question_answer1) Two guns A and B can fire bullets at speeds 1 km/s and 2 km/s respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is -
A) 1 : 16 done clear
B) 1 : 8 done clear
C) 1 : 2 done clear
D) 1 : 4 done clear
View Answer play_arrowquestion_answer2) A heat source at \[T={{10}^{3}}\] K is connected to another heat reservoir at \[T={{10}^{2}}\] K by a copper slab which is 1 m thick. Given that the thermal conductivity of copper is 0.1 \[W{{K}^{-}}^{1}{{m}^{-}}^{1}\], the energy flux through it in the steady state is -
A) 200 \[W{{m}^{-}}^{2}\] done clear
B) 65 \[W{{m}^{-}}^{2}\] done clear
C) 120 \[W{{m}^{-}}^{2}\] done clear
D) 90 \[W{{m}^{-}}^{2}\] done clear
View Answer play_arrowquestion_answer3) A satellite is moving with a constant speed v in circular orbit around the earth. An object of mass 'm' is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is -
A) \[m{{v}^{2}}\] done clear
B) \[\frac{1}{2}m{{v}^{2}}\] done clear
C) \[\frac{3}{2}m{{v}^{2}}\] done clear
D) \[2\,m{{v}^{2}}\] done clear
View Answer play_arrowquestion_answer4) A TV transmission tower has a height of 140 m and the height of the receiving antenna is 40 m. What is the maximum distance upto which signals can be broadcasted from this tower is LOS (Line of Sight) mode? (Given: radius of earth \[=\text{ }6.4\times {{10}^{6}}m)\].
A) 40 km done clear
B) 65 km done clear
C) 48 km done clear
D) 80 km done clear
View Answer play_arrowquestion_answer5) A train moves towards a stationary observer with speed 34 m/s. The train sounds a whistle and its frequency registered by the observer is\[{{f}_{1}}\]. If the speed of the train is reduced to 17 m/s, the frequency registered is\[{{f}_{2}}\]. If speed of sound is 340 m/s, then the ratio \[{{f}_{1}}/{{f}_{2}}\] is -
A) 19/18 done clear
B) 20/19 done clear
C) 21/20 done clear
D) 18/17 done clear
View Answer play_arrowquestion_answer6) In the cube of side 'a' shown in the figure, the vector from the central point of the face ABOD to the central point of the face BEFO will be -
A) \[\frac{1}{2}a\,(\widehat{k}-\widehat{i})\] done clear
B) \[\frac{1}{2}a\,(\widehat{j}-\widehat{i})\] done clear
C) \[\frac{1}{2}a\,(\widehat{j}-\widehat{k})\] done clear
D) \[\frac{1}{2}a\,(\widehat{i}-\widehat{k})\] done clear
View Answer play_arrowquestion_answer7) A parallel plate capacitor is of area \[6\text{ }c{{m}^{2}}\] and a separation 3 mm. The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constants \[{{K}_{1}}=10,\text{ }{{K}_{2}}=12\] and\[{{K}_{3}}=14\]. The dielectric constant of a material which when fully inserted in above capacitor, gives same capacitance would be -
A) 12 done clear
B) 36 done clear
C) 14 done clear
D) 4 done clear
View Answer play_arrowquestion_answer8) To mop-clean a floor, a cleaning machine presses a circular mop of radius R vertically down with a total force F and rotates it with a constant angular speed about its axis. If the force F is distributed uniformly over the mop and if coefficient of friction between the mop and the floor is u, the torque, applied by the machine on the mop is -
A) \[\mu \,FR/2\] done clear
B) \[\mu \,FR/3\] done clear
C) \[\mu \,FR/6\] done clear
D) \[\frac{2}{3}\mu \,FR\] done clear
View Answer play_arrowquestion_answer9) A block of mass m is kept on a platform which starts from rest with constant acceleration \[g/2\] acceleration \[g/2\] upward, as shown in figure. Work done by normal reaction on block in time is-
A) \[\frac{m{{g}^{2}}{{t}^{2}}}{8}\] done clear
B) \[\frac{3\,m{{g}^{2}}{{t}^{2}}}{8}\] done clear
C) \[-\frac{\,m{{g}^{2}}{{t}^{2}}}{8}\] done clear
D) 0 done clear
View Answer play_arrowquestion_answer10) Water flows into a large tank with flat bottom at the rate of\[{{10}^{-}}^{4}{{m}^{3}}{{s}^{-1}}\]. Water is also leaking out of a hole of area \[1\,c{{m}^{2}}\] at its bottom. If the height of the water in the tank remains steady, then this height is
A) 2.9 cm done clear
B) 5.1 cm done clear
C) 4 cm done clear
D) 1.7 cm done clear
View Answer play_arrowquestion_answer11) A magnet of total magnetic moment \[{{10}^{-}}^{2}\widehat{i}\,A-{{m}^{2}}\] is placed in a time varying magnetic field, \[B\widehat{i}\left( cos\text{ }\omega t \right)\] where \[B=1\] Tesla and\[\omega =0.125\text{ }rad/s\]. The work done for reversing the direction of the magnetic moment at \[t=1\] second, is-
A) 0.014 J done clear
B) 0.028 J done clear
C) 0.01 J done clear
D) 0.007 J done clear
View Answer play_arrowquestion_answer12) Two electric dipoles, A, B with respective dipole moments \[{{\overrightarrow{d}}_{A}}=-4qa\widehat{i}\] and \[{{\overrightarrow{d}}_{B}}=-2qa\widehat{i}\] are placed on the x-axis with a separation R, as shown in the figure. The distance from A at which both of them produce the same potential is -
A) \[\frac{\sqrt{2}\,R}{\sqrt{2}+1}\] done clear
B) \[\frac{\,R}{\sqrt{2}+1}\] done clear
C) \[\frac{\,\sqrt{2}\,R}{\sqrt{2}-1}\] done clear
D) \[\frac{\,\,R}{\sqrt{2}-1}\] done clear
View Answer play_arrowquestion_answer13) To get output 'I' at R, for the given logic gate circuit the input values must be-
A) \[X=0,\text{ }Y=0\] done clear
B) \[X=1,\text{ }Y=0\] done clear
C) \[X=0,\text{ }Y=1\] done clear
D) \[X=1,\text{ }Y=1\] done clear
View Answer play_arrowquestion_answer14) A solid metal cube of edge length 2 cm is moving in a positive y-direction at a constant speed of 6 m/s. There it?, a uniform magnetic field of 0.1 T in the positive z- direction. The potential difference between the two faces of the cube perpendicular to the x-axis, is -
A) 2 mV done clear
B) 12 mV done clear
C) 6 mV done clear
D) 1 mV done clear
View Answer play_arrowquestion_answer15) In a Young's double slit experiment with slit separation 0.1 mm, one observes a bright fringe at angle \[\frac{1}{40}\] rad by using light of wavelength\[{{\lambda }_{1}}\]. When the light of wavelength \[{{\lambda }_{2}}\] is used a bright fringe is seen at the same angle in the same set up. Given that \[{{\lambda }_{1}}\] and \[{{\lambda }_{2}}\] are in visible range (380 nm to 740 nm), their values are -
A) 400 nm, 500 nm done clear
B) 625 nm, 500 nm done clear
C) 380 nm, 500 nm done clear
D) 380 nm, 525 nm done clear
View Answer play_arrowquestion_answer16) The density of a material in SI units is 128 \[kg\text{ }{{m}^{-}}^{3}\]. In certain units in which the unit of length is 25 cm and the unit of mass is 50 g, the numerical value of density of the material is-
A) 40 done clear
B) 640 done clear
C) 16 done clear
D) 410 done clear
View Answer play_arrowquestion_answer17) Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At \[t=0\] it was 1600 counts per second and \[t=8\] seconds it was 100 counts per second. The count rate observed, as counts per second, at \[t=6\] seconds is close to-
A) 200 done clear
B) 150 done clear
C) 400 done clear
D) 360 done clear
View Answer play_arrowquestion_answer18) A uniform metallic wire has a resistance of \[18\,\Omega \] and is bent into an equilateral triangle. Then, the resistance between any two vertices of the triangle is-
A) \[12\,\Omega \] done clear
B) \[2\,\Omega \] done clear
C) \[4\,\Omega \] done clear
D) \[8\,\Omega \] done clear
View Answer play_arrowquestion_answer19) An insulating thin rad of length l has a linear charge density \[\rho (x)\,\,=\,\,{{\rho }_{0}}\,\frac{x}{l}\]on it. The rod is rotated about an axis passing through the origin \[(x\,\,=\,\,0)\]and perpendicular to the rod. If the rod makes n rotations per second, then the time averaged magnetic moment of the rod is-
A) \[\frac{\pi }{3}\,n\,\,\rho {{l}^{3}}\] done clear
B) \[\frac{\pi }{4}\,n\,\,\rho {{l}^{3}}\] done clear
C) \[n\,\,\rho {{l}^{3}}\] done clear
D) \[\pi n\,\,\rho {{l}^{3}}\] done clear
View Answer play_arrowquestion_answer20) A plano convex lens of refractive index \[{{\mu }_{1}}\] and focal, length \[{{f}_{1}}\] is kept in contact with another piano concave lens of refractive index \[{{\mu }_{2}}\]and focal length\[{{f}_{2}}\]. If the radius of curvature of their spherical faces is R each and \[{{f}_{1}}\,=\,2{{f}_{2}}\], then \[{{\mu }_{1}}\,and\,\,{{\mu }_{2}}\] are related as-
A) \[3{{\mu }_{2}}-2{{\mu }_{1}}=1\] done clear
B) \[{{\mu }_{1}}+{{\mu }_{2}}=3\] done clear
C) \[2{{\mu }_{1}}-{{\mu }_{2}}=1\] done clear
D) \[2{{\mu }_{2}}-{{\mu }_{1}}=1\] done clear
View Answer play_arrowquestion_answer21) In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. To resolve a width of \[7.5\times {{10}^{-}}^{12}\] m, the minimum electron required is close to-
A) 25 ke V done clear
B) 500 ke V done clear
C) 100 ke V done clear
D) 1 ke V done clear
View Answer play_arrowquestion_answer22) A homogeneous solid cylindrical roller of radius R and mass M is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is-
A) \[\frac{F}{2mR}\] done clear
B) \[\frac{2\,F}{3mR}\] done clear
C) \[\frac{3\,F}{2mR}\] done clear
D) \[\frac{F}{3mR}\] done clear
View Answer play_arrowquestion_answer23) A string of length 1 m and mass 5 g is fixed at both ends. The tension in the string is 8.0 N. The string is set into vibration using an external vibrator of frequency 100 Hz. The separation between successive nodes on the string is close to-
A) 16.6 cm done clear
B) 10.0 cm done clear
C) 20.0 cm done clear
D) 33.3 cm done clear
View Answer play_arrowquestion_answer24) A 2 W carbon resistor is color coded with green, black, red and brown respectively. The maximum current which can be passed through this resistor is-
A) 0.4 mA done clear
B) 20 mA done clear
C) 63 mA done clear
D) 100 mA done clear
View Answer play_arrowquestion_answer25) If the magnetic field of a plane electromagnetic wave is given by (the speed of light \[=~\,3~\times ~{{10}^{8}}m/s)\] \[B\,=\,100\times {{10}^{-6}}\,\sin \,\left[ 2\pi \times 2\times {{10}^{15}}\left( t-\frac{x}{c} \right) \right]\]then the maximum electric field associated with it is -
A) \[4.5\times {{10}^{4}}\,N/C\] done clear
B) \[4\times {{10}^{4}}\,N/C\] done clear
C) \[6\times {{10}^{4}}\,N/C\] done clear
D) \[3\times {{10}^{4}}\,N/C\] done clear
View Answer play_arrowquestion_answer26) In the given circuit the cells have zero internal resistance. The currents (in Amperes) passing through resistance \[{{R}_{1}}and\text{ }{{R}_{2}}\] respectively, are-
A) 0.5, 0 done clear
B) 0, 1 done clear
C) 1, 2 done clear
D) 2, 2 done clear
View Answer play_arrowquestion_answer27) Three Carnot engines operate in series between a heat source at a temperature \[{{T}_{1}}\] and a heat sink at temperature \[{{T}_{4}}\] (see figure). There are two other reservoirs at temperature\[{{T}_{2}}and\text{ }{{T}_{3}}\], as shown, with\[{{T}_{1}}>{{T}_{2}}>{{T}_{3}}>{{T}_{4}}\]. The three engines are equally efficient if -
A) \[{{T}_{2}}=\,\,{{({{T}_{1}}^{3}{{T}_{4}})}^{1/4}};\,\,=\,\,{{T}_{3}}\,\,=\,\,{{({{T}_{1}}{{T}_{4}}^{3})}^{1/4}}\] done clear
B) \[{{T}_{2}}=\,\,{{({{T}_{1}}{{T}_{4}})}^{1/2}};\,\,\,{{T}_{3}}\,\,=\,\,{{({{T}_{1}}^{2}{{T}_{4}})}^{1/3}}\] done clear
C) \[{{T}_{2}}=\,\,{{({{T}_{1}}{{T}_{4}}^{2})}^{1/3}};\,\,{{T}_{3}}\,\,=\,\,{{({{T}_{1}}^{2}{{T}_{4}})}^{1/3}}\] done clear
D) \[{{T}_{2}}=\,\,{{({{T}_{1}}^{2}{{T}_{4}})}^{1/3}};\,\,\,\,{{T}_{3}}\,\,=\,\,{{({{T}_{1}}{{T}_{4}}^{2})}^{1/3}}\] done clear
View Answer play_arrowquestion_answer28) A potentiometer wire AB having length L and resistance 12 r is joined to a cell D of emf \[\varepsilon \] and internal resistance r. A cell C having emf \[\varepsilon /2\] and internal resistance 3r is connected. The length AJ at which the galvanometer as shown in figure shows no deflection is-
A) \[\frac{11}{12}\,L\] done clear
B) \[\frac{13}{24}\,L\] done clear
C) \[\frac{5}{12}\,L\] done clear
D) \[\frac{11}{24}\,L\] done clear
View Answer play_arrowquestion_answer29) A charge Q is distributed over three concentric spherical shells of radii a, b, c \[\left( a<b<c \right)\] such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common centre, where \[r<a\], would be
A) \[\frac{Q({{a}^{2}}+{{b}^{2}}+{{c}^{2}})}{{{4}_{\pi {{\varepsilon }_{0}}}}({{a}^{3}}+{{b}^{3}}+{{c}^{3}})}\] done clear
B) \[\frac{Q}{{{4}_{\pi {{\varepsilon }_{0}}}}(a+b+c)}\] done clear
C) \[\frac{Q}{{{12}_{\pi \varepsilon {{\,}_{0}}}}}\,\,\frac{ab+bc+ca}{abc}\] done clear
D) \[\frac{Q(a+b+c)}{{{4}_{\pi \varepsilon {{\,}_{0}}}}({{a}^{2}}+{{b}^{2}}+{{c}^{2}})}\] done clear
View Answer play_arrowquestion_answer30) A piece of wood of mass 0.03 kg is dropped from the top of a 100 m height building. At the same time, a bullet of mass 0.02 kg is fired vertically upward, with a velocity \[100\text{ }m{{s}^{-1}}\]from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is - \[(g=10\,m{{s}^{-2}})\]
A) 30 m done clear
B) 40 m done clear
C) 20 m done clear
D) 10 m done clear
View Answer play_arrowquestion_answer31) The type of hybridisation and number of lone pair (s) of electrons of Xe in \[XeO{{F}_{4}}\] respectively, are:
A) \[s{{p}^{3}}d\] and 2 done clear
B) \[s{{p}^{3}}{{d}^{2}}\] and 2 done clear
C) \[s{{p}^{3}}d\] and 1 done clear
D) \[s{{p}^{3}}{{d}^{2}}\] and 1 done clear
View Answer play_arrowquestion_answer32) Which of the following is not an example of heterogeneous catalytic reaction?
A) Ostwald's process done clear
B) Combustion of coal done clear
C) Hydrogenation of vegetable oils done clear
D) Haber?s process done clear
View Answer play_arrowquestion_answer33) Which hydrogen in compound `is easily replaceable during bromination reaction in presence of light?
A) \[\beta hydrogen\] done clear
B) \[\alpha hydrogen\] done clear
C) \[\gamma hydrogen\] done clear
D) \[\delta hydrogen\] done clear
View Answer play_arrowquestion_answer34) The total number of isotopes of hydrogen and number of radioactive isotopes among them, respectively, are:
A) 3 and 2 done clear
B) 2 and 1 done clear
C) 2 and 0 done clear
D) 3 and 1 done clear
View Answer play_arrowquestion_answer35) A process has \[\Delta H=200\text{ }J\text{ }mo{{l}^{-1}}\] and\[\Delta \,S=40\text{ }J{{K}^{-1}}\,mo{{l}^{-1}}\]. Out of the values given below, choose the minimum temperature above which the process will be spontaneous:
A) 4 K done clear
B) 20 K done clear
C) 5 K done clear
D) 12 K done clear
View Answer play_arrowquestion_answer36) A mixture of 100 m mol of \[Ca{{\left( OH \right)}_{2}}\], and 2 g of sodium sulphate was dissolved in water and the volume was made up to 100 mL. The mass of calcium sulphate formed and the concentration of \[O{{H}^{-}}\]in resulting solution, respectively, are: (Molar mass \[Ca{{\left( OH \right)}_{2}}\], \[N{{a}_{2}}S{{O}_{4}}\], and \[CaS{{O}_{4}}\] are 74, 143 and \[136\text{ }g\text{ }mo{{l}^{-1}}\], respectively; \[{{K}_{sp}}\]of \[Ca{{\left( OH \right)}_{2}}\]is \[5.5\,\times \,{{10}^{-6}}\])
A) \[13.6g,\text{ }0.28\text{ }mol\text{ }{{L}^{-1}}\] done clear
B) \[13.6\,g,\text{ }0.14\,mol\,{{L}^{-\,1}}\] done clear
C) \[1.9\,g,\text{ }0.28\text{ }mol\text{ }{{L}^{-1}}\] done clear
D) \[1.9\,g,\text{ }0.14\text{ }mol\,{{L}^{-1}}\] done clear
View Answer play_arrowquestion_answer37) The increasing order of the pKa values of the following compounds is:
A) \[B<C<D<A\] done clear
B) \[B<C<A<D\] done clear
C) \[D<A<C<B\] done clear
D) \[C<B<A<D\] done clear
View Answer play_arrowquestion_answer38) Hall- Heroult's process is given by:
A) \[C{{u}^{2}}^{+}\left( aq \right)+{{H}_{2}}\left( g \right)\to Cu\left( s \right)+2{{H}^{+}}\left( aq \right)\] done clear
B) \[C{{r}_{2}}{{O}_{3}}+2Al\to A{{l}_{2}}{{O}_{3}}+2\,Cr\] done clear
C) \[2A{{l}_{2}}{{O}_{3}}+3C\to 4Al+3\text{ }C{{O}_{2}}\] done clear
D) \[ZnO+C\xrightarrow{Coke,\,1673\,K}\,\,Zn+CO\] done clear
View Answer play_arrowquestion_answer39) The electronegativity of aluminium is similar to:
A) Beryllium done clear
B) Carbon done clear
C) Boron done clear
D) Lithium done clear
View Answer play_arrowquestion_answer40) The metal used for marking X-ray tube window is:
A) Ca done clear
B) Na done clear
C) Mg done clear
D) Be done clear
View Answer play_arrowquestion_answer41) Which premitive unit cell has unequal edge lengths \[(a\ne b\ne c)\] and all axial angles different from \[90{}^\circ \]?
A) Hexagonal done clear
B) Tetragonal done clear
C) Triclinic done clear
D) Monoclinic done clear
View Answer play_arrowquestion_answer42) Which of the graphs shown below does not represent the relationship between incident light and the electron ejected from metal surface?
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer43) The major product formed in the reaction given below will be:
A) done clear
B) done clear
C) done clear
D) done clear
E) None of these done clear
View Answer play_arrowquestion_answer44) The values of \[{{K}_{p}}/{{K}_{c}}\] for the following reactions at. 300 K are, respectively: (At 300 K, \[RT=24.62\text{ }d{{m}^{3}}\] atm \[mo{{l}^{-1}}\])
\[{{N}_{2}}\left( g \right)+{{O}_{2}}\left( g \right)\rightleftharpoons 2\text{ }NO\left( g \right)\] |
\[{{N}_{2}}{{O}_{4}}(g)\,\,\rightleftharpoons \,\,2NO\,(g)\] |
\[{{N}_{2}}(g)+3{{H}_{2}}(g)\rightleftharpoons 2N{{H}_{3}}(g)\] |
A) 24.62 \[d{{m}^{3}}\] atm \[mo{{l}^{-1}}\], 606.0 \[d{{m}^{6}}\] \[at{{m}^{2}}\]\[mo{{l}^{-2}}\] \[1.65\times {{10}^{-3}}d{{m}^{-}}^{6}at{{m}^{-}}^{2}mo{{l}^{2}}\] done clear
B) \[1,4.1\times {{10}^{-}}^{2}d{{m}^{-}}^{3}\,at{{m}^{-}}^{1}\] mol, 606 \[d{{m}^{6}}\] \[at{{m}^{2}}\,mo{{l}^{-}}^{2}\] done clear
C) \[1,24.62\text{ }d{{m}^{3}}\text{ }atm\text{ }mo{{l}^{-}}^{1}\], \[1.65\times {{10}^{-3}}\] \[d{{m}^{-6}}\]\[at{{m}^{-}}^{2}\,mo{{l}^{2}}\] done clear
D) 1, 24.62 \[d{{m}^{3}}\] atm\[mo{{l}^{-}}^{1}\], 606.0 \[d{{m}^{6}}\] \[at{{m}^{2}}\]\[mo{{l}^{-}}^{2}\] done clear
View Answer play_arrowquestion_answer45) Consider the given plots for a reaction obeying Arrhenius equation \[\left( 0{}^\circ C<T<300{}^\circ C \right)\]: (K and \[{{E}_{a}}\] are rate constant and activation energy, respectively) Choose the correct option:
A) I is right but II is wrong done clear
B) Both I and II are correct done clear
C) Both I and II are wrong done clear
D) I is wrong but II is right done clear
View Answer play_arrowquestion_answer46) If dichloromethane (DCM) and water \[({{H}^{2}}O)\]are used for differential extraction, which one of the following statements is correct?
A) DCM and \[{{H}_{2}}O\] would stay as upper and lower layer respectively in the separating funnel (S.F.) done clear
B) DCM and \[{{H}_{2}}O\] will make turbid/ colloidal mixture done clear
C) DCM and \[{{H}_{2}}O\] would stay as lower and upper layer respectively in the S.F. done clear
D) DCM and \[{{H}_{2}}O\] will be miscible clearly done clear
View Answer play_arrowquestion_answer47) Which, dicarboxylic acid in presence of a dehydrating agent is least reactive to give an anhydride?
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer48) The major product of the following reaction is
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer49) The major product 'X' formed in the following reaction is:
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer50) Two pi and half sigma bonds are present in:
A) \[{{O}^{2}}\] done clear
B) \[{{N}^{+}}_{2}\] done clear
C) \[{{O}^{+}}_{2}\] done clear
D) \[{{N}_{2}}\] done clear
View Answer play_arrowquestion_answer51) The correct structure of product 'P' in the following reactions is: \[Asn-Ser+\underset{excess}{\mathop{{{\left( C{{H}_{3}}CO \right)}_{2}}O}}\,\text{ }\xrightarrow{NE{{t}_{3}}}\text{ }P\]
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer52) Wilkinson catalyst is : \[\left( Et={{C}_{2}}{{H}_{5}} \right)\]
A) \[\left[ {{\left( P{{h}_{3}}P \right)}_{3}}\text{ }RhCl \right]\] done clear
B) \[\left[ {{\left( E{{t}_{3}}P \right)}_{3}}RhCl \right]\] done clear
C) \[\left[ {{\left( E{{t}_{3}}P \right)}_{3}}IrCl \right]\] done clear
D) \[\left[ {{\left( P{{h}_{3}}P \right)}_{3}}IrCl \right]\] done clear
View Answer play_arrowquestion_answer53) The chemical nature of hydrogen peroxide is:
A) Oxidising agent in acidic medium, but not in basic medium done clear
B) Oxidising and reducing agent in both acidic and basic medium done clear
C) Reducing agent in basic medium, but not in acidic medium done clear
D) Oxidising and reducing agent in acidic medium, but not in basic medium. done clear
View Answer play_arrowquestion_answer54) The major product of the following reaction is:
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer55) The effect of lanthanoid contraction in the lanthanoid series of elements by and large means:
A) increase in atomic radii and decrease in ionic radii done clear
B) increase in both atomic and ionic radii done clear
C) decrease in both atomic and ionic radii done clear
D) decrease in atomic radii and increase in ionic radii done clear
View Answer play_arrowquestion_answer56) Water filled in two glasses A and B have BOD values of 10 and 20, respectively. The correct statement regarding them, is:
A) B is more polluted than A done clear
B) A is suitable for drinking, whereas B is not done clear
C) Both A and B are suitable for drinking done clear
D) A is more polluted than B. done clear
View Answer play_arrowquestion_answer57) The decreasing order of ease of alkaline hydrolysis for the following esters in
(I) |
(II) |
(III) |
(IV) |
A) \[III>II>IV>I\] done clear
B) \[IV>II>III>I\] done clear
C) \[III>II>I>IV\] done clear
D) \[II>III>I>IV\] done clear
View Answer play_arrowquestion_answer58) Liquids A and B form an ideal solution in the entire composition range. At 350 K, the vapor pressures of pure A and pure B are \[7\times {{10}^{3}}\]Pa and \[12\times {{10}^{3}}\] Pa, respectively. The composition of the vapor in equilibrium with a solution containing 40 mole percent of A at this temperature is:
A) \[{{x}_{A}}=0.76;\,\,{{x}_{B}}=0.24\] done clear
B) \[{{x}_{A}}=0.28;\,\,{{x}_{B}}=0.72\] done clear
C) \[{{x}_{A}}=0.4;\,\,{{x}_{B}}=0.6\] done clear
D) \[{{x}_{A}}=0.37;\,\,{{x}_{B}}=0.63\] done clear
View Answer play_arrowquestion_answer59) The total number of isomers for a square planar complex \[\left[ M\left( F \right)\left( Cl \right)\left( SCN \right)\left( N{{O}_{2}} \right) \right]\] is:
A) 16 done clear
B) 8 done clear
C) 12 done clear
D) 4 done clear
View Answer play_arrowquestion_answer60) Consider the following reduction processes:
\[Z{{n}^{2}}+2{{e}^{-}}\to Zn\left( s \right);\text{ }E{}^\circ =-\,0.76V\] |
\[C{{a}^{2+}}+2{{e}^{-}}\to Ca\left( s \right);\text{ }E{}^\circ =-\,2.87\,V\] |
\[M{{g}^{2+}}+2{{e}^{-}}\to Mg\left( s \right);\text{ }E{}^\circ =-\,2.36\,V\] |
\[N{{i}^{2}}+2{{e}^{-}}\to Ni\left( s \right);\text{ }E{}^\circ =-\,0.25\,V\] |
A) \[Ca<Mg<Zn<Ni\] done clear
B) \[Ni<Zn<Mg<Ca\] done clear
C) \[Zn<Mg<Ni<Ca\] done clear
D) \[Ca<Zn<Mg<Ni\] done clear
View Answer play_arrowquestion_answer61) In a class of 140 student numbered 1 to 140, all even numbered students opted Mathematics course, those whose number is divisible by 3 opted Physics course and those whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is:
A) 42 done clear
B) 102 done clear
C) 1 done clear
D) 38 done clear
View Answer play_arrowquestion_answer62) Let \[\overrightarrow{a}=2\widehat{i}+{{\lambda }_{1}}\widehat{j}+3\widehat{k},\text{ }\overrightarrow{b}=4\widehat{i}+(3-{{\lambda }_{2}})\widehat{j}+6\widehat{k}\] and \[\overrightarrow{c}=3\widehat{i}+6\widehat{j}+({{\lambda }_{3}}-1)\widehat{k}\] be three vectors such that \[\overrightarrow{b}=2\overrightarrow{a}\] and \[\overrightarrow{a}\] is perpendicular to\[\overrightarrow{c}\]. Then a possible value of \[({{\lambda }_{1}},\,\,{{\lambda }_{2}},\,\,{{\lambda }_{3}})\] is -
A) (1, 5, 1) done clear
B) (1, 3, 1) done clear
C) \[\left( -\frac{1}{2},\,\,4,\,\,0 \right)\] done clear
D) \[\left( \frac{1}{2},\,\,4,\,\,-2 \right)\] done clear
View Answer play_arrowquestion_answer63) Consider the statement: \[''P\left( n \right):{{n}^{2}}-n+41\] is prime?. Then which one of the following is true?
A) P(5) is false but P(3) is true done clear
B) Both P(3) and P(5) are true done clear
C) P(3) is false but P(5) is true done clear
D) Both P(3) and P(5) are false done clear
View Answer play_arrowquestion_answer64) If a circle C passing through the point (4, 0) touches the circle \[{{x}^{2}}+{{y}^{2}}+4x-6y=12\] externally at the point \[\left( 1,\,\,-1 \right)\], then the radius of C is-
A) 5 done clear
B) \[2\sqrt{5}\] done clear
C) 4 done clear
D) \[\sqrt{57}\] done clear
View Answer play_arrowquestion_answer65) If the parabolas \[{{y}^{2}}=4b\left( x-c \right)\text{ }and\text{ }{{y}^{2}}=8\,ax\] have a common normal, then which on of the following is a valid choice for the ordered triad (a, b, c)?
A) (1, 1, 3) done clear
B) (1, 1, 0) done clear
C) \[\left( \frac{1}{2},\,\,2,\,\,0 \right)\] done clear
D) \[\left( \frac{1}{2},\,\,2,\,\,3 \right)\] done clear
View Answer play_arrowquestion_answer66) The plane passing through the point \[\left( 4,\,\,-1,\text{ }2 \right)\] and parallel to the lines \[\frac{x+2}{3}\,\,=\,\frac{y-2}{-1}\,\,=\,\,\frac{z+1}{2}\] and \[\frac{x-2}{1}\,\,=\,\frac{y-3}{2}\,\,=\,\,\frac{z-4}{3}\] also passes through
A) (1, 1, -1) done clear
B) (1, 1, 1) done clear
C) (-1, -1, -I) done clear
D) (-1, -1, 1) done clear
View Answer play_arrowquestion_answer67) Let \[n\ge 2\] be a natural number and \[0<\theta <\frac{\pi }{2}\]Then \[\int{\frac{(si{{n}^{n}}\,\theta \,-\,sin\,\theta ){{\,}^{1/n}}\,\cos \,\theta }{\sin {{\,}^{n+1}}\,\theta }}\,d\theta \] is equal to -(where C is a constant of integration)
A) \[\frac{n}{{{n}^{2}}-1}\,{{\left( 1+\frac{1}{\sin {{\,}^{n-1}}\,\theta } \right)}^{\frac{n+1}{n}}}\,+C\] done clear
B) \[\frac{n}{{{n}^{2}}-1}\,{{\left( 1-\frac{1}{\sin {{\,}^{n+1}}\,\theta } \right)}^{\frac{n+1}{n}}}\,+C\] done clear
C) \[\frac{n}{{{n}^{2}}-1}\,{{\left( 1-\frac{1}{\sin {{\,}^{n-1}}\,\theta } \right)}^{\frac{n+1}{n}}}\,+C\] done clear
D) \[\frac{n}{{{n}^{2}}+1}\,{{\left( 1-\frac{1}{\sin {{\,}^{n-1}}\,\theta } \right)}^{\frac{n+1}{n}}}\,+C\] done clear
View Answer play_arrowquestion_answer68) The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two observations is -
A) 6 : 7 done clear
B) 10 : 3 done clear
C) 4 : 9 done clear
D) 5 : 8 done clear
View Answer play_arrowquestion_answer69) If the system of equations
\[x+y+z=5\] \[x+2y+3z=9\] \[x+3y+\alpha z=\beta \] |
has infinitely many solutions, then \[\beta -\alpha \] equals- |
A) 8 done clear
B) 21 done clear
C) 18 done clear
D) 5 done clear
View Answer play_arrowquestion_answer70) If 5, 5r, \[5{{r}^{2}}\] are the lengths of the sides of a triangle, then r cannot be equal to -
A) \[\frac{7}{4}\] done clear
B) \[\frac{5}{4}\] done clear
C) \[\frac{3}{4}\] done clear
D) \[\frac{3}{2}\] done clear
View Answer play_arrowquestion_answer71) An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in tail then a card from a well- shuffled pack of nine cards numbered 1, 2, 3, ....... 9 is randomly picked and the number on the card is noted. The probability that the noted number is either 7 or 8 is -
A) \[\frac{19}{36}\] done clear
B) \[\frac{15}{72}\] done clear
C) \[\frac{13}{36}\] done clear
D) \[\frac{19}{72}\] done clear
View Answer play_arrowquestion_answer72) Let \[f:R\,\to R\] be a function such that\[f\left( x \right)={{x}^{3}}+{{x}^{2}}f\,\left( 1 \right)+xf\,\left( 2 \right)+f\text{ }\left( 3 \right),\] \[x\in R\]. Then f(2) equals-
A) 30 done clear
B) - 2 done clear
C) - 4 done clear
D) 8 done clear
View Answer play_arrowquestion_answer73) The equation of a tangent to the hyperbola \[4{{x}^{2}}-5{{y}^{2}}=20\] parallel to the line \[x-y=2\] is-
A) \[x-y+9=0\] done clear
B) \[x-y-3=0\] done clear
C) \[x-y+1=0\] done clear
D) \[x-y+7=0\] done clear
View Answer play_arrowquestion_answer74) If \[\frac{dy}{dx}+\frac{3}{{{\cos }^{2}}x}y=\frac{1}{\cos {{\,}^{2}}\,x}\] \[x\in \left( \frac{-\pi }{3},\,\,\frac{\pi }{3} \right)\] and \[y\left( \frac{\pi }{4} \right)\,=\,\frac{4}{3}\] then \[y\left( -\frac{\pi }{4} \right)\,\] equals-
A) \[\frac{1}{3}+{{e}^{6}}\] done clear
B) \[\frac{1}{3}\] done clear
C) \[\frac{1}{3}+{{e}^{3}}\] done clear
D) \[-\frac{4}{3}\] done clear
View Answer play_arrowquestion_answer75) A point P moves on the line\[2x-3y+4=0\]. If Q(1, 4) and R (3, - 2) are fixed points, then the locus of the centroid of \[\Delta \,PQR\] is a line-
A) parallel to y-axis done clear
B) with slope \[\frac{2}{3}\] done clear
C) parallel to x-axis done clear
D) with slope \[\frac{3}{2}\] done clear
View Answer play_arrowquestion_answer76) The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder is-
A) 1356 done clear
B) 1256 done clear
C) 1365 done clear
D) 1465 done clear
View Answer play_arrowquestion_answer77) If \[{{\sum\limits_{i\,=\,1}^{20}{\left( \frac{^{20}{{C}_{i-1}}}{^{20}{{C}_{i}}\,{{+}^{20}}{{C}_{i\,=\,1}}} \right)}}^{3}}\,\,=\,\,\frac{k}{21}\]then k is equal to
A) 100 done clear
B) 200 done clear
C) 50 done clear
D) 400 done clear
View Answer play_arrowquestion_answer78) Consider the quadratic equation
\[(c-5){{x}^{2}}-2cx+(c-4)=0,c\ne 5\]. Let S be the set of all integral values of c for which one root of the equation lies in the integral values of c for which one root of the equation lies in the interval (0, 2) and its other root lies in the interval (2, 3). Then the number of elements in S is |
A) 12 done clear
B) 18 done clear
C) 10 done clear
D) 11 done clear
View Answer play_arrowquestion_answer79) If the area enclosed between the curves \[y=k{{x}^{2}}\] and \[x=k{{y}^{2}},\text{ }\left( k>0 \right)\], is 1 square unit. Then k is-
A) \[\sqrt{3}\] done clear
B) \[\frac{\sqrt{3}}{2}\] done clear
C) \[\frac{2}{\sqrt{3}}\] done clear
D) \[\frac{1}{\sqrt{3}}\] done clear
View Answer play_arrowquestion_answer80) Consider a triangular plot ABC with sides\[AB=7\,m\], \[BC=5\,m\] and\[CA=6\,m\]. A vertical lamp-post at the mid-point D of AC subtends an angle \[30{}^\circ \] at B. The height (in m) of the lamp-post is-
A) \[2\sqrt{21}\] done clear
B) \[\frac{3}{2}\sqrt{21}\] done clear
C) \[7\sqrt{3}\] done clear
D) \[\frac{2}{3}\sqrt{21}\] done clear
View Answer play_arrowquestion_answer81) The shortest distance between the point \[\left( \frac{3}{2},\,\,0 \right)\] and the curve \[y=\sqrt{x},\,\,(x>0)\], is -
A) \[\frac{\sqrt{3}}{2}\] done clear
B) \[\frac{5}{4}\] done clear
C) \[\frac{3}{2}\] done clear
D) \[\frac{\sqrt{5}}{2}\] done clear
View Answer play_arrowquestion_answer82) Let \[I=\int\limits_{a}^{b}{\left( {{x}^{4}}-2{{x}^{2}} \right)dx}\]. If I is minimum then the ordered pair (a, b) is -
A) \[d\in R\] done clear
B) \[\,(0,\,\,\sqrt{2})\] done clear
C) \[(-\,\sqrt{2},\,\,\sqrt{2})\] done clear
D) \[\,(-\sqrt{2},\,\,0)\] done clear
View Answer play_arrowquestion_answer83) For each \[t\in R\], let. [t] be the greatest integer less than or equal to t.
Then \[\underset{x\to 1+}{\mathop{\lim }}\,\,\frac{1-\left| x \right|+\sin \left| 1-x \right|)sin\left( \frac{\pi }{2}[1-x] \right)}{\left| 1-x \right|\,.\,[1-x]\,}\] |
A) equals -1 done clear
B) equals 1 done clear
C) equals 0 done clear
D) does not exist done clear
View Answer play_arrowquestion_answer84) Let \[{{z}_{1}}\,and\text{ }{{z}_{2}}\] be any two non-zero complex numbers such that\[3\text{ }\left| {{z}_{1}} \right|=4\text{ }\left| {{z}_{2}} \right|\]. If \[z=\frac{3{{z}_{1}}}{2{{z}_{2}}}+\frac{2{{z}_{2}}}{3{{z}_{1}}}\] then-
A) \[Im\left( z \right)=0\] done clear
B) \[\left| z \right|=\frac{\sqrt{5}}{2}\] done clear
C) \[\left| z \right|=\frac{1}{2}\frac{\sqrt{17}}{2}\] done clear
D) \[Re\left( z \right)=0\] done clear
E) None of these done clear
View Answer play_arrowquestion_answer85) If the line \[3x+4y-24=0\] intersects the x-axis at the point A and the y-axis at the point B, then the in centre of the triangle OAB, where 0 is the origin, is-
A) (3, 4) done clear
B) (2, 2) done clear
C) (4, 4) done clear
D) (4, 3) done clear
View Answer play_arrowquestion_answer86) The sum of all values of \[\theta \in \left( 0,\,\,\frac{\pi }{2} \right)\] satisfying \[{{\sin }^{2}}2\theta \,\,+\,{{\cos }^{4}}2\theta =\frac{3}{4}\,\] is
A) \[\frac{5\pi }{4}\] done clear
B) \[\frac{\pi }{2}\] done clear
C) \[\pi \] done clear
D) \[\frac{3\,\pi }{8}\] done clear
View Answer play_arrowquestion_answer87) Let A be a point on the line \[\overrightarrow{\text{r}}=\,\,\left( 1-3\mu \right)\widehat{i}+(\mu -1)\widehat{j}+\left( 2+5\mu \right)\widehat{k}\] and \[B(3,\,\,2,\,\,6)\]be a point in the space. Then the value of \[\mu \] for which the vector AB is parallel to the plane \[x-4y+3z=1\] is-
A) \[\frac{1}{8}\] done clear
B) \[\frac{1}{2}\] done clear
C) \[\frac{1}{4}\] done clear
D) \[-\frac{1}{4}\] done clear
View Answer play_arrowquestion_answer88) Let \[d\in R\], and
\[A=\left[ \begin{matrix} -2 & 4+d & (sin\,\theta )-2 \\ 1 & (sin\,\theta )+2 & d \\ 5 & (2\,sin\,\theta )-d & (-sin\,\theta )+2+2d \\ \end{matrix} \right]\] |
\[\theta \in [0,\,\,2\,\pi ]\]. If the minimum value of det is 8, then a value of d is - |
A) -7 done clear
B) \[2(\sqrt{2}+2)\] done clear
C) -5 done clear
D) \[2(\sqrt{2}+1)\] done clear
View Answer play_arrowquestion_answer89) Let \[f(x)\,=\,\,\left\{ \begin{matrix} \max \,\{\left| x \right|,\,{{x}^{2}}\} \\ 8-2\,\left| x \right| \\ \end{matrix} \right.\,\,\,\,\,\begin{matrix} \left| x \right|\,\le \,2 \\ 2<\left| x \right|\,\le \,4 \\ \end{matrix}\]
Let S be the set of points in the interval (- 4, 4) at which f is not differentiable. |
Then S |
A) equals {-2, -1, 1, 2} done clear
B) equals {- 2, - 1, 0, 1, 2} done clear
C) equals {- 2, 2} done clear
D) is an empty set done clear
View Answer play_arrowquestion_answer90) If the third term in the binomial expansion of \[{{\left( 1+{{x}^{{{\log }_{2}}x}} \right)}^{5}}\] equals 2560, then a possible value of x is-
A) \[2\sqrt{2}\] done clear
B) \[4\sqrt{2}\] done clear
C) \[\frac{1}{8}\] done clear
D) \[\frac{1}{4}\] done clear
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