Solved papers for JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2004

Jamia Millia Islamia Solved Paper-2004 Total Questions - 170

1) If masses of all molecules of a gas are halved and their speeds are doubled, then the ratio of initial and final pressures is:

A)

1:2

B)

2 : 1

C)

4 : 1

D)

1 : 4

View Answer
2)     A force \[\therefore \]N displaces the body by \[{{\upsilon }^{2}}=4rg\]in 2 sec. Power generated will be :

A)

11 watt

B)

6 watt

C)

22 watt

D)

12 watt

View Answer
3)     A   body   moving   with   uniform acceleration describes 40 m in the first 5 sec and 65 m in next 5 sec. Its initial velocity will be :

A)

4 m/s

B)

2.5 m/s

C)

5.5 m/s

D)

11 m/s

View Answer
4)     The displacement time graph for two bodies A and B are straight lines inclined at 30° and 60° respectively with the time axes. If \[\upsilon =\sqrt{4rg}\] and \[\upsilon =\sqrt{4\times 2.5\times 9.8}\] are their velocities, then \[\upsilon =\sqrt{98}\,\,m/s\]will be :

A)

\[\text{2}0\text{ g }=\text{ 2}\times \text{1}{{0}^{-\text{2}}}\text{ kg},\]

B)

\[=\frac{360\times 5}{18}=100m/s\]

C)

3 : 1

D)

1 : 3

View Answer
5)     The first excited state of hydrogen atom is 10.2 eV above its ground state. The temperature needed to excite hydrogen atoms to first excited level, is :

A)

\[=\frac{n\times \frac{1}{2}m{{\upsilon }^{2}}}{t}\]

B)

\[=\frac{360\times \frac{1}{2}\times 2\times {{10}^{-2}}\times {{(100)}^{2}}}{60}\]

C)

\[g=\frac{Gm}{{{R}^{2}}}\]

D)

\[\overrightarrow{\text{F}}=\left( \text{2\hat{i}}+\text{4\hat{j}} \right)\]

View Answer
6)     The acceleration of a train travelling with speed of 400 m/s as it goes round a curve of radius 160 m, is :

A)

\[\overrightarrow{S}=\left( \text{3\hat{j}}+\text{5\hat{k}} \right)\text{m}\]

B)

\[{{\upsilon }_{A}}\]

C)

\[{{\upsilon }_{B}}\]

D)

\[{{\upsilon }_{A}}:{{\upsilon }_{B}}\]

View Answer
7) The maximum and minimum tensions in the string whirling in a circle of radius 2.5 m are in the ratio 5:3 then its velocity is :

A)

\[\sqrt{3}:1\]

B)

7 m/s

C)

\[1:\sqrt{3}\]

D)

\[7.9\times {{10}^{4}}K\]

View Answer
8)     From an automatic gun a man fires 360 bullets per minute with a speed of 360 km/hour. If each weighs 20 g, the power of the gun is :

A)

600 W

B)

300 W

C)

150 W

D)

75 W

View Answer
9) A body has a weight 90 kg on the earths surface, the mass of the moon is 1/9 that of the earths mass and its radius is ½ that of the earths radius. On the moon the weight of the body is:

A)

45 kg

B)

202.5 kg

C)

90 kg

D)

40 kg

View Answer
10)     The amplitude of a particle executing SHM is 4 cm. At the mean position the speed of the particle is 16 cm/sec. The distance of the particle from the mean position at which the speed of the particle becomes \[3.5\times {{10}^{4}}K\] cm/s, will be :

A)

\[5.8\times {{10}^{4}}K\]

B)

\[\text{14 }\times \,\,\text{1}{{0}^{\text{4}}}\text{ K}\]

C)

1 cm

D)

2 cm

View Answer
11)     The viscous force acting on a rain drop of radius 0.35 mm falling through air with a velocity of 1 m/s, is \[\text{1 km}/{{\text{s}}^{\text{2}}}\]

A)

\[\text{1}00\text{ m}/{{\text{s}}^{\text{2}}}\]

B)

\[\text{1}0\text{ m}/{{\text{s}}^{\text{2}}}\]

C)

\[\text{1}\,\text{m}/{{\text{s}}^{\text{2}}}\]

D)

\[\sqrt{98}m/s\]

View Answer
12)     Two narrow capillary tubes A and B are of lengths ( and 111 and of same radius r. The rate of flow of water through the tube A under a constant pressure head P is 3\[\sqrt{\text{49}0}\text{ m}/\text{s}\]. If A and B are connected in series and the same pressure difference P is maintained between the ends of the composite tube, then the rate of flow of water is :

A)

\[\sqrt{\text{4}\text{.9}}\text{ m}/\text{s}\]

B)

\[8\sqrt{3}\]

C)

\[2\sqrt{3}cm\]

D)

none of these

View Answer
13) The energy of electron in the nth orbit of hydrogen atom is expressed as \[\sqrt{3}cm\]. The shortest and longest wavelength of Lyman series will be :

A)

\[\left( \eta =\text{2}\times \text{1}{{0}^{-\text{4}}}\text{Ns}/{{\text{m}}^{\text{2}}} \right):\]

B)

\[6.6\times {{10}^{-6}}N\]

C)

\[6.6\times {{10}^{-5}}N\]

D)

none of these

View Answer
14) Pitch of musical note depends on :

A)

its fundamental frequency only

B)

its harmonics only

C)

its amplitude only

D)

the instrument producing the pitch

View Answer
15) An electron is accelerated by a potential difference of 1000 volt. Its velocity will be :

A)

\[1.32\times {{10}^{-7}}N\]

B)

\[13.2\times {{10}^{-7}}N\]

C)

\[\text{c}{{\text{m}}^{\text{3}}}/\text{sec}\]

D)

\[\text{1}\text{.5}\,\,\text{c}{{\text{m}}^{\text{3}}}\text{/s}\]

View Answer
16) The energy of photon of wavelength \[5000\overset{\text{o}}{\mathop{\text{A}}}\,\] is nearly 2.5 eV. Then the energy of X-ray photon of wavelength 1 A will be nearly :

A)

\[3\,\,\text{c}{{\text{m}}^{\text{3}}}\text{/s}\]

B)

\[2\,\,\text{c}{{\text{m}}^{\text{3}}}\text{/s}\]

C)

\[{{E}_{n}}=\frac{-13.6}{{{n}^{2}}}eV\]

D)

\[\text{91}0\text{ { }\!\!\mathrm{\AA}\!\!\text{ }},\text{ 1213 { }\!\!\mathrm{\AA}\!\!\text{ }}\]

View Answer
17) The wavelength of light observed on the earth from a moving star is found to decrease by 0.05%. The star is :

A)

coming closer with a velocity of \[\text{5463}\,\overset{\text{o}}{\mathop{\text{A}}}\,,\text{ 7858}\overset{\text{o}}{\mathop{\text{A}}}\,\]

B)

moving away with a velocity of \[\text{1315}\,\overset{\text{o}}{\mathop{\text{A}}}\,,\text{ 1530}\overset{\text{o}}{\mathop{\text{A}}}\,\]

C)

coming closer with a velocity of \[\text{5}.\text{67}\times \text{l}{{0}^{\text{7}}}\text{m}/\text{s}\]

D)

moving away with a velocity of \[0.\text{95 }\times \text{ 1}{{0}^{\text{7}}}\text{ m}/\text{s}\]

View Answer
18)     A transistor is used as an amplifier in CB mode with a load resistance of \[\text{1}.\text{89 }\times \text{ 1}{{0}^{7}}\text{ m}/\text{s}\]. The current gain of amplifier is 0.98 and the input resistance is \[\text{3}.\text{78 }\times \text{l}{{0}^{\text{7}}}\text{ m}/\text{s}\], the voltage gain and power gain respectively are :

A)

70, 68.6

B)

80, 75.6

C)

60, 66.6

D)

90, 96.6

View Answer
19) A whistle of frequency 500 Hz, tied to the end of a string of length 1.2 m, revolves at 400 rev/min. A listener standing some distance away in the plane of rotation of whistle hears frequencies in the range of (speed of sound = 340 m/s):

A)

436 to 386 Hz

B)

426 to 474 Hz

C)

426 to 586 Hz

D)

436 to 586 Hz

View Answer
20) In LCR circuit, an alternating emf of angular frequency co is applied then the total impedance will be :

A)

\[2.5\times {{(5000)}^{2}}eV\]

B)

\[\text{2}.\text{5 }\times \text{ 5}000\text{ eV}\]

C)

\[\frac{2.5}{5000}eV\]

D)

\[\frac{2.5}{{{(5000)}^{2}}}eV\]

View Answer
21)     In A.C. circuit a resistance of \[\text{1}.\text{5 }\times \text{ 1}{{0}^{\text{4}}}\text{ m}/\text{s}\] is connected in series with an inductance L. If the phase difference between the current and voltage is 45°, the inductive reactance will be :

A)

R/2

B)

R/4

C)

R

D)

none of these

View Answer
22)     The output voltage of a transformer connected to 220 volt line is 1100 volt at 2 ampere current. Its efficiency is 100%. The current coming from the line is :

A)

20 A

B)

10 A

C)

11 A

D)

22 A

View Answer
23) A circular coil has 500 turns of wire and its radius is 5 cm. The self inductance of the coil is :

A)

\[\text{1}.\text{5 }\times \text{ 1}{{0}^{\text{4}}}\text{ m}/\text{s}\]

B)

25 mH

C)

\[\text{1}.\text{5 }\times \text{ 1}{{0}^{5}}\text{ m}/\text{s}\]

D)

\[\text{1}.\text{5 }\times \text{ 1}{{0}^{5}}\text{ m}/\text{s}\]

View Answer
24)     2m long wire is moved with a velocity 1 m/s in a magnetic field of intensity 0.5 Wb/m in direction perpendicular to the field. The emf induced in it will be .

A)

2V

B)

\[5K\Omega \]

C)

0.1 V

D)

0.5 V

View Answer
25) The north pole of a magnet is brought near a metallic ring as shown in the fig. The direction of induced current in the ring will be :

A)

clock wise

B)

anti-clock wise

C)

first clock wise then anti-clock wise

D)

first anti-clock wise then clock wise

View Answer
26) In the given fig. A, B and C are three identical bulbs. When the switch S is closed :

A)

the brightness of bulb A does not change and that of B decreases

B)

the brightness of bulb A increases and that of B decreases

C)

the brightness of A increases bulb B does not glow

D)

the brightness of both bulbs A and B decrease

View Answer
27) Two bulbs of 100 W and 200 W working at 220 volt are joined in series with 220 volt supply. Total power consumed will be :

A)

65 watt

B)

33 watt

C)

300 watt

D)

100 watt

View Answer
28)     An electron (\[70\Omega \]) kg and charge \[{{\left[ {{(R\omega )}^{2}}+{{\left( L\omega -\frac{1}{C\omega } \right)}^{2}} \right]}^{1/2}}\]) is moving in a circular orbit in a ^magnetic field of\[{{\left[ {{R}^{2}}+{{\left( L\omega -\frac{1}{C\omega } \right)}^{2}} \right]}^{\frac{-1}{2}}}\]. Its period of revolution is :

A)

\[{{[{{R}^{2}}+{{(L\omega -C\omega )}^{2}}]}^{1/2}}\]

B)

\[{{\left[ {{R}^{2}}+{{\left( L\omega -\frac{1}{C\omega } \right)}^{2}} \right]}^{-1/2}}\]

C)

\[R\Omega \]

D)

\[\text{25}\times \text{1}{{0}^{-\text{3}}}\text{ mH}\]

View Answer
29)     1.5 m long wire carries a current 5A. It experiences a force of 7.5 N when placed in a uniform magnetic field of intensity 2T. The angle between the magnetic field and direction of current is :

A)

\[90{}^\circ \]

B)

\[60{}^\circ \]

C)

\[45{}^\circ \]

D)

\[30{}^\circ \]

View Answer
30) Currents flow m three long straight parallel long wires as shown in fig. The force on 10 cm length of wire Q is:

A)

\[\text{5}0\times \text{1}{{0}^{-\text{3}}}\text{H}\]N towards left

B)

\[\text{5}0\times \text{1}{{0}^{-\text{3}}}\text{mH}\] N towards right

C)

\[1V\]N towards right

D)

\[\text{mass}=\text{9}.0\times \text{1}{{0}^{\text{-31}}}\] towards left

View Answer
31) An ammeter gives full scale deflection when a current of 2A flows through it. The resistance of ammeter is \[1.6\times {{10}^{-19}}C\]. If the same ammeter is to be used for measusring a maximum current of 5A, then ammeter must be connected with a resistance of :

A)

\[\text{1}\text{.0}\times \text{1}{{\text{0}}^{\text{-4}}}\text{Wb}/{{\text{m}}^{\text{2}}}\] in parallel

B)

\[\text{2}.\text{1}\times \text{1}{{0}^{-\text{6}}}\text{ s}\]. in parallel

C)

\[\text{1}.0\text{5}\times \text{1}{{0}^{-\text{6}}}\text{ s}\]. is series

D)

\[7\times \text{1}{{0}^{-7}}\text{ s}\]. is series

View Answer
32) The emf of a primary cell is 2 volt. When it is short circuited it provides 4A current then the internal resistance of cell will be :

A)

\[3.5\times {{10}^{-7}}s\]

B)

\[\text{2}.\text{6}\times \text{1}{{0}^{-\text{4}}}\]

C)

\[\text{2}.\text{6}\times \text{1}{{0}^{-\text{4}}}\]

D)

\[\text{1}.\text{4 }\times \text{1}{{0}^{-\text{4}}}\]

View Answer
33)     The equivalent resistance between the points P and Q in the given circuit is :

A)

\[\text{1}.\text{4 }\times \text{1}{{0}^{-\text{4}}}\]

B)

\[12\Omega \]

C)

2R

D)

5R

View Answer
34) The resistivity of wire depends upon :

A)

its material

B)

its shape

C)

its length

D)

its area of cross-section

View Answer
35) A rod of certain metal is 1.0 m long and 0.6 cm in diameter and its resistance is \[18\Omega \]Another disc made of same metal is 2.0 cm in dimeter and 1.0 mm long. The resistance between the round faces of the disc is :

A)

\[8\Omega \].

B)

\[18\Omega \]

C)

\[8\Omega \]

D)

\[8\Omega \]

View Answer
36)     A \[2.0\Omega \]capacitor is charged to 100 V and then its plates are connected by a conducting wire. The heat produced is :

A)

\[4\Omega \]

B)

\[0.5\Omega \]

C)

\[\frac{6R}{5}\]

D)

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

View Answer
37)     An \[3\times {{10}^{-3}}\Omega \] particle is accelerated through a p.d of 106 volt then K.E. of particle will be:

A)

8 MeV

B)

4 MeV

C)

2 MeV

D)

1 MeV

View Answer
38)     As shown m fig if the point C is earthed and the point A is given a potential of 2000 volt then the potential at point B will be :

A)

400 V

B)

500 V

C)

1000 V

D)

1300 V

View Answer
39)     The radius of nucleus of silver (atomic number = 47) is\[\text{8}.\text{1}0\times \text{1}{{0}^{-\text{5}}}\text{ }\Omega \]. The electric potential on the surface of nucleus is : \[\text{4}.0\text{5}\times \text{1}{{0}^{-\text{6}}}\text{ }\Omega \]

A)

\[\text{1}\text{.35}\times \text{1}{{0}^{-8}}\text{ }\Omega \]

B)

\[2.70\times \text{1}{{0}^{-7}}\Omega \]

C)

\[2\mu F\]

D)

\[0.00\text{1 J}\]

View Answer
40)     Two small sphere balls each carrying charge \[0.0\text{1 J}\] are suspended by two insulated threads of equal length 1 m each, from a point fixed in the ceiling. It is found that in equilibrium, threads are separated by an angle 60° between them as shown in fig., the tension in the thread is :

A)

0.18 N

B)

18 N

C)

1.8 N

D)

none of these

View Answer
41)     At a certain place the horizontal component of the earths magnetic field is \[\text{15 J}\] and the angle of dip is \[45{}^\circ \] then total intensity of field at that place will be :

A)

\[0.\text{1 J}\]

B)

\[\alpha \]

C)

\[\text{3}.\text{4}\times \text{1}{{0}^{-\text{14}}}\text{ m}\]

D)

\[(e=1.6\times {{10}^{-19}}C)\]

View Answer
42)     A diver inside water (\[\text{1}.\text{99}\times \text{1}{{0}^{\text{6}}}\text{volt}\]) should see the sun set at an angle of :

A)

\[60{}^\circ \]

B)

\[90{}^\circ \]

C)

\[0{}^\circ \]

D)

\[49{}^\circ \]

View Answer
43)     The mean distance of sun from the earth is \[\text{2}.\text{9}\times \text{1}{{0}^{\text{6}}}\text{volt}\](nearly). The time taken by the light to reach earth from the sun is :

A)

0.12 min

B)

8.33 min

C)

12.5 min

D)

6.25 min

View Answer
44) A monochromatic light ray of frequency\[\text{4}.\text{99}\times \text{1}{{0}^{\text{6}}}\text{volt}\]from vacuum enters in a medium of refractive index 1.5. Its wavelength in medium will be :

A)

\[5500\overset{\text{o}}{\mathop{\text{A}}}\,\]

B)

\[6000\overset{\text{o}}{\mathop{\text{A}}}\,\]

C)

\[5000\overset{\text{o}}{\mathop{\text{A}}}\,\]

D)

\[4000\overset{\text{o}}{\mathop{\text{A}}}\,\]

View Answer
45)     The spectrum of red hot heater will be :

A)

continuous

B)

band

C)

line

D)

absorption

View Answer
46)     The focal lengths of convex lens for red and blue light are 100 cm and 96.8 cm respectively. The dispersive power of material of lens is :

A)

0.325

B)

0.0325

C)

0.98

D)

0.968

View Answer
47)     The power of an achromatic convergent lens of two lenses is + 2D. The power of convex lens is +5D. The ratio of dispersive power of convex and concave lenses will be :

A)

5 : 3

B)

3:5

C)

2:5

D)

5 : 2

View Answer
48) The diameter of objective of a telescope is 1m. Its resolving limit for the light of wavelength \[4538\overset{\text{o}}{\mathop{\text{A}}}\,\], will be :

A)

\[2B_{0}^{{}}\]

B)

\[\sqrt{2}B_{0}^{{}}\]

C)

\[B_{0}^{{}}\]

D)

none of these

View Answer
49)     A man cannot see distinctly an object beyond 5m. He wants to see the stars. The focal length of the lens which he must use, will be :

A)

12.5 m

B)

65 m

C)

6 m

D)

5 m

View Answer
50)     For thorium A = 232, Z = 90 at the end of some radioactive disintegration we obtain an isotope of lead with A = 208 and Z = 82, then the number of emitted a and P particles are :

A)

\[\mu =\text{1}.\text{33}\]

B)

\[\text{1}.\text{5}\times \text{1}{{0}^{\text{8}}}\text{ km}\]

C)

\[\text{5}\times \text{1}0{{~}^{14}}\text{Hz}\]

D)

\[\text{55}00\text{ { }\!\!\mathrm{\AA}\!\!\text{ }}\]

View Answer
51) The k line of singly ionised calcium has a wavelength of 393.3 nm as measured on earth. In the spectrum of one of the observed galaxies, this spectral line is located at 401.8 nm. The speed with which the galaxy is moving away from us, will be :

A)

6480 km/s

B)

3240 km/s

C)

4240 km/s

D)

none of these

View Answer
52)     If unit of length, mass and time each be doubled, the unit of work done is increased by

A)

4 times

B)

6 times

C)

8 times

D)

2 times

View Answer
53) The dimensional formula of universal gas constant:

A)

\[\text{6}000\text{ { }\!\!\mathrm{\AA}\!\!\text{ }}\]

B)

\[\text{5}000\text{ { }\!\!\mathrm{\AA}\!\!\text{ }}\]

C)

\[\text{4000 { }\!\!\mathrm{\AA}\!\!\text{ }}\]

D)

none of these

View Answer
54) A geostationary satellite is orbiting the earth at the height of 6R above the surface of earth, R being radius of earth. The time period of another satellite at a height of 2.5 R from the surface of earth, is:

A)

10 hour

B)

\[\text{5}.\text{54}\times \text{1}{{0}^{-\text{7}}}\text{rad}\] hour

C)

6 hour

D)

\[\text{2}.\text{54}\times \text{1}{{0}^{-\text{4}}}\text{ rad}\] hour

View Answer
55) 5 g of ice at \[0{}^\circ C\] is dropped in a beaker containing 20 g of water at \[40{}^\circ C\]. The final temperature will be:

A)

\[32{}^\circ C\]

B)

\[16{}^\circ C\]

C)

\[8{}^\circ C\]

D)

\[24{}^\circ C\]

View Answer
56) Beryllium shows diagonal relationship with :

A)

Mg

B)

Na

C)

B

D)

Al

View Answer
57) For a reaction, the rate constant is\[\text{6}.\text{54}\times \text{1}{{0}^{-\text{7}}}\text{rad}\]. The half-life period for the inaction is :

A)

0.30 sec

B)

0.60 sec

C)

3.3 sec

D)

data is insufficient

View Answer
58) Artificial radioactivity was discovered by:

A)

Pault

B)

Rutherford

C)

Soddy

D)

Curie

View Answer
59) Electrolysis of an aqueous solution of sodium acetate, yields :

A)

ethane

B)

ethane

C)

ethane

D)

propane

View Answer
60) Ethyl acetoacetate shows, which type of isomerism?

A)

Chain

B)

Optical

C)

Metamerism

D)

Tautomerism

View Answer
61) Which of the following gas is insoluble in water?

A)

\[\alpha =\text{4},\beta =\text{6}~~~~\]

B)

\[\alpha =\text{5},\beta =\text{5}\]

C)

\[\alpha =\text{6},\beta =\text{4}\]

D)

\[\alpha =\text{6},\beta =\text{6}\]

View Answer
62)     Dual nature of particles was proposed by:

A)

Heisenberg

B)

Lowry

C)

De-Broglie

D)

Schrodinger

View Answer
63)     sp hybridisation is found in :

A)

\[[M{{L}^{2}}{{T}^{-2}}{{\theta }^{-1}}]\]

B)

\[[{{M}^{2}}L{{T}^{-2}}\theta ]\]

C)

\[[M{{L}^{3}}{{T}^{-1}}{{\theta }^{-1}}]\]

D)

\[\frac{6}{\sqrt{2}}\]

View Answer
64)     Which of the following is an ore of lead?

A)

Galena

B)

Calamine

C)

Malachite

D)

Dolomite

View Answer
65)     The compound X, in the reaction, is :\[6\sqrt{2}\]\[\text{2}.\text{34 se}{{\text{c}}^{\text{-1}}}\]

A)

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

B)

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

C)

\[{{\text{H}}_{\text{2}}}\]

D)

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

View Answer
66)     Which of the following compound give yellow precipitate with l2 and NaOH?

A)

\[\text{CO}_{3}^{2-}\]

B)

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

C)

\[\text{NO}_{3}^{-}\]

D)

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

View Answer
67)     The laws of electrolysis were proposed by:

A)

Kohlraush

B)

Faraday

C)

Nernst

D)

Berthelot

View Answer
68)     Which of the following does not react with \[X\xrightarrow{C{{H}_{3}}Mgl}Y\xrightarrow{hydrolysis}Mg(OH)I\]?

A)

\[C{{H}_{3}}COOH:\]

B)

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

C)

HCHO

D)

none of these

View Answer
69)     What is the product in the reaction, \[C{{H}_{3}}CON{{H}_{2}}\xrightarrow[{}]{NaN{{O}_{2}}HCl}X\]

A)

\[{{(C{{H}_{3}})}_{2}}CO\]

B)

\[HCHO\]

C)

\[\text{C}{{\text{H}}_{\text{3}}}\text{OH}\]

D)

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

View Answer
70)     Which of the following .is not a Lewis base?

A)

\[{{\text{C}}_{\text{2}}}{{\text{H}}_{\text{5}}}\text{O}{{\text{C}}_{\text{2}}}{{\text{H}}_{\text{5}}}\]

B)

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

C)

\[\text{NaHS}{{\text{O}}_{\text{3}}}\]

D)

\[\text{C}{{\text{H}}_{\text{3}}}\text{COC}{{\text{H}}_{\text{3}}}\]

View Answer
71) The unit of molality is :

A)

mole per litre

B)

mole per kilogram

C)

per mole per litre

D)

mole litre

View Answer
72)     What is the ratio of diffusion rate of oxygen and hydrogen?

A)

1:4

B)

4:1

C)

1 : 8

D)

8 : 1

View Answer
73)     For the gaseous reaction,\[\text{C}{{\text{H}}_{\text{3}}}\text{CHO}\]

A)

\[\text{C}{{\text{H}}_{\text{3}}}\text{CON}{{\text{H}}_{2}}\xrightarrow{NaN{{O}_{2}}/HCl}X\]

B)

\[\text{C}{{\text{H}}_{\text{3}}}\text{COOH}\]

C)

\[\overset{+}{\mathop{\text{C}{{\text{H}}_{\text{3}}}\text{CON}{{\text{H}}_{\text{3}}}{{\text{C}}^{-}}}}\,\]

D)

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

View Answer
74)     The oxidation number of Fe in\[\text{C}{{\text{H}}_{\text{3}}}\text{CHO}\]is :

A)

+3

B)

+4

C)

+2

D)

-2

View Answer
75)     Which enzyme convert glucose into alcohol?

A)

Invertase

B)

Zymase

C)

Maltase

D)

Diastase

View Answer
76) Fehling solution is :

A)

\[{{\text{H}}_{\text{2}}}\text{O}\]lime

B)

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

C)

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

D)

none of these

View Answer
77)     Glucose reacts with bromine water to produce :

A)

gluconic acid

B)

glyceraldehyde

C)

saccharic acid

D)

glucaric acid

View Answer
78) \[O{{H}^{-}}\], product X is :

A)

ethylene bromide

B)

vinyl bromide

C)

bromo ethane

D)

ethyledine bromide

View Answer
79) Glycerol reacts with potassium bisulphate to produce :

A)

allyl iodide

B)

allyl sulphate

C)

acryl aldehyde

D)

glycerol trisulphate

View Answer
80) Sorels cement is :

A)

Portland cement + MgO

B)

\[{{N}_{2}}{{O}_{4}}\xrightarrow{{}}2N{{O}_{2}}\]

C)

\[\Delta H<\Delta E\]

D)

\[\Delta H=\Delta E\]

View Answer
81)     Which of the following is the strongest acid?

A)

\[\Delta H=0\]

B)

\[\Delta H>\Delta E\]

C)

\[{{\text{K}}_{\text{4}}}\left[ \text{Fe}{{\left( \text{CN} \right)}_{\text{6}}} \right]\]

D)

\[\text{CuS}{{\text{O}}_{\text{4}}}\text{+}\]

View Answer
82)     Which law of thermodynamics help in calculating   entropy   at   different temperatures?

A)

First law

B)

Second law

C)

Third law

D)

Zeroth law

View Answer
83)     At NTP, the density of a gas, whose molecular weight is 45, is :

A)

44.8 gm/litre

B)

11.4 gm/litre

C)

2 gm /litre

D)

3 gm/litre

View Answer
84)     At equilibrium, the Gibbs free energy is :

A)

+ ve

B)

- ve

C)

zero

D)

none of these

View Answer
85) Which of the following is not an organometallic compound?

A)

Zeisses salt

B)

TEL

C)

Sodium ethoxide

D)

Ferrocene

View Answer
86)     Which of the following ions, will have maximum hydration energy?

A)

\[\text{CuS}{{\text{O}}_{\text{4}}}\text{+NaOH(aq)}\]

B)

\[\text{CuS}{{\text{O}}_{\text{4}}}+\text{N}{{\text{a}}_{\text{2}}}\text{C}{{\text{O}}_{\text{3}}}\]

C)

\[CH\equiv CH+HBr\to X\]

D)

\[\text{MgC}{{l}_{\text{2}}}.\text{CaSi}{{\text{O}}_{\text{3}}}.\text{2}{{\text{H}}_{\text{2}}}\text{O}\]

View Answer
87)     Which set of hydridisation is correct for the following compounds? \[\text{CaSi}{{\text{O}}_{\text{3}}}.\text{MgC}{{\text{O}}_{\text{3}}}\]                \[\text{MgC}{{l}_{\text{2}}}.\text{5MgO}.;x{{H}_{\text{2}}}O\] \[HCl{{O}_{4}}\]

A)

                sp,          \[HCl{{O}_{3}}\],              \[HCl{{O}_{2}}\]

B)

                sp,          \[HClO\],            \[S{{r}^{2+}}\]

C)

                \[B{{a}^{2+}}\] \[C{{a}^{2+}}\]                  \[M{{g}^{2+}}\]

D)

                \[\text{N}{{\text{O}}_{\text{2}}}\]          \[~\text{S}{{\text{F}}_{\text{4}}}\]                \[\text{P}{{\text{F}}_{\text{6}}}\]

View Answer
88)     Phenol is more acidic than :

A)



B)

C)

\[~\text{s}{{\text{p}}^{\text{2}}}\]

D)

both (a) and (c)

View Answer
89) The reaction, \[\text{s}{{\text{p}}^{\text{3}}}\]Product, is called :

A)

Perkin reaction

B)

Levit reaction

C)

Wurtz reaction

D)

Aldol condensation

View Answer
90)     PVC is prepared by the polymerization of:

A)

ethylene

B)

1-chloropopene

C)

propene

D)

1-chloroethene

View Answer
91)     \[\text{s}{{\text{p}}^{\text{3}}}\text{d}\]            The product B is :

A)

malonic acid

B)

glycolic acid

C)

lactic acid

D)

malic acid

View Answer
92)     Solder is an alloy of :

A)

\[\text{s}{{\text{p}}^{\text{3}}}{{\text{d}}^{\text{2}}}\]

B)

\[\text{s}{{\text{p}}^{\text{2}}},\]

C)

\[\text{s}{{\text{p}}^{3}},\]

D)

\[{{\text{d}}^{2}}\text{s}{{\text{p}}^{3}}\]

View Answer
93)     The maximum number of electrons in \[\text{s}{{\text{p}}^{3}},\]-orbital with n = 5, m = 1 is :

A)

6

B)

2

C)

14

D)

10

View Answer
94)     Wolf Kishner reduction, reduces :

A)

-COOH group

B)

-C= C- group

C)

-CHO group

D)

-0- group

View Answer
95) The solubility product of \[\text{s}{{\text{p}}^{3}}{{d}^{2}},\]is\[\text{s}{{\text{p}}^{3}}{{d}^{2}}\]. What is the solubility of \[{{\text{C}}_{\text{2}}}{{\text{H}}_{\text{2}}}\]?

A)

\[C{{H}_{3}}Br+Na\to \]

B)

\[C{{H}_{3}}CHO\xrightarrow{HCN}A\xrightarrow{HOH}B\]

C)

\[\text{Pb}+\text{Zn}+\text{Sn}\]

D)

\[\text{Pb}+\text{Zn}\]

View Answer
96)     For reaction, \[\text{Pb}+\text{Sn}\], the value of kc will be equal to :

A)

\[\text{Sn}+\text{Zn}\]

B)

\[p\]

C)

\[\text{A}{{\text{s}}_{\text{2}}}{{\text{S}}_{\text{3}}}\]

D)

none of these

View Answer
97) Molecular orbital theory was proposed by:

A)

Gillespie and Nyholm

B)

Pauling

C)

Slater

D)

Hund and Mulliken

View Answer
98) The correct order of basicity of amines in water is :

A)

\[\text{2}.\text{8}\times \text{l}{{\text{0}}^{\text{-72}}}\]

B)

\[\text{A}{{\text{s}}_{\text{2}}}{{\text{S}}_{\text{3}}}\]

C)

\[\text{1}.\text{92 }\times \text{1}{{\text{0}}^{\text{-15}}}\text{ mole}/\text{litre}\]

D)

\[\text{1}.7\text{2 }\times \text{1}{{\text{0}}^{\text{-15}}}\text{ mole}/\text{litre}\]

View Answer
99) A galvanic cell with electrode potential of A=+2.23V and B= 1.43V. The value of E°cell is :

A)

3.66 V

B)

0.80 V

C)

-0.80 V

D)

-3.66 V

View Answer
100) A non ideal solution was prepared by mixing 30 ml chloroform and 50 ml acetone. The volume of mixture will be :

A)

>80 ml

B)

< 80 ml

C)

= 80 ml

D)

\[\text{2}.\text{3 }\times \text{1}{{0}^{-\text{16}}}\text{ mole}/\text{litre}\]

View Answer
101) The half-life of \[\text{1}.\text{65}\times \text{1}{{0}^{-\text{36}}}\text{ mole}/\text{litre}\] is (disintegration constant,\[2A(g)3C(g)+D(s)\]) :

A)

\[{{K}_{p}}(RT)\]

B)

\[{{K}_{p}}/RT\]

C)

\[={{K}_{p}}\]

D)

\[{{\left( \text{C}{{\text{H}}_{\text{3}}} \right)}_{\text{2}}}\text{NH}>{{\left( \text{C}{{\text{H}}_{\text{3}}} \right)}_{\text{3}}}\text{N}>\text{C}{{\text{H}}_{\text{3}}}\text{N}{{\text{H}}_{\text{2}}}\]

View Answer
102) Which of the following is a protein?

A)

Pepsin

B)

Adrenaline

C)

ATP

D)

Glutamin

View Answer
103) Which of the following is a mixed oxide?

A)

\[\text{C}{{\text{H}}_{\text{3}}}\text{N}{{\text{H}}_{\text{2}}}>{{(\text{C}{{\text{H}}_{\text{3}}}\text{)}}_{2}}\text{NH}>{{\left( \text{C}{{\text{H}}_{\text{3}}} \right)}_{\text{3}}}\text{N}\]

B)

\[{{\left( \text{C}{{\text{H}}_{\text{3}}} \right)}_{\text{3}}}\text{N}>{{\left( \text{C}{{\text{H}}_{\text{3}}} \right)}_{\text{2}}}\text{NH}>\text{C}{{\text{H}}_{\text{3}}}\text{N}{{\text{H}}_{\text{2}}}\]

C)

\[{{\left( \text{C}{{\text{H}}_{\text{3}}} \right)}_{\text{3}}}\text{N}>\text{C}{{\text{H}}_{\text{3}}}\text{N}{{\text{H}}_{\text{2}}}>{{\left( \text{C}{{\text{H}}_{\text{3}}} \right)}_{\text{2}}}\text{NH}\]

D)

\[\ge \text{8}0\text{ ml}\]

View Answer
104) Which of the following has diamagnetic character?

A)

\[_{6}{{C}^{14}}\]

B)

\[\lambda =\text{2}.\text{31}\times \text{1}{{0}^{-\text{4}}}\text{ yea}{{\text{r}}^{\text{-1}}}\]

C)

\[\text{4}\times \text{1}{{0}^{\text{2}}}\text{ years}\]

D)

\[\text{3}.\text{5}\times \text{1}{{0}^{\text{4}}}\text{ years}\]

View Answer
105) An anaesthetic is :

A)

procaine

B)

chloramphenicol

C)

\[\text{2}\times \text{1}{{0}^{\text{2}}}\text{ years}\]-hexyl resorcinol

D)

cibazol

View Answer
106) Ozone with dry iodine give :

A)

\[\text{3}\times \text{1}{{0}^{\text{3}}}\text{years}\]

B)

\[\text{F}{{\text{e}}_{\text{2}}}{{\text{O}}_{\text{3}}}\]

C)

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

D)

\[\text{P}{{\text{b}}_{\text{3}}}{{\text{O}}_{\text{4}}}\]

View Answer
107) 2.76 g of silver carbonate on being strongly heated yield a residue weighing:

A)

2.16 g

B)

2.48 g

C)

2.64 g

D)

2.32 g

View Answer
108) Which of the following properties show gradual decrease with increase in atomic number across a period in the periodic table?

A)

Electron affinity

B)

lonization potential

C)

Electronegativity

D)

Size of atom

View Answer
109) When KBr is treated with concentrated \[\text{Ba}{{\text{O}}_{\text{2}}}\]redish brown gas evolved, gas is :

A)

mixture of bromine and HBr

B)

\[{{[NiC{{l}_{4}}]}^{2-}}\]

C)

bromine

D)

none of these

View Answer
110) Which of the following basic radicals will not be precipitated by H2S gas in the presence of\[{{[CO{{F}_{6}}]}^{3-}}\]?

A)

\[{{[Fe{{({{H}_{2}}O)}_{6}}]}^{2+}}\]

B)

\[{{[Ni{{(CN)}_{4}}]}^{2-}}\]

C)

\[n\]

D)

\[{{I}_{4}}{{O}_{4}}\]

View Answer
111) \[{{I}_{2}}{{O}_{3}}\] is equal to:

A)

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

B)

\[{{I}_{2}}{{O}_{4}}\]

C)

\[{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\]

D)

\[\text{HBr}\]

View Answer
112) \[\text{N}{{\text{H}}_{\text{3}}}\]will be purely imaginary, if \[M{{n}^{2+}}\] is equal to :

A)

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

B)

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

C)

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

D)

none of these

View Answer
113) If three complex number are in A.R, then they lie on :

A)

a circle in the complex plane

B)

a straight line in the complex plane

C)

a parabola in the complex plane

D)

none of these

View Answer
114) If the cube roots of unity are \[\left( \frac{1}{1-2i}+\frac{3}{1+i} \right)\left( \frac{3+4i}{2-4i} \right)\] then the roots of the equation\[\frac{1}{2}+\frac{9}{2}i\] are :

A)

\[\frac{1}{2}-\frac{9}{2}i\]

B)

\[\frac{1}{4}-\frac{9}{4}i\]

C)

\[\frac{1}{4}+\frac{9}{4}i\]

D)

\[\frac{3+2i\sin \theta }{1-2i\sin \theta }\]

View Answer
115)     99th     term     of     the     series\[\theta \]is :

A)

9998

B)

9999

C)

10000

D)

100000

View Answer
116)     If a, b, c, d and p are different real numbers such that\[2n\pi \pm \frac{\pi }{3}\]\[n\pi +\frac{\pi }{3}\], then a, b, c, d are in :

A)

A.P.

B)

G.P.

C)

H.P.

D)

none of these

View Answer
117)     The     sum     of     the     series \[n\pi \pm \frac{\pi }{3}\] upto 20 terms is :

A)

188090

B)

189080

C)

199080

D)

199089

View Answer
118)     \[1,\omega ,{{\omega }^{2}}\]equals :

A)

\[{{(x-2)}^{3}}+27=0\]

B)

\[-1,-1,-1\]

C)

\[-1,-\omega ,-{{\omega }^{2}}\]

D)

\[-1,2+3\omega ,2+3{{\omega }^{2}}\]

View Answer
119) If \[-1,2-3\omega ,2-3{{\omega }^{2}}\]and \[\text{2}+\text{7}+\text{14}+\text{23}+\text{34}...\] where \[\left( {{\text{a}}^{\text{2}}}+{{\text{b}}^{\text{2}}}+{{\text{c}}^{\text{2}}} \right){{P}^{\text{2}}}-\text{ 2}\left( \text{ab}+\text{bc}+\text{cd} \right)P\] then\[+({{b}^{2}}+{{c}^{2}}+{{d}^{2}}\le 0\] has at least :

A)

four real roots

B)

two real roots

C)

four imaginary roots

D)

none of these

View Answer
120)     The solution set of the equation \[{{1.3}^{2}}+{{2.5}^{2}}+{{3.7}^{2}}+.....\] is :

A)

\[\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{n(n+1)}\]

B)

(4)

C)

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

D)

none of these

View Answer
121)     Number of roots of the equation\[\frac{n}{(n+1)}\]is

A)

one

B)

two

C)

infinite

D)

none of these

View Answer
122)     If \[\frac{2n}{(n+1)}\]and \[\frac{2}{n(n+1)}\], then the value of r is :

A)

1

B)

2

C)

3

D)

none of these

View Answer
123)     A student is allowed to select at most n books from a collection of \[p(x)=a{{x}^{2}}+bx+c\] books. If the total number of ways in which he can select one book is 63, then the value of n is equal to :

A)

2

B)

3

C)

4

D)

1

View Answer
124)     The number of ways in which a committee can be formed of 5 members from 6 men and 4 women if the committee has at least one woman, is :

A)

186

B)

246

C)

252

D)

244

View Answer
125)     \[Q(x)=-a{{x}^{2}}+dx+c\]is equal to :

A)

\[ac\ne 0\]

B)

\[p(x).Q(x)=0\]

C)

\[{{x}^{\log x{{(1-x)}^{2}}=9}}\]

D)

none of these

View Answer
126)     The coefficient of \[(-\text{2},\text{4)}\] in the expansion of \[(0,-\text{2},\text{ 4)}\]will be :

A)

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

B)

\[^{n}{{C}_{r-1}}=36{{,}^{n}}{{C}_{r}}=84\]

C)

\[^{n}{{C}_{r-1}}=126\]

D)

\[(2n+1)\]

View Answer
127) Let n be an odd integer. If \[\sum\limits_{r=0}^{n}{^{n+r}{{C}_{n}}}\]for every value of \[^{n+m+1}{{C}_{n+1}}\],then:

A)

\[^{n+m+2}{{C}_{n}}\]

B)

\[^{n+m+3}{{C}_{n-1}}\]

C)

\[{{x}^{-7}}\]

D)

\[{{\left[ ax-\frac{1}{b{{x}^{2}}} \right]}^{11}}\]

View Answer
128) \[\frac{462{{a}^{6}}}{{{b}^{5}}}\]is equal to :

A)

\[\frac{462{{a}^{5}}}{{{b}^{6}}}\]

B)

\[-\frac{462{{a}^{5}}}{{{b}^{6}}}\]

C)

\[-\frac{462{{a}^{6}}}{{{b}^{5}}}\]

D)

0

View Answer
129)     If k is a scalar and J is a unit matrix of order 3, then adj (kl) is equal to :

A)

\[\sin n\theta =\sum\limits_{r=0}^{n}{{{b}_{r}}{{\sin }^{r}}\theta }\]

B)

\[\theta \]

C)

\[{{b}_{0}}=0,{{b}_{1}}=3\]

D)

\[{{b}_{0}}=1,{{b}_{1}}=n\]

View Answer
130)     The   value   of   the   determinant\[{{b}_{0}}=-1,{{b}_{1}}=n\]is equal to :

A)

\[{{b}_{0}}=0,{{b}_{1}}={{n}^{2}}-3n+3\]

B)

\[\left| \begin{matrix}    a+b & a+2b & a+3b \\    a+2b & a+3b & a+4b \\    a+4b & a+5b & a+6b \\ \end{matrix} \right|\]

C)

\[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}-3abc\]

D)

\[3ab\]

View Answer
131)     If \[3a+5b\], then \[{{k}^{3}}I\] is equal to :

A)

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

B)

\[-{{k}^{3}}I\]

C)

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

D)

\[\left| \begin{matrix}    1 & 1 & 1 \\    1 & 1-x & 1 \\    1 & 1 & 1+y \\ \end{matrix} \right|\]

View Answer
132) If \[3-x+y\], then \[(1-x)(1-y)\] is equal to :

A)

\[xy\]

B)

\[-xy\]

C)

\[A=\left[ \begin{matrix} 3 & 2 \\ 0 & 1 \\ \end{matrix} \right]\]

D)

none of these

View Answer
133)     If \[{{({{A}^{-1}})}^{3}}\],then the value of \[\frac{1}{27}\left( \begin{matrix}    1 & -8 \\    0 & 27 \\ \end{matrix} \right)\] is equal to :

A)

1

B)

2

C)

0

D)

\[\frac{1}{27}\left( \begin{matrix}    -1 & 26 \\    0 & 27 \\ \end{matrix} \right)\]

View Answer
134)     In a \[\frac{1}{27}\left( \begin{matrix}    1 & -26 \\    0 & -27 \\ \end{matrix} \right)\], if\[\frac{1}{27}\left( \begin{matrix}    -1 & -26 \\    0 & -27 \\ \end{matrix} \right)\], then the value of\[\alpha +\beta -\lambda =\pi \]is equal to :

A)

1

B)

2

C)

\[{{\sin }^{2}}\alpha +{{\sin }^{2}}\beta -{{\sin }^{2}}\gamma \]

D)

\[\text{2 sin }\alpha \text{ sin}\beta \text{ cos }\gamma \]

View Answer
135)     There exist a triangle ABC, satisfying the conditions :

A)

\[\text{2 cos}\alpha \text{ cos}\beta \text{ cos }\gamma \]

B)

\[\text{2sin}\alpha \text{ sin}\beta \text{ sin }\gamma \]

C)

\[x\cos \theta =y\cos \left( \theta +\frac{2\pi }{3} \right)=z\cos \left( \theta +\frac{4\pi }{3} \right)\]

D)

none of these

View Answer
136)     The number of values of x in the interval \[\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\]    satisfying    the    equation \[3\,\,\,\cos \,\,\,\theta \]is :

A)

0

B)

5

C)

6

D)

10

View Answer
137)     The angle of depression of a ship from the top of a tower 30 m high is 60°. Then the distance of ship from the base of tower is :

A)

30 m

B)

\[\Delta ABC\]

C)

\[\text{3a}=\text{b}+\text{c}\]

D)

10 m

View Answer
138)     The area of triangle formed by the points \[\cot \frac{B}{2}\cot \frac{C}{2}\]is equal to :

A)

\[\sqrt{3}\]

B)

\[\sqrt{2}\]

C)

\[b\sin A=a,A<\frac{\pi }{2}\]

D)

0

View Answer
139)     The points (1,3) and (5,1) are the opposite vertices of a rectangle. The other two vertices lie on the line \[b\sin A>a,A>\frac{\pi }{2}\], then the value of c will be :

A)

4

B)

-4

C)

2

D)

-2

View Answer
140) Given the four lines with equations \[b\sin A>a,A<\frac{\pi }{2}\]and \[[0,5\pi ]\], then these lines are :

A)

concurrent

B)

perpendicular

C)

the sides of a rectangle

D)

none of these

View Answer
141)     The angle between the lines \[3{{\sin }^{2}}x-7\sin x+2=0\] is equal to :

A)

45°

B)

60°

C)

90°

D)

180°

View Answer
142) The equation to a pair of opposite sides of a parallelogram are \[30\sqrt{3}m\] and \[10\sqrt{3}m\], the equation to its diagonals are :

A)

\[\left( \text{a},\text{b}+\text{c} \right),\left( \text{b},\text{c}+\text{a} \right),\left( \text{c},\text{a}+\text{b} \right)\]and \[abc\]

B)

\[~{{\text{a}}^{\text{2}}}+{{\text{b}}^{\text{2}}}+{{\text{c}}^{\text{2}}}\] and \[\text{ab}+\text{bc}+\text{ca}\]

C)

\[y=2x+c\] and \[x+2y=3,3x+4y=7,2x+3y=4\]

D)

\[4x+5y=6\] and y \[xy=0\]

View Answer
143) The equation of the chord of the circle, \[{{x}^{2}}-5x+6=0\] having \[{{y}^{2}}-6y+5=0\] as its mid-point, is:

A)

\[x+4y=13\]

B)

\[y=4x-7\]

C)

\[4x+y=13\]

D)

\[4y=x-7\]

View Answer
144) A circle of radius 5 touches another circle \[4x+y=13\]at (5, 5),then its equation is :

A)

\[y=4x-7\]

B)

\[y-4x=13\]

C)

\[y+4x-7\]

D)

none of these

View Answer
145)     The equation of the latus-rectum of the parabola \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\] is equal to :

A)

\[({{x}_{1}},{{y}_{1}})\]

B)

\[x{{y}_{1}}+y{{x}_{1}}={{a}^{2}}\]

C)

\[{{x}_{1}}+{{y}_{1}}=a\]

D)

\[x{{x}_{1}}+y{{y}_{1}}=x_{1}^{2}+y_{1}^{2}\]

View Answer
146)     The length of major and minor axis of an ellipse are 10 and 8 respectively and its major axis along the y-axis the equation of the ellipse referred to its centre as origin is :

A)

\[x{{x}_{1}}+y{{y}_{1}}={{a}^{2}}\]

B)

\[{{x}^{2}}+{{y}^{2}}-2x-4y-20=0\]

C)

\[{{x}^{2}}+{{y}^{2}}+18x+16y+120=0\]

D)

\[{{x}^{2}}+{{y}^{2}}-18x-16y+120=0\]

View Answer
147)     The point of intersection of tangents at the ends of the latus-rectum of the parabola \[{{x}^{2}}+{{y}^{2}}-18x+16y+120=0\] is equal to :

A)

(1,0)

B)

\[{{x}^{2}}+4x+2y=0\]

C)

\[2y+3=0\]

D)

\[3y=2\]

View Answer
148) Eccentricity of the parabola \[2y=3\] is equal to :

A)

\[3y+2=0\]

B)

\[\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{16}=1\]

C)

\[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{25}=1\]

D)

\[\frac{{{x}^{2}}}{100}+\frac{{{y}^{2}}}{64}=1\]

View Answer
149)     The angle between the lines \[\frac{{{x}^{2}}}{64}+\frac{{{y}^{2}}}{100}=1\]and \[{{y}^{2}}=4x\] is equal to :

A)

\[(-1,0)\]

B)

\[\left( 0,1 \right)\]

C)

\[\left( 0,-\text{l} \right)\]

D)

\[{{x}^{2}}-4x-4y+4=0\]

View Answer
150) \[e=0\]is equal to:

A)

\[e=1\]

B)

\[e>4\]

C)

0

D)

\[e=4\]

View Answer
151)     If the points whose position vectors are\[\frac{x}{1}=\frac{y}{0}=\frac{z}{-1}\] and \[\frac{x}{3}=\frac{y}{4}=\frac{z}{5}\]lie on a plane, then \[{{\cos }^{-1}}\left( \frac{1}{5} \right)\]is equal to :

A)

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

B)

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

C)

\[{{\cos }^{-1}}\left( \frac{1}{4} \right)\]

D)

\[(a-b).(b-c)\times (c-a)\]

View Answer
152)     If    \[2a.b\times c\] and \[a.b\times c\] \[a.b\] and \[3\hat{i}-2\hat{j}-\hat{k},2\hat{i}+3\hat{j}-4\hat{k},-\hat{i}+\hat{j}+2\hat{k}\] are non-coplanar vectors, then \[4\hat{i}+5\hat{j}+\lambda \hat{k}\]is equal to:

A)

-1

B)

0

C)

1

D)

4

View Answer
153)     In   \[\lambda \]if \[-\frac{146}{17}\],   then\[\frac{146}{17}\] equals :

A)

\[-\frac{17}{146}\]

B)

\[\frac{17}{146}\]

C)

\[\left| \begin{matrix}    a & {{a}^{2}} & 1+{{a}^{3}} \\    b & {{b}^{3}} & 1+{{b}^{3}} \\    c & {{c}^{3}} & 1+{{c}^{3}} \\ \end{matrix} \right|=0\]

D)

\[(1,a,{{a}^{2}})\]

View Answer
154)     Let \[(1,b,{{b}^{2}})\]and a unit vector \[(1,c,{{c}^{2}})\] be coplanar, if \[\text{abc}\] is perpendicular to \[\Delta ABC\] then \[2\overrightarrow{AC}=3\overrightarrow{CB}\]is equal to:

A)

\[2\overrightarrow{OA}+3\overrightarrow{OB}\]

B)

\[4\overrightarrow{OC}\]

C)

\[-\overrightarrow{OC}\]

D)

\[\overrightarrow{OC}\]

View Answer
155)     \[4\overrightarrow{OC}\]is equal to :

A)

\[\overrightarrow{a}\text{ }=\text{2\hat{i}}+\text{\hat{j}+ \hat{k}},\text{ }\overrightarrow{\text{b}}=\text{\hat{i}}+\text{2\hat{j}}-\text{\hat{k}}\]

B)

\[\overrightarrow{c}\]

C)

\[\overrightarrow{c}\]

D)

0

View Answer
156)     If\[\overrightarrow{a}\text{ }=\text{2\hat{i}}+\text{\hat{j}+ \hat{k}},\text{ }\overrightarrow{\text{b}}=\text{\hat{i}}+\text{2\hat{j}}-\text{\hat{k}}\], when \[\overrightarrow{c}\], where \[\frac{1}{\sqrt{2}}(-\hat{j}+\hat{k})\] is greatest integer function, then \[\frac{1}{\sqrt{3}}(-\hat{i}-\hat{j}-\hat{k})\] is equal to :

A)

-1

B)

1

C)

does not exist

D)

none of these

View Answer
157)     The function \[\frac{1}{\sqrt{5}}(\hat{i}-2\hat{j})\],\[\frac{1}{\sqrt{3}}(\hat{i}-\hat{j}-\hat{k})\]where\[\underset{x\to 1}{\mathop{\lim }}\,(1-x)\tan \left( \frac{\pi x}{2} \right)\]assumes its minimum value only at one point, if :

A)

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

B)

\[\pi \]

C)

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

D)

\[f(x)=\frac{\sin [x]}{[x]}\]

View Answer
158) \[[x]\ne 0\]

A)

exists and is equals \[[x]\]

B)

exists and is equals \[\underset{x\to 0}{\mathop{\lim }}\,f[x]\]

C)

does not exist because \[f(x)=|px-q|+r|x|\]

D)

does not exist because left hand limit is not equal to right hand limit

View Answer
159)     Differential coefficient of sec \[x\in (-\infty ,\infty )\] with respect to \[p>0,q>0,r>0\] at \[p\ne q\]is equal to :

A)

2

B)

4

C)

6

D)

1

View Answer
160)     The     function \[q\ne r\]increases, if :

A)

\[r\ne p\]

B)

\[p=q=r\]

C)

\[\underset{x\to 1}{\mathop{\lim }}\,\frac{\sqrt{1-\cos 2(x-1)}}{x-1}\]

D)

\[\sqrt{2}\]

View Answer
161) \[-\sqrt{2}\] is equal to :

A)

\[x-1\to 0\]

B)

\[{{\sec }^{-1}}\frac{1}{2{{x}^{2}}-1}\]

C)

\[\sqrt{1-{{x}^{2}}}\]

D)

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

View Answer
162)     Area bounded by the curve \[f(x)={{\sin }^{4}}x+{{\cos }^{4}}x\] and the straight line \[0<x<\frac{\pi }{8}\], is equal to :

A)

\[\frac{\pi }{4}<x<\frac{3\pi }{8}\] sq. units

B)

\[\frac{3\pi }{8}<x<\frac{5\pi }{8}\]sq. units

C)

\[\frac{5\pi }{8}<x<\frac{3\pi }{4}\]sq. units

D)

none of these

View Answer
163) The solution of the differential equation\[\int{\sqrt{1+\sin \frac{x}{2}}}dx\] is :

A)

\[\frac{1}{4}\left[ \cos \frac{x}{4}-\sin \frac{x}{4} \right]+C\]

B)

\[4\left[ \cos \frac{x}{4}-\sin \frac{x}{4} \right]+C\]

C)

\[4\left[ \sin \frac{x}{4}-\cos \frac{x}{4} \right]+C\]

D)

\[4\left[ \sin \frac{x}{4}+\cos \frac{x}{4} \right]+C\]

View Answer
164)     In a binomial distribution, mean is 3 and standard deviation is \[x=4y\], then the probability distribution is :

A)

\[x=4y-2\]

B)

\[\frac{8}{9}\]

C)

\[\frac{9}{8}\]

D)

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

View Answer
165)     The probability of India winning a test match against West indies is \[({{x}^{2}}-y{{x}^{2}})\frac{dy}{dx}+{{y}^{2}}+x{{y}^{2}}=0\] assuming independence from match to match the probability that in a 5 match series Indias second win occurs at the third test, is :

A)

2/3

B)

½

C)

1/4

D)

1/8

View Answer
166)     If both the regression lines intersect perpendicularly, then :

A)

\[\log \left( \frac{x}{y} \right)=\frac{1}{x}+\frac{1}{y}+c\]

B)

\[\log \left( \frac{y}{x} \right)=\frac{1}{x}+\frac{1}{y}+c\]

C)

\[\log (xy)=\frac{1}{x}+\frac{1}{y}+c\]

D)

\[\log (xy)+\frac{1}{x}+\frac{1}{y}=c\]

View Answer
167)     If\[\frac{3}{2}\], \[{{\left( \frac{3}{4}+\frac{1}{4} \right)}^{12}}\], and \[{{\left( \frac{1}{4}+\frac{3}{4} \right)}^{12}}\], then the coefficient of correlation is :

A)

0.1

B)

0.3

C)

0.2

D)

0.1

View Answer
168) For any two independent events \[{{\left( \frac{1}{4}+\frac{3}{4} \right)}^{9}}\] anc \[{{\left( \frac{3}{4}+\frac{1}{4} \right)}^{9}}\], \[\frac{1}{2}\]) is equal to :

A)

\[r<-1\]

B)

\[r=-1\]

C)

\[r=0\]

D)

none of these

View Answer
169)     The degree of the differential equation \[r=\frac{1}{2}\]is equal to:

A)

1

B)

2

C)

3

D)

6

View Answer
170) \[\overline{x}+\overline{y}=0\] is equal to :

A)

\[\sum {{x}_{i}}{{y}_{i}}=12,{{\sigma }_{x}}=2,{{\sigma }_{y}}=3\]

B)

0

C)

1

D)

\[n=10\]

View Answer

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done Jamia Millia Islamia Solved Paper-2004 Total Questions - 170

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Jamia Millia Islamia Solved Paper-2004 Total Questions - 170