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_arrow
A)
0.5m
done
clear
B)
5m
done
clear
C)
6mm
done
clear
D)
7cm
done
clear
View Answer play_arrow
A)
\[\frac{T}{8}\]
done
clear
B)
\[\frac{T}{6}\]
done
clear
C)
\[\frac{T}{3}\]
done
clear
D)
\[\frac{T}{12}\]
done
clear
View Answer play_arrow
A)
\[\frac{\pi }{3}\]
done
clear
B)
\[\frac{2\pi }{3}\]
done
clear
C)
\[\pi \]
done
clear
D)
\[\frac{\pi }{6}\]
done
clear
View Answer play_arrow
A)
W
done
clear
B)
2W
done
clear
C)
\[\sqrt{2}W\]
done
clear
D)
\[{{4}^{1/3}}W\]
done
clear
View Answer play_arrow
A)
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_arrow
A)
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_arrow
A)
\[1\,\,m{{s}^{-2}}\]
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_arrow
A)
45 cm
done
clear
B)
30 cm
done
clear
C)
40 cm
done
clear
D)
25 cm
done
clear
View Answer play_arrow
A)
448 Hz
done
clear
B)
455 Hz
done
clear
C)
440 Hz
done
clear
D)
468 Hz
done
clear
View Answer play_arrow
A)
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_arrow
A)
\[40\,\,k\Omega \]
done
clear
B)
\[4\,k\Omega \]
done
clear
C)
\[200\,\,\Omega \]
done
clear
D)
\[400\,\,\Omega \]
done
clear
View Answer play_arrow
A)
a b c \[[{{L}^{2}}]\] \[[T]\] \[[L{{T}^{2}}]\]
done
clear
B)
a b c \[[L{{T}^{2}}]\] \[[LT]\] \[[T]\]
done
clear
C)
a b c \[[L{{T}^{-2}}]\] \[[L]\] \[[T]\]
done
clear
D)
a b c \[[L]\] \[[LT]\] \[[{{T}^{2}}]\]
done
clear
View Answer play_arrow
A)
80 J
done
clear
B)
-180 J
done
clear
C)
100 J
done
clear
D)
+180 J
done
clear
View Answer play_arrow
A)
2 : 1
done
clear
B)
1 : 2
done
clear
C)
4 :1
done
clear
D)
1 : 4
done
clear
View Answer play_arrow
A)
\[\frac{1}{3}\,\mu F\]
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_arrow
A)
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_arrow
A)
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_arrow
A)
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_arrow
Direction: 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_arrow
Direction: 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_arrow
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_arrow
A)
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_arrow
A)
\[3.62\times {{10}^{4}}\,Hz\]
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_arrow
A)
zero
done
clear
B)
infinite
done
clear
C)
one
done
clear
D)
information insufficient
done
clear
View Answer play_arrow
Direction: 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_arrow
Direction: 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_arrow
Direction: 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
The correct relation between P and \[{{B}_{0}}\] is
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_arrow
Direction: 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
Considering the instant of crossing origin at \[t=0,\] the Z-coordinate of location of electron as a function of time is
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_arrow
Direction: 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
The plot between X-coordinates of location of electron as a function of time for different frequencies v of the incident light, is
A)
done
clear
B)
done
clear
C)
done
clear
D)
done
clear
View Answer play_arrow
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_arrow
A)
\[1\times {{10}^{-5}}\]
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_arrow
Direction: 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.
The EAN of \[Co\] in \[Co{{(CO)}_{4}}\] is 35 and it is less stable. It attains stability by
A)
oxidation of Co
done
clear
B)
reduction of Co
done
clear
C)
dimerization
done
clear
D)
tetramerization
done
clear
View Answer play_arrow
Direction: 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.
Which one of the following does not follow EAN rule?
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_arrow
Direction: 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.
Which complex is most stable where \[{{K}_{d}}\] is un stability constant?
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_arrow
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_arrow
A)
\[\frac{2{{E}_{1}}}{{{N}_{0}}},\,\,\frac{2({{E}_{1}}-{{E}_{2}})}{{{N}_{0}}}\]
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_arrow
Statement 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_arrow
A)
\[\left( 1-\frac{a}{RTV} \right)\]
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_arrow
A)
\[\frac{\Delta H}{nF}\]
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_arrow
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_arrow
Using the following Latimer diagram for bromine,\[pH=0;\,\,Br{{O}_{2}}\xrightarrow{1.82\,V}\,BrO_{3}^{-}\xrightarrow{1.50\,V}\,\] \[HBr{{O}_{2}}\xrightarrow{1.595\,V}\,B{{r}_{2}}\xrightarrow{1.652\,V}B{{r}^{-}}\] The species undergoing dispropotionation is
A)
\[Br{{O}_{4}}\]
done
clear
B)
\[BrO_{3}^{-}\]
done
clear
C)
\[HBrO\]
done
clear
D)
\[B{{r}_{2}}\]
done
clear
View Answer play_arrow
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_arrow
A)
EDTA
done
clear
B)
oxalate
done
clear
C)
phosphate
done
clear
D)
None of these
done
clear
View Answer play_arrow
A)
done
clear
B)
done
clear
C)
done
clear
D)
All are correct
done
clear
View Answer play_arrow
A)
\[C{{H}_{3}}-C{{H}_{2}}-C\equiv CH\] 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_arrow
A)
\[C{{H}_{3}}OH\]
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_arrow
A)
1%
done
clear
B)
2%
done
clear
C)
4%
done
clear
D)
8%
done
clear
View Answer play_arrow
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_arrow
A)
done
clear
B)
done
clear
C)
done
clear
D)
done
clear
View Answer play_arrow
Statement 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_arrow
A)
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_arrow
A)
\[0.66\times {{10}^{-9}}\,mol\,{{L}^{-1}}\]
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_arrow
A)
1
done
clear
B)
2
done
clear
C)
4
done
clear
D)
0
done
clear
View Answer play_arrow
A)
\[N{{H}_{2}}\]
done
clear
B)
\[NO\]
done
clear
C)
\[NH_{4}^{+}\]
done
clear
D)
\[C{{l}^{-}}\]
done
clear
View Answer play_arrow
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_arrow
A)
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_arrow
A)
done
clear
B)
done
clear
C)
done
clear
D)
done
clear
View Answer play_arrow
[Five such products are possible] How many structures of Fare possible?
A)
2
done
clear
B)
5
done
clear
C)
6
done
clear
D)
3
done
clear
View Answer play_arrow
A)
done
clear
B)
done
clear
C)
done
clear
D)
done
clear
View Answer play_arrow
A)
0
done
clear
B)
1
done
clear
C)
\[\frac{1}{2011}\]
done
clear
D)
can't be determined
done
clear
View Answer play_arrow
Let \[{{x}^{2006}}{{y}^{2007}}{{z}^{2008}},\]\[{{x}^{2007}}{{y}^{2008}}{{z}^{2009}},\]\[{{x}^{2008}}{{y}^{2009}}{{z}^{2010}}\] be in AP, where, \[x,\,\,y,\,\,z>0\]. Te least value of \[x+y+z\] is
A)
1
done
clear
B)
2
done
clear
C)
3
done
clear
D)
2009
done
clear
View Answer play_arrow
A)
338
done
clear
B)
329
done
clear
C)
330
done
clear
D)
331
done
clear
View Answer play_arrow
A)
\[\frac{15}{286}\]
done
clear
B)
\[\frac{7}{286}\]
done
clear
C)
\[\frac{105}{286}\]
done
clear
D)
\[\frac{35}{286}\]
done
clear
View Answer play_arrow
A)
\[\frac{\pi }{3}\,{{e}^{\pi /9}}\]
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_arrow
The maximum number of solutions of the equation\[5\,\,\cos \,x+\frac{5}{2\,\cos \,x}-5\,=2\,{{\cos }^{2}}\,x+\frac{1}{2\,{{\cos }^{2}}x},\]\[x\,\in [0,\,2\pi ]\]
A)
3
done
clear
B)
4
done
clear
C)
5
done
clear
D)
2
done
clear
View Answer play_arrow
A)
12 units
done
clear
B)
13 units
done
clear
C)
\[\sqrt{149}\] units
done
clear
D)
\[\sqrt{49}\] units
done
clear
View Answer play_arrow
A)
4
done
clear
B)
3
done
clear
C)
2
done
clear
D)
1
done
clear
View Answer play_arrow
A)
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_arrow
A)
a circle
done
clear
B)
a parabola
done
clear
C)
a straight line
done
clear
D)
a hyperbola
done
clear
View Answer play_arrow
A)
\[\theta =\phi =\psi \]
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_arrow
A)
\[3x+2y=0\] 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_arrow
A)
2
done
clear
B)
3
done
clear
C)
1
done
clear
D)
8
done
clear
View Answer play_arrow
A)
\[a+b=10\]
done
clear
B)
\[|b-a|\,=10\]
done
clear
C)
\[|a\pm b|\,=2009\]
done
clear
D)
\[|b-a|\,=4\]
done
clear
View Answer play_arrow
A)
1
done
clear
B)
4
done
clear
C)
8
done
clear
D)
3
done
clear
View Answer play_arrow
A)
\[a+b=10\]
done
clear
B)
\[a+b=6\]
done
clear
C)
\[|b-a|\,=\,14\]
done
clear
D)
\[|a\pm b|\,=\,2009\]
done
clear
View Answer play_arrow
A)
16
done
clear
B)
6
done
clear
C)
8
done
clear
D)
20
done
clear
View Answer play_arrow
A)
\[k\]
done
clear
B)
\[k+10\]
done
clear
C)
\[k+\sqrt{10}\]
done
clear
D)
\[10k\]
done
clear
View Answer play_arrow
A)
3
done
clear
B)
1
done
clear
C)
4
done
clear
D)
8
done
clear
View Answer play_arrow
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_arrow
A)
\[\frac{1}{3!}+\frac{1}{(2010)!}\]
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_arrow
A)
\[\left( \frac{1}{2},\,\frac{15}{4} \right)\]
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_arrow
A)
4
done
clear
B)
5
done
clear
C)
6
done
clear
D)
7
done
clear
View Answer play_arrow
A)
1
done
clear
B)
2
done
clear
C)
3
done
clear
D)
0
done
clear
View Answer play_arrow
Direction: 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\[15{{x}^{2}}+4{{y}^{2}}=60\].
The equation of a tangent common to both the parabola and the ellipse is
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_arrow
Direction: 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\[15{{x}^{2}}+4{{y}^{2}}=60\].
The equation of the normal at the point of contact of the common tangent which makes an acute angle with the positive direction of \[x-\]axis to the parabola is
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_arrow
Direction: 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_arrow
Direction: 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_arrow
Direction: 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_arrow
Direction: 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
View Answer play_arrow