan }^{-1}}{{x}^{2}}]}^{2}}+C\]

C)

       \[2{{[{{\tan }^{-1}}{{x}^{2}}]}^{2}}+C\]

D)

       None of above

View Answer
142) \[\int_{0}^{\pi /2}{\frac{d\theta }{1+\tan \theta }}\]is equal to

A)

\[\pi \]

B)

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

C)

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

D)

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

View Answer
143) \[\int_{-4}^{4}{|x+2|}dx\] is equal to

A)

50

B)

       24

C)

       20

D)

       None of these

View Answer
144) The area bounded by the curve \[y=x,\]\[x-\] axis and ordinates \[x=-1\]to \[x=2\] is

A)

0

B)

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

C)

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

D)

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

View Answer
145) The area enclosed between the curve \[y={{\log }_{e}}(x+e)\]and the coordinate axes is

A)

3

B)

       4

C)

       1

D)

       2

View Answer
146) The solution of \[\frac{dy}{dx}+\sqrt{\left( \frac{1-{{y}^{2}}}{1-{{x}^{2}}} \right)}=0\]is

A)

\[{{\tan }^{-1}}x+{{\cot }^{-1}}x=C\]

B)

       \[{{\sin }^{-1}}x+{{\sin }^{-1}}y=C\]

C)

       \[{{\sec }^{-1}}x+\cos e{{c}^{-1}}x=C\]

D)

       None of the above

View Answer
147) The dice are thrown. The probability that the sum of the points on two dice will be 7, is

A)

\[\frac{5}{36}\]

B)

       \[\frac{6}{36}\]

C)

       \[\frac{7}{36}\]

D)

       \[\frac{8}{36}\]

View Answer
148) A horizontal force F is applied to a small object P of mass m on a smooth plane inclined to the horizontal at an angle \[\theta .\]If F is just enough to keep P in equilibrium, then F is equal to

A)

\[mg{{\cos }^{2}}\theta \]

B)

       \[mg{{\sin }^{2}}\theta \]

C)

       \[mg\cos \theta \]

D)

       \[mg\tan \theta \]

View Answer
149) Let R be the relation on the set R, of all real numbers defined by aRb iff \[mg\tan \theta \] Then, R is

A)

reflexive and symmetric

B)

       symmetric only

C)

       transitive only

D)

       anti-symmetric only

View Answer
150) The converse of the contrapositive of the conditional\[p\to \tilde{\ }q\] is

A)

\[p\to q\]

B)

       \[\tilde{\ }p\to \tilde{\ }q\]

C)

       \[\tilde{\ }q\to p\]

D)

       \[\tilde{\ }p\to q\]

View Answer