MCQOPTIONS
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MCQOPTIONS
This section includes 8666 Mcqs, each offering curated multiple-choice questions to sharpen your Joint Entrance Exam - Main (JEE Main) knowledge and support exam preparation. Choose a topic below to get started.
| 5101. |
Family of curves \[y={{e}^{x}}(A\cos x+B\sin x)\], represents the differential equation [MP PET 1999] |
| A. | \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=2\frac{dy}{dx}-y\] |
| B. | \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=2\frac{dy}{dx}-2y\] |
| C. | \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=\frac{dy}{dx}-2y\] |
| D. | \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=2\frac{dy}{dx}+y\] |
| Answer» C. \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=\frac{dy}{dx}-2y\] | |
| 5102. |
Differential equation whose solution is \[y=cx+c-{{c}^{3}}\], is [MP PET 1997] |
| A. | \[\frac{dy}{dx}=c\] |
| B. | \[y=x\frac{dy}{dx}+\frac{dy}{dx}-{{\left( \frac{dy}{dx} \right)}^{3}}\] |
| C. | \[\frac{dy}{dx}=c-3{{c}^{2}}\] |
| D. | None of these |
| Answer» C. \[\frac{dy}{dx}=c-3{{c}^{2}}\] | |
| 5103. |
The differential equation of all the lines in the xy-plane is |
| A. | \[\frac{dy}{dx}-x=0\] |
| B. | \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-x\frac{dy}{dx}=0\] |
| C. | \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=0\] |
| D. | \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+x=0\] |
| Answer» D. \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+x=0\] | |
| 5104. |
The differential equation found by the elimination of the arbitrary constant K from the equation \[y=(x+K){{e}^{-x}}\]is |
| A. | \[\frac{dy}{dx}-y={{e}^{-x}}\] |
| B. | \[\frac{dy}{dx}-y{{e}^{x}}=1\] |
| C. | \[\frac{dy}{dx}+y{{e}^{x}}=1\] |
| D. | \[\frac{dy}{dx}+y={{e}^{-x}}\] |
| Answer» E. | |
| 5105. |
The differential equation of all parabolas whose axes are parallel to y-axis is |
| A. | \[\frac{{{d}^{3}}y}{d{{x}^{3}}}=0\] |
| B. | \[\frac{{{d}^{2}}x}{d{{y}^{2}}}=c\] |
| C. | \[\frac{{{d}^{3}}y}{d{{x}^{3}}}+\frac{{{d}^{2}}x}{d{{y}^{2}}}=0\] |
| D. | \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+2\frac{dy}{dx}=c\] |
| Answer» B. \[\frac{{{d}^{2}}x}{d{{y}^{2}}}=c\] | |
| 5106. |
The differential equation of displacement of all "Simple harmonic motions" of given period \[2\pi /n\], is |
| A. | \[\frac{{{d}^{2}}x}{d{{t}^{2}}}+nx=0\] |
| B. | \[\frac{{{d}^{2}}x}{d{{t}^{2}}}+{{n}^{2}}x=0\] |
| C. | \[\frac{{{d}^{2}}x}{d{{t}^{2}}}-{{n}^{2}}x=0\] |
| D. | \[\frac{{{d}^{2}}x}{d{{t}^{2}}}+\frac{1}{{{n}^{2}}}x=0\] |
| Answer» C. \[\frac{{{d}^{2}}x}{d{{t}^{2}}}-{{n}^{2}}x=0\] | |
| 5107. |
The differential equation of all circles which passes through the origin and whose centre lies on y-axis, is [MNR 1986; DCE 2000] |
| A. | \[({{x}^{2}}-{{y}^{2}})\frac{dy}{dx}-2xy=0\] |
| B. | \[({{x}^{2}}-{{y}^{2}})\frac{dy}{dx}+2xy=0\] |
| C. | \[({{x}^{2}}-{{y}^{2}})\frac{dy}{dx}-xy=0\] |
| D. | \[({{x}^{2}}-{{y}^{2}})\frac{dy}{dx}+xy=0\] |
| Answer» B. \[({{x}^{2}}-{{y}^{2}})\frac{dy}{dx}+2xy=0\] | |
| 5108. |
The differential equation of the family of curves \[{{y}^{2}}=4a(x+a)\], where a is an arbitrary constant, is |
| A. | \[y\text{ }\left[ 1+{{\left( \frac{dy}{dx} \right)}^{2}} \right]=2x\frac{dy}{dx}\] |
| B. | \[y\text{ }\left[ 1-{{\left( \frac{dy}{dx} \right)}^{2}} \right]=2x\frac{dy}{dx}\] |
| C. | \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+2\frac{dy}{dx}=0\] |
| D. | \[{{\left( \frac{dy}{dx} \right)}^{3}}+3\,\frac{dy}{dx}+y=0\] |
| Answer» C. \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+2\frac{dy}{dx}=0\] | |
| 5109. |
The differential equation of all straight lines passing through the point \[(1,\,-1)\]is [MP PET 1994] |
| A. | \[y=(x+1)\frac{dy}{dx}+1\] |
| B. | \[y=(x+1)\frac{dy}{dx}-1\] |
| C. | \[y=(x-1)\frac{dy}{dx}+1\] |
| D. | \[y=(x-1)\frac{dy}{dx}-1\] |
| Answer» E. | |
| 5110. |
The differential equation of the family of curves \[v=\frac{A}{r}+B,\]where A and B are arbitrary constants, is |
| A. | \[\frac{{{d}^{2}}v}{d{{r}^{2}}}+\frac{1}{r}\frac{dv}{dr}=0\] |
| B. | \[\frac{{{d}^{2}}v}{d{{r}^{2}}}-\frac{2}{r}\frac{dv}{dr}=0\] |
| C. | \[\frac{{{d}^{2}}v}{d{{r}^{2}}}+\frac{2}{r}\frac{dv}{dr}=0\] |
| D. | None of these |
| Answer» D. None of these | |
| 5111. |
The differential equation for the line \[y=mx+c\] is (where c is arbitrary constant) |
| A. | \[\frac{dy}{dx}=m\] |
| B. | \[\frac{dy}{dx}+m=0\] |
| C. | \[\frac{dy}{dx}=0\] |
| D. | None of these |
| Answer» B. \[\frac{dy}{dx}+m=0\] | |
| 5112. |
The differential equation whose solution is \[y={{c}_{1}}\cos ax+{{c}_{2}}\sin ax\] is (Where \[{{c}_{1}},\ {{c}_{2}}\]are arbitrary constants) [MP PET 1996] |
| A. | \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+{{y}^{2}}=0\] |
| B. | \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+{{a}^{2}}y=0\] |
| C. | \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+a{{y}^{2}}=0\] |
| D. | \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-{{a}^{2}}y=0\] |
| Answer» C. \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+a{{y}^{2}}=0\] | |
| 5113. |
The differential equation corresponding to primitive \[y={{e}^{cx}}\]is or The elimination of the arbitrary constant m from the equation \[y={{e}^{mx}}\]gives the differential equation [MP PET 1995, 2000; Pb. CET 2000] |
| A. | \[\frac{dy}{dx}=\left( \frac{y}{x} \right)\log x\] |
| B. | \[\frac{dy}{dx}=\left( \frac{x}{y} \right)\log y\] |
| C. | \[\frac{dy}{dx}=\left( \frac{y}{x} \right)\log y\] |
| D. | \[\frac{dy}{dx}=\left( \frac{x}{y} \right)\log x\] |
| Answer» D. \[\frac{dy}{dx}=\left( \frac{x}{y} \right)\log x\] | |
| 5114. |
The point (4, 1)undergoes the following two successive transformation (i) Reflection about the line \[y=x\] (ii) Translation through a distance 2 units along the positive x-axis Then the final coordinates of the point are [MNR 1987; UPSEAT 2000] |
| A. | (4, 3) |
| B. | (3, 4) |
| C. | (1, 4) |
| D. | \[\left( \frac{7}{2},\frac{7}{2} \right)\] |
| Answer» C. (1, 4) | |
| 5115. |
One vertex of the equilateral triangle with centroid at the origin and one side as \[x+y-2=0\]is |
| A. | \[(-1,-1)\] |
| B. | \[(2,2)\] |
| C. | \[(-2,-2)\] |
| D. | None of these |
| Answer» D. None of these | |
| 5116. |
The line \[2x+3y=12\]meets the x-axis at A and y-axis at B. The line through (5, 5) perpendicular to \[AB\]meets the x- axis , y axis and the \[AB\] at C, D and E respectively. If O is the origin of coordinates, then the area of \[OCEB\]is [IIT 1976] |
| A. | \[23\] sq. units |
| B. | \[\frac{23}{2}sq.\]units |
| C. | \[\frac{23}{3}sq.\]units |
| D. | None of these |
| Answer» D. None of these | |
| 5117. |
The co-ordinates of the foot of perpendicular from the point (2, 3) on the line \[x+y-11=0\]are [MP PET 1986] |
| A. | \[(-6,\,5)\] |
| B. | \[(5,\,6)\] |
| C. | \[(-5,\,6)\] |
| D. | \[(6,\,5)\] |
| Answer» C. \[(-5,\,6)\] | |
| 5118. |
The foot of the coordinates drawn from (2, 4) to the line \[x+y=1\] is [Roorkee 1995] |
| A. | \[\left( \frac{1}{3},\frac{3}{2} \right)\] |
| B. | \[\left( -\frac{1}{2},\frac{3}{2} \right)\] |
| C. | \[\left( \frac{4}{3},\frac{1}{2} \right)\] |
| D. | \[\left( \frac{3}{4},\,\,-\frac{1}{2} \right)\] |
| Answer» C. \[\left( \frac{4}{3},\frac{1}{2} \right)\] | |
| 5119. |
The coordinates of the foot of the perpendicular from \[({{x}_{1}},{{y}_{1}})\]to the line \[ax+by+c=0\] are [Dhanbad Engg. 1973] |
| A. | \[\left( \frac{{{b}^{2}}{{x}_{1}}-ab{{y}_{1}}-ac}{{{a}^{2}}+{{b}^{2}}},\frac{{{a}^{2}}{{y}_{1}}-ab{{x}_{1}}-bc}{{{a}^{2}}+{{b}^{2}}} \right)\] |
| B. | \[\left( \frac{{{b}^{2}}{{x}_{1}}+ab{{y}_{1}}+ac}{{{a}^{2}}+{{b}^{2}}},\frac{{{a}^{2}}{{y}_{1}}+ab{{x}_{1}}+bc}{{{a}^{2}}+{{b}^{2}}} \right)\] |
| C. | \[\left( \frac{a{{x}_{1}}+b{{y}_{1}}+ab}{a+b},\frac{a{{x}_{1}}-b{{y}_{1}}-ab}{a+b} \right)\] |
| D. | None of these |
| Answer» B. \[\left( \frac{{{b}^{2}}{{x}_{1}}+ab{{y}_{1}}+ac}{{{a}^{2}}+{{b}^{2}}},\frac{{{a}^{2}}{{y}_{1}}+ab{{x}_{1}}+bc}{{{a}^{2}}+{{b}^{2}}} \right)\] | |
| 5120. |
If for a variable line \[\frac{x}{a}+\frac{y}{b}=1\], the condition \[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{1}{{{c}^{2}}}\] (c is a constant) is satisfied, then locus of foot of perpendicular drawn from origin to the line is [RPET 1999] |
| A. | \[{{x}^{2}}+{{y}^{2}}={{c}^{2}}/2\] |
| B. | \[{{x}^{2}}+{{y}^{2}}=2{{c}^{2}}\] |
| C. | \[{{x}^{2}}+{{y}^{2}}={{c}^{2}}\] |
| D. | \[{{x}^{2}}-{{y}^{2}}={{c}^{2}}\] |
| Answer» D. \[{{x}^{2}}-{{y}^{2}}={{c}^{2}}\] | |
| 5121. |
Coordinates of the foot of the perpendicular drawn from (0,0) to the line joining \[(a\cos \alpha ,a\sin \alpha )\] and \[(a\cos \beta ,a\sin \beta )\] are [IIT 1982] |
| A. | \[\left( \frac{a}{2},\frac{b}{2} \right)\] |
| B. | \[\left[ \frac{a}{2}(\cos \alpha +\cos \beta ),\frac{a}{2}(\sin \alpha +\sin \beta ) \right]\] |
| C. | \[\left( \cos \frac{\alpha +\beta }{2},\sin \frac{\alpha +\beta }{2} \right)\] |
| D. | None of these |
| Answer» C. \[\left( \cos \frac{\alpha +\beta }{2},\sin \frac{\alpha +\beta }{2} \right)\] | |
| 5122. |
If (- 2, 6) is the image of the point (4, 2) with respect to line L = 0, then L = [EAMCET 2002] |
| A. | 3x ? 2y + 5 |
| B. | 3x ? 2y + 10 |
| C. | 2x + 3y ? 5 |
| D. | 6x ? 4y ? 7 |
| Answer» B. 3x ? 2y + 10 | |
| 5123. |
A straight line passes through a fixed point \[(h,k)\]. The locus of the foot of perpendicular on it drawn from the origin is |
| A. | \[{{x}^{2}}+{{y}^{2}}-hx-ky=0\] |
| B. | \[{{x}^{2}}+{{y}^{2}}+hx+ky=0\] |
| C. | \[3{{x}^{2}}+3{{y}^{2}}+hx-ky=0\] |
| D. | None of these |
| Answer» B. \[{{x}^{2}}+{{y}^{2}}+hx+ky=0\] | |
| 5124. |
The reflection of the point (4, -13) in the line \[5x+y+6=0\] is [EAMCET 1994] |
| A. | \[(-1,-14)\] |
| B. | (3 ,4) |
| C. | (1, 2) |
| D. | (- 4, 13) |
| Answer» B. (3 ,4) | |
| 5125. |
The image of a point \[A(3,\,8)\]in the line \[x+3y-7=0\], is [RPET 1991] |
| A. | \[(-1,-4)\] |
| B. | \[(-3\,,\,\,-8)\] |
| C. | \[(1,-4)\] |
| D. | \[(3,\,8)\] |
| Answer» B. \[(-3\,,\,\,-8)\] | |
| 5126. |
The pedal points of a perpendicular drawn from origin on the line \[3x+4y-5=0\], is [RPET 1990] |
| A. | \[\left( \frac{3}{5},2 \right)\] |
| B. | \[\left( \frac{3}{5},\frac{4}{5} \right)\] |
| C. | \[\left( -\frac{3}{5},-\frac{4}{5} \right)\] |
| D. | \[\left( \frac{30}{17},\frac{19}{17} \right)\] |
| Answer» C. \[\left( -\frac{3}{5},-\frac{4}{5} \right)\] | |
| 5127. |
Line L has intercepts a and b on the co-ordinate axes. When the axes are rotated through a given angle keeping the origin fixed, the same line L has intercepts p and q, then [IIT 1990; Kurukshetra CEE 1998] |
| A. | \[{{a}^{2}}+{{b}^{2}}={{p}^{2}}+{{q}^{2}}\] |
| B. | \[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{1}{{{p}^{2}}}+\frac{1}{{{q}^{2}}}\] |
| C. | \[{{a}^{2}}+{{p}^{2}}={{b}^{2}}+{{q}^{2}}\] |
| D. | \[\frac{1}{{{a}^{2}}}+\frac{1}{{{p}^{2}}}=\frac{1}{{{b}^{2}}}+\frac{1}{{{q}^{2}}}\] |
| Answer» C. \[{{a}^{2}}+{{p}^{2}}={{b}^{2}}+{{q}^{2}}\] | |
| 5128. |
Let L be the line \[2x+y=2\]. If the axes are rotated by \[{{45}^{o}}\], then the intercepts made by the line L on the new axes are respectively [Roorkee Qualifying 1998] |
| A. | \[\sqrt{2}\]and 1 |
| B. | 1 and \[\sqrt{2}\] |
| C. | \[2\sqrt{2}\]and \[2\sqrt{2}/3\] |
| D. | \[2\sqrt{2}/3\]and \[2\sqrt{2}\] |
| Answer» D. \[2\sqrt{2}/3\]and \[2\sqrt{2}\] | |
| 5129. |
The coordinates of the foot of the perpendicular from the point (2, 3) on the line \[y=3x+4\] are given by [MP PET 1984] |
| A. | \[\left( \frac{37}{10},-\frac{1}{10} \right)\] |
| B. | \[\left( -\frac{1}{10},\frac{37}{10} \right)\] |
| C. | \[\left( \frac{10}{37},-10 \right)\] |
| D. | \[\left( \frac{2}{3},-\frac{1}{3} \right)\] |
| Answer» C. \[\left( \frac{10}{37},-10 \right)\] | |
| 5130. |
\[\frac{2}{1\,!}+\frac{2+4}{2\,!}+\frac{2+4+6}{3\,!}+....\infty =\] [MNR 1985] |
| A. | \[e\] |
| B. | \[2\,e\] |
| C. | \[3\,e\] |
| D. | None of these |
| Answer» D. None of these | |
| 5131. |
In the expansion of \[\frac{{{e}^{7x}}+{{e}^{3x}}}{{{e}^{5x}}}\] , the constant term is |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | None of these |
| Answer» D. None of these | |
| 5132. |
In the expansion of \[(1+x+{{x}^{2}}){{e}^{-x}}\], the coefficient of \[{{x}^{2}}\] is |
| A. | 1 |
| B. | \[-1\] |
| C. | 44228 |
| D. | -0.5 |
| Answer» D. -0.5 | |
| 5133. |
The coefficients of \[{{x}^{3}}\] in the expansion of \[{{3}^{x}}\] is [Kerala (Engg.) 2005] |
| A. | \[\frac{{{3}^{3}}}{6}\] |
| B. | \[\frac{{{(\log 3)}^{3}}}{3}\] |
| C. | \[\frac{\log ({{3}^{3}})}{6}\] |
| D. | \[\frac{{{(\log 3)}^{3}}}{6}\] |
| E. | \[\frac{3}{3\,!}\] |
| Answer» E. \[\frac{3}{3\,!}\] | |
| 5134. |
In the expansion of \[\frac{{{e}^{5x}}+{{e}^{x}}}{{{e}^{3x}}}\], the coefficient of \[{{x}^{4}}\]is |
| A. | - \[6/5\] |
| B. | 44259 |
| C. | -1.33333333333333 |
| D. | None of these |
| Answer» C. -1.33333333333333 | |
| 5135. |
\[(1+3){{\log }_{e}}3+\frac{1+{{3}^{2}}}{2\,!}{{({{\log }_{e}}3)}^{2}}+\frac{1+{{3}^{3}}}{3\,!}{{({{\log }_{e}}3)}^{3}}+.....\infty =\] [Roorkee 1989] |
| A. | 28 |
| B. | 30 |
| C. | 25 |
| D. | 0 |
| Answer» B. 30 | |
| 5136. |
\[1+\frac{{{\log }_{e}}x}{1\,!}+\frac{{{({{\log }_{e}}x)}^{2}}}{2\,!}+\frac{{{({{\log }_{e}}x)}^{3}}}{3\,!}+.....\infty =\] [Kurukshetra CEE 1998; JMI CET 2000] |
| A. | \[{{\log }_{e}}x\] |
| B. | \[x\] |
| C. | \[{{x}^{-1}}\] |
| D. | \[-{{\log }_{e}}(1+x)\] |
| Answer» C. \[{{x}^{-1}}\] | |
| 5137. |
\[\frac{2}{1\,!}{{\log }_{e}}2+\frac{{{2}^{2}}}{2\,!}{{({{\log }_{e}}2)}^{2}}+\frac{{{2}^{3}}}{3\,!}{{({{\log }_{e}}2)}^{3}}+.....\infty =\] |
| A. | 2 |
| B. | 3 |
| C. | 4 |
| D. | None of these |
| Answer» C. 4 | |
| 5138. |
The sum of the series \[\frac{{{1}^{2}}}{1\cdot 2\,!}+\frac{{{1}^{2}}+{{2}^{2}}}{2\cdot 3\,!}+\frac{{{1}^{2}}+{{2}^{2}}+{{3}^{2}}}{3\cdot 4\,!}+..+\frac{{{1}^{2}}+{{2}^{2}}+...+{{n}^{2}}}{n\cdot (n+1)\,!}+...\infty \]equals [AMU 2002] |
| A. | \[{{e}^{2}}\] |
| B. | \[\frac{1}{2}{{(e+{{e}^{-1}})}^{2}}\] |
| C. | \[\frac{3e-1}{6}\] |
| D. | \[\frac{4e+1}{6}\] |
| Answer» D. \[\frac{4e+1}{6}\] | |
| 5139. |
If \[i=\sqrt{-1}\], then \[\frac{{{e}^{xi}}+{{e}^{-xi}}}{2}=\] |
| A. | \[1+\frac{{{x}^{2}}}{2\,!}+\frac{{{x}^{4}}}{4\,!}+.....\infty \] |
| B. | \[1-\frac{{{x}^{2}}}{2\,!}+\frac{{{x}^{4}}}{4\,!}-.....\infty \] |
| C. | \[x+\frac{{{x}^{3}}}{3\,!}+\frac{{{x}^{5}}}{5\,!}+....\infty \] |
| D. | \[i\,\left[ x-\frac{{{x}^{3}}}{3\,!}+\frac{{{x}^{5}}}{5\,!}-.....\infty \right]\] |
| Answer» C. \[x+\frac{{{x}^{3}}}{3\,!}+\frac{{{x}^{5}}}{5\,!}+....\infty \] | |
| 5140. |
\[\frac{1}{2\,!}+\frac{1+2}{3\,!}+\frac{1+2+3}{4\,!}+......\infty =\] [EAMCET 2003] |
| A. | \[e\] |
| B. | \[2\,e\] |
| C. | e/2 |
| D. | None of these |
| Answer» D. None of these | |
| 5141. |
\[1+\frac{2}{3\,!}+\frac{3}{5\,!}+\frac{4}{7\,!}+......\infty =\,\] |
| A. | e |
| B. | \[2\,e\] |
| C. | e/2 |
| D. | e/3 |
| Answer» D. e/3 | |
| 5142. |
\[1+\frac{{{2}^{2}}}{1\,!}+\frac{{{3}^{2}}}{2\,!}+\frac{{{4}^{2}}}{3\,!}+......\infty =\] |
| A. | \[2\,e\] |
| B. | \[3\,e\] |
| C. | \[(0.5)-\frac{{{(0.5)}^{2}}}{2}+\frac{{{(0.5)}^{3}}}{3}-\frac{{{(0.5)}^{4}}}{4}+....\] |
| D. | \[5\,e\] |
| Answer» E. | |
| 5143. |
If \[y=x-\frac{{{x}^{2}}}{2\,!}+\frac{{{x}^{3}}}{3!}-\frac{{{x}^{4}}}{4\,!}+......,\] then \[x=\] |
| A. | \[{{\log }_{e}}(1-y)\] |
| B. | \[\frac{1}{{{\log }_{e}}(1-y)}\] |
| C. | \[{{\log }_{e}}\frac{1}{1-y}\] |
| D. | \[{{\log }_{e}}(1+y)\] |
| Answer» D. \[{{\log }_{e}}(1+y)\] | |
| 5144. |
In the expansion of \[\frac{a+bx}{{{e}^{x}}}\], the coefficient of \[{{x}^{r}}\] is |
| A. | \[\frac{a-b}{r\,!}\] |
| B. | \[\frac{a-br}{r\,!}\] |
| C. | \[{{(-1)}^{r}}\frac{a-br}{r\,!}\] |
| D. | None of these |
| Answer» D. None of these | |
| 5145. |
\[1+\frac{1+x}{2\,!}+\frac{1+x+{{x}^{2}}}{3\,!}+\frac{1+x+{{x}^{2}}+{{x}^{3}}}{4\,!}+.....\infty =\] |
| A. | \[\frac{{{e}^{x}}+1}{x+1}\] |
| B. | \[\frac{{{e}^{x}}+1}{x-1}\] |
| C. | \[\frac{{{e}^{x}}-e}{x+1}\] |
| D. | \[\frac{{{e}^{x}}-e}{x-1}\] |
| Answer» E. | |
| 5146. |
\[1+\frac{3}{1\,!}+\frac{5}{2\,!}+\frac{7}{3\,!}+....\infty =\] |
| A. | \[e\] |
| B. | \[2\,e\] |
| C. | \[3\,e\] |
| D. | \[4\,e\] |
| Answer» D. \[4\,e\] | |
| 5147. |
\[\frac{2}{1\,!}+\frac{4}{3\,!}+\frac{6}{5\,!}+\frac{8}{7\,!}+......\infty =\] [JMI CET 2000] |
| A. | \[1/e\] |
| B. | \[e\] |
| C. | \[2\,e\] |
| D. | \[3e\] |
| Answer» C. \[2\,e\] | |
| 5148. |
\[1+\frac{{{2}^{4}}}{2\,!}+\frac{{{3}^{4}}}{3\,!}+\frac{{{4}^{4}}}{4\,!}+.....\infty =\] |
| A. | \[5\,e\] |
| B. | \[e\] |
| C. | \[15\,e\] |
| D. | \[2\,e\] |
| Answer» D. \[2\,e\] | |
| 5149. |
\[\frac{1+\frac{{{2}^{2}}}{2\,!}+\frac{{{2}^{4}}}{3\,!}+\frac{{{2}^{6}}}{4\,!}+.....\infty }{1+\frac{1}{2\,!}+\frac{2}{3\,!}+\frac{{{2}^{2}}}{4\,!}+....\infty }=\] |
| A. | \[{{e}^{2}}\] |
| B. | \[{{e}^{2}}-1\] |
| C. | \[{{e}^{3/2}}\] |
| D. | None of these |
| Answer» C. \[{{e}^{3/2}}\] | |
| 5150. |
\[1+x{{\log }_{e}}a+\frac{{{x}^{2}}}{2\,!}{{({{\log }_{e}}a)}^{2}}+\frac{{{x}^{3}}}{3\,!}{{({{\log }_{e}}a)}^{3}}+...=\] [EAMCET 2002] |
| A. | \[{{a}^{x}}\] |
| B. | x |
| C. | \[{{a}^{{{\log }_{a}}x}}\] |
| D. | a |
| Answer» B. x | |