Solved papers for JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2009

Jamia Millia Islamia Solved Paper-2009 Total Questions - 170

1) The magnitude of resultant of two equal forces is equal to either of two forces. The angle between forces is

A)

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

B)

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

C)

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

D)

\[\frac{3\pi }{4}\]

View Answer
2)     A particle projected vertically upwards attains a maximum height H. If the ratio of the times to attain a height\[h(h<H)\]is\[\frac{1}{3}\]then,

A)

\[4h=3H\]

B)

\[3h=4H\]

C)

\[3h=H\]

D)

\[4h=H\]

View Answer
3)     A force vector applied on a body is given by \[\overrightarrow{F}=6\hat{i}-8\hat{j}+10\hat{k}\]and acquires an acceleration of\[1\text{ }m{{s}^{2}}\]. Then the mass of the body is

A)

\[10\sqrt{2}\]kg

B)

\[2\sqrt{10}\]

C)

\[10\,kg\]

D)

\[20\,kg\]

View Answer
4)     In the adjoining figure, AB,BC and AC are light metallic rods hinged at B. The tension on rod BC is

A)

150 N

B)

180 N

C)

500 N

D)

\[166\frac{1}{3}N\]

View Answer
5)     A 2 kg block is dropped from a height of 0.4m on a spring of force constant\[k=1960\text{ }N{{m}^{-1}}\]. The maximum compression of the spring is

A)

0.1 m

B)

0.2 M

C)

0.3 M

D)

0.4 M

View Answer
6)     A solid sphere of mass 2 kg rolls up a\[30{}^\circ \]incline with an initial speed\[10\text{ }m{{s}^{-1}}\]. The maximum height reached by the sphere is\[(g=10\text{ }m{{s}^{-2}})\]

A)

3.5m

B)

7.0m

C)

10.5m

D)

14.5m

View Answer
7)     A body is moving in a vertical circle of radius r such that the string is just tout at its highest point. The speed of the particle when the string is horizontal is

A)

\[\sqrt{gr}\]

B)

\[\sqrt{2gr}\]

C)

\[\sqrt{3gr}\]

D)

\[\sqrt{5gr}\]

View Answer
8)     In some region, the gravitational field is zero. The gravitational potential in this region

A)

may be zero

B)

cannot be zero

C)

must be change

D)

None of these

View Answer
9) Some gas at 300K is enclosed in a container. Now, the container is placed on a fast moving train. While the trains is in motion, the temperature of gas

A)

rises above 300K

B)

falls below 300K

C)

remains unchanged

D)

becomes unsteady

View Answer
10)     The ratio of the adiabatic bulk modulus to the isothermal bulk modulus of a perfect gas is equal to (symbols have their usual meanings)

A)

\[{{C}_{p}}-{{C}_{V}}\]

B)

\[\frac{{{C}_{P}}}{{{C}_{V}}}\]

C)

\[\frac{{{C}_{V}}}{{{C}_{P}}}\]

D)

\[\sqrt{\frac{{{C}_{P}}}{{{C}_{V}}}}\]

View Answer
11) The volume of a block of metal changed by 0.12% when heated through\[20{}^\circ C\]. Then a is

A)

\[2.0\times {{10}^{-5}}/{}^\circ C\]

B)

\[4.0\times {{10}^{-5}}/{}^\circ C\]

C)

\[6.0\times {{10}^{-5}}/{}^\circ C\]

D)

\[8.0\times {{10}^{-5}}/{}^\circ C\]

View Answer
12)     A simple pendulum has time period T. The pendulum is completely immersed in a non-viscous liquid whose density is one-tenth of that of the material of the bob. The time period of the pendulum immersed in liquid is

A)

\[T\]

B)

\[\sqrt{\frac{9}{10}}T\]

C)

\[\sqrt{\frac{10}{9}}T\]

D)

\[\frac{T}{10}\]

View Answer
13)     How many times more intense is a 90 dB sound than a 40 dB sound?

A)

2.5

B)

5

C)

50

D)

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

View Answer
14)     The minimum distance of a reflector to hear the echo of monosyllabic sound is (speed of sound is\[330\text{ }m{{s}^{-1}}\])

A)

16.5 m

B)

33 m

C)

165 m

D)

330m

View Answer
15)     If\[X=\frac{{{\varepsilon }_{0}}lV}{t},\]where\[{{\varepsilon }_{0}}\]is the permittivity of free space,\[l\]is light, V is potential difference and\[t\]is time. The dimensions of\[X\]are the same as that of

A)

charge

B)

resistance

C)

voltage

D)

current

View Answer
16)     An electric dipole placed in a uniform electric field will have minimum potential energy when the dipole moment is inclined to the field at an angle

A)

\[\pi \]

B)

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

C)

zero

D)

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

View Answer
17)     In the figure, the equivalent capacitance between A and B is

A)

\[3.75\text{ }\mu F\]

B)

\[5.25\text{ }\mu F\]

C)

\[6.5\text{ }\mu F\]

D)

\[10.5\text{ }\mu F\]

View Answer
18)     Potential at appoint at a distance r from the centre of uniformly charged sphere of radius a \[a(<r)\] is proportional to

A)

\[{{a}^{3}}\]

B)

r

C)

\[\frac{1}{r}\]

D)

\[\frac{1}{{{a}^{3}}}\]

View Answer
19) If we add impurity to a metal those atoms also deflect electrons. Therefore,

A)

the electrical and thermal conductivity both increase

B)

the electrical and thermal conductivity both decrease

C)

the electrical conductivity increases but thermal conductivity decreases

D)

the electrical conductivity decreases but thermal conductivity increases

View Answer
20)     The voltage V and current\[I\]graph for a conductor at two different temperatures\[{{T}_{1}}\]and\[{{T}_{2}}\]are shown in figure. The relations between\[{{T}_{1}}\]and\[{{T}_{2}}\]is

A)

\[{{T}_{1}}>{{T}_{2}}\]

B)

\[{{T}_{1}}<{{T}_{2}}\]

C)

\[{{T}_{1}}={{T}_{2}}\]

D)

\[{{T}_{1}}\approx {{T}_{2}}\]

View Answer
21)     \[1\,Wb/{{m}^{2}}\]is equal to

A)

\[10{{\,}^{4}}G\]

B)

\[10{{\,}^{2}}G\]

C)

\[10{{\,}^{-2}}G\]

D)

\[10{{\,}^{-4}}G\]

View Answer
22)     A bar magnet has coercively\[4\times {{10}^{3}}A\text{ }{{m}^{-1}}\]. It is desired to demagnetize 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)

2 A

B)

4A

C)

6 A

D)

8 A

View Answer
23)     A thyroidal solenoid with an air core has an average radius of 15 cm, are of cross-section 12cm2 and 1200 turns. Ignoring the field variation across the cross-section of the toroid the self-inductance of the toroid is

A)

4.6 mH

B)

6.9 mH

C)

2.3 mH

D)

9.2 mH

View Answer
24)     If\[\phi \]is phase difference between current and voltage the wattless component of current is

A)

\[I\,\cos \phi \]

B)

\[I\sin \phi \]

C)

\[I\tan \phi \]

D)

\[I{{\cos }^{2}}\phi \]

View Answer
25)     To double the covering range of a TV transmitter tower, its height should be made

A)

2 times

B)

4 times

C)

V2 times

D)

8 times

View Answer
26)     A bulb is placed between two plane mirrors inclined at an angle of\[60{}^\circ \]. The number of images formed is

A)

5

B)

6

C)

4

D)

3

View Answer
27) Two plane mirrors are placed perpendicular to each other. A ray strikes one mirror and after reflection from the second mirror will be

A)

perpendicular to the original ray

B)

parallel to the original ray

C)

at\[45{}^\circ \]to the original ray

D)

can be at any angle to the original ray

View Answer
28)     An electron moving with velocity\[2\times {{10}^{7}}m{{s}^{-1}}\] describes a circle in a magnetic field of strength\[2\times {{10}^{-2}}T\].If\[\left( \frac{e}{m} \right)\]of electrons is\[1.76\times {{10}^{11}}K\,k{{g}^{-1}},\]then the diameter of the circle is nearly

A)

1.1 cm

B)

1.1 mm

C)

1.1 m

D)

11 cm

View Answer
29) A neutron is confined to a nucleus of size\[{{10}^{-14}}m\]. The minimum momentum of the electron may be

A)

\[6.6\times {{10}^{-20}}kg\text{ }m{{s}^{-1}}\]

B)

\[3.3\times {{10}^{-20}}kg\text{ }m{{s}^{-1}}\]

C)

\[3.3\times {{10}^{-48}}kg\text{ }m{{s}^{-1}}\]

D)

\[6.6\times {{10}^{-48}}kg\text{ }m{{s}^{-1}}\]

View Answer
30)     An electron makes transition inside a hydrogen atom. The orbital angular momentum of the electron may change by

A)

\[h\]

B)

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

C)

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

D)

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

View Answer
31)     If 1 mg of\[{{U}^{235}}\]is completely annihilated, the energy liberated is

A)

\[9\times {{10}^{10}}J\]

B)

\[9\times {{10}^{19}}J\]

C)

\[9\times {{10}^{18}}J\]

D)

\[9\times {{10}^{17}}J\]

View Answer
32)     The transfer ratio\[\beta \]of a transistor is 50. The input resistance of the transistor when used in the common emitter mode is\[1\,k\Omega \]. The peak value of the collector alternating current for an input peak voltage of 0.01 V is

A)

\[100\text{ }\mu A\]

B)

\[\text{500 }\mu A\]

C)

\[\text{0}\text{.01 }\mu A\]

D)

\[\text{0}\text{.25 }\mu A\]

View Answer
33)     It is possible to observe total internal reflection when a ray travels from

A)

air into water

B)

air into glass

C)

water into glass

D)

glass into water

View Answer
34)     A combination of convex and concave lenses has power 4D. If the convex lens has power 5D the focal length of the concave lens will be

A)

100 cm

B)

\[-100cm\]

C)

\[-1\,cm\]

D)

\[-\frac{100}{9}\,cm\]

View Answer
35) A liquid of refractive index 1.62 is placed between two plano-convex identical lenses, the medium of which has refractive index 1.54. Two possible arrangement P and Q are shown. The system is

A)

divergent in P, convergent in Q

B)

convergent in P, divergent ion Q

C)

convergent in both

D)

divergent in both

View Answer
36)     A scooter of mass 120 kg is moving with a uniform velocity of\[108\text{ }km{{h}^{-1}}\]. The force required to stop the vehicle in 10 s is

A)

360 N

B)

720 N

C)

180 N

D)

\[120\times 10.8\text{ }N\]

View Answer
37)     Energy required to accelerate a car from \[10\text{ }m{{s}^{-1}}\]to\[20\text{ }m{{s}^{-1}}\]compared with that. required to accelerate from 0 to\[10\text{ }m{{s}^{-1}}\]is

A)

twice

B)

three times

C)

four times

D)

same

View Answer
38)     The moment of inertia of the body about on axis is\[1.2\text{ }kg\text{ }{{m}^{2}}\]. Initially the body is at rest. In order to produce a rotational kinetic energy of 1500 J, an angular acceleration of 25 rads-2 must be applied about the axis for the duration of

A)

2 s

B)

4 s

C)

8s

D)

10s

View Answer
39) A cooking pot should have

A)

high specific heat and low conductivity

B)

high specific heat and high conductivity

C)

low specific heat and low conductivity

D)

low specific heat and high conductivity

View Answer
40)     A certain force gives a 2 kg object an acceleration of\[0.5\text{ }m{{s}^{-2}}\]. What acceleration would the same force give to a 10 kg object?

A)

\[0.1m{{s}^{-2}}\]

B)

\[0.2m{{s}^{-2}}\]

C)

\[0.5m{{s}^{-2}}\]

D)

\[1.0m{{s}^{-2}}\]

View Answer
41)     A heat engine absorbs heat at\[327{}^\circ C\]and exhausts heat at\[127{}^\circ C\]. The efficiency of engine is\[\eta \]and the maximum amount of work performed by the engine per kilocalorie of heat input is W. Then

A)

\[\eta =0.38\]

B)

\[\eta =0.88\]

C)

\[W=1596J\]

D)

\[W=1400J\]

View Answer
42)     A simple pendulum with length L and mass of the bob is vibrating with an amplitude a. Then the maximum tension in the string is

A)

\[mg\]

B)

\[mg\left[ 1{{\left( \frac{a}{1} \right)}^{2}} \right]\]

C)

\[mg{{\left[ 1+\frac{a}{2L} \right]}^{2}}\]

D)

\[mg{{\left[ 1+\left( \frac{a}{L} \right) \right]}^{2}}\]

View Answer
43) A sonometer wire is vibrating in the second overtone. In the wire there are

A)

two nodes and two antinodes

B)

one node and two antinodes

C)

four nodes and three antinodes

D)

three nodes and three antinodes

View Answer
44)     Two charged conducting spheres of radii\[{{R}_{1}}\] and\[{{R}_{2}},\]separated by a large distance, are connected by a long wire. The ratio of the charges on, them is

A)

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

B)

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

C)

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

D)

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

View Answer
45)     A proton and an\[\alpha -\]particle, accelerated through the same potential difference, enter a region of uniform magnetic field normally. If the radius of the proton orbit is 10 cm the radius of\[\alpha -\]orbit is

A)

10cm

B)

\[10\sqrt{2}cm\]

C)

20cm

D)

\[5\sqrt{2}cm\]

View Answer
46)     In a noiseless transformer an alternating current of 2 A is flowing in the primary coil. The number of turns on the primary and secondary coils are 100 and 20 respectively. The value of the current in the secondary coil is

A)

0.08 A

B)

0.4 A

C)

5 A

D)

10 A

View Answer
47)     Two photons of energy 2.5 eV each are incident on a metal plate whose work function is 4.0 eV, then the number of electrons emitted from the metal surface will be

A)

one

B)

two

C)

more than two

D)

None of these

View Answer
48)     The ratio of areas between the electron orbits for the first excited state to the ground state for hydrogen atom is

A)

\[2:1\]

B)

\[4:1\]

C)

\[8:1\]

D)

\[16:1\]

View Answer
49)     The voltage gain of an amplifier without feedback is 100. If a negative feedback is introduced with a feedback fraction\[p=0.1,\] then the gain of the feedback amplifier is

A)

9.09

B)

10

C)

100.1

D)

90.0

View Answer
50)     The sun subtends an angle of half a degree at the pole of a concave mirror which has a radius of curvature of 15 m. Then the size (diameter) of the image of the sun formed by the concave mirror is

A)

7.5 cm

B)

6.55 cm

C)

3.7cm

D)

13.1cm

View Answer
51)     Two bodies of equal masses are connected by a light inextensible string passing over a smooth frictionless pulley. The amount of mass that should be transferred from one to another so that both the masses mole 50 m in 5 s is

A)

30 %

B)

40 %

C)

70%

D)

50%

View Answer
52)     In the following\[p-V\]diagram, two Aetobatus cut two isothermal at\[{{T}_{1}}\]and\[{{T}_{2}}\]The value of\[{{V}_{b}}/{{V}_{c}}\]is

A)

\[{{V}_{a}}/{{V}_{d}}\]

B)

\[<\frac{{{V}_{a}}}{{{V}_{d}}}\]

C)

\[>\frac{{{V}_{a}}}{{{V}_{d}}}\]

D)

cannot say

View Answer
53)     A copper wire of cross-sectional area \[=2.0\text{ }m{{m}^{2}},\]resistivity\[=1.7\times {{10}^{-8}}\Omega m,\]carries a current of 1 A. The electric field in the copper wire is

A)

\[8.5\times {{10}^{-5}}V{{m}^{-1}}\]

B)

\[8.5\times {{10}^{-4}}V{{m}^{-1}}\]

C)

\[8.5\times {{10}^{-3}}V{{m}^{-1}}\]

D)

\[8.5\times {{10}^{-2}}V{{m}^{-1}}\]

View Answer
54)     A solenoid 30 cm long is made by winding 2000 loops of wire on an iron rod whose cross section is\[1.5\text{ }c{{m}^{2}}\]. If the relative permeability of the iron is 6000, what is the self-inductance of the solenoid?

A)

1.5 H

B)

2.5 H

C)

3.5 H

D)

0.5 H

View Answer
55)     A luminous object is placed 20 cm from surface of a convex mirror and a plane mirror is set, so that virtual mirror is at a distance of 12 cm from object, then focal length of convex mirror is

A)

5 cm

B)

10 cm

C)

20cm

D)

40cm

View Answer
56) The optically active tartaric acid is named as\[D-(+)-\]tartaric acid because it has a positive

A)

optical rotation and derived from D-glucose

B)

pH in organic solvent

C)

optical rotation and is derived from\[D-(+)-\]glyceraldehyde

D)

optical rotation when substituted by deuterium

View Answer
57) Which one of the following pairs is not correctly matched?

A)

Clemmnensen reduction

B)

Wolff-Kishner reduction

C)

\[-COCl\to -CHO\]Rosemond reduction

D)

\[-C\equiv N\to -CHO\]Stephen reduction

View Answer
58)     Which of the following radical is precipitated as sulphide when treated with hydrogen sulphide in ammonia Cal solution?

A)

\[B{{a}^{2+}}\]

B)

\[N{{i}^{2+}}\]

C)

\[M{{g}^{2+}}\]

D)

\[C{{a}^{2+}}\]

View Answer
59)     Isomerism which arises due to the presence of two different atoms in the same ligand is called

A)

linkage

B)

hydrate

C)

salt

D)

Both (a) and (b)

View Answer
60) The black compound formed during the reaction between sodium thiosulphate and silver nitrate is

A)

silver thiosulphate

B)

silver sulphide

C)

silver sulphate

D)

silver sulphite

View Answer
61)     Electrode potential data are given below \[F{{e}^{3+}}(aq)++{{e}^{-}}F{{e}^{2+}}(aq)\]    \[E{}^\circ =+0.77V\] \[A{{l}^{3+}}(aq)+3{{e}^{-}}\xrightarrow[{}]{{}}Al(s)\]    \[E{}^\circ =-1.66\,V\] \[B{{r}_{2}}(aq)+2{{e}^{-}}\xrightarrow[{}]{{}}2B{{r}^{-}}(aq)\]   \[E{}^\circ =+1.08\,V\] Based on the data given above, reducing power of\[F{{e}^{2+}},Al\]and\[B{{r}^{-}},\]will increase, in the order

A)

\[B{{r}^{-}}<F{{e}^{2+}}<Al\]

B)

\[F{{e}^{2+}}<Al<B{{r}^{-}}\]

C)

\[Al<B{{r}^{-}}<F{{e}^{2+}}\]

D)

\[Al<F{{e}^{2+}}<B{{r}^{-}}\]

View Answer
62) Which of the following volume (V)\[-\]temperature (T) plots represent the behaviour of one mole of an ideal gas at one atmospheric pressure?

A)

B)

C)

D)

View Answer
63)     Amongst the following, identify the species with an atom in\[+6\]oxidation state

A)

\[MnO_{4}^{-}\]

B)

\[Cr(CN)_{6}^{3-}\]

C)

\[NiF_{6}^{2-}\]

D)

\[Cr{{O}_{2}}C{{l}_{2}}\]

View Answer
64)     What is the concentration of nitrate ions if equal-volumes of\[0.1M\,AgN{{O}_{3}}\]and\[0.1\text{ }M\text{ }NaCl\]are mixed together?

A)

0.1 N

B)

0.2 M

C)

0.05 M

D)

0.25 M

View Answer
65)     Consider the following statements (I) A sigma\[(\sigma )\] bond is formed when two\[s-\] orbitals overlap (II) A pi\[(\pi )\]bond is formed when two\[p-\] orbitals axially overlap (III) A\[\sigma \] bond is weaker than\[\pi -\]bond Which of the above statements is/are correct?

A)

II and III

B)

I and II

C)

I alone

D)

II alone

View Answer
66)     Speed of decomposition of\[{{H}_{2}}{{O}_{2}}\]is reduced by

A)

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

B)

\[NaOH\]

C)

alcohol

D)

\[Pt\]

View Answer
67)     The correct order of radii is

A)

\[N<Be<B\]

B)

\[{{F}^{-1}}<{{O}^{2-}}<{{N}^{3-}}\]

C)

\[Na<Li<K\]

D)

\[F{{e}^{3+}}<F{{e}^{2+}}<F{{e}^{4+}}\]

View Answer
68) Amalgamation method is used for the extraction of

A)

noble metals

B)

alkali metals

C)

alkaline earth metals

D)

transition elements

View Answer
69)     The alkali metal that reacts with nitrogen directly to form nitride is

A)

\[Li\]

B)

\[Na\]

C)

K

D)

\[Rb\]

View Answer
70) Fluid magnesia is

A)

a solution of magnesium

B)

a solution of magnesium carbonate

C)

a solution of magnesium bicarbonate

D)

a solution of magnesium sulphate

View Answer
71) A compound with the molecular formula \[{{C}_{3}}{{H}_{8}}O\]on vigorous oxidation produces an acid \[{{C}_{3}}{{H}_{6}}{{O}_{2}}\]. It is

A)

a tertiary alcohol

B)

a secondary alcohol

C)

a primary alcohol

D)

not necessarily an alcohol

View Answer
72)     The correct order of basic ties of the following compounds is (1)          (2) \[C{{H}_{3}}-C{{H}_{2}}-N{{H}_{2}}\] (3) \[{{(C{{H}_{3}})}_{2}}NH\]                     (4) \[C{{H}_{3}}-\overset{\begin{smallmatrix} O \\ |\,\,| \end{smallmatrix}}{\mathop{C}}\,-N{{H}_{2}}\]

A)

\[2>1>3>4\]

B)

\[1>3>2>4\]

C)

\[3>1>2>4\]

D)

\[1>2>3>4\]

View Answer
73)     \[R-\overset{\begin{smallmatrix} O \\ |\,| \end{smallmatrix}}{\mathop{C}}\,-OH\xleftarrow[{}]{{{H}_{3}}{{O}^{+}}}X\xrightarrow[{}]{[H]}RC{{H}_{2}}N{{H}_{2}}\] Here X is

A)

isonitrile

B)

nitrile

C)

nitrite

D)

oxime

View Answer
74) Identify\[X\]\[{{C}_{6}}{{H}_{6}}\xrightarrow[reflux]{HN{{O}_{3}}/{{H}_{2}}S{{O}_{4}}}\]Intermediate\[\xrightarrow[heat]{Sn/HCl}X\]

A)

B)

C)

D)

View Answer
75) Rutherfords a-particle dispersion experiment concludes

A)

all positive ions are deposited at small part

B)

all negative ions are deposited at small part

C)

proton moves around the electron

D)

neutrons are charged particles

View Answer
76) Identify the correct statement when following compounds are given\[HF,HBr,{{H}_{2}}Se,{{H}_{2}}Te,{{H}_{3}}P\]

A)

HF is strong acid

B)

\[{{H}_{2}}Te\]is strong alkali

C)

\[HBr\]is strong acid

D)

\[{{H}_{3}}P\]is strong alkali

View Answer
77) Calcium is obtained by

A)

electrolysis of molten \[CaC{{l}_{2}}\]

B)

electrolysis of aq solution of \[CaC{{l}_{2}}\]

C)

reduction of\[CaC{{l}_{2}}\]with carbon

D)

roasting of lime stone

View Answer
78)     Heat of dissociation of benzene to elements in\[5535\text{ }kJ\text{ }mo{{l}^{-1}}\]. The bond enthalpies of\[C-C,\] \[C=C,\]and\[C-H\]are 347.3, 615.0 and 416.2 kJ respectively resonance energy of benzene is

A)

1.51 kJ

B)

15.1 kJ

C)

151 kJ

D)

1511 kJ

View Answer
79)     The rate constant for the reaction,\[2{{N}_{2}}{{O}_{5}}\xrightarrow[{}]{{}}4N{{O}_{2}}+{{O}_{2}}\]\[3.0\times {{10}^{-5}}{{s}^{-1}}\]. If the rate is\[2.40\times {{10}^{-5}}\]mol \[{{L}^{-1}}{{s}^{-1}},\]Then the concentration of\[{{N}_{2}}{{O}_{5}}\](in mol \[{{L}^{-1}}\]) is

A)

1.4

B)

1.2

C)

0.04

D)

0.8

View Answer
80) Which one of the following has highest pH?

A)

Distilled water

B)

\[1M\,N{{H}_{3}}\]

C)

\[1M\,NaOH\]

D)

Water saturated with chlorine

View Answer
81)     Which of the following element of\[IIIA\]group form alum with aluminum like alkali metals?

A)

\[B\]

B)

\[Ca\]

C)

\[In\]

D)

\[Te\]

View Answer
82) Which of the following is used as a test for detecting the presence of carbon monoxide?

A)

Reduction of metallic oxides to metals

B)

Reduction of water to hydrogen

C)

Reduction of\[PdC{{l}_{2}}\]to\[Pd\](Black)

D)

All of the above

View Answer
83)     Nitrogen can exists in two forms which are correct about them? (i) \[\alpha -\]nitrogen with cubic crystalline structure (ii)\[\beta -\]nitrogen with cubic crystalline structure (iii)\[\beta -\]nitrogen with hexagonal crystalline structure

A)

Both (i) and (iii)

B)

Both (i) and (ii)

C)

Both (ii) and (iii)

D)

None of these

View Answer
84)     Which of the following mixture Is called black ash?

A)

\[{{K}_{2}}C{{O}_{3}}+CuS\]

B)

\[N{{a}_{2}}C{{O}_{3}}+CaS\]

C)

\[{{K}_{2}}C{{O}_{3}}+N{{a}_{2}}S\]

D)

\[N{{a}_{2}}C{{O}_{3}}+N{{a}_{2}}S\]

View Answer
85)     In phosphorus pentoxide each P atoms is linked to

A)

4 oxygen atom

B)

2 oxygen atom

C)

3 oxygen atom

D)

10 oxygen atom

View Answer
86) When glucose is warmed with dilute alkali solution converted into a mixture of

A)

glucose and manose

B)

glucose and fructose

C)

manose and fructose

D)

glucose and manose and fructose

View Answer
87)     Methyl amine reacts with nitrous acid to form

A)

methyl nitrile

B)

dimethyle ether

C)

Both (a) and (b)

D)

None of these

View Answer
88) Which order is correct about acidity?

A)

\[{{C}_{6}}{{H}_{5}}OH>{{C}_{6}}{{H}_{5}}COOH>C{{H}_{3}}COOH\]

B)

\[{{C}_{6}}{{H}_{5}}COOH>C{{H}_{3}}COOH>{{C}_{6}}{{H}_{5}}OH\]

C)

\[C{{H}_{3}}COOH>{{C}_{6}}{{H}_{5}}COOH>{{C}_{6}}{{H}_{5}}OH\]

D)

\[{{C}_{6}}{{H}_{5}}OH>C{{H}_{3}}COOH>{{C}_{6}}{{H}_{5}}COOH\]

View Answer
89)     Which of the following is most reactive towards nucleophilic addition reaction?

A)

\[HCHO\]

B)

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

C)

\[{{C}_{2}}{{H}_{5}}CHO\]

D)

\[C{{H}_{3}}.CO.C{{H}_{3}}\]

View Answer
90)     Meta formaldehyde is a

A)

polymer

B)

tetramer

C)

trimer

D)

dimer

View Answer
91)     An aqueous solution of urea freezes at 272.8 K. An equimolar solution of acetic acid in water will freeze at

A)

272.8 K

B)

272.79 K

C)

272.81 K

D)

272.6 K

View Answer
92)     A mixture of 0.3 mol of H2 and 0. 3 mole of 12 is allowed to react in a 10 L evacuated flask at\[500{}^\circ C\]. The reaction is\[{{H}_{2}}+{{I}_{2}}2HI\].The K is found to be 64. The amount of unreacted 12 at equilibrium is

A)

0.15 mol

B)

0.06 mol

C)

0.03 mol

D)

0.2 mol

View Answer
93)     \[IF{{N}_{2}}+3{{H}_{2}}2N{{K}_{3}}-K\]and \[2{{N}_{2}}+6{{H}_{2}}4N{{H}_{3}}-{{k}^{-1}}\] then\[{{k}^{-1}}\] will be

A)

\[{{k}^{2}}\]

B)

\[\sqrt{k}\]

C)

\[\frac{1}{\sqrt{k}}\]

D)

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

View Answer
94) With the rise in temperature, the surface tension of a liquid

A)

increases

B)

decreases

C)

remain constant

D)

first increase then decrease

View Answer
95) At STP a container has 1 mole of Ar, 2 mol of \[C{{O}_{2}},\]3 mol of\[{{O}_{2}}\]and 4 mol of\[{{N}_{2}}\]without changing the total pressure if one mole of\[{{O}_{2}}\]is removed, the partical pressure of\[{{O}_{2}}\]

A)

is change by about 16%

B)

is halved

C)

is changed by 26%

D)

is unchanged

View Answer
96)     Due to Frenkel defect, the density of ionic solid

A)

decreases

B)

increases

C)

does not change

D)

charge

View Answer
97) A semiconductor of Ge can be made p-type by adding

A)

trivalent impurity

B)

tetravalent impurity

C)

pentavaient impurity

D)

divalent impurity

View Answer
98)     0.45 g of acid of molecular weight 90 was neutralised by 20 mL of 0.5 N Caustic potash. The basicity of the acid is

A)

1

B)

2

C)

3

D)

4

View Answer
99)     Which of the following cannot give iodometric titrations?

A)

\[F{{e}^{3+}}\]

B)

\[C{{u}^{2+}}\]

C)

\[P{{b}^{2+}}\]

D)

\[A{{g}^{+}}\]

View Answer
100)     Oxidation state of Fe in\[F{{e}_{3}}{{O}_{4}}\]is

A)

2/3

B)

4/5

C)

5/4

D)

8/3

View Answer
101)     A compound contains atoms of three elements AB and C. If the oxidation number of A is\[+2,\]B is\[+5,\]and that of C is\[-2,\]the possible formula of the compound is

A)

\[{{A}_{3}}{{(B{{C}_{4}})}_{2}}\]

B)

\[{{A}_{3}}{{({{B}_{4}}C)}_{2}}\]

C)

\[AB{{C}_{2}}\]

D)

\[{{A}_{2}}{{(B{{C}_{3}})}_{2}}\]

View Answer
102)     For the redox reaction,\[MnO_{4}^{-}+{{C}_{2}}O_{4}^{2-}+{{H}^{+}}\xrightarrow[{}]{{}}M{{n}^{2+}}+C{{O}_{2}}+{{H}_{2}}O\]the correct coefficient of the reactants for the balanced reaction are                 \[MnO_{4}^{-}\]                              \[{{C}_{2}}O_{4}^{2-}\]                 \[{{H}^{+}}\]

A)

                2                              5                              16

B)

                16                           5                              2

C)

                5                              16                           2

D)

                2                              16                           5

View Answer
103)     An example of Lewis acid is

A)

\[NaCl\]

B)

\[MgC{{l}_{2}}\]

C)

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

D)

\[AlC{{l}_{3}}\]

View Answer
104)     The conjugate acid of\[NH_{2}^{-}\]is

A)

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

B)

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

C)

\[NH_{4}^{+}\]

D)

\[{{N}_{2}}{{H}_{4}}\]

View Answer
105)     Which of the following is hot paramagnetic?

A)

\[NO\]

B)

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

C)

\[CO\]

D)

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

View Answer
106)     The values of electronegativitys of atom A and B are 1.20 and 4.0 respectively. The percentage of ionic character of\[A-B\]bond is

A)

50%

B)

72.24%

C)

55.3%

D)

43%

View Answer
107)     A sample of wood decayed to 1/16 of its, original value. What is the number of\[{{t}_{1/2}}\]?

A)

3

B)

4

C)

8

D)

16

View Answer
108) The phenomenon of radioactivity arises from the

A)

binary fission

B)

nuclear fission

C)

stable nuclei

D)

decay of unstable nuclei

View Answer
109)     The kinetic energy of an electron accelerated from rest through a potential difference of 5V will be

A)

5eV

B)

5J

C)

5 erg

D)

80 eV

View Answer
110)     A 2.5 mol sample of hydrazine,\[{{N}_{2}}{{H}_{4}}\]loses 25 mole of electrons in being converted to a new compound\[X\]. Assuming that all of the nitrogen appears in the new compound, what is the oxidation state of nitrogen in compound\[X\]?

A)

\[-1\]

B)

\[-2\]

C)

\[+3\]

D)

\[+4\]

View Answer
111) If the expression\[\frac{\left[ \sin \left( \frac{x}{2} \right)+\cos \left( \frac{x}{2} \right)-i\tan (x) \right]}{\left[ 1+2i\sin \left( \frac{x}{2} \right) \right]}\]is real the set of all possible value of\[x\]is

A)

\[n\pi +\alpha \]

B)

\[2n\pi \]

C)

\[\frac{n\pi }{2}+\alpha \]

D)

None of these

View Answer
112) If\[{{t}_{1}},{{t}_{2}}\]and\[{{t}_{3}}\]are distinct, points\[({{t}_{1}},2a{{t}_{3}}+at_{1}^{3}),\]\[({{t}_{2}},2a{{t}_{2}}+at_{2}^{3})\]and\[({{t}_{3}},2a{{t}_{3}}+at_{3}^{3})\]are collinear, if

A)

\[{{t}_{1}}{{t}_{2}}{{t}_{3}}=1\]

B)

\[{{t}_{1}}+{{t}_{2}}+{{t}_{3}}={{t}_{1}}{{t}_{2}}{{t}_{3}}\]

C)

\[{{t}_{1}}+{{t}_{2}}+{{t}_{3}}=0\]

D)

\[{{t}_{1}}+{{t}_{2}}+{{t}_{3}}=-1\]

View Answer
113)     If the pair of straight lines\[a{{x}^{2}}+2hxy-a{{y}^{2}}=0\] and \[b{{x}^{2}}+2gxy-b{{y}^{2}}=0,\]be such that each bisect the angle between the other, then

A)

\[hg+ab=0\]

B)

\[ah+bg=0.\]

C)

\[{{h}^{2}}-ab=0\]

D)

\[ag+bh=0.\]

View Answer
114)     The locus of a points which moves such that the sum of the squares of its distance from three vertices of the triangle is constant is a/an

A)

circle

B)

straight line

C)

ellipse

D)

None of these

View Answer
115)     AB is a chord of the parabola\[{{y}^{2}}=4ax\]with vertex at A. BC is drawn perpendicular to AB meeting the axis at C. The projection of BC on the axis of the parabola is

A)

2

B)

\[2a\]

C)

\[4a\]

D)

\[8a\]

View Answer
116) If\[\tan {{\theta }_{1}},\tan {{\theta }_{2}}=-\frac{{{a}^{2}}}{{{b}^{2}}},\] then the chord joining two points\[{{\theta }_{1}}\]and\[{{\theta }_{2}}\]on the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] will subtend a right angle at

A)

focus

B)

centre

C)

end of the major axis

D)

end of the minor axis

View Answer
117)     The largest interval for which\[{{x}^{2}}-{{x}^{9}}+{{x}^{4}}-x+1>0\]is

A)

\[-4<x<0\]

B)

\[0<x<1\]

C)

\[-100<x<100\]

D)

\[-\infty <x<\infty \]

View Answer
118)     The eccentricity of the conic represented by \[{{x}^{2}}-{{y}^{2}}-4x+4y+16=0\]is

A)

1

B)

\[\sqrt{2}\]

C)

2

D)

\[1/2\]

View Answer
119)     Let\[f\]be a twice differentiable function such that\[f(x)=-f(x)\]and\[f(x)=g(x)\]. If\[h(x)=[f{{(x)}^{2}}+g{{(x)}^{2}}]h(1)=8\]and\[h(0)=2,\]then\[h(2)\]is equal to

A)

1

B)

2

C)

3

D)

None of these

View Answer
120) The equation of\[f\]those tangents to \[4{{x}^{2}}-9{{y}^{2}}=36\]which are perpendicular to the straight line\[5x+2y-10=0\]are

A)

\[5(y-3)=2\left( x-\frac{\sqrt{117}}{2} \right)\]

B)

\[2x-5y+10-2\sqrt{18}=0\]

C)

\[2x-5y-10-2\sqrt{18}=0\]

D)

None of the above

View Answer
121)     If\[f(x)=a\log |x|+b{{x}^{2}}+x\]has its extremum value at\[x=-1\]and\[x=2,\]then

A)

\[a=2,b=-1\]

B)

\[a=2,b=\frac{-1}{2}\]

C)

\[a=-2,b=\frac{1}{2}\]

D)

None of these

View Answer
122) If\[\int{\frac{1}{(\sin x+4)(\sin x-1)}}dx\]\[=A=\frac{1}{\tan \frac{x}{2}-1}+B{{\tan }^{-1}}(f(x))+{{C}_{1}}\]. Then

A)

\[A=\frac{1}{5},B=\frac{-2}{5\sqrt{15}},f(x)=\frac{4\tan x+3}{\sqrt{15}}\]

B)

\[A=-\frac{1}{5},B=\frac{1}{\sqrt{15}},f(x)=\frac{4\tan x\left( \frac{x}{2} \right)+1}{\sqrt{15}}\]

C)

\[A=\frac{2}{5},B=\frac{-2}{5},f(x)=\frac{4\tan x+1}{5}\]

D)

\[A=\frac{2}{5},B=\frac{-2}{5\sqrt{15}},f(x)=\frac{4\tan \frac{x}{2}+1}{\sqrt{15}}\]

View Answer
123)     If\[{{a}_{1}},{{a}_{2}},.....,{{a}_{n}}\]On are in arithmetic progression, where\[{{a}_{i}}>0\]for all\[i\]. Then \[\frac{1}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{2}}}}+\frac{1}{\sqrt{{{a}_{2}}}+\sqrt{{{a}_{3}}}}+...+\frac{1}{\sqrt{{{a}_{n-1}}}+\sqrt{{{a}_{n}}}}\]is equal to

A)

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

B)

\[\frac{n-1}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{n}}}}\]

C)

\[\frac{n(n-1)}{2}\]

D)

None of these

View Answer
124)     Let\[f\]be a positive function. Let\[{{I}_{1}}=\int_{1-k}^{k}{xf\{x(1-x)\}}dx,\]\[{{I}_{2}}=\int_{1-k}^{k}{f\{x(1-x)\}}dx\]where\[2k-1>0\]. Then, \[\frac{{{I}_{1}}}{{{I}_{2}}}\]is

A)

2

B)

\[k\]

C)

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

D)

1

View Answer
125)     The area bounded by the curve\[y=x|x|,\]\[x-\]axis and the ordinates\[x=1,\text{ }x=-1\]is given by

A)

6

B)

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

C)

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

D)

None of these

View Answer
126)     The degree of the differential equation satisfying\[\sqrt{1-{{x}^{2}}}+\sqrt{1-{{y}^{2}}}=a(x-y)\]is

A)

1

B)

2

C)

3

D)

None of these

View Answer
127)     7 relatives of a man comprises 4 ladies and 3 gentlemen his wife has also 7 relatives, 3 of them are ladies and 4 gentlemen. In how many ways can they invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of mans relative and 3 of the wifes relative?

A)

485

B)

500

C)

486

D)

102

View Answer
128)     If\[\overrightarrow{\alpha }=x(\overrightarrow{a}\times \overrightarrow{b})+y(\overrightarrow{b}\times \overrightarrow{c})+z(\overrightarrow{c}\times \overrightarrow{a})\]and\[[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}]=\frac{1}{8},\]then\[x+y+z\]is equal to

A)

\[8\overrightarrow{\alpha }.(\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c})\]

B)

\[\overrightarrow{\alpha }.(\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c})\]

C)

\[8(\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c})\]

D)

None of these

View Answer
129) The\[xy-\]plane divides the line joining the points\[(-1,3,4)\]and\[(2,-5,6)\]

A)

internally in the ratio \[2:3\]

B)

externally in the ratio\[2:3\]

C)

internally in the ratio\[3:2\]

D)

externally in the ratio\[3:2\]

View Answer
130) The plane\[2x-(1+\lambda )y+3\lambda z=0\]passes through the intersection of the plane

A)

\[2x-y=0\]and \[y+3z=0\]

B)

\[2x-y=0\]and \[y-3z=0\]

C)

\[2x+3z=0\]and \[y=0\]

D)

None of the above

View Answer
131)     In a triangle ABC,\[sin\text{ }A-cos\,B=cosC,\]then angle B is

A)

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

B)

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

C)

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

D)

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

View Answer
132)     Eight chair are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chair marked 1 to 4; and then the men select the chairs from amongst the remaining.   The   number   of possible arrangements is

A)

\[^{6}{{C}_{3}}{{\times }^{4}}{{C}_{2}}\]

B)

\[^{4}{{P}_{2}}{{\times }^{6}}{{P}_{3}}\]

C)

\[^{4}{{C}_{2}}{{\times }^{4}}{{P}_{3}}\]

D)

None of these

View Answer
133)     In a \[\Delta ABC,\tan \frac{A}{2}=\frac{5}{6},\tan \frac{C}{2}=\frac{2}{5},\]then

A)

a, c, b are in AP

B)

a, b, c are in AP

C)

b, a, c are in AP

D)

a, b, c are in GP

View Answer
134)     \[\Sigma {{a}^{3}}\cos (B-C)\]is equal to

A)

\[3abc\]

B)

\[3(cz+b+c)\]

C)

\[abc(a+b+c)\]

D)

0

View Answer
135)     If\[\alpha ,\beta ,\gamma \in \left[ 0,\frac{\pi }{2} \right],\] then the value of \[\frac{\sin (\alpha +\beta +\gamma )}{sin\text{ }\alpha +sin\,\beta +sin\text{ }\gamma }\]is

A)

\[<1\]

B)

\[=-1\]

C)

\[<0\]

D)

None of these

View Answer
136)     If \[f(x)=\]\[\left| \begin{matrix}    1 & x & x+1 \\    2x & x(x-1) & (x+1)x \\    3x(x-1) & x(x-1)(x-2) & (x+1)x(x-1) \\ \end{matrix} \right|\]then\[f(100)\]is equal to

A)

0

B)

1

C)

100

D)

\[-100\]

View Answer
137)     The general value of 6 satisfying the equation \[2si{{n}^{2}}\theta -3sin\theta -2=0\]is

A)

\[n\pi +{{(-1)}^{n+1}}\frac{\pi }{6}\]

B)

\[n\pi +{{(-1)}^{n}}\frac{\pi }{2}\]

C)

\[n\pi +{{(-1)}^{n}}\frac{5\pi }{6}\]

D)

\[n\pi +{{(-1)}^{n}}\frac{7\pi }{6}\]

View Answer
138)     In a right angled triangle the hypotenuse is\[2\sqrt{2}\]times the length of perpendicular drawn from the opposite vertex on the hypotenuse, then the other two angles are

A)

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

B)

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

C)

\[\frac{\pi }{8},\frac{3\pi }{8}\]

D)

\[\frac{\pi }{12},\frac{5\pi }{12}\]

View Answer
139)     lf \[x+y+z=xyz,\]then \[ta{{n}^{-1}}x+ta{{n}^{-1}}y+ta{{n}^{-1}}z\] is equal to

A)

\[\pi \]

B)

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

C)

1

D)

None of these

View Answer
140)     If two events A and B are such\[P({{A}^{c}})=0.3\] \[P(B)=0.4\]and\[P(A\cap {{B}^{c}})=0.5,\]then \[P[B/{{(A\cup B)}^{c}}]\]is equal to

A)

1/2

B)

¼

C)

0

D)

None of these

View Answer
141)     If\[{{x}_{1}},{{x}_{2}},{{x}_{3}},{{x}_{4}}\]are roots of the equation\[{{x}^{4}}-{{x}^{3}}\] \[\sin 2\beta +{{x}^{2}}\cos 2\beta -x\cos \beta -\sin \beta =0,\] then \[{{\tan }^{-1}}{{x}_{1}}+{{\tan }^{-1}}{{x}_{2}}+{{\tan }^{-1}}{{x}_{3}}+{{\tan }^{-1}}{{x}_{4}}\]is equal to

A)

\[\beta \]

B)

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

C)

\[\pi -\beta \]

D)

\[-\beta \]

View Answer
142)     The value of\[\cos (2{{\cos }^{-1}}0.8)\]is

A)

0.48

B)

0.96

C)

0.6

D)

None of these

View Answer
143)     ABC is a triangular park with\[AB=AC=100\text{ }m\]A clock tower is situated at the mid point of BC. The angle of elevation if the top of the tower at A and B are\[co{{t}^{-1}}3.2\]and\[\cos e{{c}^{-1}}2.6\] respectively. The height of the tower is

A)

16 m

B)

25 m

C)

50 m

D)

None of these

View Answer
144) The equation\[\frac{3}{4}{{({{\log }_{2}}x)}^{2}}+{{\log }_{2}}x-\frac{5}{4}={{\log }_{x}}\sqrt{2}\]has

A)

at least one real solutions

B)

exactly three real solutions

C)

exactly one irrational solution

D)

complex roots

View Answer
145) If G is the GM of the product of r set of observation with geometric means\[{{G}_{1}},{{G}_{2}},....{{G}_{r}}\]respectively, then G is equal to

A)

\[\log {{G}_{1}}+\log {{G}_{2}}+....+\log {{G}_{n}}\]

B)

\[{{G}_{1}}{{G}_{2}}....{{G}_{n}}\]

C)

\[\log {{G}_{1}},\log {{G}_{2}},....,\log {{G}_{n}}\]

D)

None of the above

View Answer
146) If\[Z=aX+bY\]and r the correlation coefficient between\[X\]and\[Y\],then\[\sigma _{z}^{2}\]is equal to

A)

\[{{a}^{2}}\sigma _{X}^{2}+{{b}^{2}}\sigma _{Y}^{2}+2abr\,{{\sigma }_{X}}{{\sigma }_{Y}}\]

B)

\[{{a}^{2}}\sigma _{X}^{2}+{{b}^{2}}\sigma _{Y}^{2}-2abr\,{{\sigma }_{X}}{{\sigma }_{Y}}\]

C)

\[2abr\,{{\sigma }_{X}}{{\sigma }_{Y}}\]

D)

None of the above

View Answer
147)     If\[{{\log }_{2}}({{5.2}^{x}}+1),{{\log }_{4}}({{2}^{1-x}}+1)\]and 1 are in AP, then\[x\]equals

A)

\[lo{{g}_{2}}5\]

B)

\[1-lo{{g}_{2}}5\]

C)

\[lo{{g}_{5}}2\]

D)

None of these

View Answer
148)     If\[A=\left[ \begin{matrix}    \alpha & 0 \\    1 & 1 \\ \end{matrix} \right]\]and\[B=\left[ \begin{matrix}    1 & 0 \\    5 & 1 \\ \end{matrix} \right],\]then value of a for which\[{{A}^{2}}=B\]is

A)

1

B)

\[-1\]

C)

4

D)

no real value

View Answer
149)     The maximum value of\[|z|\]when z satisfies the condition\[\left| 2+\frac{2}{z} \right|=2\]is

A)

\[\sqrt{3}-1\]

B)

\[\sqrt{3}\]

C)

\[\sqrt{3}+1\]

D)

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

View Answer
150)     The value\[1+\sum\limits_{k=0}^{14}{\left\{ \cos \frac{(2k+1)\pi }{15}+i\sin \frac{(2k+1)\pi }{15} \right\}}\]is

A)

0

B)

\[-1\]

C)

1

D)

\[i\]

View Answer
151) The sum to n terms of the infinite series \[{{1.3}^{2}}+{{2.5}^{2}}+{{3.7}^{2}}+...\infty \]is

A)

\[\frac{n}{6}(n+1)(6{{n}^{2}}+14n+7)\]

B)

\[\frac{n}{6}(n+1)(2n+1)(3n+1)\]

C)

\[4{{n}^{3}}+4{{n}^{2}}+n\]

D)

None of the above

View Answer
152)     If\[f(x)={{\sin }^{2}}x+{{\sin }^{2}}\left( x+\frac{\pi }{3} \right)\]\[+\cos x\cos \left( x+\frac{\pi }{3} \right)\] and\[g\left( \frac{5}{4} \right)=1,\]then\[gof(x)\]is equal to

A)

0

B)

2

C)

1

D)

3

View Answer
153)     If the roots of the quadratic equation\[{{x}^{2}}-4x-lo{{g}_{3}}a=0\]are real, then the least value of a is

A)

81

B)

1/81

C)

1/64

D)

None of these

View Answer
154)     The exponent of 12 in 100 is

A)

48

B)

49

C)

96

D)

None of these

View Answer
155)     The value of\[1.1!+2.2!+3.3!+...+n.n!\]is

A)

\[(n+1)!\]

B)

\[(n+1)!+1\]

C)

\[(n+1)!-1\]

D)

None of these

View Answer
156)     \[\underset{n\to \infty }{\mathop{\lim }}\,\frac{1}{n}\sum\limits_{r=1}^{2n}{\frac{r}{\sqrt{{{n}^{2}}+{{r}^{2}}}}}\]equals

A)

\[1+\sqrt{5}\]

B)

\[-1+\sqrt{5}\]

C)

\[-1+\sqrt{2}\]

D)

\[1+\sqrt{2}\]

View Answer
157)     If\[{{(1+2x+3{{x}^{2}})}^{10}}={{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}\]\[+...+{{a}_{20}}{{x}^{20}},\]then\[{{a}_{1}}\]equals

A)

10

B)

20

C)

210

D)

None of these

View Answer
158)     The sum of series\[\sum\limits_{n-1}^{\infty }{\frac{2n}{(2n+1)!}}\]is

A)

\[e\]

B)

\[-1\]

C)

\[2e\]

D)

None of these

View Answer
159)     If the value of the determinants\[\left| \begin{matrix}    a & 1 & 1 \\    1 & b & 1 \\    1 & 1 & c \\ \end{matrix} \right|\]is positive, then

A)

\[abc>1\]

B)

      \[abc>-8\]

C)

\[abc<-8\]

D)

\[abc>-2\]

View Answer
160)     The function\[f(x)=\frac{ln(1+ax)-ln(1-bx)}{x}\]is not defined at\[x=0\]. The value which should be assigned to\[f\]at\[x=0\]so that it is continuous at\[x=0,\]is

A)

\[a-b\]

B)

\[a+b\]

C)

\[ln\text{ }a+ln\text{ }b\]

D)

None of these

View Answer
161)     If\[f(x+2y,x,x-2y)=xy,\]then\[f(x,y)\]equals

A)

\[\frac{{{x}^{2}}-{{y}^{2}}}{8}\]

B)

\[\frac{{{x}^{2}}-{{y}^{2}}}{4}\]

C)

\[\frac{{{x}^{2}}+{{y}^{2}}}{4}\]

D)

\[\frac{{{x}^{2}}-{{y}^{2}}}{2}\]

View Answer
162)     If\[\underset{x\to \infty }{\mathop{\lim }}\,\left[ \frac{{{x}^{3}}+1}{{{x}^{2}}+1}-(ax+b) \right]=2,\]then

A)

\[a=1,\text{ }b=-2\]

B)

\[a=-1,\text{ }b=2\]

C)

\[a=-1,\text{ }b=-2\]

D)

None of these

View Answer
163)     \[\underset{x\to \infty }{\mathop{\lim }}\,\frac{\sqrt{{{x}^{2}}+1}-\sqrt[3]{{{x}^{3}}+1}}{\sqrt{{{x}^{4}}+1}-\sqrt[3]{{{x}^{4}}+1}}\]equals

A)

1

B)

0

C)

\[-1\]

D)

None of these

View Answer
164)     The tangent at (1,7) to the curve\[{{x}^{2}}=y-6\]touches the circle\[{{x}^{2}}+{{y}^{2}}+16x+12y+c=0\]at

A)

(6, 7)

B)

\[(-6,7)\]

C)

\[(6,-7)\]

D)

\[(-6,-7)\]

View Answer
165)     The set of points where the function\[f(x)=x|x|\]is differentiable is

A)

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

B)

\[(-\infty ,0)\cup (0,\infty )\]

C)

\[(0,\infty )\]

D)

\[[0,\infty )\]

View Answer
166) If\[f(x)=|{{\log }_{e}}|x||,\]then\[{{f}_{0}}(x)\]equals

A)

\[\frac{1}{|x|},x\ne 0\]

B)

\[\frac{1}{x}\]for \[|x|>1\]and\[\frac{-1}{x}\]for \[|x|<1\]

C)

\[\frac{-1}{x}\]for \[|x|>1\]and \[\frac{1}{x}\]for \[|x|<1\]

D)

\[\frac{1}{x}\]for\[x>0\]and\[-\frac{1}{x}\]for \[x<0\]

View Answer
167)     The equation of the tangent to the curve \[y=(2x-1){{e}^{2(1-x)}}\]at the points its maximum, is

A)

\[y-1=0\]

B)

\[x-1=0\]

C)

\[x+y-1=0\]

D)

\[x-y+1=0\]

View Answer
168) A function\[f(x)=\left\{ \begin{matrix} 1+x,\,\,x\le 2 \\ 5-x,\,\,x>2 \\ \end{matrix} \right.\]is

A)

not continuous at \[x=2\]

B)

differentiable at\[x=2\]

C)

continuous but not differentiable at\[x=2\]

D)

None of the above

View Answer
169)     The interval of increase of the function\[f(x)=x-{{e}^{x}}+\tan (2\pi /7)\]is

A)

\[(0,\infty )\]

B)

\[(-\infty ,0)\]

C)

\[(1,\infty )\]

D)

\[(-\infty ,-1)\]

View Answer
170) Let\[P(x)={{a}_{0}}+{{a}_{1}}{{x}^{2}}+{{a}_{2}}{{x}^{4}}+...+{{a}_{n}}{{x}^{2n}}\]be a polynomial in a real variable\[x\]with \[0<{{a}_{0}}<{{a}_{1}}<{{a}_{2}}<...<{{a}_{n}}\].The function\[P(x)\]has

A)

neither a maximum nor a minimum

B)

only one maximum

C)

only one minimum

D)

only one maximum and only one minimum

View Answer