A) \[V-ER\theta \] done clear
B) \[V-2ER\,\sin \,\frac{\theta }{2}\] done clear
C) \[V+ER\theta \] done clear
D) \[V+2ER\,\sin \,\frac{\theta }{2}\] done clear
View Answer play_arrowA) At \[t=\frac{{{T}_{0}}}{2},\] coordinates of charge are \[\left( \frac{{{P}_{0}}}{2},\,0,\,-2{{R}_{0}} \right)\] done clear
B) At\[t=\frac{3{{T}_{0}}}{2},\] coordinates of charge are \[\left( \frac{3{{P}_{0}}}{2},\,0,\,2{{R}_{0}} \right)\] done clear
C) Two extremes from x-axis are at a distance \[2{{R}_{0}}\] from each other done clear
D) Two extremes from x-axis are at a distance \[4{{R}_{0}}\] from each other done clear
View Answer play_arrowquestion_answer3) Find frictional force on block 30 kg
A) 20 N done clear
B) 30 N done clear
C) 40 N done clear
D) 50 N done clear
View Answer play_arrowA) \[x=f-d,\,\,y=f\,\theta \] done clear
B) \[x=d+f,\,\,y=f\,\theta \] done clear
C) \[x=f-d,\,\,y=-f\theta \] done clear
D) \[x=d-f,\]\[y=-f\,\theta \] done clear
View Answer play_arrowA) 8 A done clear
B) 4 A done clear
C) 5 A done clear
D) 6 A done clear
View Answer play_arrowA) \[\alpha =\beta \] done clear
B) \[\alpha >\beta \] done clear
C) \[\alpha <\beta \] done clear
D) All are possible, depending upon \[\alpha \] done clear
View Answer play_arrowA) \[10\,\mu C\] done clear
B) \[20\,\mu C\] done clear
C) \[25\,\mu C\] done clear
D) \[30\,\mu C\] done clear
View Answer play_arrowA) \[\frac{\pi }{3\omega }\] done clear
B) \[\frac{3\pi }{\omega }\] done clear
C) \[\frac{\pi }{6\omega }\] done clear
D) \[\frac{2\pi }{3\omega }\] done clear
View Answer play_arrowA) \[2.5\,mCi\] done clear
B) \[1\,mCi\] done clear
C) \[3.2\,mCi\] done clear
D) \[3\,mCi\] done clear
View Answer play_arrowA) \[30{}^\circ \] done clear
B) \[45{}^\circ \] done clear
C) \[60{}^\circ \] done clear
D) \[90{}^\circ \] done clear
View Answer play_arrowA) charge on \[2\mu F\] capacitor is approximately\[13\mu C\] done clear
B) potential difference across \[3\mu C\]capacitor is approximately 4.3 V done clear
C) potential difference across \[1\mu F\] capacitor is approximately 11 V done clear
D) All of the above done clear
View Answer play_arrowA) 64 J done clear
B) zero done clear
C) - 64 J done clear
D) None of these done clear
View Answer play_arrowA) \[\left[ 0,\,\left( \frac{2}{\pi } \right)R \right]\] done clear
B) \[\left[ 0,\,\left( \frac{\sqrt{2}}{\pi } \right)R \right]\] done clear
C) \[\left[ 0,\,\left( \frac{2\sqrt{2}}{\pi } \right)R \right]\] done clear
D) \[\left[ 0,\,\left( \frac{4}{\pi } \right)R \right]\] done clear
View Answer play_arrowquestion_answer14) When a body roils without sliding up an inclined plane, the frictional force is
A) directed up the plane done clear
B) directed down the plane done clear
C) zero done clear
D) dependent on its velocity done clear
View Answer play_arrowquestion_answer15) Find \[{{V}_{A}}-{{V}_{B}}\] in steady state
A) 8V done clear
B) 16V done clear
C) 24V done clear
D) Data is insufficient done clear
View Answer play_arrowA) maximum current through inductor equals \[\frac{{{l}_{0}}}{2}\] done clear
B) maximum current through inductor equals \[\frac{{{C}_{1}}{{l}_{0}}}{{{C}_{1}}+{{C}_{2}}}\] done clear
C) maximum charge on \[\frac{{{C}_{1}}{{l}_{0}}\sqrt{L{{C}_{2}}}}{{{C}_{1}}+{{C}_{2}}}\] done clear
D) maximum charge on \[{{C}_{1}}={{C}_{1}}{{l}_{0}}\sqrt{\frac{L}{{{C}_{1}}+{{C}_{2}}}}\] done clear
View Answer play_arrowA) \[\frac{\sqrt{3}}{4}\frac{{{l}^{2}}}{R}\] done clear
B) \[\frac{4}{\sqrt{3}}\frac{{{l}^{2}}}{R}\] done clear
C) \[\frac{\sqrt{3}}{4}\frac{R}{{{l}^{2}}}\] done clear
D) \[\frac{4}{\sqrt{3}}\frac{R}{{{l}^{2}}}\] done clear
View Answer play_arrowA) \[\frac{\pi }{3}\] done clear
B) \[\frac{4\pi }{3}\] done clear
C) \[\frac{3\pi }{3}\] done clear
D) \[\frac{5\pi }{6}\] done clear
View Answer play_arrowA) 12 m/s done clear
B) 6.6 m/s done clear
C) 4.2 m/s done clear
D) 5.9 m/s done clear
View Answer play_arrowA) \[{{T}_{1}}>{{T}_{2}}\] done clear
B) \[{{T}_{1}}<{{T}_{2}}\] done clear
C) \[{{T}_{1}}={{T}_{2}}\] done clear
D) Cannot be predicted done clear
View Answer play_arrowI. Molar heat capacity of the gas is \[-\frac{3R}{2}\] |
II. Molar heat capacity of the gas is \[\frac{3R}{2}\] |
III. Work done is \[-3R{{T}_{0}}\] |
IV. Work done is 3 \[R{{T}_{0}}\] |
A) Statements I and IV are correct done clear
B) Statements I and III are correct done clear
C) Statements II and IV are correct done clear
D) Statements II and III are correct done clear
View Answer play_arrowA) \[\sqrt{\frac{3T}{g(2d-\rho )}}\] done clear
B) \[\sqrt{\frac{3T}{g(d-\rho )}}\] done clear
C) \[\sqrt{\frac{6T}{g(2d-\rho )}}\] done clear
D) \[\sqrt{\frac{6T}{g(d-\rho )}}\] done clear
View Answer play_arrowA) \[\frac{aL}{2g}\] done clear
B) \[\frac{gL}{2a}\] done clear
C) \[\frac{gL}{a}\] done clear
D) \[\frac{aL}{g}\] done clear
View Answer play_arrowA) \[\sqrt{\frac{3}{2}}{{v}_{0}}\] done clear
B) \[\sqrt{\frac{2}{3}}\,{{v}_{0}}\] done clear
C) \[\sqrt{\frac{5}{3}}\,{{v}_{0}}\] done clear
D) None of these done clear
View Answer play_arrowA) \[4.2\times {{10}^{6}}\,J\] done clear
B) \[8.4\times {{10}^{6}}J\] done clear
C) \[16.8\times {{10}^{6}}J\] done clear
D) zero done clear
View Answer play_arrowDirection: A voltage source \[V={{V}_{0}}\,\sin \,(100t)\] is connected to a black box in which there can he either one element out of L, C, R or any two of them connected in series. |
At steady state the variation of current in the circuit and the source voltage are plotted together with time, using an oscilloscope, as shown. |
A) only C done clear
B) L and C done clear
C) L and R done clear
D) L and C done clear
View Answer play_arrowDirection: A voltage source \[V={{V}_{0}}\,\sin \,(100t)\] is connected to a black box in which there can he either one element out of L, C, R or any two of them connected in series. |
At steady state the variation of current in the circuit and the source voltage are plotted together with time, using an oscilloscope, as shown. |
A) \[R=50\,\Omega ,\,\,C=200\,\mu F\] done clear
B) \[R=50\,\Omega ,\,\,L=2\,m\mu \] done clear
C) \[R=400\,\Omega ,\,C=50\,\mu F\] done clear
D) \[R=50\,\Omega ,\,\,L=02H\] done clear
View Answer play_arrowDirection: A voltage source \[V={{V}_{0}}\,\sin \,(100t)\] is connected to a black box in which there can he either one element out of L, C, R or any two of them connected in series. |
At steady state the variation of current in the circuit and the source voltage are plotted together with time, using an oscilloscope, as shown. |
A) increase exponentially with constant \[=4\times {{10}^{-3}}s\] done clear
B) decrease exponentially with time constant \[=1\times {{10}^{-2}}s\] done clear
C) oscillate with angular frequency \[20\,{{s}^{-1}}\] done clear
D) first increase and then decrease done clear
View Answer play_arrowDirection: For the following questions choose the correct answers from the codes [a], [b], [c] and [d] defined as follows. |
Statement I When the separation between the slits in Young's double slit experiment is made equal to wavelength used, fringes disappear. |
Statement II In this case, central fringe will cover the entire field of view. |
A) Statement I is true, Statement II is also true and Statement II is the correct explanation or Statement I. done clear
B) Statement I is true, Statement II is also true but Statement II is not the correct explanation of Statement I. done clear
C) Statement I is true, Statement II is false. done clear
D) Statement I is false, Statement II is true. done clear
View Answer play_arrowDirection: For the following questions choose the correct answers from the codes [a], [b], [c] and [d] defined as follows. |
Statement I If there is no slipping between pulley and string, in an at wood machine the tangential acceleration of a point on the rim of the pulley does not depend upon the radius of the pulley. |
Statement II The linear acceleration of the masses in an at wood machine depends upon the mass of pulley but not on the radius of the pulley. |
A) Statement I is true, Statement II is also true and Statement II is the correct explanation or Statement I. done clear
B) Statement I is true, Statement II is also true but Statement II is not the correct explanation of Statement I. done clear
C) Statement I is true, Statement II is false. done clear
D) Statement I is false, Statement II is true. done clear
View Answer play_arrowA) 1.425 done clear
B) - 0.0843 done clear
C) 0.0843 done clear
D) 1.366 done clear
View Answer play_arrowA) 0.9542 done clear
B) 0.5924 done clear
C) 0.9245 done clear
D) 0.5294 done clear
View Answer play_arrowA) aluminium done clear
B) sodium done clear
C) bromine done clear
D) iodine done clear
View Answer play_arrowquestion_answer34) Consider the following endothermic reaction,
\[F{{e}^{3+}}(aq)+C{{l}^{-}}\,FeC{{l}^{2+}}(aq)\] |
Equilibrium may be disturbed by |
I. Addition of ferric nitrate |
II. Addition of silver nitrate |
III. Change in temperature |
IV. Addition of catalyst |
A) I and III only done clear
B) I, II and III only done clear
C) II and III only done clear
D) I, II, III and IV done clear
View Answer play_arrowA) \[C{{H}_{3}}CHO\] done clear
B) \[C{{H}_{3}}CON{{H}_{2}}\] done clear
C) \[C{{H}_{3}}COOH\] done clear
D) \[C{{H}_{3}}-C{{H}_{2}}-NHOH\] done clear
View Answer play_arrowquestion_answer36) The compounds (X) and (Y) may be separated by dissolving in
A) \[NaOH\] done clear
B) ether done clear
C) \[NaHC{{O}_{3}}\] done clear
D) alcohol done clear
View Answer play_arrowquestion_answer37) Aspartame on hydrolysis forms two amino acids
I.\[{{H}_{2}}N\cdot \underset{\begin{smallmatrix} | \\ C{{H}_{2}} \end{smallmatrix}}{\mathop{C}}\,H\cdot COOH\] |
II. \[{{H}_{2}}N\cdot \overset{\begin{smallmatrix} C{{H}_{2}}{{C}_{6}}{{H}_{5}} \\ | \end{smallmatrix}}{\mathop{C}}\,H\cdot COOH\] |
III. \[{{H}_{2}}N\cdot \underset{\begin{smallmatrix} | \\ C{{H}_{2}}COOH \end{smallmatrix}}{\mathop{C}}\,H\cdot CON{{H}_{2}}\] |
IV.\[{{H}_{2}}N\cdot CHCOHN\cdot \overset{\begin{smallmatrix} C{{H}_{2}}{{C}_{6}}{{H}_{5}} \\ | \end{smallmatrix}}{\mathop{C}}\,H\cdot COOH\] |
A) I, II done clear
B) III, IV done clear
C) I, III done clear
D) II, IV done clear
View Answer play_arrowquestion_answer38) In the chemical reaction, Identify the compound 'B'.
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowA) 110000 and 10538 done clear
B) 36000 and 43333 done clear
C) 140000 and 156000 done clear
D) 228000 and 56000 done clear
View Answer play_arrowA) The pink colour is decolorized by acidified \[FeS{{O}_{4}}\] solution done clear
B) The black residue [c] is same as compound [a] done clear
C) When \[{{O}_{3}}\] gas is passed through the green colour solution, it changes to pink done clear
D) All of the above done clear
View Answer play_arrowquestion_answer41) Actinides have greater tendency to form complexes than lanthanides because
A) the energies of 5f and 6d orbitals are very close done clear
B) actinides are good reducing agents done clear
C) the 5f orbitals are more diffuse than 4f orbital done clear
D) of high charge/size ratio of actinide ions done clear
View Answer play_arrowA) \[\frac{1}{2}\] done clear
B) \[\frac{1}{3}\] done clear
C) \[\frac{3}{5}\] done clear
D) \[\frac{2}{3}\] done clear
View Answer play_arrowA) \[3,\,\,0,\,\,0,\,+\frac{1}{2}\] done clear
B) \[3,\,1,\,\,-1,\,+\frac{1}{2}\] done clear
C) \[21-1-\frac{1}{2}\] done clear
D) \[3,\,1,\,-1,\,-\frac{1}{2}\] done clear
View Answer play_arrowA) \[C{{H}_{3}}C{{H}_{2}}Br<{{(C{{H}_{3}})}_{3}}CCl<\] \[CHCl-C{{H}_{3}}\] done clear
B) \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}l<C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}Br\]\[<C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}Cl\] done clear
C) \[{{C}_{6}}{{H}_{5}}CCl{{(C{{H}_{3}})}_{2}}<{{C}_{6}}{{H}_{5}}CHClC{{H}_{3}}\]\[<{{C}_{6}}{{H}_{5}}C{{H}_{2}}Cl\] done clear
D) \[C{{H}_{2}}=CHCl<C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}Cl<C{{H}_{2}}=\]\[CH-C{{H}_{2}}Cl\] done clear
View Answer play_arrowquestion_answer45) Which of the following has the highest \[p{{K}_{a}}\]?
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowA) reduce the silver bromide grains to metallic silver done clear
B) convert the metallic silver to silver salt done clear
C) remove un decomposed \[AgBr\] as soluble silver thiosulphate complex done clear
D) remove reduced silver done clear
View Answer play_arrowDirection: The bond dissociation energy of a diatomic molecule is also called bond energy. Bond energy is also called, the heat of formation of the bond from the gaseous atoms constituting the bond with reverse sign. |
Example\[H(g)+Cl(g)\xrightarrow{\,}\,H-Cl(g),\]\[\Delta {{H}_{f}}=-431\,\,kJ\,\,mo{{l}^{-1}}\]or bond energy of \[H-Cl=-(\Delta {{H}_{f}})\]\[=-(431)=+431\,kJ\,mo{{l}^{-1}}\] When a compound shows resonance there occurs a fair agreement between the calculated values of heat of formation obtained from bond enthalpies and any other method. However deviation occur incase of compounds having alternate double bonds. |
Example \[\underset{(g)}{\mathop{{{C}_{6}}{{H}_{6}}}}\,\xrightarrow{\,}\underset{(g)}{\mathop{\,6C}}\,+\underset{(g)}{\mathop{6H}}\,\] |
Resonance energy = experimental heat of formation - calculated heat of formation |
A) 309.17 kJ done clear
B) 206 kJ done clear
C) 109.2 kJ done clear
D) 275.8 kJ done clear
View Answer play_arrowDirection: The bond dissociation energy of a diatomic molecule is also called bond energy. Bond energy is also called, the heat of formation of the bond from the gaseous atoms constituting the bond with reverse sign. |
Example\[H(g)+Cl(g)\xrightarrow{\,}\,H-Cl(g),\]\[\Delta {{H}_{f}}=-431\,\,kJ\,\,mo{{l}^{-1}}\]or bond energy of \[H-Cl=-(\Delta {{H}_{f}})\]\[=-(431)=+431\,kJ\,mo{{l}^{-1}}\] When a compound shows resonance there occurs a fair agreement between the calculated values of heat of formation obtained from bond enthalpies and any other method. However deviation occur incase of compounds having alternate double bonds. |
Example \[\underset{(g)}{\mathop{{{C}_{6}}{{H}_{6}}}}\,\xrightarrow{\,}\underset{(g)}{\mathop{\,6C}}\,+\underset{(g)}{\mathop{6H}}\,\] |
Resonance energy = experimental heat of formation - calculated heat of formation |
A) - 132 kJ done clear
B) - 72 kJ done clear
C) + 80 kJ done clear
D) + 162 kJ done clear
View Answer play_arrowDirection: The bond dissociation energy of a diatomic molecule is also called bond energy. Bond energy is also called, the heat of formation of the bond from the gaseous atoms constituting the bond with reverse sign. |
Example\[H(g)+Cl(g)\xrightarrow{\,}\,H-Cl(g),\]\[\Delta {{H}_{f}}=-431\,\,kJ\,\,mo{{l}^{-1}}\]or bond energy of \[H-Cl=-(\Delta {{H}_{f}})\]\[=-(431)=+431\,kJ\,mo{{l}^{-1}}\] When a compound shows resonance there occurs a fair agreement between the calculated values of heat of formation obtained from bond enthalpies and any other method. However deviation occur incase of compounds having alternate double bonds. |
Example \[\underset{(g)}{\mathop{{{C}_{6}}{{H}_{6}}}}\,\xrightarrow{\,}\underset{(g)}{\mathop{\,6C}}\,+\underset{(g)}{\mathop{6H}}\,\] |
Resonance energy = experimental heat of formation - calculated heat of formation |
If (i) \[\Delta H_{f}^{o}\] (benzene) \[=-358.5\,\,kJ\,\,mo{{l}^{-1}}\]. |
(ii) Heat of atomization of graphite \[=716.8\,\,kJ\,mo{{l}^{-1}}\]. |
(iii) Bond energy of \[C-H,\,\,C-C,\,\,C=C\] and \[H-H\]bonds are 490, 340, 620 and\[436.9\,\,kJ\,\,mo{{l}^{-1}}\] respectively. The resonance energy (in \[kJ\,\,mo{{l}^{-1}}\]) of \[{{C}_{6}}{{H}_{6}}\] using Kekule formula is |
A) - 150 done clear
B) - 50 done clear
C) - 250 done clear
D) +150 done clear
View Answer play_arrowA) 83.9 done clear
B) 93.8 done clear
C) 98.3 done clear
D) 89.3 done clear
View Answer play_arrowA) 8 done clear
B) 10 done clear
C) 12 done clear
D) 18 done clear
View Answer play_arrowStatement I Solubility of \[AgCl\] in \[N{{H}_{3}}\,(aq),\] is greater than in pure water. |
Statement II When \[AgCl\] dissolve in\[N{{H}_{3}}\,(aq),\] complex ions formation of \[Ag(N{{H}_{3}})_{2}^{+}\]takes place and solubility equilibrium of \[AgCl\] shifted in forward direction. |
A) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I. done clear
B) Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I. done clear
C) Statement I is true, Statement II is false. done clear
D) Statement I is false, Statement II is true. done clear
View Answer play_arrowquestion_answer53) Increasing value of magnetic moment of the following species is
(i) \[{{[Fe{{(CN)}_{6}}]}^{4-}}\] |
(ii) \[{{[Fe{{(CN)}_{6}}]}^{3-}}\] |
(iii) \[{{[Cr{{(N{{H}_{3}})}_{6}}]}^{3+}}\] |
(iv) \[{{[Ni{{({{H}_{2}}O)}_{6}}]}^{2+}}\] |
A) I < II < III < IV done clear
B) IV < III < II < I done clear
C) II < III < I < IV done clear
D) I < II < IV < III done clear
View Answer play_arrowquestion_answer54) Which of the following is the weakest base in aqueous solution?
A) Diisopropylamine done clear
B) Benzylamine done clear
C) Aniline done clear
D) Cyclohexylamine done clear
View Answer play_arrowquestion_answer55) The reagents/conditions A, B, and C are respectively
A) \[Ba{{(OH)}_{2}},\,KCN\]and\[CHC{{l}_{3}}/NaOH\] heat, \[{{H}_{3}}{{O}^{+}}\] done clear
B) \[{{H}_{2}}O(boil),\,C{{O}_{2}}/KOH\]and\[A{{c}_{2}}O-AcONa,\] heat done clear
C) Steam; \[CHC{{l}_{3}}/NaOH,\] heat, \[{{H}_{3}}{{O}^{+}}\] and \[A{{c}_{2}}O-AcONa,\] heat done clear
D) \[C{{u}_{2}}C{{l}_{2}}/HCl,\,\,NaOH/\]high pressure and \[C{{O}_{2}}/NaOH\] heat, done clear
View Answer play_arrowquestion_answer56) Considering \[NO,\,N{{O}^{+}}\] and \[N{{O}^{-}}\] we say that
A) the three, the one isoelectronic with \[{{N}_{2}}\] alone is diamagnetic done clear
B) among the three, the one isoelectronic with \[{{O}_{2}}\] alone is paramagnetic done clear
C) all the three species are paramagnetic done clear
D) the three overlaps are stronger than \[{{N}_{3}}\] or \[{{O}_{2}}\] done clear
View Answer play_arrowquestion_answer57) Identify the incorrect statement.
A) The oxidation of iodide ions by ozone can be used as a method to estimate ozone. done clear
B) Bromine does not liberate nitrogen gas from ammonia like chlorine. done clear
C) With hot concentrated alkali, chlorine produces the chloride and chlorate. done clear
D) Only fluorine attacks \[Si{{O}_{2}}\]to give \[Si{{F}_{4}}\]. done clear
View Answer play_arrowStatement I A solution of sucrose in water is dextrorotatory but on hydrolysis in presence of acid, the solution of the product becomes laevorotatory. |
Statement II Sucrose on hydrolysis produces an equimolar mixture of D (-) glucose and D(-) fructose. |
A) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I. done clear
B) Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I. done clear
C) Statement I is true, Statement II is false. done clear
D) Statement I is false, Statement II is true. done clear
View Answer play_arrowquestion_answer59) The bleaching action of bleaching powder is due to the formation of
A) \[CaC{{l}_{2}}\] done clear
B) \[CaS{{O}_{4}}\] done clear
C) \[HClO\] done clear
D) \[Ca{{(Cl{{O}_{3}})}_{2}}\] done clear
View Answer play_arrowA) 20 done clear
B) 30 done clear
C) 40 done clear
D) 50 done clear
View Answer play_arrowA) 0 done clear
B) 2 done clear
C) 4 done clear
D) 6 done clear
View Answer play_arrowquestion_answer62) The propositions \[(p\Rightarrow \sim p)\,\wedge \,(\sim p\Rightarrow p)\] is
A) tautology and contradiction done clear
B) neither tautology nor contradiction done clear
C) contradiction done clear
D) tautology done clear
View Answer play_arrowA) \[np\] done clear
B) \[nq\] done clear
C) \[n(p+q)\] done clear
D) None of these done clear
View Answer play_arrowA) 0 done clear
B) 1 done clear
C) \[\tan \,\,10-10\] done clear
D) \[\infty \] done clear
View Answer play_arrowA) \[\left\{ \frac{\pi }{2},\,\frac{3\pi }{4} \right\}\] done clear
B) \[\left\{ \frac{3\pi }{4},\,\frac{7\pi }{4} \right\}\] done clear
C) \[\left\{ \frac{2\pi }{3},\,\frac{5\pi }{3} \right\}\] done clear
D) \[\left\{ \frac{5\pi }{4},\,\frac{7\pi }{3} \right\}\] done clear
View Answer play_arrowA) -2 done clear
B) -1 done clear
C) 0 done clear
D) 1 done clear
View Answer play_arrowA) \[t=0\] done clear
B) \[t=\infty \] done clear
C) \[t=\frac{1}{\sqrt{3}}\] done clear
D) \[t=\frac{-1}{\sqrt{3}}\] done clear
View Answer play_arrowA) \[\left( \frac{-1}{2},\,0 \right)\] done clear
B) \[\left( \frac{-1}{2},\,2 \right)\] done clear
C) \[\left( \frac{-1}{2},\,-2 \right]\] done clear
D) \[\left( \frac{1}{2},\,\infty \right)\] done clear
View Answer play_arrowA) \[f(x)\]has local maxima at \[x=1\] done clear
B) \[f(x)\]has local minima at \[x=1\] done clear
C) \[f(x)\]doesn't have any local extrema at \[x=1\] done clear
D) \[f(x)\]has global minima at \[x=1\] done clear
View Answer play_arrowA) \[{{\log }^{r+1}}(x)+C\] done clear
B) \[\frac{{{\log }^{(r+1)}}(x)}{r+1}+C\] done clear
C) \[{{\log }^{r}}(x)+C\] done clear
D) None of these done clear
View Answer play_arrowA) 0 done clear
B) 2/9 done clear
C) 1/3 done clear
D) 2/3 done clear
View Answer play_arrowA) \[\frac{-\pi }{4}\] done clear
B) \[\frac{\pi }{4}\] done clear
C) \[\frac{+\pi }{2}\] done clear
D) \[\frac{-3\pi }{4}\] done clear
View Answer play_arrowA) \[2\pi \]sq units done clear
B) \[3\pi \]sq units done clear
C) \[4\pi \]sq units done clear
D) \[5\pi \]sq units done clear
View Answer play_arrowA) a = 1, b = 2 done clear
B) a = 1, b = 1 done clear
C) a = 2, b = 1 done clear
D) a = 2, b = 2 done clear
View Answer play_arrowA) 6 done clear
B) 5 done clear
C) 4 done clear
D) 11 done clear
View Answer play_arrowquestion_answer76) The equations of the circles which touch both the axes and the line \[x=a\] are
A) \[{{x}^{2}}+{{y}^{2}}\pm ax\pm ay+\frac{{{a}^{2}}}{4}=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}+ax\pm ay+\frac{{{a}^{2}}}{4}=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-ax\pm ay+\frac{{{a}^{2}}}{4}=0\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer77) Which of the following line is tangent to the curve, \[y={{x}^{2}}-x\]
A) \[x-y=0\] done clear
B) \[x+y=0\] done clear
C) \[x-y=2\] done clear
D) \[x+y=1\] done clear
View Answer play_arrowA) 0 done clear
B) 1 done clear
C) 2 done clear
D) 4 done clear
View Answer play_arrowA) \[(1,\,\,-3)\] done clear
B) \[(2,\,\,2)\] done clear
C) \[(-2,\,\,4)\] done clear
D) \[(1,\,\,2)\] done clear
View Answer play_arrowA) \[\sqrt{19}\] done clear
B) \[\frac{1}{2}\sqrt{19}\] done clear
C) \[\frac{1}{2}\sqrt{38}\] done clear
D) \[\frac{1}{2}\sqrt{57}\] done clear
View Answer play_arrowA) 1 done clear
B) \[1+{{\sin }^{2}}1\] done clear
C) \[1+{{\cos }^{2}}1\] done clear
D) None of these done clear
View Answer play_arrowA) \[\frac{-\pi }{2},\,0\] done clear
B) \[\frac{-\pi }{2},\,0\,\frac{\pi }{2}\] done clear
C) \[\frac{\pi }{2},\,0\] done clear
D) \[0,\frac{\pi }{2},\,\frac{\pi }{2}\] done clear
View Answer play_arrowA) 0 done clear
B) - 1 done clear
C) - 2 done clear
D) - 3 done clear
View Answer play_arrowA) \[\Pi \,\,\tan \,\,A\] done clear
B) \[\Pi \,\,\cot \,\,A\] done clear
C) \[\Sigma \,{{\tan }^{2}}A\] done clear
D) \[\Sigma \,{{\cot }^{2}}A\] done clear
View Answer play_arrowDirection: We have, | |
\[x<0\] | \[x\ge 0\] |
\[\frac{-\pi }{2}\le {{\sin }^{-1}}x<0\] | \[0\le \,{{\sin }^{-1}}x\le \frac{\pi }{2}\] |
\[\frac{\pi }{2}<{{\cos }^{-1}}x\le \pi \] | \[0\le {{\cos }^{-1}}x\le \frac{\pi }{2}\] |
Then, |
A) \[\frac{8\pi }{3}\] done clear
B) \[\frac{4\pi }{3}\] done clear
C) \[\frac{2\pi }{3}\] done clear
D) \[\frac{\pi }{3}\] done clear
View Answer play_arrowDirection: We have, | |
\[x<0\] | \[x\ge 0\] |
\[\frac{-\pi }{2}\le {{\sin }^{-1}}x<0\] | \[0\le \,{{\sin }^{-1}}x\le \frac{\pi }{2}\] |
\[\frac{\pi }{2}<{{\cos }^{-1}}x\le \pi \] | \[0\le {{\cos }^{-1}}x\le \frac{\pi }{2}\] |
Then, |
A) 0 done clear
B) \[2\pi -10\] done clear
C) \[-\pi \] done clear
D) \[3\pi -10\] done clear
View Answer play_arrowDirection: For the following questions, chose the correct answer from the codes [a], [b] [c] and [d] defined as follows. |
Let there are three points P, Q and R having position vectors a, b and c, respectively. |
Statement I If \[2a+3b-5c=0\], then points P, Q and R must be collinear. |
Statement II For three points A, B and C; \[AB=\lambda AC,\] then the points A, B and C must be collinear. |
A) Statement I is true, Statement II is also true and Statement II is the correct explanation of Statement I. done clear
B) Statement I is true, Statement II is true and Statement II is not the correct explanation of Statement I. done clear
C) Statement I is true, Statement II is false. done clear
D) Statement I is false, Statement II is true. done clear
View Answer play_arrowDirection: For the following questions, chose the correct answer from the codes [a], [b] [c] and [d] defined as follows. |
Using the identity \[{{\sin }^{-1}}(\sin \,x)\,=x,\,\frac{\pi }{2}\le x\le \frac{\pi }{2}\]. |
Statement I\[{{\sin }^{-1}}(\sin \,2)=2\] |
Statement II The principal value of \[{{\sin }^{-1}}\,(\sin \,x)=x\] |
A) Statement I is true, Statement II is also true and Statement II is the correct explanation of Statement I. done clear
B) Statement I is true, Statement II is true and Statement II is not the correct explanation of Statement I. done clear
C) Statement I is true, Statement II is false. done clear
D) Statement I is false, Statement II is true. done clear
View Answer play_arrowDirection: For the following questions, chose the correct answer from the codes [a], [b] [c] and [d] defined as follows. |
Let us define a two events A and B such that \[0<P(A),\,P(B)<1\]. |
Statement I The conditional probability relation between A and B is \[P\left( \frac{A}{B} \right)+P\left( \frac{\overline{A}}{\overline{B}} \right)=\frac{3}{2}\] |
Statement II If the event B is already occurred, then \[P\left( \frac{A}{B} \right)=\frac{P(A\cap B)}{P(B)}\]and\[P(\overline{B})=P(A\cap B)+P(\overline{A}\cap \overline{B})\]. |
A) Statement I is true, Statement II is also true and Statement II is the correct explanation of Statement I. done clear
B) Statement I is true, Statement II is true and Statement II is not the correct explanation of Statement I. done clear
C) Statement I is true, Statement II is false. done clear
D) Statement I is false, Statement II is true. done clear
View Answer play_arrowDirection: For the following questions, chose the correct answer from the codes [a], [b] [c] and [d] defined as follows. |
Statement I The function \[f(x)=x\,\sin \,x\] and \[f'(x)=x\,\cos \,x+\sin \,x\] are both non-periodic. |
Statement II The derivative of differentiable non-periodic function is not be periodic function. |
A) Statement I is true, Statement II is also true and Statement II is the correct explanation of Statement I. done clear
B) Statement I is true, Statement II is true and Statement II is not the correct explanation of Statement I. done clear
C) Statement I is true, Statement II is false. done clear
D) Statement I is false, Statement II is true. done clear
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