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

done Jamia Millia Islamia Solved Paper-2004

• question_answer1) 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

• question_answer2) 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

• question_answer3) 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

• question_answer4) 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

• question_answer5) 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) $\overrightarrow{\text{F}}=\left( \text{2\hat{i}}+\text{4\hat{j}} \right)$

• question_answer6) 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) ${{\upsilon }_{A}}:{{\upsilon }_{B}}$

• question_answer7) 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) $7.9\times {{10}^{4}}K$

• question_answer8) 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

• question_answer9) 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 1/2 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

• question_answer10) 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

• question_answer11) 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) $\sqrt{98}m/s$

• question_answer12) 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

• question_answer13) 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

• question_answer14) 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

• question_answer15) 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) $\text{1}\text{.5}\,\,\text{c}{{\text{m}}^{\text{3}}}\text{/s}$

• question_answer16) 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) $\text{91}0\text{ { }\!\!\mathrm{\AA}\!\!\text{ }},\text{ 1213 { }\!\!\mathrm{\AA}\!\!\text{ }}$

• question_answer17) 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 $0.\text{95 }\times \text{ 1}{{0}^{\text{7}}}\text{ m}/\text{s}$

• question_answer18) 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

• question_answer19) 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

• question_answer20) 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) $\frac{2.5}{{{(5000)}^{2}}}eV$

• question_answer21) 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

• question_answer22) 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

• question_answer23) 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) $\text{1}.\text{5 }\times \text{ 1}{{0}^{5}}\text{ m}/\text{s}$

• question_answer24) 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

• question_answer25) 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

• question_answer26) 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

• question_answer27) 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

• question_answer28) 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) $\text{25}\times \text{1}{{0}^{-\text{3}}}\text{ mH}$

• question_answer29) 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) $30{}^\circ$

• question_answer30) 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

• question_answer31) 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

• question_answer32) 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) $\text{1}.\text{4 }\times \text{1}{{0}^{-\text{4}}}$

• question_answer33) 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

• question_answer34) The resistivity of wire depends upon :

A) its material

B) its shape

C) its length

D) its area of cross-section

• question_answer35) 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) $8\Omega$

• question_answer36) 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) $\frac{R}{2}$

• question_answer37) 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

• question_answer38) 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

• question_answer39) 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) $0.00\text{1 J}$

• question_answer40) 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

• question_answer41) 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) $(e=1.6\times {{10}^{-19}}C)$

• question_answer42) 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) $49{}^\circ$

• question_answer43) 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

• question_answer44) 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) $4000\overset{\text{o}}{\mathop{\text{A}}}\,$

• question_answer45) The spectrum of red hot heater will be :

A) continuous

B) band

C) line

D) absorption

• question_answer46) 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

• question_answer47) 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

• question_answer48) 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

• question_answer49) 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

• question_answer50) 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) $\text{55}00\text{ { }\!\!\mathrm{\AA}\!\!\text{ }}$

• question_answer51) 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

• question_answer52) 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

• question_answer53) 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

• question_answer54) 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

• question_answer55) 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) $24{}^\circ C$

• question_answer56) Beryllium shows diagonal relationship with :

A) Mg

B) Na

C) B

D) Al

• question_answer57) 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

• question_answer58) Artificial radioactivity was discovered by:

A) Pault

B) Rutherford

C) Soddy

D) Curie

• question_answer59) Electrolysis of an aqueous solution of sodium acetate, yields :

A) ethane

B) ethane

C) ethane

D) propane

• question_answer60) Ethyl acetoacetate shows, which type of isomerism?

A) Chain

B) Optical

C) Metamerism

D) Tautomerism

• question_answer61) 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) $\alpha =\text{6},\beta =\text{6}$

• question_answer62) Dual nature of particles was proposed by:

A) Heisenberg

B) Lowry

C) De-Broglie

D) Schrodinger

• question_answer63) 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) $\frac{6}{\sqrt{2}}$

• question_answer64) Which of the following is an ore of lead?

A) Galena

B) Calamine

C) Malachite

D) Dolomite

• question_answer65) 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) $\text{C}{{\text{O}}_{\text{2}}}$

• question_answer66) 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) $N{{H}_{3}}$

• question_answer67) The laws of electrolysis were proposed by:

A) Kohlraush

C) Nernst

D) Berthelot

• question_answer68) 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

• question_answer69) 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) $\text{C}{{\text{H}}_{\text{3}}}\text{C}{{\text{H}}_{\text{2}}}\text{C}{{\text{H}}_{\text{2}}}\text{OH}$

• question_answer70) 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) $\text{C}{{\text{H}}_{\text{3}}}\text{COC}{{\text{H}}_{\text{3}}}$

• question_answer71) The unit of molality is :

A) mole per litre

B) mole per kilogram

C) per mole per litre

D) mole litre

• question_answer72) What is the ratio of diffusion rate of oxygen and hydrogen?

A) 1:4

B) 4:1

C) 1 : 8

D) 8 : 1

• question_answer73) 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) $\text{C}{{\text{H}}_{\text{3}}}\text{N}{{\text{H}}_{\text{2}}}$

• question_answer74) The oxidation number of Fe in$\text{C}{{\text{H}}_{\text{3}}}\text{CHO}$is :

A) +3

B) +4

C) +2

D) -2

• question_answer75) Which enzyme convert glucose into alcohol?

A) Invertase

B) Zymase

C) Maltase

D) Diastase

• question_answer76) 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

• question_answer77) Glucose reacts with bromine water to produce :

A) gluconic acid

B) glyceraldehyde

C) saccharic acid

D) glucaric acid

• question_answer78) $O{{H}^{-}}$, product X is :

A) ethylene bromide

B) vinyl bromide

C) bromo ethane

D) ethyledine bromide

• question_answer79) Glycerol reacts with potassium bisulphate to produce :

A) allyl iodide

B) allyl sulphate

C) acryl aldehyde

D) glycerol trisulphate

• question_answer80) Sorels cement is :

A) Portland cement + MgO

B) ${{N}_{2}}{{O}_{4}}\xrightarrow{{}}2N{{O}_{2}}$

C) $\Delta H<\Delta E$

D) $\Delta H=\Delta E$

• question_answer81) 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) $\text{CuS}{{\text{O}}_{\text{4}}}\text{+}$

• question_answer82) Which law of thermodynamics help in calculating entropy at different temperatures?

A) First law

B) Second law

C) Third law

D) Zeroth law

• question_answer83) 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

• question_answer84) At equilibrium, the Gibbs free energy is :

A) + ve

B) - ve

C) zero

D) none of these

• question_answer85) Which of the following is not an organometallic compound?

A) Zeisses salt

B) TEL

C) Sodium ethoxide

D) Ferrocene

• question_answer86) 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) $\text{MgC}{{l}_{\text{2}}}.\text{CaSi}{{\text{O}}_{\text{3}}}.\text{2}{{\text{H}}_{\text{2}}}\text{O}$

• question_answer87) 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) $\text{N}{{\text{O}}_{\text{2}}}$ $~\text{S}{{\text{F}}_{\text{4}}}$ $\text{P}{{\text{F}}_{\text{6}}}$

• question_answer88) Phenol is more acidic than :

A)

B)

C) $~\text{s}{{\text{p}}^{\text{2}}}$

D) both (a) and (c)

• question_answer89) The reaction, $\text{s}{{\text{p}}^{\text{3}}}$Product, is called :

A) Perkin reaction

B) Levit reaction

C) Wurtz reaction

D) Aldol condensation

• question_answer90) PVC is prepared by the polymerization of:

A) ethylene

B) 1-chloropopene

C) propene

D) 1-chloroethene

• question_answer91) $\text{s}{{\text{p}}^{\text{3}}}\text{d}$ The product B is :

A) malonic acid

B) glycolic acid

C) lactic acid

D) malic acid

• question_answer92) 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) ${{\text{d}}^{2}}\text{s}{{\text{p}}^{3}}$

• question_answer93) 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

• question_answer94) Wolf Kishner reduction, reduces :

A) -COOH group

B) -C= C- group

C) -CHO group

D) -0- group

• question_answer95) 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) $\text{Pb}+\text{Zn}$

• question_answer96) 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

• question_answer97) Molecular orbital theory was proposed by:

A) Gillespie and Nyholm

B) Pauling

C) Slater

D) Hund and Mulliken

• question_answer98) 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) $\text{1}.7\text{2 }\times \text{1}{{\text{0}}^{\text{-15}}}\text{ mole}/\text{litre}$

• question_answer99) 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

• question_answer100) 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) $\text{2}.\text{3 }\times \text{1}{{0}^{-\text{16}}}\text{ mole}/\text{litre}$

• question_answer101) 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) ${{\left( \text{C}{{\text{H}}_{\text{3}}} \right)}_{\text{2}}}\text{NH}>{{\left( \text{C}{{\text{H}}_{\text{3}}} \right)}_{\text{3}}}\text{N}>\text{C}{{\text{H}}_{\text{3}}}\text{N}{{\text{H}}_{\text{2}}}$

• question_answer102) Which of the following is a protein?

A) Pepsin

C) ATP

D) Glutamin

• question_answer103) 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) $\ge \text{8}0\text{ ml}$

• question_answer104) 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) $\text{3}.\text{5}\times \text{1}{{0}^{\text{4}}}\text{ years}$

• question_answer105) An anaesthetic is :

A) procaine

B) chloramphenicol

C) $\text{2}\times \text{1}{{0}^{\text{2}}}\text{ years}$-hexyl resorcinol

D) cibazol

• question_answer106) 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) $\text{P}{{\text{b}}_{\text{3}}}{{\text{O}}_{\text{4}}}$

• question_answer107) 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

• question_answer108) 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

• question_answer109) 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

• question_answer110) 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) ${{I}_{4}}{{O}_{4}}$

• question_answer111) ${{I}_{2}}{{O}_{3}}$ is equal to:

A) $I{{O}_{2}}$

B) ${{I}_{2}}{{O}_{4}}$

C) ${{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}$

D) $\text{HBr}$

• question_answer112) $\text{N}{{\text{H}}_{\text{3}}}$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

• question_answer113) 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

• question_answer114) 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) $\frac{3+2i\sin \theta }{1-2i\sin \theta }$

• question_answer115) 99th term of the series$\theta$is :

A) 9998

B) 9999

C) 10000

D) 100000

• question_answer116) 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

• question_answer117) The sum of the series $n\pi \pm \frac{\pi }{3}$ upto 20 terms is :

A) 188090

B) 189080

C) 199080

D) 199089

• question_answer118) $1,\omega ,{{\omega }^{2}}$equals :

A) ${{(x-2)}^{3}}+27=0$

B) $-1,-1,-1$

C) $-1,-\omega ,-{{\omega }^{2}}$

D) $-1,2+3\omega ,2+3{{\omega }^{2}}$

• question_answer119) 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

• question_answer120) 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

• question_answer121) Number of roots of the equation$\frac{n}{(n+1)}$is

A) one

B) two

C) infinite

D) none of these

• question_answer122) 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

• question_answer123) 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

• question_answer124) 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

• question_answer125) $Q(x)=-a{{x}^{2}}+dx+c$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

• question_answer126) 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) $(2n+1)$

• question_answer127) 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) ${{\left[ ax-\frac{1}{b{{x}^{2}}} \right]}^{11}}$

• question_answer128) $\frac{462{{a}^{6}}}{{{b}^{5}}}$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

• question_answer129) 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) ${{b}_{0}}=1,{{b}_{1}}=n$

• question_answer130) 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) $3ab$

• question_answer131) If $3a+5b$, then ${{k}^{3}}I$ is equal to :

A) ${{k}^{2}}I$

B) $-{{k}^{3}}I$

C) $-{{k}^{2}}I$

D) $\left| \begin{matrix} 1 & 1 & 1 \\ 1 & 1-x & 1 \\ 1 & 1 & 1+y \\ \end{matrix} \right|$

• question_answer132) 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

• question_answer133) 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) $\frac{1}{27}\left( \begin{matrix} -1 & 26 \\ 0 & 27 \\ \end{matrix} \right)$

• question_answer134) 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) $\text{2 sin }\alpha \text{ sin}\beta \text{ cos }\gamma$

• question_answer135) 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

• question_answer136) 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

• question_answer137) 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

• question_answer138) 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

• question_answer139) 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

• question_answer140) 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

• question_answer141) 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?

• question_answer142) 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 $xy=0$

• question_answer143) 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) $4y=x-7$

• question_answer144) 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

• question_answer145) 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) $x{{x}_{1}}+y{{y}_{1}}=x_{1}^{2}+y_{1}^{2}$

• question_answer146) 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) ${{x}^{2}}+{{y}^{2}}-18x-16y+120=0$

• question_answer147) 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) $3y=2$

• question_answer148) 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) $\frac{{{x}^{2}}}{100}+\frac{{{y}^{2}}}{64}=1$

• question_answer149) 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) ${{x}^{2}}-4x-4y+4=0$

• question_answer150) $e=0$is equal to:

A) $e=1$

B) $e>4$

C) 0

D) $e=4$

• question_answer151) 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) $(a-b).(b-c)\times (c-a)$

• question_answer152) 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

• question_answer153) 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) $(1,a,{{a}^{2}})$

• question_answer154) 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) $\overrightarrow{OC}$

• question_answer155) $4\overrightarrow{OC}$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

• question_answer156) 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

• question_answer157) 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) $f(x)=\frac{\sin [x]}{[x]}$

• question_answer158) $[x]\ne 0$

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

• question_answer159) 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

• question_answer160) 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) $\sqrt{2}$

• question_answer161) $-\sqrt{2}$ is equal to :

A) $x-1\to 0$

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

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

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

• question_answer162) 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

• question_answer163) 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) $4\left[ \sin \frac{x}{4}+\cos \frac{x}{4} \right]+C$

• question_answer164) 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) $\frac{4}{3}$

• question_answer165) 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) 1/2

C) 1/4

D) 1/8

• question_answer166) 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) $\log (xy)+\frac{1}{x}+\frac{1}{y}=c$

• question_answer167) 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

• question_answer168) 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

• question_answer169) The degree of the differential equation $r=\frac{1}{2}$is equal to:

A) 1

B) 2

C) 3

D) 6

• question_answer170) $\overline{x}+\overline{y}=0$ is equal to :

A) $\sum {{x}_{i}}{{y}_{i}}=12,{{\sigma }_{x}}=2,{{\sigma }_{y}}=3$

B) 0

C) 1

D) $n=10$