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question_answer1) Matrix A is such that\[T\propto \frac{1}{V}\], where is the identity matrix. Then, for\[\text{6}\times \text{1}{{0}^{-\text{7}}}\text{A}-{{\text{m}}^{\text{2}}}\],\[{{A}^{n}}\] is equal to
A)
\[\text{5 g}/\text{c}{{\text{m}}^{\text{3}}}\]
done
clear
B)
\[nA-l\]
done
clear
C)
\[\text{1}.\text{2}\times \text{1}{{0}^{-\text{7}}}\]
done
clear
D)
\[\text{3}\times \text{1}{{0}^{-\text{6}}}\]
done
clear
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question_answer2) The number of solutions of the system of equations \[CaC{{l}_{2}}\],\[\text{MgS}{{\text{O}}_{\text{4}}}\] and\[\text{MgS}{{\text{O}}_{\text{4}}}\] is
A)
zero
done
clear
B)
one
done
clear
C)
two
done
clear
D)
infinite
done
clear
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question_answer3) Let\[CaC{{l}_{2}}\] be a function defined by \[x+3y-11=0\], where [ ] denotes the greatest integer function. Then, \[P({{x}_{1}},{{y}_{1}})\]is equal to
A)
\[Q\left( \text{4},-\text{3} \right)\]
done
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B)
\[\therefore \]
done
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C)
\[PQ\]
done
clear
D)
\[\frac{1}{x+\left[ \frac{\pi }{2} \right]}\]
done
clear
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question_answer4) Let \[y=x\] be a function defined by \[\therefore \]The\[\frac{{{x}_{1}}+4}{2}=\frac{{{y}_{1}}-3}{2}\]is
A)
one-one onto
done
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B)
one-one but not onto
done
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C)
onto but not one-one
done
clear
D)
None of these
done
clear
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question_answer5) If the conjugate of \[\Rightarrow \]be \[{{x}_{1}}-{{y}_{1}}=-7\],then
A)
\[PQ=\frac{-3-{{y}_{1}}}{4-{{x}_{1}}}\]
done
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B)
\[y=x\]
done
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C)
\[\because \]
done
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D)
\[PQ\]
done
clear
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question_answer6) In the argand plane, the complex number \[y=x\] is turned in the clockwise sense through 180° and stretched three times. The complex number represented by the new number is
A)
\[\therefore \]
done
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B)
\[\left( \frac{-3-{{y}_{1}}}{4-{{x}_{1}}} \right)(1)=-1\]
done
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C)
\[\Rightarrow \]
done
clear
D)
\[{{y}_{1}}+{{x}_{1}}=1\]
done
clear
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question_answer7) If the sum of roots of equation \[{{x}_{1}}=-3\,\,\,and\,\,\,{{y}_{1}}=4\] is equal to sum of squares of their reciprocals, then \[\underset{x\to \infty }{\mathop{\lim }}\,{{\left( \frac{x+1}{x+2} \right)}^{2x+1}}=\underset{x\to \infty }{\mathop{\lim }}\,{{\left( 1-\frac{1}{x+2} \right)}^{2x+1}}\]and \[=\underset{x\to \infty }{\mathop{\lim }}\,{{\left[ {{\left( 1-\frac{1}{x+2} \right)}^{x+2}} \right]}^{\frac{2x+1}{x+2}}}\]are in
A)
GP
done
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B)
HP
done
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C)
AP
done
clear
D)
None of these
done
clear
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question_answer8) If the roots of the equation \[=\underset{x\to \infty }{\mathop{\lim }}\,\frac{2+1/x}{1+2/x}={{e}^{-2}}\] are real and less than 3,then
A)
\[[-1,\infty )-\{0\}\]
done
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B)
\[\text{x}=0\]
done
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C)
\[\therefore \]
done
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D)
\[Rf'(0)=\underset{h\to 0}{\mathop{\lim }}\,\frac{f(0+h)-f(0)}{h}\]
done
clear
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question_answer9) If \[=\underset{h\to 0}{\mathop{\lim }}\,\frac{\sqrt{h+1}-1}{{{h}^{3/2}}}\times \frac{\sqrt{h+1}+1}{\sqrt{h+1}+1}\], y and z are in HP, then the value of expression \[=\underset{h\to 0}{\mathop{\lim }}\,\frac{h}{{{h}^{3/2}}(\sqrt{h+1}+1)}\] will be
A)
\[=\underset{h\to 0}{\mathop{\lim }}\,\frac{h}{\sqrt{h}(\sqrt{h+1}+1)}\]
done
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B)
\[=\frac{1}{0(\sqrt{0+1}+1)}=\frac{1}{0}=\infty \]
done
clear
C)
\[\underset{x\to 0}{\mathop{\lim }}\,\frac{\cos (\sin x)-1}{{{x}^{2}}}\]
done
clear
D)
\[\mu \]
done
clear
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question_answer10) The term independent of. r in the expansion of \[W\]is
A)
\[\frac{4W}{3}\]
done
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B)
\[\frac{5W}{2}\]
done
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C)
\[\frac{\pi }{2}\]
done
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D)
None of these
done
clear
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question_answer11) The largest term in the expansion of\[\sigma =\text{5}.\text{67}\times \text{1}{{0}^{-\text{8}}}\text{W}-{{\text{m}}^{\text{2}}}{{\text{K}}^{\text{-4}}}\], where \[y=5\sin \frac{\pi x}{3}\cos 40\pi t\], is
A)
5th
done
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B)
3rd
done
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C)
7th
done
clear
D)
6th
done
clear
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question_answer12) \[t\]is equal to
A)
0
done
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B)
\[{{(Kg)}^{1/2}}\]
done
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C)
\[{{(Kg)}^{-1/2}}\]
done
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D)
\[{{(Kg)}^{2}}\]
done
clear
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question_answer13) If A and B are square matrices of order 3 such that \[{{(Kg)}^{-2}}\]and\[\frac{pV}{nT}\], then \[\frac{pV}{nT}\frac{pV}{nT}\upsilon ersus\] is equal to
A)
-9
done
clear
B)
-81
done
clear
C)
-27
done
clear
D)
81
done
clear
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question_answer14) If\[{{T}_{1}}>{{T}_{2}}\] , then r , is equal to
A)
3
done
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B)
4
done
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C)
8
done
clear
D)
6
done
clear
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question_answer15) The number of ways in which \[\frac{pV}{nT}\] students can be distributed equal among n sections, is
A)
\[4\times {{10}^{3}}A{{m}^{-1}}\]
done
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B)
\[\text{1}{{0}^{-\text{2}}}\]
done
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C)
\[\text{1}{{0}^{-3}}\]
done
clear
D)
\[1\mu V\]
done
clear
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question_answer16) The origin is shifted to (1, 2). The equation \[\text{1}.\text{96}\times \text{1}{{0}^{-\text{8}}}\text{ m}/\text{s}\] changes to \[\text{2}.\text{12}\times \text{1}{{0}^{\text{8}}}\text{ m}/\text{s}\] Then, \[\text{3}.\text{18}\times \text{1}{{0}^{8}}m/s\] is equal to
A)
1
done
clear
B)
2
done
clear
C)
-2
done
clear
D)
-1
done
clear
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question_answer17) Given points are A (0,4) and\[\text{3}.\text{33}\times {{10}^{\text{8}}}\text{ m}/\text{s}\]. Then, locus of \[\theta =\text{45}{}^\circ \] such that \[\frac{1}{3}M{{L}^{2}}\]is
A)
\[\frac{3}{2}M{{L}^{2}}\]
done
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B)
\[\frac{3}{4}M{{L}^{2}}\]
done
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C)
\[M{{L}^{2}}\]
done
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D)
None of these
done
clear
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question_answer18) The equation of straight line perpendicular to a line \[{{R}_{1}}\] and passes through (5, 2) is
A)
\[{{R}_{2}}\]
done
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B)
\[{{Q}_{1}}\]
done
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C)
\[{{Q}_{2}}\]
done
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D)
None of these
done
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question_answer19) The image of the point (4, -3) with respect to the line \[{{Q}_{1}}{{R}_{2}}\ne {{Q}_{2}}{{R}_{1}}\] is
A)
\[(-4,-3)\]
done
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B)
\[(3,4)\]
done
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C)
\[(-4,\text{ }3)\]
done
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D)
\[(-3,\text{ }4)\]
done
clear
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question_answer20) \[{{Q}_{1}}{{R}_{2}}={{Q}_{2}}{{R}_{1}}\] is equal to
A)
\[s=\frac{{{t}^{2}}}{4}\]
done
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B)
e
done
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C)
\[T\propto V\]
done
clear
D)
None of these
done
clear
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question_answer21) The set of points of differentiability of the function \[T\propto {{V}^{2}}\] is
A)
R
done
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B)
\[T\propto \frac{1}{{{V}^{2}}}\]
done
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C)
\[T\propto \frac{1}{V}\]
done
clear
D)
\[\text{6}\times \text{1}{{0}^{-\text{7}}}\text{A}-{{\text{m}}^{\text{2}}}\]
done
clear
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question_answer22) \[\text{5 g}/\text{c}{{\text{m}}^{\text{3}}}\]is equal to
A)
1
done
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B)
\[\text{8}\text{.3}\times \text{1}{{0}^{\text{6}}}\]
done
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C)
\[\text{1}.\text{2}\times \text{1}{{0}^{-\text{7}}}\]
done
clear
D)
\[\text{3}\times \text{1}{{0}^{-\text{6}}}\]
done
clear
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question_answer23) Let \[CaC{{l}_{2}}\] and \[\text{MgS}{{\text{O}}_{\text{4}}}\]where \[CaC{{l}_{2}}\]is continuous. Then, \[CaC{{l}_{2}}\]is equal to
A)
\[f(x)g(0)\]
done
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B)
\[\text{MgS}{{\text{O}}_{\text{4}}}\]
done
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C)
\[\upsilon /\text{1}0\]
done
clear
D)
\[f\]
done
clear
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question_answer24) The equation of a tangent parallel to\[1.11f\]drawn to\[1.22f\]is
A)
\[f\]
done
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B)
\[1.27f\]
done
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C)
\[\text{1}.0\text{1}\times \text{1}{{0}^{\text{5}}}\text{ N}/{{\text{m}}^{\text{2}}}\]
done
clear
D)
None of these
done
clear
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question_answer25) The lengths of the axes of the conic \[\text{9}.\text{13}\times \text{1}{{0}^{\text{4}}}\text{ N}/{{\text{m}}^{\text{2}}}\] are
A)
\[\text{9}.\text{13}\times \text{1}{{0}^{\text{3}}}\text{N}/{{\text{m}}^{\text{2}}}\]
done
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B)
\[\text{18}.\text{26 N}/{{\text{m}}^{\text{2}}}\]
done
clear
C)
\[\text{2}.\text{25}\times \text{1}{{0}^{\text{3}}}\text{min}\]
done
clear
D)
3,2
done
clear
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question_answer26) If a chord which is normal to the parabola at one end, subtends a right angle at the vertex, then angle to the axis is
A)
\[\text{3}.\text{97}\times \text{1}{{0}^{\text{3}}}\text{min}\]
done
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B)
0
done
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C)
\[9.13\times {{10}^{3}}N/{{m}^{2}}\]
done
clear
D)
\[\text{5}.\text{25}\times \text{1}{{0}^{\text{3}}}\text{min}\]
done
clear
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question_answer27) Two cards are drawn without replacement from a well-shuffled pack. The probability that one of them is an ace of heart, is
A)
\[\left[ \text{FL}{{\text{T}}^{-\text{2}}} \right]\]
done
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B)
\[\left[ \text{F}{{\text{L}}^{\text{2}}}{{T}^{-\text{2}}} \right]\]
done
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C)
\[\left[ \text{F}{{\text{L}}^{-\text{1}}}{{\text{T}}^{\text{2}}} \right]\]
done
clear
D)
None of these
done
clear
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question_answer28) If\[\left[ {{\text{F}}^{2}}\text{L}{{\text{T}}^{\text{-2}}} \right]\]and \[-\text{273}.\text{15}{}^\circ \text{F}\]then \[-\text{453}.\text{15}{}^\circ \text{F}\] is equal to
A)
\[-\text{459}.\text{67}{}^\circ \text{F}\]
done
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B)
\[-\text{491}.\text{67}{}^\circ \text{F}\]
done
clear
C)
\[\text{52}00\text{{ }\!\!\mathrm{\AA}\!\!\text{ }}\]
done
clear
D)
\[\text{Vc}=\text{1}.\text{5V}\]
done
clear
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question_answer29) The value of\[[a-b\,b-c\,c-a]\] is
A)
0
done
clear
B)
1
done
clear
C)
2
done
clear
D)
3
done
clear
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question_answer30) Let \[\text{15}0\text{ }\mu \text{A}\] and \[\text{5 mA}\]be unit vectors at an angle \[\text{10 mA}\] \[\text{ }\!\!\beta\!\!\text{ }\] from each other. Then, \[\left( \frac{1}{V(volume)} \right)\], if
A)
\[\frac{3}{4}\text{m}/\text{s}\]
done
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B)
\[\frac{1}{3}\text{m}/\text{s}\]
done
clear
C)
\[\frac{3}{2}\text{m}/\text{s}\]
done
clear
D)
\[\frac{2}{3}\text{m}/\text{s}\]
done
clear
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question_answer31) The angle between the planes \[{{\lambda }_{0}},\]and \[\frac{25}{16}{{\lambda }_{0}}\] is
A)
\[\frac{27}{20}{{\lambda }_{0}}\]
done
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B)
\[\frac{20}{27}{{\lambda }_{0}}\]
done
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C)
\[\frac{16}{25}{{\lambda }_{0}}\]
done
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D)
\[3\Omega \]
done
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question_answer32) The equation of the plane which bisects the line joining (2, 3, 4) and (6, 7, 8), is
A)
\[4\Omega \]
done
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B)
\[4.5\Omega \]
done
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C)
\[5\Omega \]
done
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D)
\[\frac{\sqrt{3}}{1}\]
done
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question_answer33) The point on the line \[\frac{(\sqrt{3}+1)}{(\sqrt{3}-1)}\]at a distance of 6 from the point (2, -3, -5) is
A)
(3,-5,-3)
done
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B)
(4,-7.-9)
done
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C)
(0,2,-1)
done
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D)
(-3,5,3)
done
clear
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question_answer34) The maximum value of \[\frac{(\sqrt{3}+1)}{1}\]is
A)
\[\frac{4}{3}\]
done
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B)
\[4\mu F\]
done
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C)
\[10\mu F\]
done
clear
D)
\[8\mu F\]
done
clear
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question_answer35) If \[120\mu F\]then the value of \[\omega \] is
A)
1
done
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B)
2
done
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C)
0
done
clear
D)
\[R/2\]
done
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question_answer36) The number of solutions of the equation \[\frac{4\omega }{5}\] in \[\frac{2\omega }{5}\]is
A)
zero
done
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B)
one
done
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C)
two
done
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D)
three
done
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question_answer37) If in a \[\frac{3\omega }{5}\]\[\frac{2\omega }{3}\], then \[\mu =\frac{3}{2}\] is equal to
A)
\[30{}^\circ \]
done
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B)
\[60{}^\circ \]
done
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C)
\[90{}^\circ \]
done
clear
D)
None of these
done
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question_answer38) In \[\mu =\frac{4}{3}\] then a, b and care in
A)
AP
done
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B)
GP
done
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C)
HP
done
clear
D)
None of these
done
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question_answer39) \[{{\sin }^{-1}}\left( \frac{9}{8} \right)\] is equal to
A)
\[{{\cos }^{-1}}\left( \frac{x-4}{5} \right)+C\]
done
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B)
\[si{{n}^{-1}}\left( \frac{x-4}{5} \right)+C\]
done
clear
C)
\[si{{n}^{-1}}\left( \frac{5}{x-4} \right)+C\]
done
clear
D)
None of these
done
clear
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question_answer40) \[\beta =0.\text{1}\]is equal to
A)
\[\frac{{{x}^{2}}}{2}+C\]
done
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B)
\[-\frac{{{x}^{2}}}{2}+C\]
done
clear
C)
\[x|x|+C\]
done
clear
D)
\[\frac{x|x|}{2}+C\]
done
clear
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question_answer41) \[\text{2}\times \text{1}{{0}^{\text{7}}}\text{m}/\text{s}\]is equal to
A)
\[\text{2}\times \text{1}{{0}^{-2}}T\]
done
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B)
\[\left( \frac{e}{m} \right)\]
done
clear
C)
\[\text{1}.\text{76}\times \text{1}{{0}^{\text{11}}}\text{C}/\text{kg}\]
done
clear
D)
\[2B\]
done
clear
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question_answer42) \[\frac{B}{4}\] is equal to
A)
\[\frac{B}{2}\]
done
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B)
\[y=A\sin (Bx+Ct+D)\]
done
clear
C)
\[[{{m}^{0}}{{L}^{-1}}{{T}^{0}}]\]
done
clear
D)
\[[{{m}^{0}}{{L}^{0}}{{T}^{-1}}]\]
done
clear
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question_answer43) The area bounded by \[[{{m}^{0}}{{L}^{-1}}{{T}^{-2}}]\] and X-axis is
A)
\[[{{m}^{0}}{{L}^{0}}{{T}^{0}}]\]
done
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B)
\[1.5\mu \]
done
clear
C)
\[\mu \]
done
clear
D)
None of the above
done
clear
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question_answer44) A man on the top of a cliff 100 m high observes the angles of depression of two points on the opposite sides of the cliff as 30° and 60°, respectively. Then, the distance between the two points is
A)
400 m
done
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B)
\[W\]
done
clear
C)
\[\frac{4W}{3}\]
done
clear
D)
None of these
done
clear
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question_answer45) The solution set of the equation \[\frac{5W}{2}\]is
A)
[0,1]
done
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B)
[-1,1]
done
clear
C)
[1.3]
done
clear
D)
None of these
done
clear
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question_answer46) If \[\frac{\pi }{2}\],then the value of \[\sigma =\text{5}.\text{67}\times \text{1}{{0}^{-\text{8}}}\text{W}-{{\text{m}}^{\text{2}}}{{\text{K}}^{\text{-4}}}\] will be
A)
2abc
done
clear
B)
abc
done
clear
C)
\[y=5\sin \frac{\pi x}{3}\cos 40\pi t\]
done
clear
D)
\[t\]
done
clear
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question_answer47) The. solution of the differential equation \[{{(Kg)}^{1/2}}\] is
A)
\[{{(Kg)}^{-1/2}}\]
done
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B)
\[{{(Kg)}^{2}}\]
done
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C)
\[{{(Kg)}^{-2}}\]
done
clear
D)
None of these
done
clear
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question_answer48) The integrating factor of the differential equation \[\frac{pV}{nT}\]is
A)
\[{{x}^{\log x}}\]
done
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B)
\[{{(\sqrt{x})}^{\log x}}\]
done
clear
C)
\[{{(\sqrt{e})}^{{{(\log x)}^{2}}}}\]
done
clear
D)
\[{{e}^{{{x}^{2}}}}\]
done
clear
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question_answer49) If \[\text{1}{{0}^{-\text{2}}}\].then \[\text{1}{{0}^{-3}}\] is equal to
A)
\[1\mu V\]
done
clear
B)
\[\text{1}.\text{96}\times \text{1}{{0}^{-\text{8}}}\text{ m}/\text{s}\]
done
clear
C)
\[{{(\tan x)}^{\sin x}}[\sec x+\cos x\log \tan x]\]
done
clear
D)
None of the above
done
clear
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question_answer50) If\[\text{3}.\text{18}\times \text{1}{{0}^{8}}m/s\] and \[\text{3}.\text{33}\times {{10}^{\text{8}}}\text{ m}/\text{s}\] then \[\theta =\text{45}{}^\circ \] is equal to
A)
\[\frac{-y}{x}\]
done
clear
B)
\[\frac{y}{x}\]
done
clear
C)
\[-\frac{x}{y}\]
done
clear
D)
\[\frac{x}{y}\]
done
clear
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question_answer51) The equation of the tangent to the curve\[{{R}_{1}}\]at the point, where the ordinate and the abscissa are equal, is
A)
\[{{R}_{2}}\]
done
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B)
\[{{Q}_{1}}\]
done
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C)
\[{{Q}_{2}}\]
done
clear
D)
None of the above
done
clear
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question_answer52) The function \[{{Q}_{1}}{{R}_{2}}\ne {{Q}_{2}}{{R}_{1}}\]has
A)
no maxima and minima
done
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B)
one maximum and one minimum
done
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C)
two maxima
done
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D)
two minima
done
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question_answer53) If \[{{Q}_{1}}{{R}_{2}}={{Q}_{2}}{{R}_{1}}\]and f(0) = 0, then the value of a for which Rolle's theorem can be applied in [0,1], is
A)
-2
done
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B)
-1
done
clear
C)
0
done
clear
D)
\[s=\frac{{{t}^{2}}}{4}\]
done
clear
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question_answer54) The algebraic sum of the deviation of 20 observations measured from 30 is 2. Then mean of observations is
A)
28.5
done
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B)
30.1
done
clear
C)
30.5
done
clear
D)
29.6
done
clear
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question_answer55) The standard deviation of 15 items is 6 and if each item is decreased by 1, then standard deviation will be
A)
5
done
clear
B)
7
done
clear
C)
\[T\propto V\]
done
clear
D)
6
done
clear
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question_answer56) If \[T\propto {{V}^{2}}\]is equal to
A)
2
done
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B)
0
done
clear
C)
\[T\propto \frac{1}{{{V}^{2}}}\]
done
clear
D)
0
done
clear
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question_answer57) The equation of the smallest circle passing through the intersection of the line \[T\propto \frac{1}{V}\] and the circle \[\text{6}\times \text{1}{{0}^{-\text{7}}}\text{A}-{{\text{m}}^{\text{2}}}\] is
A)
\[\text{5 g}/\text{c}{{\text{m}}^{\text{3}}}\]
done
clear
B)
\[\text{8}\text{.3}\times \text{1}{{0}^{\text{6}}}\]
done
clear
C)
\[\text{1}.\text{2}\times \text{1}{{0}^{-\text{7}}}\]
done
clear
D)
None of the above
done
clear
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question_answer58) The complex number \[\text{3}\times \text{1}{{0}^{-\text{6}}}\] in polar form is
A)
\[CaC{{l}_{2}}\]
done
clear
B)
\[\text{MgS}{{\text{O}}_{\text{4}}}\]
done
clear
C)
\[\text{MgS}{{\text{O}}_{\text{4}}}\]
done
clear
D)
None of the above
done
clear
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question_answer59) If \[CaC{{l}_{2}}\]and \[A\to B,B\to C\], then\[C\to A\]is equal to
A)
\[\upsilon /\text{1}0\]
done
clear
B)
\[f\]
done
clear
C)
\[1.11f\]
done
clear
D)
\[1.22f\]
done
clear
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question_answer60) The orthocentre of the triangle formed by (0,0), (8, 0) and (4, 6) is
A)
\[f\]
done
clear
B)
\[1.27f\]
done
clear
C)
\[\text{1}.0\text{1}\times \text{1}{{0}^{\text{5}}}\text{ N}/{{\text{m}}^{\text{2}}}\]
done
clear
D)
\[\text{9}.\text{13}\times \text{1}{{0}^{\text{4}}}\text{ N}/{{\text{m}}^{\text{2}}}\]
done
clear
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