question_answer1) What is the position and nature of image formed by lens combination shown in figure? (\[{{f}_{1}},{{f}_{2}}\]are focal lengths)
A) 70 cm from point B at right; real done clear
B) \[\frac{20}{3}cm\]from point B at right, real done clear
C) 40 cm from point B at right, real done clear
D) 70 cm from point B at left, virtual done clear
View Answer play_arrowquestion_answer2) A particle of mass m moves in a circular orbit in a central potential field \[U(r)=\frac{1}{2}k{{r}^{2}}.\]If Bohr's quantization conditions are applied, radii of possible orbitals and energy levels vary with quantum number n as
A) \[{{r}_{n}}\propto {{n}^{2}},{{E}_{n}}\propto \frac{1}{{{n}^{2}}}\] done clear
B) \[{{r}_{n}}\propto \sqrt{n},{{E}_{n}}\propto n\] done clear
C) \[{{r}_{n}}\propto \sqrt{n},{{E}_{n}}\propto \frac{1}{n}\] done clear
D) \[{{r}_{n}}\propto n,{{E}_{n}}\propto n\] done clear
View Answer play_arrowquestion_answer3) The galvanometer deflection, when key \[{{K}_{1}}\]is closed but \[{{K}_{2}}\] is open, equals \[{{\theta }_{0}},\] (see figure). On closing \[{{K}_{2}}\]also and adjusting \[{{R}_{2}}\] to \[5\Omega ,\]the deflection in galvanometer becomes\[\frac{{{\theta }_{0}}}{5}.\] The resistance of the galvanometer is, then, given by [Neglect the internal resistance of battery]
A) \[25\Omega \] done clear
B) \[22\Omega \] done clear
C) \[5\Omega \] done clear
D) \[12\Omega \] done clear
View Answer play_arrowquestion_answer4) In the figure shown, after the switch S is turned from position A to position B the energy dissipated in the circuit in terms of capacitance C and total charge Q is
A) \[\frac{5}{8}\frac{{{Q}^{2}}}{C}\] done clear
B) \[\frac{1}{8}\frac{{{Q}^{2}}}{C}\] done clear
C) \[\frac{3}{8}\frac{{{Q}^{2}}}{C}\] done clear
D) \[\frac{3}{4}\frac{{{Q}^{2}}}{C}\] done clear
View Answer play_arrowquestion_answer5) There is a uniform spherically symmetric surface charge density at a distance \[{{R}_{0}}\] from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed V(R(t)) of the distribution as a function of its instantaneous radius R(t) is
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer6) A point source of light, S is placed at a distance L in front of the centre of plane mirror of width d which is hanging vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror, at a distance 2L as shown below The distance over which the man can see the image of the light source in the mirror is
A) 3d done clear
B) 2d done clear
C) d done clear
D) \[\frac{d}{2}\] done clear
View Answer play_arrowquestion_answer7) Two light identical springs of spring constant k are attached horizontally at the two ends of a uniform horizontal rod AB of length l and mass m. The rod is pivoted at its centre O and can rotate freely in horizontal plane. The other ends of the two springs are fixed to rigid supports as shown in figure. The rod is gently pushed through a small angle and released. The frequency of resulting oscillation is
A) \[\frac{1}{2\pi }\sqrt{\frac{k}{m}}\] done clear
B) \[\frac{1}{2\pi }\sqrt{\frac{6k}{m}}\] done clear
C) \[\frac{1}{2\pi }\sqrt{\frac{3k}{m}}\] done clear
D) \[\frac{1}{2\pi }\sqrt{\frac{2k}{m}}\] done clear
View Answer play_arrowquestion_answer8) As shown in, the figure, two infinitely long, identical wires are bent by \[90{}^\circ \] and placed in such a way that the segments LP and QM are along the x-axis, while segments PS and QN are parallel to the y-axis. If OP=OQ=4cm, and the magnitude of the magnetic field at C) is\[{{10}^{-4}}T,\] and the two wires carry equal currents (see figure), the magnitude of the current in each wire and the direction of the magnetic field at O will be \[({{\mu }_{0}}=4\pi \times {{10}^{-7}}N{{A}^{-2}})\]
A) 20 A, perpendicular into the page done clear
B) 40 A, perpendicular into the page done clear
C) 20 A, perpendicular out of the page done clear
D) 40 A, perpendicular out of the page. done clear
View Answer play_arrowquestion_answer9) A passenger train of length 60 m travels at a speed of 80 km/hr. Another freight train of length 120 m travels at a speed of 30 km/hr, The ratio of times taken by the passenger train to completely cross the freight train when: (i) they are moving in the same direction, and (ii) in the opposite direction is
A) \[\frac{25}{11}\] done clear
B) \[\frac{3}{2}\] done clear
C) \[\frac{5}{2}\] done clear
D) \[\frac{11}{5}\] done clear
View Answer play_arrowquestion_answer10) The position vector of the centre of mass \[\vec{r}cm\]of an asymmetric uniform bar of negligible area of cross-section as shown in figure is
A) \[\vec{r}\,cm=\frac{11}{8}L\hat{x}+\frac{3}{8}L\,\hat{y}\] done clear
B) \[\vec{r}\,cm=\frac{13}{8}L\hat{x}+\frac{5}{8}L\,\hat{y}\] done clear
C) \[\vec{r}\,cm=\frac{3}{8}L\hat{x}+\frac{11}{8}L\,\hat{y}\] done clear
D) \[\vec{r}\,cm=\frac{5}{8}L\hat{x}+\frac{13}{8}L\,\hat{y}\] done clear
View Answer play_arrowquestion_answer11) An ideal battery of 4 V and resistance R are connected in series in the primary circuit of a potentiometer of length 1 m and resistance \[5\Omega .\] The value of R, to give a potential difference of mV across 10 cm of potentiometer wire is
A) \[490\,\Omega \] done clear
B) \[495\,\Omega \] done clear
C) \[395\,\Omega \] done clear
D) \[480\,\Omega \] done clear
View Answer play_arrowquestion_answer12) Determine the electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle, as shown in the figure.
A) \[2ql\,\hat{j}\] done clear
B) \[(ql)\,\frac{\hat{i}+\,\hat{j}}{\sqrt{2}}\] done clear
C) \[\sqrt{3}ql\,\frac{\,\hat{j}-\hat{i}}{\sqrt{2}}\] done clear
D) \[-\sqrt{3}ql\,\hat{j}\] done clear
View Answer play_arrowquestion_answer13) A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely in elastically. The speeds of the satellite and meteorite are the same, just before the collision. The subsequent motion of the combined body will be
A) in an elliptical orbit done clear
B) in the same circular orbit of radius R done clear
C) in a circular orbit of a different radius done clear
D) such that it escapes to infinity. done clear
View Answer play_arrowquestion_answer14) A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The thermal conductivity of the material of the inner cylinder is \[{{K}_{1}}\]and that of the outer cylinder is\[{{K}_{2}}\]. Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is
A) \[\frac{2{{K}_{1}}+3{{K}_{2}}}{5}\] done clear
B) \[\frac{{{K}_{1}}+{{K}_{2}}}{2}\] done clear
C) \[{{K}_{1}}+{{K}_{2}}\] done clear
D) \[\frac{{{K}_{1}}+3{{K}_{2}}}{4}\] done clear
View Answer play_arrowquestion_answer15) A light wave is incident normally on a glass slab of refractive index 1.5. If 4% of light gets reflected and the amplitude of the electric field of the incident light is \[30V\,{{m}^{-1}},\]then the amplitude of the electric field for the wave propagating in the glass medium will be
A) \[24V\,{{m}^{-1}}\] done clear
B) \[10V\,{{m}^{-1}}\] done clear
C) \[30V\,{{m}^{-1}}\] done clear
D) \[6V\,{{m}^{-1}}\] done clear
View Answer play_arrowquestion_answer16) A travelling harmonic wave is represented by the equation \[y(x,t)={{10}^{-3}}\sin (50t+2x),\]where x and t are in meter and t is in seconds. Which of the following is a correct statement about the wave?
A) The wave is propagating along the positive x-axis with speed \[25\,m\,{{s}^{-1}}\]. done clear
B) The wave is propagating along the positive x-axis with speed \[100\,m\,{{s}^{-1}}\]. done clear
C) The wave is propagating along the negative x-axis with speed \[25\,m\,{{s}^{-1}}\]. done clear
D) The wave is propagating along the negative x-axis with speed \[100\,m\,{{s}^{-1}}\]. done clear
View Answer play_arrowquestion_answer17) A simple pendulum, made of a string of length I and a bob of mass m, is released from a small angle \[{{\theta }_{0}}.\]It strikes a block of mass M, kept on a horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle \[{{\theta }_{1}}.\]Then M is given by
A) \[\frac{m}{2}\left( \frac{{{\theta }_{0}}-{{\theta }_{1}}}{{{\theta }_{0}}+{{\theta }_{1}}} \right)\] done clear
B) \[m\left( \frac{{{\theta }_{0}}+{{\theta }_{1}}}{{{\theta }_{0}}-{{\theta }_{1}}} \right)\] done clear
C) \[\frac{m}{2}\left( \frac{{{\theta }_{0}}+{{\theta }_{1}}}{{{\theta }_{0}}-{{\theta }_{1}}} \right)\] done clear
D) \[m\left( \frac{{{\theta }_{0}}-{{\theta }_{1}}}{{{\theta }_{0}}+{{\theta }_{1}}} \right)\] done clear
View Answer play_arrowquestion_answer18) For the given cyclic process CAB as shown for a gas, the work done is
A) 10 J done clear
B) 1 J done clear
C) 5 J done clear
D) 30 J done clear
View Answer play_arrowquestion_answer19) In a meter bridge, the wire of length 1 m has a non-uniform cross-section such that the variation \[\frac{dR}{dl}\]of its resistance R with length l is \[\frac{dR}{dl}\propto \frac{1}{\sqrt{l}}.\] Two equal resistances are connected as shown in the figure. The galvanometer has zero deflection when the jockey is at point P. What is the length AP?
A) 0.35 m done clear
B) 0.2 m done clear
C) 0.25 m done clear
D) 0.3 m done clear
View Answer play_arrowquestion_answer20) The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on its circular scale required to measure \[5\mu m\]diameter of a wire is
A) 50 done clear
B) 100 done clear
C) 200 done clear
D) 500 done clear
View Answer play_arrowquestion_answer21) A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle \[60{}^\circ \] with ground level. But he finds the aeroplane right vertically above his position. If v is the speed of sound, speed of the plane is
A) v done clear
B) \[\frac{\sqrt{3}}{2}v\] done clear
C) \[\frac{2v}{\sqrt{3}}\] done clear
D) \[\frac{v}{2}\] done clear
View Answer play_arrowquestion_answer22) Two electric bulbs, rated at (25 W, 220 V) and (100 W, 220 V), are connected in series across a 220 V voltage source. If the 25 W and 100 W bulbs draw powers \[{{P}_{1}}\]and \[{{P}_{2}}\]respectively, then
A) \[{{P}_{1}}=9W,{{P}_{2}}=16W\] done clear
B) \[{{P}_{1}}=16\,W,{{P}_{2}}=4W\] done clear
C) \[{{P}_{1}}=4\,W,{{P}_{2}}=16W\] done clear
D) \[{{P}_{1}}=16\,W,{{P}_{2}}=9W\] done clear
View Answer play_arrowquestion_answer23) The output of the given logic circuit is
A) \[\bar{A}B\] done clear
B) \[A\bar{B}\] done clear
C) \[AB+\overline{AB}\] done clear
D) \[A\overline{B}+\overline{A}B\] done clear
View Answer play_arrowquestion_answer24) A proton and an \[\alpha -\]particle (with their masses in the ratio 1 : 4 and charges in the ratio of 1 : 2) are accelerated from rest through a potential difference V. If a uniform, magnetic field is set up perpendicular to their' velocities, the ratio of the radii \[{{r}_{p}}:{{r}_{\alpha }}\]of the circular paths described by them will be
A) \[1:3\] done clear
B) \[1:\sqrt{2}\] done clear
C) \[1:2\] done clear
D) \[1:\sqrt{3}\] done clear
View Answer play_arrowquestion_answer25) An ideal gas occupies a volume of \[2{{m}^{3}}\] at a pressure of\[3\times {{10}^{6}}Pa\]. The energy of the gas is
A) \[9\times {{10}^{6}}J\] done clear
B) \[3\times {{10}^{2}}J\] done clear
C) \[6\times {{10}^{4}}J\] done clear
D) \[{{10}^{8}}J\] done clear
View Answer play_arrowquestion_answer26) A 100 V carrier wave is made to vary between 160 V and 40 V by a modulating signal. What is the modulation index?
A) 0.4 done clear
B) 0.5 done clear
C) 0.6 done clear
D) 0.3 done clear
View Answer play_arrowquestion_answer27) A straight rod of length L extends from x=a to \[x=L+a.\] The gravitational force it exerts on a point mass m at x=0, if the mass per unit length of the rod is \[A+B{{x}^{2}},\], is given by
A) \[Gm\left[ A\left( \frac{1}{a}-\frac{1}{a+L} \right)-BL \right]\] done clear
B) \[Gm\left[ A\left( \frac{1}{a+L}-\frac{1}{a} \right)-BL \right]\] done clear
C) \[Gm\left[ A\left( \frac{1}{a+L}-\frac{1}{a} \right)+BL \right]\] done clear
D) \[Gm\left[ A\left( \frac{1}{a}-\frac{1}{a+L} \right)+BL \right]\] done clear
View Answer play_arrowquestion_answer28) In the figure shown, a circuit contains two identical resistors with resistance \[R=5\Omega \] and an inductance with L=2mH. An ideal battery of 15 V is connected in the circuit. What will be the current through the battery long after the switch is closed?
A) 3 A done clear
B) 5.5 A done clear
C) 7.5 A done clear
D) 6 A done clear
View Answer play_arrowquestion_answer29) Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer radius 20 cm), about its axis be I. The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also J, is
A) 14 cm done clear
B) 16 cm done clear
C) 12 cm done clear
D) 18 cm done clear
View Answer play_arrowquestion_answer30) A particle A of mass m and charge q is accelerated by a potential difference of 50 V. Another particle B of mass 4 m and charge q is accelerated by a potential difference of 2500 V. The ratio of de-Broglie wavelengths\[\frac{{{\lambda }_{A}}}{{{\lambda }_{B}}}\] is close to
A) 14.14 done clear
B) 0.07 done clear
C) 4.47 done clear
D) 10.00 done clear
View Answer play_arrowquestion_answer31) In the Hall-Heroult process, aluminium is formed at the cathode. The cathode is made out of
A) platinum done clear
B) pure aluminium done clear
C) copper done clear
D) carbon. done clear
View Answer play_arrowquestion_answer32) What is the work function of the metal if the light of wavelength \[4000\text{ }\overset{o}{\mathop{\text{A}}}\,\] generates photoelectrons of velocity \[6\times {{10}^{5}}m\,{{s}^{-1}}\]from it?
(Mass of electron \[=9\times {{10}^{-31}}kg,\] |
Velocity of light\[=3\times {{10}^{8}}m\,{{s}^{-1}},\] |
Planck?s constant \[=6.626\times {{10}^{-34}}Js,\] |
Charge of electron\[=1.6\times {{10}^{-19}}Je{{V}^{-1}}\]) |
A) 4.0 eV done clear
B) 2.1 Ev done clear
C) 0.9 eV done clear
D) 3.1 eV done clear
View Answer play_arrowquestion_answer33) A metal on combustion in excess air forms X. X upon hydrolysis with water yields \[{{H}_{2}}{{O}_{2}}\]and \[{{O}_{2}}\] along with another product. The metal is
A) Li done clear
B) Rb done clear
C) Mg done clear
D) Na done clear
View Answer play_arrowquestion_answer34) Two solids dissociate as follows
\[{{A}_{(s)}}{{B}_{(g)}}+{{C}_{(g)}};{{K}_{P1}}=x\,at{{m}^{2}}\] |
\[{{D}_{(s)}}{{C}_{(g)}}+{{E}_{(g)}};{{K}_{P2}}=y\,at{{m}^{2}}\] |
A) \[\sqrt{x+y}atm\] done clear
B) \[{{x}^{2}}+{{y}^{2}}atm\] done clear
C) \[2\left( \sqrt{x+y} \right)atm\] done clear
D) \[(x+y)atm\] done clear
View Answer play_arrowquestion_answer35) \[C{{H}_{3}}C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ Ph \end{smallmatrix}}{\overset{\begin{smallmatrix} OH \\ | \end{smallmatrix}}{\mathop{C}}}\,-C{{H}_{3}}\] cannot be prepared by
A) \[PhCOC{{H}_{3}}+C{{H}_{3}}C{{H}_{2}}MgX\] done clear
B) \[HCHO+PhCH(C{{H}_{3}})C{{H}_{2}}MgX\] done clear
C) \[PhCOC{{H}_{2}}C{{H}_{3}}+C{{H}_{3}}MgX\] done clear
D) \[C{{H}_{3}}C{{H}_{2}}COC{{H}_{3}}+PhMgX\] done clear
View Answer play_arrowquestion_answer36) Water samples with BOD values of 4 ppm and 18 ppm, respectively, are
A) clean and highly polluted done clear
B) highly polluted and highly polluted done clear
C) highly polluted and clean done clear
D) clean and clean. done clear
View Answer play_arrowquestion_answer37) The element with Z = 120 (not yet discovered) will be an/a
A) inner-transition metal done clear
B) alkaline earth metal done clear
C) alkali metal done clear
D) transition metal. done clear
View Answer play_arrowquestion_answer38) Given
Gas | \[{{H}_{2}}\] | \[C{{H}_{4}}\] | \[C{{O}_{2}}\] | \[S{{O}_{2}}\] |
Critical | 33 | 190 | 304 | 630 |
Temperature/K |
A) \[{{H}_{2}}\] done clear
B) \[C{{H}_{4}}\] done clear
C) \[C{{O}_{2}}\] done clear
D) \[S{{O}_{2}}\] done clear
View Answer play_arrowquestion_answer39) The main product of the following reaction is
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer40) In a chemical reaction, \[A+2B2C+D,\]the initial concentration of B was 1.5 times of the concentration of A, but the equilibrium concentrations of A and B were found to be equal. The equilibrium constant (K) for the aforesaid chemical reaction is
A) 1 done clear
B) \[\frac{1}{4}\] done clear
C) 4 done clear
D) 16 done clear
View Answer play_arrowquestion_answer41) Among the following four aromatic compounds, which one will have the lowest melting point?
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer42) The standard electrode potential \[E{}^\circ \]and its temperature coefficient \[\left( \frac{d{{E}^{o}}}{dT} \right)\]for a cell are 2 V and \[-5\times {{10}^{-4}}V\,{{K}^{-1}}\]at 300 K respectively.
The cell reaction is |
\[Z{{n}_{(s)}}+Cu_{(aq)}^{2+}\xrightarrow[{}]{{}}Zn_{(aq)}^{2+}+C{{u}_{(s)}}\] |
A) \[-412.8\] done clear
B) 192.0 done clear
C) \[-384.0\] done clear
D) 206.4 done clear
View Answer play_arrowquestion_answer43) The hardness of a water sample (in terms of equivalents of \[CaC{{O}_{3}}\]) containing \[{{10}^{-3}}M\,CaS{{O}_{4}}\]is (molar mass of \[\,CaS{{O}_{4}}=136g\,mo{{l}^{-1}}\])
A) 10 ppm done clear
B) 100 ppm done clear
C) 50 ppm done clear
D) 90 ppm done clear
View Answer play_arrowquestion_answer44) Decomposition of X exhibits a rate constant of\[0.05\,\,\mu g/year\]. How many years are required for the decomposition of \[5\mu g\]of X into\[2.5\mu g\]?
A) 25 done clear
B) 50 done clear
C) 20 done clear
D) 40 done clear
View Answer play_arrowquestion_answer45) The increasing order of reactivity of the following compounds towards reaction with alkyl halides directly is
[A] |
[B] |
[C] |
[D] |
A) \[(B)<(A)<(D)<(C)\] done clear
B) \[(A)<(C)<(D)<(B)\] done clear
C) \[(B)<(A)<(C)<(D)\] done clear
D) \[(A)<(B)<(C)<(D)\] done clear
View Answer play_arrowquestion_answer46) Iodine reacts with concentrated \[HN{{O}_{3}}\]to yield Y along with other products. The oxidation state of iodine in Y, is
A) 5 done clear
B) 1 done clear
C) 7 done clear
D) 3 done clear
View Answer play_arrowquestion_answer47) For a diatomic ideal gas in a closed system, which of the following plots does not correctly describe the relation between various thermodynamic quantities?
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer48) \[M{{n}_{2}}{{(CO)}_{10}}\]is an organometallic compound due to the presence of
A) \[C-O\text{ }bond\] done clear
B) \[Mn-O\text{ }bond\] done clear
C) \[Mn-C\text{ }bond\] done clear
D) \[Mn-Mn\text{ }bond\] done clear
View Answer play_arrowquestion_answer49) The main product of the following reaction is
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer50) The volume of gas A is twice than that of gas B. The compressibility factor of gas A is thrice than that of gas B at same temperature. The pressures of the gases for equal number of moles are
A) \[2{{P}_{A}}=3{{P}_{B}}\] done clear
B) \[3{{P}_{A}}=2{{P}_{B}}\] done clear
C) \[{{P}_{A}}=2{{P}_{B}}\] done clear
D) \[{{P}_{A}}=3{{P}_{B}}\] done clear
View Answer play_arrowquestion_answer51) Among the following compounds most basic amino acid is
A) histidine done clear
B) serine done clear
C) asparagine done clear
D) lysine. done clear
View Answer play_arrowquestion_answer52) The correct order for acid strength of compounds \[CH\equiv CH,C{{H}_{3}}-C\equiv CH\] and \[C{{H}_{2}}=C{{H}_{2}}\]is as follows
A) \[C{{H}_{3}}-C\equiv CH>CH\equiv CH>C{{H}_{2}}=C{{H}_{2}}\] done clear
B) \[C{{H}_{3}}-C\equiv CH>C{{H}_{2}}=C{{H}_{2}}>HC\equiv CH\] done clear
C) \[HC\equiv CH>C{{H}_{3}}-C\equiv CH>C{{H}_{2}}=C{{H}_{2}}\] done clear
D) \[CH\equiv CH>C{{H}_{2}}=C{{H}_{2}}>C{{H}_{3}}-C\equiv CH\] done clear
View Answer play_arrowquestion_answer53) Poly-\[\beta \]-hydroxybutyrate- co-\[\beta \]-hydroxyvalerate (PHBV) is a copolymer of
A) 2-hydroxybutanoic acid and 3-hydroxypentanoic acid done clear
B) 3-hydroxybutanoic acid and 3-hydroxypentanoic acid done clear
C) 3-hydroxybutanoic acid and 2-hydroxypentanoic acid done clear
D) 3-hydroxybutanoic acid and 4-hydroxypentanoic acid. done clear
View Answer play_arrowquestion_answer54) A and B in the following reactions is
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer55) The metal d- orbital that are directly facing the ligands in \[{{K}_{3}}[Co{{(CN)}_{6}}]\]are
A) \[{{d}_{xy}}and\,{{d}_{{{x}^{2}}-{{y}^{2}}}}\] done clear
B) \[{{d}_{xy'}}{{d}_{xz}}\,and\,{{d}_{yz}}\] done clear
C) \[{{d}_{{{x}^{2}}-{{y}^{2}}}}\,and\,{{d}_{{{z}^{2}}}}\] done clear
D) \[{{d}_{xy'}}{{d}_{yz}}\,and\,{{d}_{{{z}^{2.}}}}\] done clear
View Answer play_arrowquestion_answer56) The pair of metal ions that can give a spin- only magnetic moment of 3.9 B.M. for the complex \[[M{{({{H}_{2}}O)}_{6}}]C{{l}_{2}}\] is
A) \[C{{r}^{2+}}and\,M{{n}^{2+}}\] done clear
B) \[{{V}^{2+}}and\,C{{o}^{2+}}\] done clear
C) \[{{V}^{2+}}and\,F{{e}^{2+}}\] done clear
D) \[C{{o}^{2+}}and\,F{{e}^{2+}}\] done clear
View Answer play_arrowquestion_answer57) 50 mL of 0.5 M oxalic acid is needed to neutralise 25 mL of sodium hydroxide solution. The amount of NaOH in 50 mL of the given sodium hydroxide solution is
A) 10 g done clear
B) 80 g done clear
C) 40 g done clear
D) 20 g done clear
E) None of these done clear
View Answer play_arrowquestion_answer58) The molecule that has minimum/no role in the formation of photochemical smog, is
A) \[C{{H}_{2}}=O\] done clear
B) \[{{N}_{2}}\] done clear
C) \[{{O}_{3}}\] done clear
D) NO done clear
View Answer play_arrowquestion_answer59) In the following reaction
Aldehyde + Alcohol \[\xrightarrow[{}]{HCl}\]Acetal | |
Aldehyde | Alcohol |
\[HClO\] | \[t-BuOH\] |
\[C{{H}_{3}}CHO\] | \[MeOH\] |
A) \[HCHO\,and\,t-BuOH\] done clear
B) \[C{{H}_{3}}CHO\,\,and\,\,t-BuOH\] done clear
C) \[C{{H}_{3}}CHO\,and\,MeOH\] done clear
D) \[HCHO\,\,and\,\,MeOH\] done clear
View Answer play_arrowquestion_answer60) Freezing point of a 4% aqueous solution of X is equal to freezing point of 12% aqueous solution of Y. If molecular weight of X is A, then molecular weight of Y is
A) 2A done clear
B) 3A done clear
C) A done clear
D) 4A done clear
View Answer play_arrowquestion_answer61) The sum of the distinct real values of \[\mu \], for which the vectors, \[\mu \hat{i}+\hat{j}+\hat{k},\hat{i}+\mu \hat{j}+\hat{k},\hat{i}+\hat{j}+\mu \,\hat{k}\]are co-planar, is
A) 2 done clear
B) 0 done clear
C) -1 done clear
D) 1 done clear
View Answer play_arrowquestion_answer62) The area (in sq. units) of the region bounded by the parabola, \[y={{x}^{2}}+2\] and the lines, \[y=x+1,x=0\]and \[x=3,\] is
A) 15/2 done clear
B) 17/4 done clear
C) 21/2 done clear
D) 15/4 done clear
View Answer play_arrowquestion_answer63) Let \[{{C}_{1}}\]and \[{{C}_{2}}\]be the centres of the circles \[{{x}^{2}}+{{y}^{2}}-2x-2y-2=0\]and \[{{x}^{2}}+{{y}^{2}}-6x-6y+14=0\]respectively. If P and Q are the points of intersection of these circles, then the area (in sq. units) of the Quadrilateral \[P{{C}_{1}}Q{{C}_{2}}\] is
A) 8 done clear
B) 4 done clear
C) 6 done clear
D) 9 done clear
View Answer play_arrowquestion_answer64) Consider three boxes, each containing 10 balls labelled 1, 2, ..... 10. Suppose one ball is randomly drawn from each of the boxes. Denote by \[{{n}_{i}},\]the label of the ball drawn from the \[{{i}^{th}}\] box, (i = 1, 2, 3). Then, the number of ways in which the balls can be chosen such that \[{{n}_{1}}<{{n}_{2}}<{{n}_{3}}\] is
A) 120 done clear
B) 164 done clear
C) 240 done clear
D) 82 done clear
View Answer play_arrowquestion_answer65) Considering only the principal values of inverse functions, the set
\[A=\left\{ x\ge 0:{{\tan }^{-1}}(2x)+ta{{n}^{-1}}(3x)=\frac{\pi }{4} \right\}\] |
A) contains two elements done clear
B) contains more than two elements done clear
C) is an empty set done clear
D) is a singleton done clear
View Answer play_arrowquestion_answer66) The perpendicular distance from the origin to the plane containing the two lines,\[\frac{x+2}{3}=\frac{y-2}{5}=\frac{z+5}{7}\]and\[\frac{x-1}{1}=\frac{y-4}{4}=\frac{z+4}{7},\]is
A) 11 done clear
B) \[6\sqrt{11}\] done clear
C) \[\frac{11}{\sqrt{6}}\] done clear
D) \[11\sqrt{6}\] done clear
View Answer play_arrowquestion_answer67) If \[\frac{z-\alpha }{z+\alpha }(\alpha \in R)\]is a purely imaginary number and \[|z|=2,\] then a value of \[\alpha \] is
A) 1 done clear
B) \[\sqrt{2}\] done clear
C) \[\frac{1}{2}\] done clear
D) 2 done clear
View Answer play_arrowquestion_answer68) If the straight line, \[2x-3y+17=0\] is perpendicular to the line passing through the points (7, 17) and \[(15,\beta ),\] then \[\beta \]equals
A) 5 done clear
B) \[\frac{35}{3}\] done clear
C) \[-\frac{35}{3}\] done clear
D) \[-5\] done clear
View Answer play_arrowquestion_answer69) The Boolean expression \[((p\wedge q)\vee (p\vee \tilde{\ }q))\]\[\wedge (\tilde{\ }p\wedge \tilde{\ }q)\]is equivalent to
A) \[(\tilde{\ }p)\wedge (\tilde{\ }q)\] done clear
B) \[p\wedge (\tilde{\ }q)\] done clear
C) \[p\wedge q\] done clear
D) \[p\vee (\tilde{\ }q)\] done clear
View Answer play_arrowquestion_answer70) Let\[{{S}_{k}}=\frac{1+2+3+...+k}{k}.\]If \[S_{1}^{2}+S_{2}^{2}+...+S_{10}^{2}\]\[=\frac{5}{12}A,\] then A is equal to
A) 303 done clear
B) 283 done clear
C) 301 done clear
D) 156 done clear
View Answer play_arrowquestion_answer71) An ordered pair \[(\alpha ,\beta )\]for which the system of linear equations \[(1+\alpha )x+\beta y+z=2,\]\[\alpha x+(1+\beta )y+z=3,\]\[\alpha x+\beta y+2z=2\] has a unique solution, is
A) \[(-3,\text{ }1)\] done clear
B) \[(2,\text{ 4})\] done clear
C) \[(1,\text{ }-3)\] done clear
D) \[(-4,\text{ 2})\] done clear
View Answer play_arrowquestion_answer72) The maximum area (in sq. units) of a rectangle having its base on the x-axis and its other two vertices on the parabola, \[y=12-{{x}^{2}}\]such that the rectangle lies inside the parabola, is
A) 36 done clear
B) \[18\sqrt{3}\] done clear
C) \[20\sqrt{2}\] done clear
D) 32 done clear
View Answer play_arrowquestion_answer73) Let S = {1, 2, 3, ..., 100}. The number of non- empty subsets A of S such that the product of elements in A is even is
A) \[{{2}^{50}}({{2}^{50}}-1)\] done clear
B) \[{{2}^{50}}-1\] done clear
C) \[{{2}^{50}}+1\] done clear
D) \[{{2}^{100}}-1\] done clear
View Answer play_arrowquestion_answer74) Let f and g be continuous functions on [0, a] such that \[f(x)=f(a-x)\]and \[g(x)=g(a-x)=4,\]then \[\int\limits_{0}^{a}{f(x)g(x)dx}\]is equal to
A) \[2\int\limits_{0}^{a}{f(x)dx}\] done clear
B) \[4\int\limits_{0}^{a}{f(x)dx}\] done clear
C) \[-3\int\limits_{0}^{a}{f(x)dx}\] done clear
D) \[\int\limits_{0}^{a}{f(x)dx}\] done clear
View Answer play_arrowquestion_answer75) If\[x>1\]for\[{{(2x)}^{2y}}=4{{e}^{2x-2y}},\]then\[{{(1+lo{{g}_{e}}2x)}^{2}}\frac{dy}{dx}\]equals
A) \[\frac{x\,{{\log }_{e}}2x-{{\log }_{e}}2}{x}\] done clear
B) \[{{\log }_{e}}2x\] done clear
C) \[\frac{x\,{{\log }_{e}}2x+{{\log }_{e}}2}{x}\] done clear
D) \[x\,{{\log }_{e}}2x\] done clear
View Answer play_arrowquestion_answer76) If a variable line, \[3x+4y-\lambda =0\]is such that the two circles \[{{x}^{2}}+{{y}^{2}}-2x-2y+1=0\]and\[{{x}^{2}}+{{y}^{2}}-18x\]\[-2y+78=0\]are on its opposite sides, then the set of all values of \[\lambda \] is the interval
A) (23, 31) done clear
B) (2, 17) done clear
C) [13, 23] done clear
D) [12, 21] done clear
View Answer play_arrowquestion_answer77) If X be the ratio of the roots of the quadratic equation in \[x,3{{m}^{2}}{{x}^{2}}+m(m-4)x+2=0,\]then the least value of m for which \[\lambda +\frac{1}{\lambda }=1,\]is
A) \[-2+\sqrt{2}\] done clear
B) \[4-3\sqrt{2}\] done clear
C) \[4-2\sqrt{3}\] done clear
D) \[2-\sqrt{3}\] done clear
View Answer play_arrowquestion_answer78) In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to
A) \[\frac{150}{{{6}^{5}}}\] done clear
B) \[\frac{225}{{{6}^{5}}}\] done clear
C) \[\frac{175}{{{6}^{5}}}\] done clear
D) \[\frac{200}{{{6}^{5}}}\] done clear
View Answer play_arrowquestion_answer79) The maximum value of the expression \[3\cos \theta +5\sin \left( \theta -\frac{\pi }{6} \right)\]for any real value of \[\theta \]is
A) \[\frac{\sqrt{79}}{2}\] done clear
B) \[\sqrt{31}\] done clear
C) \[\sqrt{34}\] done clear
D) \[\sqrt{19}\] done clear
View Answer play_arrowquestion_answer80) If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observations is
A) 30 done clear
B) 51 done clear
C) 31 done clear
D) 50 done clear
View Answer play_arrowquestion_answer81) Let \[y=y(x)\]be the solution of the differential equation, \[x\frac{dy}{dx}+y=x{{\log }_{e}}x,\]\[(x>1)\]. If \[2y(2)=lo{{g}_{e}}4-1,\]then\[y(e)\]is equal to
A) \[\frac{{{e}^{2}}}{4}\] done clear
B) \[-\frac{{{e}^{2}}}{2}\] done clear
C) \[-\frac{e}{2}\] done clear
D) \[\frac{e}{4}\] done clear
View Answer play_arrowquestion_answer82) If the vertices of a hyperbola be at \[(-2,\text{ }0)\,\,\,and\,\,\,(2,\text{ }0)\]and one of its foci be at\[(-3,\text{ }0)\], then which one of the following points does not lie on this hyperbola?
A) \[(2\sqrt{6},5)\] done clear
B) \[(-6,2\sqrt{10})\] done clear
C) \[(6,5\sqrt{2})\] done clear
D) \[(4,\sqrt{15})\] done clear
View Answer play_arrowquestion_answer83) Let \[P=\left[ \begin{matrix} 1 & 0 & 0 \\ 3 & 1 & 0 \\ 9 & 3 & 1 \\ \end{matrix} \right]\]and \[Q=[{{q}_{ij}}]\]be two \[3\times 3\]matrices such that \[Q-{{P}^{5}}={{I}_{3}}.\]Then \[\frac{{{q}_{21}}+{{q}_{31}}}{{{q}_{32}}}\]is equal to
A) 10 done clear
B) 135 done clear
C) 9 done clear
D) 15 done clear
View Answer play_arrowquestion_answer84) Integral \[\int_{{}}^{{}}{\cos (lo{{g}_{e}}x)}dx\]equals (where C is the constant of integration)
A) \[\frac{x}{2}[sin(lo{{g}_{e}}x)-cos(lo{{g}_{e}}x)]+C\] done clear
B) \[x[cos(lo{{g}_{e}}x)-\sin (lo{{g}_{e}}x)]+C\] done clear
C) \[\frac{x}{2}[cos(lo{{g}_{e}}x)+\sin (lo{{g}_{e}}x)]+C\] done clear
D) \[x[cos(lo{{g}_{e}}x)+\sin (lo{{g}_{e}}x)]+C\] done clear
View Answer play_arrowquestion_answer85) Let \[P(4,-4)\]and \[Q(9,6)\]be two points on the parabola, \[{{y}^{2}}=4x\] and let X be any point on the arc POQ of this parabola, where O is the vertex of this parabola, such that the area of APXQ is maximum. Then this maximum area (in sq. units) is
A) \[\frac{125}{2}\] done clear
B) \[\frac{125}{4}\] done clear
C) \[\frac{625}{4}\] done clear
D) \[\frac{75}{2}\] done clear
View Answer play_arrowquestion_answer86) The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now form an A.P. Then the sum of the original three terms of the given G.P. is
A) 36 done clear
B) 24 done clear
C) 28 done clear
D) 32 done clear
View Answer play_arrowquestion_answer87) \[\underset{x\to \pi /4}{\mathop{\lim }}\,\frac{{{\cot }^{3}}x-\tan x}{\cos \left( x+\frac{\pi }{4} \right)}\] is
A) \[4\sqrt{2}\] done clear
B) \[8\sqrt{2}\] done clear
C) 4 done clear
D) 8 done clear
View Answer play_arrowquestion_answer88) A ratio of the \[{{5}^{th}}\] term from the beginning to the \[{{5}^{th}}\] term from the end in the binomial is expansion of \[{{\left( {{2}^{1/3}}+\frac{1}{2{{(3)}^{1/3}}} \right)}^{10}}\] is
A) \[4{{(36)}^{1/3}}:1\] done clear
B) \[1:2{{(6)}^{1/3}}\] done clear
C) \[2{{(36)}^{1/3}}:1\] done clear
D) \[1:4{{(16)}^{1/3}}\] done clear
View Answer play_arrowquestion_answer89) Let 5 be the set of all points in \[(-\pi ,\pi )\]at which the function, \[f(x)=\min \{\sin x,\cos x\}\]is not differentiable. Then S is a subset of which of the following?
A) \[\left\{ -\frac{\pi }{4},0,\frac{\pi }{4} \right\}\] done clear
B) \[\left\{ -\frac{3\pi }{4},-\frac{\pi }{4},\frac{3\pi }{4},\frac{\pi }{4} \right\}\] done clear
C) \[\left\{ -\frac{3\pi }{4},-\frac{\pi }{2},\frac{\pi }{2},\frac{3\pi }{4} \right\}\] done clear
D) \[\left\{ -\frac{\pi }{2},-\frac{\pi }{4},\frac{\pi }{4},\frac{\pi }{2} \right\}\] done clear
View Answer play_arrowquestion_answer90) A tetrahedron has vertices \[P(1,2,1),Q(2,1,3),\]\[R(-1,1,2)\]and \[O(0,0,0).\]The angle between the faces OPQ and PQR is
A) \[{{\cos }^{-1}}\left( \frac{7}{31} \right)\] done clear
B) \[{{\cos }^{-1}}\left( \frac{17}{31} \right)\] done clear
C) \[{{\cos }^{-1}}\left( \frac{19}{35} \right)\] done clear
D) \[{{\cos }^{-1}}\left( \frac{9}{35} \right)\] done clear
View Answer play_arrow
You need to login to perform this action.
You will be redirected in
3 sec