Solved papers for VIT Engineering VIT Engineering Solved Paper-2009

VIT Engineering Solved Paper-2009 Total Questions - 120

1) When a wave traverses a medium, the displacement of a particle located at\[x\] at a time \[t\] is given by \[y=a\text{ }sin\left( bt-\text{c}x \right)\], where \[a\],\[b\]and\[c\] are constants of the wave, which of the following is a quantity with dimensions?

A)

\[\frac{y}{a}\]

B)

\[bt\]

C)

\[cx\]

D)

\[\frac{b}{c}\]

View Answer
2) A body is projected vertically upwards at time \[t=0\] and it is seen at a height \[H\]at timer, and \[{{t}_{1}}\] and \[{{t}_{2}}\] second during its flight. The maximum height attained is (g is acceleration due to gravity)

A)

\[\frac{g{{\left( {{t}_{2}}-{{t}_{1}} \right)}^{2}}}{8}\]

B)

\[\frac{g{{\left( {{t}_{1}}-{{t}_{2}} \right)}^{2}}}{4}\]

C)

\[\frac{g{{\left( {{t}_{1}}-{{t}_{2}} \right)}^{2}}}{8}\]

D)

\[\frac{g{{\left( {{t}_{2}}-{{t}_{1}} \right)}^{2}}}{4}\]

View Answer
3) A particle is projected up from a point at an angle with the horizontal direction. At any time \[t\], if \[p\] is the linear momentum, \[y\] is the vertical displacement, \[x\] is horizontal displacement, the graph among the following which does not represent the variation of kinetic energy of the particle is

[A]

[B]

[C]

[d]

A)

graph [A]

B)

graph [B]

C)

graph [C]

D)

graph [D]

View Answer
4) A motor of power \[{{P}_{0}}\] is used to deliver water at a certain rate through a given horizontal pipe. To increase the rate of flow of water through the same pipe \[n\] times, the power of the motor is increased top. The ratio of \[{{P}_{1}}\], to \[{{P}_{0}}\] is

A)

\[n:1~\]

B)

\[{{n}^{2}}:1\]

C)

\[{{n}^{3}}:1\]

D)

\[{{n}^{4}}:1\]

View Answer
5) A body of mass 5 kg makes an elastic collision with another body at rest and continues to move in the original direction after collision with a velocity equal to \[\frac{1}{10}th\] of its original velocity. Then the mass of the second body is

A)

4.09 kg

B)

0.5 kg

C)

5 kg

D)

5.09 kg

View Answer
6) A particle of mass \[4m\] explodes into three pieces of masses\[m\], \[m\] and \[2m.\] the equal masses move along X-axis and V-axis with velocities \[4\text{ }m{{s}^{-1}}\] and \[6m{{s}^{-1}}\] respectively. The magnitude of the velocity of the heavier mass is

A)

\[\sqrt{17}m{{s}^{-1}}\]

B)

\[2\sqrt{13}\,m{{s}^{-1}}\]

C)

\[\sqrt{13}\,m{{s}^{-1}}\]

D)

\[\frac{\sqrt{13}}{2}\,m{{s}^{-1}}\]

View Answer
7) A body is projected vertically upwards from the surface of the earth with a velocity equal to half the escape velocity. If R is the radius of the earth, maximum height attained by the body from the surface of the earth is

A)

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

B)

\[\frac{R}{3}\]

C)

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

D)

\[R\]

View Answer
8) The displacement of a particle executing SHM is given by \[y=\,5\,\sin \,\left( 4t+\frac{\pi }{3} \right)\] If T is the time period and the mass of the particle is 2g, the kinetic energy of the particle when \[t=\frac{T}{4}\] is given by

A)

0.4 J

B)

0.5 J

C)

3 J

D)

0.3 J

View Answer
9) If the ratio of lengths, radii and Youngs modulus of steel and brass wires shown in the figure are a, b and c respectively, the ratio between the increase in lengths of brass and steel wires would be

A)

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

B)

\[\frac{bc}{2{{a}^{2}}}\]

C)

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

D)

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

View Answer
10) A soap bubble of radius \[r\] is blown up to form a bubble of radius \[2r\] under isothermal conditions. If T is the surface tension of soap solution, the energy spent in the blowing

A)

\[3\pi T{{r}^{2}}\]

B)

\[6\pi T{{r}^{2}}\]

C)

\[12\pi T{{r}^{2}}\]

D)

\[24\pi T{{r}^{2}}\]

View Answer
11) Eight spherical rain drops of the same mass and radius are falling down with a terminal speed of\[6\text{ }cm-{{s}^{-1}}\]. If they coalesce to form one big drop, what will be the terminal speed of bigger drop? (Neglect the buoyancy of the air)

A)

\[1.5\text{ }cm-{{s}^{-1}}\]

B)

\[6\text{ }c{{m}^{-1}}\]

C)

\[24\text{ }cm-{{s}^{-1}}\]

D)

\[32\text{ }cm-{{s}^{-1}}\]

View Answer
12) A clock pendulum made of invar has a period of 0.5 s, at \[20{}^\circ C\]. If the clock is used in a climate where the temperature averages to\[30{}^\circ C\], how much time does the clock lose in each oscillation? \[(\text{For invar},\alpha =9\times {{10}^{-7}}{{/}^{0}}C,\,g=cons\tan t)\]

A)

\[2.25\times {{10}^{-6}}s~\]

B)

\[2.5\times {{10}^{-7}}s\]

C)

\[5\times {{10}^{-7}}s~\]

D)

\[1.125\times {{10}^{-6}}s\]

View Answer
13) A piece of metal weighs \[45g\] in air and \[25g\] in a liquid of density \[1.5\times {{10}^{3}}kg-{{m}^{-3}}\] kept at \[30{}^\circ C\]. When the temperature of the liquid is raised to \[40{}^\circ C\], the metal piece weighs \[27g\]. The density of liquid at \[40{}^\circ C\] is \[1.25\times {{10}^{3}}kg-{{m}^{-3}}\]. The coefficient of linear expansion of metal is

A)

\[1.3\times {{10}^{-3}}{{/}^{\text{o}}}C~\]

B)

\[5.2\times {{10}^{-3}}{{/}^{\text{o}}}C\]

C)

\[2.6\times {{10}^{-3}}{{/}^{\text{o}}}C\]

D)

\[0.26\times {{10}^{-3}}{{/}^{\text{o}}}C\]

View Answer
14) An ideal gas is subjected to a cyclic process ABCD as depicted in the\[p-V\]diagram given below: Which of the following curves represents the equivalent cyclic process?

A)

B)

C)

D)

View Answer
15) An ideal gas is subjected to cyclic process involving four thermodynamic states, the amounts of heat \[\left( Q \right)\] and work \[\left( W \right)\] involved in each of these states are \[{{Q}_{1}}~=\text{ }6000\text{ }J\], \[{{Q}_{2}}=-5500\text{ }J\]; \[{{Q}_{3}}=-3000\text{ }J\]; \[{{Q}_{4}}~=3500\text{ }J\] \[{{W}_{1}}=2500\text{ }J\]; \[{{W}_{2}}=-1000\text{ }J\]; \[{{W}_{3}}=-1200\text{ }J\]; \[{{W}_{4}}=x\text{ }J\]. The ratio of the net work done by the gas to the total heat absorbed by the gas is r). The values of x and n respectively are

A)

500; 7.5 %

B)

700; 10.5 %

C)

1000; 21 %

D)

1500; 15 %

View Answer
16) Two cylinders A and B fitted with pistons contain equal number of moles of an ideal monoatomic gas at 400 K. The piston of A is free to move while that of B is held fixed. Same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in A is 42 K, the rise in temperature of the gas in B is

A)

21 K

B)

35 K

C)

42 K

D)

70 K

View Answer
17) Three rods of same dimensional have thermal conductivity 3 K, 2 K and K. They are arranged as shown in the figure below Then, the temperature of the junction in steady state is

A)

\[2.0\,m{{s}^{-1}}\]

B)

\[2.5\,m{{s}^{-1}}\]

C)

\[75{}^\circ C\]

D)

\[\frac{50}{3}\] °C

View Answer
18) Two sources A and B are sending notes of frequency 680 Hz. A listener moves from A and B with a constant velocity u. If the speed of sound in air is \[340\text{ }m{{s}^{-1}}\], what must be the value of us that he hears 10 beats per second?

A)

\[2.0m{{s}^{-1}}\]

B)

\[2.5m{{s}^{-1}}\]

C)

\[3.0m{{s}^{-1}}\]

D)

\[3.5m{{s}^{-1}}\]

View Answer
19) Two identical piano wires have a fundamental frequency of 600 cycle per second when kept under the same tension. What fractional increase in the tension of one wires will lead to the occurrence of 6 beats per second when both wires vibrate simultaneously?

A)

0.01

B)

0.02

C)

0.03

D)

0.04

View Answer
20) In the Youngs double slit experiment, the intensities at two points \[{{P}_{1}}\] and \[{{P}_{2}}\] on the screen are respectively \[{{I}_{1}}\] and \[{{I}_{2}}\]. If \[{{P}_{1}}\] is located at the centre of a bright fringe and \[{{P}_{2}}\] is located at a distance equal to a quarter of fringe width from \[{{P}_{1}}\], then \[\frac{{{I}_{1}}}{{{I}_{2}}}\] is

A)

2

B)

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

C)

4

D)

16

View Answer
21) In Youngs double slit experiment, the 10th maximum of wavelength \[{{\lambda }_{1}}\]is at a distance of \[{{y}_{1}}\] from the central maximum- When the wavelength of the source is changed to \[{{\lambda }_{2}}\], 5th maximum is at a distance of \[{{y}_{2}}\] from its central maximum. The ratio \[\left( \frac{{{y}_{1}}}{{{y}_{2}}} \right)\] is

A)

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

B)

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

C)

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

D)

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

View Answer

22) Four light sources produce the following four waves:

(i) \[{{y}_{1}}\,=a\,\sin \,(\omega t+{{\phi }_{1}})\]

(ii) \[{{y}_{2}}\,=a\,\sin \,2\omega t\]

(iii) \[{{y}_{3}}\,={{a}^{}}\,\sin \,(\omega t+{{\phi }_{2}})\]

(iv) \[{{y}_{4}}\,={{a}^{}}\,\sin \,(3\omega t+\phi )\]

Superposition of which two waves give rise to interference?

(i) and (ii)

(ii) and (iii)

(i) and (iii)

(iii) and (iv)

View Answer

23) The two lenses of an achromatic doublet should have

A)

equal powers

B)

equal dispersive powers

C)

equal ratio of their power and dispersive power

D)

sum of the product of their powers and dispersive power equal to zero

View Answer
24) Two bar magnets A and Bare placed one over the other and are allowed to vibrate in a vibration magnetometer. They make 20 oscillations per minute when the similar poles of A and B are on the same side, while they make 15 oscillations per minute when their opposite poles lie on the same side. If \[{{\text{M}}_{\text{A}}}\] and \[{{\text{M}}_{\text{B}}}\]are the magnetic moments of A and B and if \[{{\text{M}}_{\text{A}}}\text{}{{\text{M}}_{\text{B}}}\], the ratio of \[{{\text{M}}_{\text{A}}}\] and \[{{\text{M}}_{\text{B}}}\]is

A)

4 : 3

B)

25 : 7

C)

7 : 5

D)

25 : 16

View Answer
25) A bar magnet is 10 cm long is kept with its north (N)-pole pointing north. A neutral point is formed at a distance of 15 cm from each pole. Given the horizontal component of earths field is 0.4 Gauss, the pole strength of the magnet is

A)

9 A-m

B)

6.75 A-m

C)

27 A-m

D)

1.35 A-m

View Answer
26) An infinitely long thin straight wire has uniform linear charge density of\[\frac{1}{3}C{{m}^{-1}}.\]. Then, the magnitude of the electric intensity at a point 18 cm away is \[(given\,{{\varepsilon }_{0}}=8.8\,\times \,{{10}^{-12}}\,{{C}^{2}}\,N{{m}^{-2}})\]

A)

\[0.33\times {{10}^{11}}N{{C}^{-1}}\]

B)

\[3\times {{10}^{11}}N{{C}^{-1}}\]

C)

\[0.66\times {{10}^{11}}N{{C}^{-1~~}}\]

D)

\[1.32\times {{10}^{11}}N{{C}^{-1}}\]

View Answer
27) Two point charges \[-q\] and \[+q\] are located at points (0, 0, \[-a\]) and (0, 0, \[a\]) respectively. The electric potential at a point (0, 0, \[z\]), where \[z<a\] is

A)

\[\frac{qa}{4\pi {{\varepsilon }_{_{0}}}{{z}^{2}}}\]

B)

\[\frac{q}{4\pi {{\varepsilon }_{_{0}}}a}\]

C)

\[\frac{2qa}{4\pi {{\varepsilon }_{_{0}}}a\left( {{z}^{2}}-{{a}^{2}} \right)}\]

D)

\[\frac{2qa}{4\pi {{\varepsilon }_{_{0}}}a\left( {{z}^{2}}+{{a}^{2}} \right)}\]

View Answer
28) In the adjacent shown circuit, a voltmeter of internal resistance R, when connected across B and C reads \[\frac{100}{3}\]V. Neglecting the internal resistance of the battery, the value of R

A)

\[100k\,\Omega \]

B)

\[75k\,\Omega \]

C)

\[50k\,\Omega \]

D)

\[25k\,\Omega \]

View Answer
29) A cell in secondary circuit gives null deflection for 2.5 m length of potentiometer having 10 m length of wire. If the length of the potentiometer wire is increased by 3 m without changing the cell in the primary, the position of the null point now is

A)

3.5 m

B)

3 m

C)

2.75 m

D)

2.0 m

View Answer
30) The following series L-C-R circuit, when driven by an emf source of angular frequency 70 kilo-radians per second, the circuit effectively behaves like

A)

purely resistive circuit

B)

series R-L circuit

C)

series R-C circuit

D)

series L-C circuit with R = 0

View Answer
31) A wire of length \[l\] is bent into a circular loop of radius R and carries a current\[I\]. The magnetic field at the centre of the loop is\[B\]. The same wire is now bent into a double loop of equal radii. If both loops carry the same current \[I\] and it is in the same direction, the magnetic field at the centre of the double loop will be

A)

Zero

B)

2 B

C)

4 B

D)

8 B

View Answer
32) An infinitely long straight conductor is bent into the shape as shown below. It carries a current of I ampere and the radius of the circular loop is R metre. Then, the magnitude of magnetic induction at the centre of the circular loop is

A)

\[\frac{{{\mu }_{0}}I}{2\pi R}\]

B)

\[\frac{{{\mu }_{0}}nI}{2R}\]

C)

\[\frac{{{\mu }_{0}}nI}{2\pi R}\left( \pi +1 \right)\]

D)

\[\frac{{{\mu }_{0}}nI}{2\pi R}\left( \pi -1 \right)\]

View Answer
33) The work function of a certain metal is \[3.31\times {{10}^{-19}}J\]. Then, the maximum kinetic energy of photoelectrons emitted by incident radiation of wavelength \[\text{5000 }\overset{\text{o}}{\mathop{\text{A}}}\,\] is (Given, \[h=6.62\times {{10}^{-34}}J-s\], \[c=3\times {{10}^{8}}m{{s}^{-1}}\],\[e=1.6\times {{10}^{-19}}C\])

A)

\[2.48\text{ }eV\]

B)

\[0.41\text{ }eV\]

C)

\[2.07\text{ }eV\]

D)

\[0.82\text{ }eV\]

View Answer
34) A photon of energy E ejects a photoelectron from a metal surface whose work function is \[{{W}_{0}}\]. If this electron enters into a uniform magnetic field of induction B in a direction perpendicular to the field and describes a circular path of radius \[r\], then the radius \[r\] is given by, (in the usual notation)

A)

\[\frac{\sqrt{2m\left( E-{{W}_{0}} \right)}}{eB}\]

B)

\[\sqrt{2m\left( E-{{W}_{0}} \right)}eB\]

C)

\[\frac{\sqrt{2e\left( E-{{W}_{0}} \right)}}{mB}\]

D)

\[\frac{\sqrt{2m\left( E-{{W}_{0}} \right)}}{eB}\]

View Answer
35) Two radioactive materials \[{{X}_{1}}\] and \[{{X}_{2}}\] have decay constants \[10\lambda \] and \[\lambda \] respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of \[{{X}_{1}}\] to that of \[{{X}_{2}}\] will be \[1/e\]after a time

A)

\[(1/10\lambda )\]

B)

\[1/(11\lambda )\]

C)

\[11/(10\lambda )~\]

D)

\[1/(9\lambda )\]

View Answer
36) Currents flowing in each of the following circuits A and B respectively are

A)

1 A, 2 A

B)

2 A, 1 A

C)

4 A, 2 A

D)

2 A, 4 A

View Answer
37) A bullet of mass 0.02 kg travelling horizontally with velocity \[250\text{ }m{{s}^{-1}}\]strikes a block of wood of mass 0.23 kg which rests on a rough horizontal surface. After the impact, the block and bullet move together and come to rest after travelling a distance of 40 m. The coefficient of sliding friction of the rough surface is \[\left( g=9.8\text{ }m{{s}^{-2}} \right)\]

A)

0.75

B)

0.61

C)

0.51

D)

0.30

View Answer
38) Two persons A and B are located in X-Y plane at the points (0, 0) and (0, 10) respectively. (The distances are measured in MKS unit). At a time (\[t=0\], they start moving simultaneously with velocities \[{{\mathbf{\vec{v}}}_{A}}=2\mathbf{j}m{{s}^{-1}}\] and \[{{\mathbf{\vec{v}}}_{B}}=2\mathbf{\hat{i}}m{{s}^{-1}}\]respectively. The time after which\[A\]and\[B\]are at their closest distance is

A)

2.5s

B)

4 s

C)

1 s

D)

\[\frac{10}{\sqrt{2}}\]s

View Answer
39) A rod of length; is held vertically stationary with its lower end located at a point P, on the horizontal plane. When the rod is released to topple about P, the velocity of the upper end of the rod with which it hits the ground is

A)

\[\sqrt{\frac{g}{I}}\]

B)

\[\sqrt{3gI}\]

C)

\[3\sqrt{\frac{g}{I}}\]

D)

\[\sqrt{\frac{3g}{I}}\]

View Answer
40) A wheel of radius 0.4 m can rotate freely about its axis as shown in the figure. \[A\]String is wrapped over its rim and a mass of 4 kg is hung. An angular acceleration of \[8\text{ }rad-{{s}^{-2}}\] is produced in it due to the torque. Then, moment of inertia of the wheel is \[(g=10m{{s}^{-2}})\]

A)

\[2\text{ }kg-{{m}^{2}}\]

B)

\[1\text{ }kg-{{m}^{2}}\]

C)

\[4\text{ }kg-{{m}^{2}}\]

D)

\[8\text{ }kg-{{m}^{2}}\]

View Answer
41) Given that \[Alkyne\xrightarrow[Lindlars\,\,catalyst]{{{H}_{2}}}A\xrightarrow{Ozonolysis}\underset{only}{\mathop{B}}\,\], express the \[\xleftarrow[\Pr ocess]{Wac\ker }C{{H}_{2}}=C{{H}_{2}}\] bond energy in kcal/mol.

A)

\[{{H}_{3}}C-C\equiv C-C{{H}_{3}}\]

B)

\[{{H}_{3}}C-C{{H}_{2}}-C\equiv CH\]

C)

\[{{H}_{2}}C=CH-C\equiv CH\]

D)

\[HC\equiv C-C{{H}_{2}}-C\equiv CH\]

View Answer
42) Identify the alkyne in the following sequence of reactions, \[NaOH\] \[{{104}^{o}}40\]

A)

\[{{103}^{o}}\]

B)

\[{{107}^{o}}\]

C)

\[{{109}^{o}}28\]

D)

\[\underline{X}\]

View Answer
43) Fluorine reacts with dilute \[\underline{X}\] and forms a gaseous product A The bond angle in the molecule of A is

A)

\[\underline{X}\]

B)

\[\Delta {{H}_{f}}(H)=218kJ/mol\]

C)

\[H-H\]

D)

\[52.15\]

View Answer
44) One mole of alkene \[911\] on ozonolysis gave one mole of acetaldehyde and one mole of acetone. The IUPAC name of \[104\] is

A)

2-methyl-2-butene

B)

2-methyl-l-butene

C)

2-butene

D)

1-butene

View Answer
45) The number of \[52153\] pi bonds present in \[Alkyne\xrightarrow[Lindlars\,\,catalyst]{{{H}_{2}}}A\xrightarrow{Ozonolysis}\underset{only}{\mathop{B}}\,\]and \[\xleftarrow[\Pr ocess]{Wac\ker }C{{H}_{2}}=C{{H}_{2}}\] molecules, respectively are

A)

3 , 4

B)

4,2

C)

2,3

D)

3,2

View Answer
46) The wavelengths of electron waves in two orbits is \[{{H}_{3}}C-C\equiv C-C{{H}_{3}}\]. The ratio of kinetic energy of electrons will be

A)

\[{{H}_{3}}C-C{{H}_{2}}-C\equiv CH\]

B)

\[{{H}_{2}}C=CH-C\equiv CH\]

C)

\[HC\equiv C-C{{H}_{2}}-C\equiv CH\]

D)

\[NaOH\]

View Answer
47) Which one of the following sets correctly represents the increase in the paramagnetic property of the ions?

A)

\[{{104}^{o}}40\]

B)

\[{{103}^{o}}\]

C)

\[{{107}^{o}}\]

D)

\[{{109}^{o}}28\]

View Answer
48) Electrons with a kinetic energy of \[\underline{X}\]are evolved from the surface of a metal, when it is exposed to radiation of wavelength of 600 nm. The minimum amount of energy required to remove an electron from the metal atom is

A)

\[\underline{X}\]

B)

\[\Delta {{H}_{f}}(H)=218kJ/mol\]

C)

\[H-H\]

D)

\[52.15\]

View Answer
49) The chemical entities present in thermosphere of the atmosphere are

A)

\[911\]

B)

\[104\]

C)

\[52153\]

D)

\[Alkyne\xrightarrow[Lindlars\,\,catalyst]{{{H}_{2}}}A\xrightarrow{Ozonolysis}\underset{only}{\mathop{B}}\,\]

View Answer
50) The type of bonds present in sulphuric anhydride are

A)

\[\xleftarrow[\Pr ocess]{Wac\ker }C{{H}_{2}}=C{{H}_{2}}\] and three \[{{H}_{3}}C-C\equiv C-C{{H}_{3}}\]

B)

\[{{H}_{3}}C-C{{H}_{2}}-C\equiv CH\], one \[{{H}_{2}}C=CH-C\equiv CH\] and two \[HC\equiv C-C{{H}_{2}}-C\equiv CH\]

C)

\[NaOH\] and three \[{{104}^{o}}40\]

D)

\[{{103}^{o}}\] and two \[{{107}^{o}}\]

View Answer
51) In Gattermann reaction, a diazonium group is replaced by \[{{109}^{o}}28\] using \[\underline{X}\]. \[\underline{X}\] and \[\Delta {{H}_{f}}(H)=218kJ/mol\] are

A)

\[H-H\]- \[911\]             \[52.15\]-\[104\]

B)

\[H-H\]-\[52153\]             \[52.15\]-\[Alkyne\xrightarrow[Lindlars\,\,catalyst]{{{H}_{2}}}A\xrightarrow{Ozonolysis}\underset{only}{\mathop{B}}\,\]

C)

\[H-H\]-\[\xleftarrow[\Pr ocess]{Wac\ker }C{{H}_{2}}=C{{H}_{2}}\]             \[52.15\]-\[{{H}_{3}}C-C\equiv C-C{{H}_{3}}\]

D)

\[H-H\]-\[{{H}_{3}}C-C{{H}_{2}}-C\equiv CH\]               \[52.15\]-\[{{H}_{2}}C=CH-C\equiv CH\]

View Answer
52) Which pair of oxyacids of phosphorus contains \[HC\equiv C-C{{H}_{2}}-C\equiv CH\] bonds?

A)

\[NaOH\]

B)

\[{{104}^{o}}40\]

C)

\[{{103}^{o}}\]

D)

\[{{107}^{o}}\]

View Answer
53) Dipole moment of \[{{109}^{o}}28\] \[\underline{X}\]Bond length of \[\underline{X}\] and \[p\pi .d\pi \]. The ratio of fraction of electric charge, \[p\pi .d\pi \], existing on each atom in \[\Delta {{H}_{f}}(H)=218kJ/mol\] and \[H-H\] is

A)

\[52.15\]

B)

\[911\]

C)

\[104\]

D)

\[52153\]

View Answer
54) \[Alkyne\xrightarrow[Lindlars\,\,catalyst]{{{H}_{2}}}A\xrightarrow{Ozonolysis}\underset{only}{\mathop{B}}\,\] on hydrolysis forms X and \[\xleftarrow[\Pr ocess]{Wac\ker }C{{H}_{2}}=C{{H}_{2}}\]. Compound X loses water at \[{{H}_{3}}C-C\equiv C-C{{H}_{3}}\] and gives Y\ Compounds X and Y respectively are

A)

\[{{H}_{3}}C-C{{H}_{2}}-C\equiv CH\]

B)

\[{{H}_{2}}C=CH-C\equiv CH\]

C)

\[HC\equiv C-C{{H}_{2}}-C\equiv CH\]

D)

\[NaOH\]

View Answer
55) 1.5 g of \[{{104}^{o}}40\] was found to contain 0.9 g of Cd. Calculate the atomic weight of Cd.

A)

\[{{103}^{o}}\]

B)

\[{{107}^{o}}\]

C)

\[{{109}^{o}}28\]

D)

\[\underline{X}\]

View Answer
56) Aluminium reacts with \[\underline{X}\] and forms compound X. If the coordination number of aluminium in X is 6, the correct formula of X is

A)

\[p\pi .d\pi \]

B)

\[\Delta {{H}_{f}}(H)=218kJ/mol\]

C)

\[H-H\]

D)

\[52.15\]

View Answer
57) The average kinetic energy of one molecule of an ideal gas at \[27{}^\circ \] and 1 atm pressure is

A)

\[104\]

B)

\[52153\]

C)

\[Alkyne\xrightarrow[Lindlars\,\,catalyst]{{{H}_{2}}}A\xrightarrow{Ozonolysis}\underset{only}{\mathop{B}}\,\]

D)

\[\xleftarrow[\Pr ocess]{Wac\ker }C{{H}_{2}}=C{{H}_{2}}\]

View Answer
58) Assertion [A] K, Rb and Cs form superoxides. Reason [R] The stability of the superoxides increases from K to Cs due to decrease in lattice energy. The correct answer is

A)

Both [A] and [R] are true and [R] is the correct explanation of [A]

B)

Both [A] and [R] are true but [R] is not the correct explanation of [A]

C)

[A] is true but [R] is not true

D)

[A] is not true but [R] is true

View Answer
59) How many \[\text{ }\!\!\!\!\text{ mL }\!\!\!\!\text{ }\] of perhydrol is required to produce sufficient oxygen which can be used to completely convert 2 L of \[{{H}_{3}}C-C\equiv C-C{{H}_{3}}\] gas to \[{{H}_{3}}C-C{{H}_{2}}-C\equiv CH\] gas?

A)

\[{{H}_{2}}C=CH-C\equiv CH\]

B)

\[HC\equiv C-C{{H}_{2}}-C\equiv CH\]

C)

\[NaOH\]

D)

\[{{104}^{o}}40\]

View Answer
60)  \[\text{pH}\] of a buffer solution decreases by 0.02 units when 0.12 g of acetic acid is added to 250 mL of a buffer solution of acetic acid and potassium acetate at \[27{}^\circ \]. The buffer capacity of the solution is

A)

\[{{107}^{o}}\]

B)

\[{{109}^{o}}28\]

C)

\[\underline{X}\]

D)

\[\underline{X}\]

View Answer

61) Match the following.

	List-I		List-II
[A]	Flespar	(I)	\[p\pi .d\pi \]
[B]	Asbestos	(II)	\[Xe{{O}_{3}}\]
[C]	Pyrargyrite	(III)	\[Xe{{O}_{3}}\]
[D]	Diaspore	(IV)	\[\Delta {{H}_{f}}(H)=218kJ/mol\]
		(V)	\[H-H\]

The correct answer is

[A]-IV [B]-V [C]-II [D]-I

[A]-IV [B]-V [C]-I [D]-II

[A]-IV [B]-I [C]- III [D]- II

[A]-II [B]-V [C]- IV [D]-I

View Answer

62) Which one of the following order is correct for the first ionisation energies of the elements?

A)

\[52.15\]

B)

\[911\]

C)

\[104\]

D)

\[52153\]

View Answer
63) What are X and Y in the following reaction sequence? \[Alkyne\xrightarrow[Lindlars\,\,catalyst]{{{H}_{2}}}A\xrightarrow{Ozonolysis}\underset{only}{\mathop{B}}\,\]

A)

\[\xleftarrow[\Pr ocess]{Wac\ker }C{{H}_{2}}=C{{H}_{2}}\]

B)

\[{{H}_{3}}C-C\equiv C-C{{H}_{3}}\]

C)

\[{{H}_{3}}C-C{{H}_{2}}-C\equiv CH\]

D)

\[{{H}_{2}}C=CH-C\equiv CH\]

View Answer

64) What are \[HC\equiv C-C{{H}_{2}}-C\equiv CH\]\[NaOH\]\[{{104}^{o}}40\] in the following reactions?

(I) \[{{103}^{o}}\]

(II) \[{{107}^{o}}\]

(III) \[{{109}^{o}}28\]

\[\underline{X}\]	\[\underline{X}\]	\[p\pi .d\pi \]
[a] \[Xe{{O}_{3}}\]	\[Xe{{O}_{4}}\]	\[Xe{{O}_{4}}\]

\[\underline{X}\]	\[\underline{X}\]	\[p\pi .d\pi \]
[b] \[\Delta {{H}_{f}}(H)=218kJ/mol\]	\[H-H\]	\[52.15\]

\[\underline{X}\]	\[\underline{X}\]	\[p\pi .d\pi \]
[c] \[911\]	\[104\]	\[52153\]

\[\underline{X}\]	\[\underline{X}\]	\[p\pi .d\pi \]
[d] \[Alkyne\xrightarrow[Lindlars\,\,catalyst]{{{H}_{2}}}A\xrightarrow{Ozonolysis}\underset{only}{\mathop{B}}\,\]	\[\xleftarrow[\Pr ocess]{Wac\ker }C{{H}_{2}}=C{{H}_{2}}\]	\[{{H}_{3}}C-C\equiv C-C{{H}_{3}}\]

View Answer

65) One per cent composition of an organic compound A is, carbon: 85.71% and hydrogen 14.29%. Its vapour density is 14. Consider the following reaction sequence \[{{H}_{3}}C-C{{H}_{2}}-C\equiv CH\] Identify , \[{{H}_{2}}C=CH-C\equiv CH\]

A)

\[HC\equiv C-C{{H}_{2}}-C\equiv CH\]

B)

\[NaOH\]

C)

\[{{104}^{o}}40\]

D)

\[{{103}^{o}}\]

View Answer
66) How many tripeptides can be prepared by linking the amino acids glycine, alanine and phenyl alanine?

A)

One

B)

Three

C)

Six

D)

Twelve

View Answer
67) A codon has a sequence of \[{{107}^{o}}\], and specifies a particular B that is to be incorporated into a \[{{109}^{o}}28\]. What are \[\underline{X}\],\[\underline{X}\],\[p\pi .d\pi \]?

A)

\[Xe{{O}_{3}}\] \[Xe{{O}_{4}}\]            \[\Delta {{H}_{f}}(H)=218kJ/mol\]

[a] 3 bases amino acid carbohydrate

B)

\[Xe{{O}_{3}}\] \[Xe{{O}_{4}}\]            \[\Delta {{H}_{f}}(H)=218kJ/mol\]

[b] 3 acids carbohydrate protein

C)

\[Xe{{O}_{3}}\] \[Xe{{O}_{4}}\]            \[\Delta {{H}_{f}}(H)=218kJ/mol\]

[c] 3 bases protein amino acid

D)

\[Xe{{O}_{3}}\] \[Xe{{O}_{4}}\]            \[\Delta {{H}_{f}}(H)=218kJ/mol\]

[d] 3 bases amino acid protein

View Answer
68) Parkinsons disease is linked to abnormalities in the levels of dopamine in the body. The structure of dopamine is

A)

B)

C)

D)

View Answer
69) During the depression in freezing point experiment, an equilibrium is established between the molecules of

A)

liquid solvent and solid solvent

B)

liquid solute and solid solvent

C)

liquid solute and solid solute

D)

liquid solvent and solid solute

View Answer
70) Consider the following reaction, \[H-H\] Which one of the following statements is true for \[52.15\]?

(I) It gives propionic acid on hydrolysis

(II) It has an ester functional group

(III) It has a nitrogen linked to, ethyl carbon

(IV) It has a cyanide group

A)

IV

B)

III

C)

II

D)

I

View Answer
71) For the following cell reaction, \[911\] \[104\] \[52153\] \[Alkyne\xrightarrow[Lindlars\,\,catalyst]{{{H}_{2}}}A\xrightarrow{Ozonolysis}\underset{only}{\mathop{B}}\,\] \[\xleftarrow[\Pr ocess]{Wac\ker }C{{H}_{2}}=C{{H}_{2}}\] of the cell is

A)

\[{{H}_{3}}C-C\equiv C-C{{H}_{3}}\]

B)

\[{{H}_{3}}C-C{{H}_{2}}-C\equiv CH\]

C)

\[{{H}_{2}}C=CH-C\equiv CH\]

D)

None of these

View Answer
72) The synthesis of crotonaldehyde from acetaldehyde is an example of ...... reaction.

A)

nucleophilic addition

B)

elimination

C)

electrophilic addition

D)

nucleophilic addition-elimination

View Answer
73) At \[HC\equiv C-C{{H}_{2}}-C\equiv CH\], the molar conductances at infinite dilution for the strong electrolytes \[NaOH\], \[{{104}^{o}}40\] and \[{{103}^{o}}\] are \[{{107}^{o}}\], \[{{109}^{o}}28\] and \[\underline{X}\]respectively, \[\underline{X}\] in \[p\pi .d\pi \] is

A)

\[Xe{{O}_{3}}\]

B)

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

C)

\[3:5\]

D)

\[3:5\]

View Answer
74) The cubic unit cell of a metal (molar mass \[\Delta {{H}_{f}}(H)=218kJ/mol\]) has an edge length of 362 pm. Its density is \[H-H\]. The type of unit cell is

A)

primitive

B)

face centred

C)

body centred

D)

end centred

View Answer
75) The equilibrium constant for the given reaction is 100. \[52.15\] What is the equilibrium constant for the reaction given below? \[911\]

A)

\[104\]

B)

\[52153\]

C)

\[Alkyne\xrightarrow[Lindlars\,\,catalyst]{{{H}_{2}}}A\xrightarrow{Ozonolysis}\underset{only}{\mathop{B}}\,\]

D)

\[\xleftarrow[\Pr ocess]{Wac\ker }C{{H}_{2}}=C{{H}_{2}}\]

View Answer
76) For a first order reaction at \[27{}^\circ C\], the ratio of time required for 75% completion to 25% completion of reaction is

A)

\[{{H}_{3}}C-C{{H}_{2}}-C\equiv CH\]

B)

\[{{H}_{2}}C=CH-C\equiv CH\]

C)

\[HC\equiv C-C{{H}_{2}}-C\equiv CH\]

D)

\[NaOH\]

View Answer
77) The concentration of an organic compound in chloroform is 6.15 g per 100 mL of solution. A portion of this solution in a 5 cm polarimeter tube causes an observed rotation of \[{{104}^{o}}40\]. What is the specific rotation of the compound?

A)

\[{{103}^{o}}\]

B)

\[{{107}^{o}}\]

C)

\[{{109}^{o}}28\]

D)

\[\underline{X}\]

View Answer
78) 20 mL of 0.1 M acetic acid is mixed with 50 mL of potassium acetate. \[\underline{X}\] of acetic acid \[p\pi .d\pi \] at \[Xe{{O}_{3}}\]. Calculate concentration of potassium acetate if pH of the mixture is 4.8.

A)

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

B)

\[3:5\]

C)

\[\Delta {{H}_{f}}(H)=218kJ/mol\]

D)

\[H-H\]

View Answer
79) Calculate \[52.15\] for the reaction, \[911\] given the following : [A] \[104\] \[52153\] [B] \[Alkyne\xrightarrow[Lindlars\,\,catalyst]{{{H}_{2}}}A\xrightarrow{Ozonolysis}\underset{only}{\mathop{B}}\,\] \[\xleftarrow[\Pr ocess]{Wac\ker }C{{H}_{2}}=C{{H}_{2}}\] [C] \[{{H}_{3}}C-C\equiv C-C{{H}_{3}}\] \[{{H}_{3}}C-C{{H}_{2}}-C\equiv CH\]

A)

\[{{H}_{2}}C=CH-C\equiv CH\]

B)

\[HC\equiv C-C{{H}_{2}}-C\equiv CH\]

C)

\[NaOH\]

D)

\[{{104}^{o}}40\]

View Answer
80) Which one of the following is most effective in causing the coagulation of an \[{{103}^{o}}\] sol?

A)

\[{{107}^{o}}\]

B)

\[{{109}^{o}}28\]

C)

\[\underline{X}\]

D)

\[\underline{X}\]

View Answer
81) If \[f:[2,\,3]\to R\] is defined by \[f(x)={{x}^{3}}+3x-2,\] then the range \[f(x)\] is contained in the interval

A)

[1, 12]

B)

[12, 34]

C)

[35, 50]

D)

[-12, 12]

View Answer
82) The number of subsets of {1, 2, 3,..., 9} containing at least one odd number is

A)

324

B)

396

C)

496

D)

512

View Answer
83) A binary sequence is an array of 0s and 1s. The number of n-digit binary sequences which contain even number of 0s is

A)

\[{{2}^{n-1}}\]

B)

\[{{2}^{n}}-1\]

C)

\[{{2}^{n-1}}-1\]

D)

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

View Answer
84) If\[x\]is numerically so small so that\[{{x}^{2}}\]and higher powers of\[x\]can be neglected, then \[{{\left( 1+\frac{2x}{3} \right)}^{3/2}}\cdot {{(32+5x)}^{-1/5}}\] is approximately equal to

A)

\[\frac{32+31x}{64}\]

B)

\[\frac{31+32x}{64}\]

C)

\[\frac{31-32x}{64}\]

D)

\[\frac{1-2x}{64}\]

View Answer
85) The roots of \[\left( x-a \right)\left( x-a-1 \right)+\left( x-a-1 \right)\left( x-a-2 \right)\] \[+\left( x-a \right)\left( x-a-2 \right)=0\] \[a\in R\]are always

A)

equal

B)

imaginary

C)

real and distinct

D)

rational and equal

View Answer
86) Let \[f(x)={{x}^{2}}+ax+b,\] where \[a,b\in R.\] If \[f(x)=0\] has all its roots imaginary, then the roots of \[f(x)+f(x)+f(x)=0\]are

A)

real and distinct

B)

imaginary

C)

equal

D)

rational and equal

View Answer
87) If \[f(x)=2{{x}^{4}}-13{{x}^{2}}+ax+b\]is divisible by\[{{x}^{2}}-3x+2,\] then (a, b) is equal to

A)

(-9, -2)

B)

(6, 4)

C)

(9, 2)

D)

(2, 9)

View Answer
88) If x, y, z are all positive and are the \[p\text{th},\] \[q\text{th}\]and \[r\text{th}\]terms of a geometric progression respectively, then the value of the determinant \[\left| \begin{matrix} \log x & p & 1 \\ \log y & q & 1 \\ \log z & r & 1 \\ \end{matrix} \right|\,\,\text{equals}\]

A)

\[\log xyz\]

B)

\[(p-q)\,(q-1)\,(r-1)\]

C)

\[pqr\]

D)

\[0\]

View Answer
89) The locus of z satisfying the inequality\[\left| \frac{z+2i}{2z+i} \right|<1,\] where \[z=x+iy,\]is

A)

\[{{x}^{2}}+{{y}^{2}}<1\]

B)

\[{{x}^{2}}-{{y}^{2}}<1\]

C)

\[{{x}^{2}}+{{y}^{2}}>1\]

D)

\[2{{x}^{2}}+3{{y}^{2}}<1\]

View Answer
90) If n is an integer which leaves remainder one when divided by three, then \[{{(1+\sqrt{3}i)}^{n}}+{{(1-\sqrt{3}i)}^{n}}\] equals

A)

\[-{{2}^{n+1}}\]

B)

\[{{2}^{n+1}}\]

C)

\[-{{(-2)}^{n}}\]

D)

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

View Answer
91) The period of \[\text{si}{{\text{n}}^{4}}x+\text{co}{{\text{s}}^{4}}x\] is

A)

\[\frac{{{\pi }^{4}}}{2}\]

B)

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

C)

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

D)

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

View Answer
92) If \[3\cos x\ne 2\sin x,\]then the general solution of \[{{\sin }^{2}}x-\cos 2x=2-\sin 2x\]is

A)

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

B)

\[\frac{n\pi }{2},\,n\in Z\]

C)

\[(4n\pm 1)\frac{\pi }{2},\,n\in Z\]

D)

\[(2n-1)\pi ,\,n\in Z\]

View Answer
93) \[{{\cos }^{-1}}\left( \frac{-1}{2} \right)-2{{\sin }^{-1}}\left( \frac{1}{2} \right)+3{{\cos }^{-1}}\left( \frac{-1}{\sqrt{2}} \right)\] \[-4{{\tan }^{-1}}(-1)\]equals

A)

\[\frac{19\pi }{12}\]

B)

\[\frac{35\pi }{12}\]

C)

\[\frac{47\pi }{12}\]

D)

\[\frac{43\pi }{12}\]

View Answer
94) In a \[\Delta \,ABC\] \[\frac{\left( a+b+c \right)\left( b+c-a \right)\left( c+a-b \right)\left( a+b-c \right)}{4{{b}^{2}}{{c}^{2}}}\]equals

A)

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

B)

\[{{\cos }^{2}}B\]

C)

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

D)

\[{{\sin }^{2}}B\]

View Answer
95) The angle between the lines whose direction cosines satisfy the equations \[l+m+n=0,\] \[{{l}^{2}}+{{m}^{2}}-{{n}^{2}}=0\]is

A)

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

B)

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

C)

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

D)

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

View Answer
96) If \[{{m}_{1}},\] \[{{m}_{2}},\] \[{{m}_{3}}\]and \[{{m}_{4}}\] are respectively the magnitudes of the vectors \[{{\overrightarrow{a}}_{1}}=2\hat{i}-\hat{j}+\hat{k},\text{ }{{\overrightarrow{a}}_{2}}=3\hat{i}-4\hat{j}-4\hat{k},\] \[{{\overrightarrow{a}}_{3}}=\hat{i}+\hat{j}-\hat{k},\]and \[{{\overrightarrow{a}}_{4}}=-\hat{i}+3\hat{j}+\hat{k},\] then the correct order of \[{{m}_{1}},{{m}_{2}},{{m}_{3}}\]and \[{{m}_{4}}\]is

A)

\[{{m}_{3}}<{{m}_{1}}<{{m}_{4}}<{{m}_{2}}\]

B)

\[{{m}_{3}}<{{m}_{1}}<{{m}_{2}}<{{m}_{4}}\]

C)

\[{{m}_{3}}<{{m}_{4}}<{{m}_{1}}<{{m}_{2}}\]

D)

\[{{m}_{3}}<{{m}_{4}}<{{m}_{2}}<{{m}_{1}}\]

View Answer
97) If X is a binomial variate with the range {0,1, 2, 3, 4, 5, 6} and \[P\left( X=2 \right)=4P\left( X=4 \right),\] then the parameter p of X is

A)

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

B)

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

C)

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

D)

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

View Answer
98) The area (in square unit) of the circle which touches the lines \[4x\text{ }+\text{ }3y\text{ }=\text{ }15\] and \[4x\text{ }+\text{ }3y\text{ }=\text{ }5\] is

A)

\[4\pi \]

B)

\[3\pi \]

C)

\[2\pi \]

D)

\[\pi \]

View Answer
99) The area (in square unit) of the triangle formed by\[x+y+1=0\] and the pair of straight lines\[{{x}^{2}}-3xy+2{{y}^{2}}=0\]is

A)

\[\frac{7}{12}\]

B)

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

C)

\[\frac{1}{12}\]

D)

\[\frac{1}{6}\]

View Answer
100) The pairs of straight lines \[{{x}^{2}}-3xy+2{{y}^{2}}=0\]and\[{{x}^{2}}-3xy+2{{y}^{2}}+x-2=0\]form a

A)

square but not rhombus

B)

rhombus

C)

parallelogram

D)

rectangle but not a square

View Answer
101) The equations of the circle which pass through the origin and makes intercepts of lengths 4 and 8 on the x and y-axes respectively are

A)

\[{{x}^{2}}+{{y}^{2}}\pm 4x\pm 8y=0\]

B)

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

C)

\[{{x}^{2}}+{{y}^{2}}\pm 8x\pm 16y=0\]

D)

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

View Answer
102) The point\[\left( 3,\,-4 \right)\]lies on both the circles \[{{x}^{2}}+{{y}^{2}}-2x+8y+13=0\] and \[{{x}^{2}}+{{y}^{2}}-4x+6y+11=0\] Then, the angle between the circles is

A)

\[60{}^\circ \]

B)

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

C)

\[{{\tan }^{-1}}\left( \frac{3}{5} \right)\]

D)

\[135{}^\circ \]

View Answer
103) The equation of the circle which passes through the origin and cuts orthogonally each of the circles \[{{x}^{2}}+{{y}^{2}}-6x+8=0\] and\[{{x}^{2}}+{{y}^{2}}-2x-2y=7\]is

A)

\[3{{x}^{2}}+3{{y}^{2}}-8x-13y=0\]

B)

\[3{{x}^{2}}+3{{y}^{2}}-8x+29y=0\]

C)

\[3{{x}^{2}}+3{{y}^{2}}+8x+29y=0\]

D)

\[3{{x}^{2}}+3{{y}^{2}}-8x-29y=0\]

View Answer
104) The number of normal drawn to the parabola \[{{y}^{2}}=4x\]from the point (1, 0) is

A)

0

B)

1

C)

2

D)

3

View Answer
105) If the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\] intersects the hyperbola\[xy={{c}^{2}}\]in four points \[({{x}_{i}},\,{{y}_{i}}),\]for \[i=\] 1, 2, 3 and 4, then \[{{y}_{1}}+{{y}_{2}}+{{y}_{3}}+{{y}_{4}}\] equals

A)

0

B)

\[c\]

C)

\[a\]

D)

\[{{c}^{4}}\]

View Answer
106) The mid-point of the chord\[4x-3y=5\]of the hyperbola\[2{{x}^{2}}-3{{y}^{2}}=12\]is

A)

\[\left( 0,\,-\frac{5}{3} \right)\]

B)

\[\left( 2,\,\,1 \right)\]

C)

\[\left( \frac{5}{4},\,\,0 \right)\]

D)

\[\left( \frac{11}{4},\,\,2 \right)\]

View Answer
107) The perimeter of the triangle with vertices at (1, 0, 0), (0, 1, 0) and (0, 0, 1) is

A)

3

B)

2

C)

\[2\sqrt{2}\]

D)

\[3\sqrt{2}\]

View Answer
108) If a line in the space makes angle \[\alpha ,\]\[\beta \]and \[\gamma \] with the coordinate axes, then \[\cos 2\alpha +\cos 2\beta +\cos 2\gamma +{{\sin }^{2}}\alpha +{{\sin }^{2}}\beta \] \[+{{\sin }^{2}}\gamma \]equals

A)

-1

B)

0

C)

1

D)

2

View Answer
109) The radius of the sphere \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=12x+4y+3z\] is

A)

13/2

B)

13

C)

26

D)

52

View Answer
110) \[\underset{x\to \infty }{\mathop{\lim }}\,{{\left( \frac{x+5}{x+2} \right)}^{x+3}}\]equals

A)

\[e\]

B)

\[{{e}^{2}}\]

C)

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

D)

\[{{e}^{5}}\]

View Answer
111) If \[f:R\to R\]is defined by \[f(x)=\left\{ \begin{matrix}    \frac{2\sin x-\sin 2x}{2x\,\cos x}, & \text{if}\,x\ne 0 \\    a, & \text{if}\,x=0 \\ \end{matrix} \right.\] then the value of a so that\[f\]is continuous at 0 is

A)

2

B)

1

C)

-1

D)

0

View Answer
112) \[x={{\cos }^{-1}}\left( \frac{1}{\sqrt{1+{{t}^{2}}}} \right),\] \[y={{\sin }^{-1}}\left( \frac{t}{\sqrt{1+{{t}^{2}}}} \right)\Rightarrow \frac{dy}{dx}\]is equal to

A)

0

B)

\[\text{tan}\,t\]

C)

1

D)

\[\text{sin}\,t\text{ cos}\,t\]

View Answer
113) \[\frac{d}{dx}\left[ a\,{{\tan }^{-1}}x+b\log \left( \frac{x-1}{x+1} \right) \right]=\frac{1}{{{x}^{4}}+1}\]\[\Rightarrow a-2b\] is equal to

A)

1

B)

-1

C)

0

D)

2

View Answer
114) \[y={{e}^{a\,{{\sin }^{-1}}x}}\Rightarrow (1-{{x}^{2}})\,{{y}_{n+2}}-(2n+1)\,x{{y}_{n+1}}\] is equal to

A)

\[-\,({{n}^{2}}+{{a}^{2}})\,{{y}_{n}}\]

B)

\[\,({{n}^{2}}-{{a}^{2}})\,{{y}_{n}}\]

C)

\[\,({{n}^{2}}+{{a}^{2}})\,{{y}_{n}}\]

D)

\[-\,({{n}^{2}}-{{a}^{2}})\,{{y}_{n}}\]

View Answer
115) The function \[f(x)={{x}^{3}}+a{{x}^{2}}+bx+c,\]\[{{a}^{2}}\le 3b\]has

A)

one maximum value

B)

one minimum value

C)

no extreme value

D)

one maximum and one minimum value

View Answer
116) \[\int{\left( \frac{2-\sin 2x}{1-\cos 2x} \right)}\,\,{{e}^{x}}dx\] is equal to

A)

\[-{{e}^{x}}\cot x+c\]

B)

\[{{e}^{x}}\cot x+c\]

C)

\[2{{e}^{x}}\cot x+c\]

D)

\[-2{{e}^{x}}\cot x+c\]

View Answer
117) If \[{{I}_{n}}=\int{{{\sin }^{n}}x\,dx},\] then \[n{{I}_{n}}-(n-1)\,{{l}_{n-2}}\]equals

A)

\[{{\sin }^{n-1}}x\,\cos x\]

B)

\[{{\cos }^{n-1}}x\,\,\sin x\]

C)

\[-{{\sin }^{n-1}}x\,\,\cos x\]

D)

\[-{{\cos }^{n-1}}x\,\,\sin x\]

View Answer
118) The line \[x=\frac{\pi }{4}\]divides the area of the region bounded by \[y=\text{sin }x,\] \[y=\text{cos }x\] and x-axis \[\left( 0\le x\le \frac{\pi }{2} \right)\] into two regions of areas \[{{A}_{1}}\] and \[{{A}_{2}}\]. Then\[{{A}_{1}}:{{A}_{2}}\]equals

A)

4 : 1

B)

3 : 1

C)

2 : 1

D)

1 : 1

View Answer
119) The solution of the differential equation\[\frac{dy}{dx}=\sin \,(x+y)\,\tan \,(x+y)-1\]is

A)

\[\text{cosec}\left( x+y \right)+\text{tan}\left( x+y \right)=x+c\]

B)

\[x+\text{cosec}\left( x+y \right)=c\]

C)

\[x+\text{tan}\left( x+y \right)=c\]

D)

\[x+\text{sec}\left( x+y \right)=c\]

View Answer
120) If \[p\Rightarrow (\tilde{\ }p\vee q)\]is false, the truth value of p and q are respectively

A)

F, T

B)

F, F

C)

T, F

D)

T, T

View Answer

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