A) \[\left[ 1-\frac{1}{\mu t} \right]\] done clear
B) \[\left[ t-\frac{\mu }{t} \right]\] done clear
C) \[t\left[ 1-\frac{t}{\mu } \right]\] done clear
D) \[[\mu t-1]\] done clear
View Answer play_arrowA) 0.5m done clear
B) 5m done clear
C) 6mm done clear
D) 7cm done clear
View Answer play_arrowA) \[\frac{T}{8}\] done clear
B) \[\frac{T}{6}\] done clear
C) \[\frac{T}{3}\] done clear
D) \[\frac{T}{12}\] done clear
View Answer play_arrowA) \[\frac{\pi }{3}\] done clear
B) \[\frac{2\pi }{3}\] done clear
C) \[\pi \] done clear
D) \[\frac{\pi }{6}\] done clear
View Answer play_arrowA) W done clear
B) 2W done clear
C) \[\sqrt{2}W\] done clear
D) \[{{4}^{1/3}}W\] done clear
View Answer play_arrowA) liquid will form foundation done clear
B) liquid will not rise done clear
C) the meniscus will adjust itself so that the water does not spill done clear
D) None of the above done clear
View Answer play_arrowA) Pascal's law done clear
B) Stoke's law done clear
C) Bernoulli's principle done clear
D) Archimedes' principle done clear
View Answer play_arrowA) \[1\,\,m{{s}^{-2}}\] done clear
B) \[2.5\,\,m{{s}^{-2}}\] done clear
C) \[10\,\,m{{s}^{-2}}\] done clear
D) \[5\,\,m{{s}^{-2}}\] done clear
View Answer play_arrowA) 45 cm done clear
B) 30 cm done clear
C) 40 cm done clear
D) 25 cm done clear
View Answer play_arrowA) 448 Hz done clear
B) 455 Hz done clear
C) 440 Hz done clear
D) 468 Hz done clear
View Answer play_arrowA) becomes half done clear
B) remains the same done clear
C) becomes 6 times done clear
D) becomes 4 times done clear
View Answer play_arrowA) \[40\,\,k\Omega \] done clear
B) \[4\,k\Omega \] done clear
C) \[200\,\,\Omega \] done clear
D) \[400\,\,\Omega \] done clear
View Answer play_arrowA)
a | b | c |
\[[{{L}^{2}}]\] | \[[T]\] | \[[L{{T}^{2}}]\] |
B)
a | b | c |
\[[L{{T}^{2}}]\] | \[[LT]\] | \[[T]\] |
C)
a | b | c |
\[[L{{T}^{-2}}]\] | \[[L]\] | \[[T]\] |
D)
a | b | c |
\[[L]\] | \[[LT]\] | \[[{{T}^{2}}]\] |
A) 80 J done clear
B) -180 J done clear
C) 100 J done clear
D) +180 J done clear
View Answer play_arrowA) 2 : 1 done clear
B) 1 : 2 done clear
C) 4 :1 done clear
D) 1 : 4 done clear
View Answer play_arrowA) \[\frac{1}{3}\,\mu F\] done clear
B) \[2\,\mu F\] done clear
C) \[\frac{3}{2}\,\mu F\] done clear
D) \[3\,\mu F\] done clear
View Answer play_arrowA) v0 is 8j + 4k done clear
B) position vector of location where two particles collide is 16i + 32k done clear
C) Both [a] and [b] are correct done clear
D) it is not possible that B and C collide with each other for any value of v0 done clear
View Answer play_arrowA) Particle is moving along +ve X-axis done clear
B) Particle may move along+ve X-axis done clear
C) Particle may move along -ve X-axis done clear
D) When particle crosses x =-2 m, the speed of particle is \[\sqrt{60}\,m/s\] done clear
View Answer play_arrowA) the tension in the string GH is 6 g done clear
B) the tension in the string GH is zero done clear
C) the tension in string GH is\[\frac{21g}{4}\] done clear
D) the 2 kg block remains in equilibrium 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 we cover one slit in YDSE by an opaque plate then, interference pattern wouldn't be observed on screen. |
Statement II In YDSE, for interference pattern to be observable, the two slits may be of different intensities, but each has to be non-zero. |
A) Statement I is true. Statement II is also true and Statement n is the correct explanation of Statement I. done clear
B) Statement I is true. Statement II is also 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, choose the correct answers from the codes [a], [b], [c] and [d] defined as follows |
Statement I An ideal black body always appears black irrespective of me temperature of the black body. |
Statement II An ideal black body absorbs all the radiations falling on it and no radiant energy has been reflected. |
A) Statement I is true. Statement II is also true and Statement n is the correct explanation of Statement I. done clear
B) Statement I is true. Statement II is also 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_arrowquestion_answer22) Young's modulus for quartz is
A) \[7\times {{10}^{11}}\,N/{{m}^{2}}\] done clear
B) \[8.76\times {{10}^{12}}\,N/{{m}^{2}}\] done clear
C) \[2\times {{10}^{12}}N/{{m}^{2}}\] done clear
D) Information insufficient done clear
View Answer play_arrowA) 71.75 cm done clear
B) 7.175 cm done clear
C) 6.02 cm done clear
D) 0.07 cm done clear
View Answer play_arrowA) \[3.62\times {{10}^{4}}\,Hz\] done clear
B) \[5.74\times {{10}^{4}}Hz\] done clear
C) \[28.7\times {{10}^{4}}Hz\] done clear
D) None of these done clear
View Answer play_arrowA) zero done clear
B) infinite done clear
C) one done clear
D) information insufficient 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 Xenon-139 has a half-life of 41 s, and is produced at a constant rate during the fission of a particular sample of U-235. (Assume that number xenon-139 atom escape d from the sample). Then in this situation, number of nuclei of xenon-139 atom becomes constant after a certain time. |
Statement II Half-life of U-235 to decay to xenon-139 is very near to 41 s. |
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 n is also 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 choose the correct answers from the codes [a], [b], [c] and [d] defined as follows. |
Statement I Systematic errors have same size and sign for all measurements. |
Statement II While computing systematic error in some physical quantity, say X, which AB depends on other physical quantities, say A, B and C, by the expression \[X=\frac{AB}{{{C}^{2}}}\], we won't consider the worst case. |
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 n is also 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: Light having photons energy \[hv\] is incident on a metallic plate having work function \[\phi \] to eject the electrons. |
The most energetic electrons are then allowed to enter in a region of uniform magnetic field B as shown in the figure. |
The electrons are projected in XZ-plane making an angle of\[\theta \] with X-axis and magnetic field is \[\mathbf{B}={{B}_{0}}\,i\] along X-axis. Maximum pitch of the helix described by electron is found to be p. Take mass of electron as m and charge as q. Based on above information, answer the following questions |
A) \[qP{{B}_{0}}=2\pi \,\cos \,\theta \,\sqrt{2\,(hv-\phi )\,m}\] done clear
B) \[qP{{B}_{0}}=2\pi \,\cos \,\theta \,\sqrt{\frac{2\,(hv-\phi )}{m}}\] done clear
C) \[qP{{B}_{0}}=2\pi \,\sqrt{2\,(hv-\phi )\,m}\,\] done clear
D) \[P=\frac{2gm}{q{{B}_{0}}}\times \sqrt{hv-\phi }\] done clear
View Answer play_arrowDirection: Light having photons energy \[hv\] is incident on a metallic plate having work function \[\phi \] to eject the electrons. |
The most energetic electrons are then allowed to enter in a region of uniform magnetic field B as shown in the figure. |
The electrons are projected in XZ-plane making an angle of\[\theta \] with X-axis and magnetic field is \[\mathbf{B}={{B}_{0}}\,i\] along X-axis. Maximum pitch of the helix described by electron is found to be p. Take mass of electron as m and charge as q. Based on above information, answer the following questions |
A) \[-\frac{-\sqrt{2m\,(hv-\phi )}}{q{{B}_{0}}}\sin \,\theta \,\left[ 1-\cos \,\left( \frac{q{{B}_{0}}t}{m} \right) \right]\] done clear
B) \[\frac{\sqrt{2m\,(hv-\phi )}}{q{{B}_{0}}}\sin \,\theta \,\times \sin \,\left[ \frac{q{{B}_{0}}t}{m} \right]\] done clear
C) \[\frac{-\sqrt{2m\,(hv-\phi )}}{q{{B}_{0}}}\sin \,\theta \,\times \sin \,\left[ \frac{q{{B}_{0}}t}{m} \right]\] done clear
D) \[\frac{\sqrt{2m\,(hv-\phi )}}{q{{B}_{0}}}\times \sin \,\left( \frac{q{{B}_{0}}t}{m} \right)\] done clear
View Answer play_arrowDirection: Light having photons energy \[hv\] is incident on a metallic plate having work function \[\phi \] to eject the electrons. |
The most energetic electrons are then allowed to enter in a region of uniform magnetic field B as shown in the figure. |
The electrons are projected in XZ-plane making an angle of\[\theta \] with X-axis and magnetic field is \[\mathbf{B}={{B}_{0}}\,i\] along X-axis. Maximum pitch of the helix described by electron is found to be p. Take mass of electron as m and charge as q. Based on above information, answer the following questions |
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer31) Which of the following carboxylic acids undergoes decarboxylation easily?
A) \[{{C}_{6}}{{H}_{5}}-CO-C{{H}_{2}}-COOH\] done clear
B) \[{{C}_{6}}{{H}_{5}}-CO-COOH\] done clear
C) \[{{C}_{6}}{{H}_{5}}-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{CH}}\,-COOH\] done clear
D) \[{{C}_{6}}{{H}_{5}}-\underset{\begin{smallmatrix} | \\ N{{H}_{2}} \end{smallmatrix}}{\mathop{CH}}\,-COOH\] done clear
View Answer play_arrowA) \[1\times {{10}^{-5}}\] done clear
B) \[2\times {{10}^{-5}}\] done clear
C) \[1\times {{10}^{-5}}\,{{a}^{2}}\] done clear
D) \[1\times {{10}^{-5}}\,\times \,\,{{a}^{-1}}\] done clear
View Answer play_arrowDirection: The dissociation of complex may be expressed as \[{{[M{{L}_{x}}]}^{4+}}\,+xL\] and equilibrium constant of this is known as instability constant which is a measure of stability. The stability of complex depends on EAN of central atom, charge on metalion, basic nature of ligand and chelation. |
A) oxidation of Co done clear
B) reduction of Co done clear
C) dimerization done clear
D) tetramerization done clear
View Answer play_arrowDirection: The dissociation of complex may be expressed as \[{{[M{{L}_{x}}]}^{4+}}\,+xL\] and equilibrium constant of this is known as instability constant which is a measure of stability. The stability of complex depends on EAN of central atom, charge on metalion, basic nature of ligand and chelation. |
A) \[Fe{{(CO)}_{5}}\] done clear
B) \[V{{(CO)}_{6}}\] done clear
C) \[{{K}_{4}}[Fe{{(CN)}_{6}}]\] done clear
D) \[M{{n}_{2}}{{(CO)}_{10}}\] done clear
View Answer play_arrowDirection: The dissociation of complex may be expressed as \[{{[M{{L}_{x}}]}^{4+}}\,+xL\] and equilibrium constant of this is known as instability constant which is a measure of stability. The stability of complex depends on EAN of central atom, charge on metalion, basic nature of ligand and chelation. |
A) \[{{[Cu\,{{(CN)}_{2}}]}^{-}}\,{{K}_{d}}=1\times {{10}^{-16}}\] done clear
B) \[{{[Fe{{(CN)}_{6}}]}^{4-}}{{K}_{d}}=1\times {{10}^{-37}}\] done clear
C) \[{{[Fe{{(CN)}_{6}}]}^{3-}}{{K}_{d}}=1\times {{10}^{-44}}\] done clear
D) \[[Ag{{(CN)}_{2}}^{-}{{K}_{d}}=1\times {{10}^{-20}}\] done clear
View Answer play_arrowquestion_answer36) The compound which does not show paramagnetic is
A) \[[Cu{{(N{{H}_{3}})}_{4}}]C{{l}_{2}}\] done clear
B) \[[Ag{{(N{{H}_{3}})}_{2}}]Cl\] done clear
C) \[NO\] done clear
D) \[N{{O}_{2}}\] done clear
View Answer play_arrowA) \[\frac{2{{E}_{1}}}{{{N}_{0}}},\,\,\frac{2({{E}_{1}}-{{E}_{2}})}{{{N}_{0}}}\] done clear
B) \[\frac{2{{E}_{1}}}{{{N}_{0}}},\,\,\frac{2{{E}_{2}}}{{{N}_{0}}}\] done clear
C) \[\frac{{{E}_{1}}-{{E}_{2}}}{{{N}_{0}}},\,\,\frac{2{{E}_{1}}}{{{N}_{0}}}\] done clear
D) None of these done clear
View Answer play_arrowStatement I Be can form \[{{[Be{{F}_{3}}]}^{-}}\] and \[{{[Be{{F}_{4}}]}^{2-}}\] but Mg cannot. |
Statement II Be due to large charge to size ratio can form stable complex but magnesium cannot. |
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 also 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_arrowA) \[\left( 1-\frac{a}{RTV} \right)\] done clear
B) \[\left( 1-\frac{RTV}{a} \right)\] done clear
C) \[\left( 1+\frac{a}{RTV} \right)\] done clear
D) \[\left( 1+\frac{RTV}{a} \right)\] done clear
View Answer play_arrowA) \[\frac{\Delta H}{nF}\] done clear
B) \[\frac{\Delta G}{nF}\] done clear
C) \[\frac{\Delta S}{nF}\] done clear
D) \[\frac{-\Delta S}{nF}\] done clear
View Answer play_arrowquestion_answer41) Percentage ionization of a weak acid can be calculated by using the formula
A) \[100\sqrt{\frac{{{K}_{a}}}{C}}\] done clear
B) \[\frac{100}{1+{{10}^{(p{{K}_{a}}-pH)}}}\] done clear
C) Both [a] and [b] are correct done clear
D) None of these done clear
View Answer play_arrowA) \[Br{{O}_{4}}\] done clear
B) \[BrO_{3}^{-}\] done clear
C) \[HBrO\] done clear
D) \[B{{r}_{2}}\] done clear
View Answer play_arrowquestion_answer43) If \[{{H}_{2}}{{O}_{2}}\] is ?5. 6 volume?, then
A) it is 1.7% weight by volume done clear
B) it is 1 N done clear
C) Both [a] and [b] done clear
D) None of these done clear
View Answer play_arrowquestion_answer44) Estimation of calcium and magnesium is done by
A) EDTA done clear
B) oxalate done clear
C) phosphate done clear
D) None of these done clear
View Answer play_arrowA) done clear
B) done clear
C) done clear
D) All are correct done clear
View Answer play_arrowA) \[C{{H}_{3}}-C{{H}_{2}}-C\equiv CH\] and \[C{{H}_{2}}=CH-CH=C{{H}_{2}}\] done clear
B) \[C{{H}_{3}}-C\equiv C-C{{H}_{3}}\] and \[C{{H}_{3}}-CH=C=C{{H}_{2}}\] done clear
C) and done clear
D) done clear
View Answer play_arrowA) \[C{{H}_{3}}OH\] done clear
B) \[{{C}_{2}}{{H}_{5}}OH\] done clear
C) \[{{C}_{3}}{{H}_{7}}OH\] done clear
D) All are same done clear
View Answer play_arrowA) 1% done clear
B) 2% done clear
C) 4% done clear
D) 8% done clear
View Answer play_arrow1. Plots AD and BC show that Raoult's law is obeyed for the solution in which B is a solvent and A is the solute and as well as for that in which A is solvent and B is solute. |
2. Plot CD shows that Dalton's law of partial pressure is observed by the binary solution of components A and B. |
3.\[EF+EG+EH\]; and AC and BD corresponds to the vapour pressure of the pure solvents A and B respectively. |
A) 1 and 2 done clear
B) 2 and 3 done clear
C) 1 and 3 done clear
D) 1, 2 and 3 done clear
View Answer play_arrowquestion_answer50) Which, if any, of the following alcohols cannot be prepared from an alkene?
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowStatement I \[Sn\] on heating with dilute nitric acid gives \[Sn{{(N{{O}_{3}})}_{2}},\]\[N{{H}_{4}}N{{O}_{3}}\]and \[{{H}_{2}}\] gas. |
Statement II \[Sn\] although a metal, does not produce Hg gas on reaction with dilute nitric acid. |
A) Statement I is true, Statement II is also true and Statement II is the correct explanation of Statement I. done clear
B) Statement is true, Statement II is also 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_arrowA) 0.00 V done clear
B) + 0.8274 V done clear
C) - 0.8274V done clear
D) can't be said done clear
View Answer play_arrowA) \[0.66\times {{10}^{-9}}\,mol\,{{L}^{-1}}\] done clear
B) \[105\times {{10}^{-5}}\,mo{{l}^{-1}}\,L\] done clear
C) \[2.0\times {{10}^{-4}}\,{{s}^{-1}}\] done clear
D) \[3.0\times {{10}^{5}}\,mo{{l}^{-1}}\,{{s}^{-1}}\] done clear
View Answer play_arrowA) 1 done clear
B) 2 done clear
C) 4 done clear
D) 0 done clear
View Answer play_arrowquestion_answer55) \[{{K}_{2}}[Hg{{l}_{4}}]\] detects the ion/group
A) \[N{{H}_{2}}\] done clear
B) \[NO\] done clear
C) \[NH_{4}^{+}\] done clear
D) \[C{{l}^{-}}\] done clear
View Answer play_arrowquestion_answer56) In the dichromate anion
A) 4Cr?O bonds are equivalent done clear
B) 6Cr?O bonds are equivalent done clear
C) All Cr?O bonds are equivalent done clear
D) All Cr?O bonds are non-equivalent done clear
View Answer play_arrowA) is added to dilute the solution of the dye done clear
B) oxidizes the dye to give the desired colour done clear
C) reduce the dye to give the desire colour done clear
D) acidifies the solution of the dye done clear
View Answer play_arrowquestion_answer58) The reaction of
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowA) 2 done clear
B) 5 done clear
C) 6 done clear
D) 3 done clear
View Answer play_arrowA) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowA) 0 done clear
B) 1 done clear
C) \[\frac{1}{2011}\] done clear
D) can't be determined done clear
View Answer play_arrowA) 1 done clear
B) 2 done clear
C) 3 done clear
D) 2009 done clear
View Answer play_arrowA) 338 done clear
B) 329 done clear
C) 330 done clear
D) 331 done clear
View Answer play_arrowA) \[\frac{15}{286}\] done clear
B) \[\frac{7}{286}\] done clear
C) \[\frac{105}{286}\] done clear
D) \[\frac{35}{286}\] done clear
View Answer play_arrowA) \[\frac{\pi }{3}\,{{e}^{\pi /9}}\] done clear
B) \[\frac{\pi }{9}\,{{e}^{\pi /3}}\] done clear
C) \[\frac{9}{\pi }\,{{e}^{\pi /3}}\] done clear
D) \[\frac{3}{\pi }\,{{e}^{\pi /9}}\] done clear
View Answer play_arrowA) 3 done clear
B) 4 done clear
C) 5 done clear
D) 2 done clear
View Answer play_arrowA) 12 units done clear
B) 13 units done clear
C) \[\sqrt{149}\] units done clear
D) \[\sqrt{49}\] units done clear
View Answer play_arrowA) 4 done clear
B) 3 done clear
C) 2 done clear
D) 1 done clear
View Answer play_arrowA) circle circumscribing the \[\Delta PQR\] passes through the vertex of the parabola. done clear
B) the algebraic sum of slopes of the tangents at P, Q and R vanishes. done clear
C) the algebraic sum of the ordinates of the points P vanishes. done clear
D) circumcentre of \[\Delta PQR\] lies on the axis of the parabola. done clear
View Answer play_arrowA) a circle done clear
B) a parabola done clear
C) a straight line done clear
D) a hyperbola done clear
View Answer play_arrowA) \[\theta =\phi =\psi \] done clear
B) \[\theta =\frac{\pi }{2}\] done clear
C) \[\phi =\psi =\pi \] done clear
D) any one of \[\theta ,\,\,\phi \,\,\psi \] is \[\frac{\pi }{3}\] done clear
View Answer play_arrowA) \[3x+2y=0\] and \[x+3y=0\] done clear
B) \[x=3y\] and \[3x+2y=0\] done clear
C) \[2x-3y=0\] and \[x+3y=0\] done clear
D) \[y-3x=0\] and \[2x-4y=0\] done clear
View Answer play_arrowA) 2 done clear
B) 3 done clear
C) 1 done clear
D) 8 done clear
View Answer play_arrowA) \[a+b=10\] done clear
B) \[|b-a|\,=10\] done clear
C) \[|a\pm b|\,=2009\] done clear
D) \[|b-a|\,=4\] done clear
View Answer play_arrowA) 1 done clear
B) 4 done clear
C) 8 done clear
D) 3 done clear
View Answer play_arrowA) \[a+b=10\] done clear
B) \[a+b=6\] done clear
C) \[|b-a|\,=\,14\] done clear
D) \[|a\pm b|\,=\,2009\] done clear
View Answer play_arrowA) 16 done clear
B) 6 done clear
C) 8 done clear
D) 20 done clear
View Answer play_arrowA) \[k\] done clear
B) \[k+10\] done clear
C) \[k+\sqrt{10}\] done clear
D) \[10k\] done clear
View Answer play_arrowA) 3 done clear
B) 1 done clear
C) 4 done clear
D) 8 done clear
View Answer play_arrowquestion_answer80) \[(p\wedge \sim q)\,\wedge \,(\sim p\wedge q)\] is
A) tautology done clear
B) a contradiction done clear
C) both a tautology and a contradiction done clear
D) neither a tautology nor a contradiction done clear
View Answer play_arrowA) \[\frac{1}{3!}+\frac{1}{(2010)!}\] done clear
B) \[\frac{1}{2}+\frac{1}{(2010)!}\] done clear
C) \[\frac{1}{2}-\frac{1}{(2009)!}\] done clear
D) \[\frac{1}{3!}-\frac{1}{(2009)!}\] done clear
View Answer play_arrowA) \[\left( \frac{1}{2},\,\frac{15}{4} \right)\] done clear
B) \[\left( -\frac{1}{2},\,\frac{15}{4} \right)\] done clear
C) \[\left( \frac{1}{2},-\,\frac{15}{4} \right)\] done clear
D) \[\left( -\frac{1}{2},-\,\frac{15}{2} \right)\] done clear
View Answer play_arrowA) 4 done clear
B) 5 done clear
C) 6 done clear
D) 7 done clear
View Answer play_arrowA) 1 done clear
B) 2 done clear
C) 3 done clear
D) 0 done clear
View Answer play_arrowDirection: A straight line will touch a given conic if there is only one point of intersection of the line and the given conic. If the conic is specified by quadratic equation in\[x\] and \[y,\] then the straight line will touch if the discriminant of the equation obtained by the elimination of one of the variable is zero. Let us consider parabola \[{{y}^{2}}=8x\] and an ellipse\[15{{x}^{2}}+4{{y}^{2}}=60\]. |
A) \[2x-y-8=0\] done clear
B) \[x-2y+8=0\] done clear
C) \[2x-y+8=0\] done clear
D) \[x+2y-8=0\] done clear
View Answer play_arrowDirection: A straight line will touch a given conic if there is only one point of intersection of the line and the given conic. If the conic is specified by quadratic equation in\[x\] and \[y,\] then the straight line will touch if the discriminant of the equation obtained by the elimination of one of the variable is zero. Let us consider parabola \[{{y}^{2}}=8x\] and an ellipse\[15{{x}^{2}}+4{{y}^{2}}=60\]. |
A) \[2x+y-24=0\] done clear
B) \[2x+y-48=0\] done clear
C) \[2x+y+48=0\] done clear
D) \[2x+y+24=0\] 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. |
Consider the statements |
p: Delhi is in India, |
q: Mumbai is not in Italy. |
Statement I The negation of the statement \[p\vee q\] Delhi is not in India and Mumbai is in Italy'. |
Statement II For any two statements p and \[q\,\sim (p\vee q)\,=\,\sim \,p\,\vee \sim q\] |
A) Statement I is true. Statement II is also true and Statement n is the correct explanation of Statement I. done clear
B) Statement I is true. Statement II is also true and Statement n 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. |
Let the vectors PQ,QR, RS, ST, TU and UP represent the sides of a regular hexagon. |
Statement I\[PQ\times \,(RS+ST)\ne 0\] |
Statement II\[PQ\times RS=0\] and \[PQ\times ST\ne \,0\] |
A) Statement I is true. Statement II is also true and Statement n is the correct explanation of Statement I. done clear
B) Statement I is true. Statement II is also true and Statement n 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. |
Let \[f(x)\] be a function such that \[f'(x)\,=\,\prod\limits_{n\,=\,1}^{10}{{{(x-n)}^{n}}}\]. |
Statement I The sum of all values of \[x\]at which \[f(x)\] attains minima is 15. |
Statement II\[f(x)\] has inflectional points at \[x=2,\,4,\,6,\,\,8,\,\,10\] |
A) Statement I is true. Statement II is also true and Statement n is the correct explanation of Statement I. done clear
B) Statement I is true. Statement II is also true and Statement n 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. |
Consider the principal argument of a complex number z is 9. |
Statement I Principal argument of \[{{z}^{2}}\] is \[2\theta \]. |
Statement II\[\arg \,({{z}^{2}})=2\,\arg \,(z)\]. |
A) Statement I is true. Statement II is also true and Statement n is the correct explanation of Statement I. done clear
B) Statement I is true. Statement II is also true and Statement n 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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