MCQOPTIONS
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MCQOPTIONS
This section includes 150 Mcqs, each offering curated multiple-choice questions to sharpen your 11th Class knowledge and support exam preparation. Choose a topic below to get started.
| 101. |
\[{{\log }_{e}}(1+x)=\sum\limits_{i=1}^{\infty }{\left[ \frac{{{(-1)}^{i+1}}{{x}^{i}}}{i} \right]}\] is defined for [Roorkee 1990] |
| A. | \[x\in (-1,\,1)\] |
| B. | Any positive (+) real x |
| C. | \[x\in (-1,\,1]\] |
| D. | Any positive (+) real \[x(x\ne 1)\] |
| Answer» D. Any positive (+) real \[x(x\ne 1)\] | |
| 102. |
If \[a\,\cos 2\theta +b\,\sin 2\theta =c\]has a and b as its solution, then the value of \[\tan \alpha +\tan \beta \] is [Kurukshetra CEE 1998] |
| A. | \[\frac{c+a}{2b}\] |
| B. | \[\frac{2b}{c+a}\] |
| C. | \[\frac{c-a}{2b}\] |
| D. | \[\frac{b}{c+a}\] |
| Answer» C. \[\frac{c-a}{2b}\] | |
| 103. |
Let P be a variable point on the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] with foci \[{{F}_{1}}\] and \[{{F}_{2}}\]. If A is the area of the triangle \[P{{F}_{1}}{{F}_{2}}\], then maximum value of A is [IIT 1994; Kerala (Engg.) 2005] |
| A. | ab |
| B. | abe |
| C. | \[\frac{e}{ab}\] |
| D. | \[\frac{ab}{e}\] |
| Answer» C. \[\frac{e}{ab}\] | |
| 104. |
The centre of an ellipse is C and PN is any ordinate and A, A? are the end points of major axis, then the value of \[\frac{P{{N}^{2}}}{AN\ .\ A'N}\] is |
| A. | \[\frac{{{b}^{2}}}{{{a}^{2}}}\] |
| B. | \[\frac{{{a}^{2}}}{{{b}^{2}}}\] |
| C. | \[{{a}^{2}}+{{b}^{2}}\] |
| D. | 1 |
| Answer» B. \[\frac{{{a}^{2}}}{{{b}^{2}}}\] | |
| 105. |
If \[{{z}_{1}},{{z}_{2}},{{z}_{3}}\]be three non-zero complex number, such that \[{{z}_{2}}\ne {{z}_{1}},a=|{{z}_{1}}|,b=|{{z}_{2}}|\] and \[c=|{{z}_{3}}|\] suppose that \[\left| \begin{matrix} a & b & c \\ b & c & a \\ c & a & b \\ \end{matrix} \right|=0\], then \[arg\left( \frac{{{z}_{3}}}{{{z}_{2}}} \right)\] is equal to |
| A. | \[arg{{\left( \frac{{{z}_{2}}-{{z}_{1}}}{{{z}_{3}}-{{z}_{1}}} \right)}^{2}}\] |
| B. | \[arg\left( \frac{{{z}_{2}}-{{z}_{1}}}{{{z}_{3}}-{{z}_{1}}} \right)\] |
| C. | \[arg{{\left( \frac{{{z}_{3}}-{{z}_{1}}}{{{z}_{2}}-{{z}_{1}}} \right)}^{2}}\] |
| D. | \[arg\left( \frac{{{z}_{3}}-{{z}_{1}}}{{{z}_{2}}-{{z}_{1}}} \right)\] |
| Answer» D. \[arg\left( \frac{{{z}_{3}}-{{z}_{1}}}{{{z}_{2}}-{{z}_{1}}} \right)\] | |
| 106. |
If the product of roots of the equation\[{{x}^{2}}-3kx+2{{e}^{2\log k}}-1=0\]is 7, then its roots will real when [IIT 1984] |
| A. | \[k=1\] |
| B. | \[k=2\] |
| C. | \[k=3\] |
| D. | None of these |
| Answer» C. \[k=3\] | |
| 107. |
The value of \[{{\log }_{e}}\left( 1+a{{x}^{2}}+{{a}^{2}}+\frac{a}{{{x}^{2}}} \right)\] is |
| A. | \[a\,\left( {{x}^{2}}-\frac{1}{{{x}^{2}}} \right)-\frac{{{a}^{2}}}{2}\,\left( {{x}^{4}}-\frac{1}{{{x}^{4}}} \right)+\frac{{{a}^{3}}}{3}\,\left( {{x}^{6}}-\frac{1}{{{x}^{6}}} \right)-.....\] |
| B. | \[a\,\left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right)-\frac{{{a}^{2}}}{2}\,\left( {{x}^{4}}+\frac{1}{{{x}^{4}}} \right)+\frac{{{a}^{3}}}{3}\,\left( {{x}^{6}}+\frac{1}{{{x}^{6}}} \right)-.....\] |
| C. | \[a\,\left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right)+\frac{{{a}^{2}}}{2}\,\left( {{x}^{4}}+\frac{1}{{{x}^{4}}} \right)+\frac{{{a}^{3}}}{3}\,\left( {{x}^{6}}+\frac{1}{{{x}^{6}}} \right)+.....\] |
| D. | \[a\,\left( {{x}^{2}}-\frac{1}{{{x}^{2}}} \right)+\frac{{{a}^{2}}}{2}\,\left( {{x}^{4}}-\frac{1}{{{x}^{4}}} \right)+\frac{{{a}^{3}}}{3}\,\left( {{x}^{6}}-\frac{1}{{{x}^{6}}} \right)+.....\] |
| Answer» C. \[a\,\left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right)+\frac{{{a}^{2}}}{2}\,\left( {{x}^{4}}+\frac{1}{{{x}^{4}}} \right)+\frac{{{a}^{3}}}{3}\,\left( {{x}^{6}}+\frac{1}{{{x}^{6}}} \right)+.....\] | |
| 108. |
If \[\alpha ,\,\beta ,\,\gamma \in \,\left( 0,\,\frac{\pi }{2} \right)\], then \[\frac{\sin \,(\alpha +\beta +\gamma )}{\sin \alpha +\sin \beta +\sin \gamma }\] is |
| A. | < 1 |
| B. | >1 |
| C. | 1 |
| D. | None of these |
| Answer» B. >1 | |
| 109. |
If \[{{z}_{1}}=10+6i,{{z}_{2}}=4+6i\] and \[z\] is a complex number such that \[amp\left( \frac{z-{{z}_{1}}}{z-{{z}_{2}}} \right)=\frac{\pi }{4},\] then the value of \[|z-7-9i|\] is equal to [IIT 1990] |
| A. | \[\sqrt{2}\] |
| B. | \[2\sqrt{2}\] |
| C. | \[3\sqrt{2}\] |
| D. | \[2\sqrt{3}\] |
| Answer» D. \[2\sqrt{3}\] | |
| 110. |
If \[n\] geometric means between \[a\] and \[b\]be \[{{G}_{1}},\ {{G}_{2}},\ .....\]\[{{G}_{n}}\] and a geometric mean be \[G\], then the true relation is |
| A. | \[{{G}_{1}}.{{G}_{2}}........{{G}_{n}}=G\] |
| B. | \[{{G}_{1}}.{{G}_{2}}........{{G}_{n}}={{G}^{1/n}}\] |
| C. | \[{{G}_{1}}.{{G}_{2}}........{{G}_{n}}={{G}^{n}}\] |
| D. | \[{{G}_{1}}.{{G}_{2}}........{{G}_{n}}={{G}^{2/n}}\] |
| Answer» D. \[{{G}_{1}}.{{G}_{2}}........{{G}_{n}}={{G}^{2/n}}\] | |
| 111. |
If the roots of the equations \[{{x}^{2}}-bx+c=0\] and \[{{x}^{2}}-cx+b=0\] differ by the same quantity, then \[b+c\] is equal to [BIT Ranchi 1969; MP PET 1993] |
| A. | 4 |
| B. | 1 |
| C. | 0 |
| D. | -4 |
| Answer» E. | |
| 112. |
\[1+\frac{2}{3}-\frac{2}{4}+\frac{2}{5}-......\infty =\] |
| A. | \[{{\log }_{e}}3\] |
| B. | \[{{\log }_{e}}4\] |
| C. | \[{{\log }_{e}}\left( \frac{e}{2} \right)\] |
| D. | \[{{\log }_{e}}\left( \frac{2}{3} \right)\] |
| Answer» C. \[{{\log }_{e}}\left( \frac{e}{2} \right)\] | |
| 113. |
The equation of a circle passing through the vertex and the extremities of the latus rectum of the parabola \[{{y}^{2}}=8x\] is [MP PET 1998] |
| A. | \[{{x}^{2}}+{{y}^{2}}+10x=0\] |
| B. | \[{{x}^{2}}+{{y}^{2}}+10y=0\] |
| C. | \[{{x}^{2}}+{{y}^{2}}-10x=0\] |
| D. | \[{{x}^{2}}+{{y}^{2}}-5x=0\] |
| Answer» D. \[{{x}^{2}}+{{y}^{2}}-5x=0\] | |
| 114. |
If both the roots of the quadratic equation\[{{x}^{2}}-2kx+{{k}^{2}}+k-5=0\]are less than 5, then \[k\] lies in the interval [AIEEE 2005] |
| A. | \[(-\infty ,\,4)\] |
| B. | [4, 5] |
| C. | (5, 6] |
| D. | (6, \[\infty \]) |
| Answer» B. [4, 5] | |
| 115. |
The sum of the series \[1+\frac{3}{2\,!}+\frac{7}{3\,!}+\frac{15}{4\,!}+.....\text{to}\,\infty \] is [Kerala (Engg.) 2005] |
| A. | \[e(e+1)\] |
| B. | \[e\,(1-e)\] |
| C. | \[3e-1\] |
| D. | \[3e\] |
| E. | (e) \[e\,(e-1)\] |
| Answer» F. | |
| 116. |
The locus of mid point of that chord of parabola which subtends right angle on the vertex will be [UPSEAT 1999] |
| A. | \[{{y}^{2}}-2ax+8{{a}^{2}}=0\] |
| B. | \[{{y}^{2}}=a(x-4a)\] |
| C. | \[{{y}^{2}}=4a(x-4a)\] |
| D. | \[{{y}^{2}}+3ax+4{{a}^{2}}=0\] |
| Answer» B. \[{{y}^{2}}=a(x-4a)\] | |
| 117. |
If \[\sin \alpha ,\cos \alpha \] are the roots of the equation \[a{{x}^{2}}+bx+c=0\], then [MP PET 1993] |
| A. | \[{{a}^{2}}-{{b}^{2}}+2ac=0\] |
| B. | \[{{(a-c)}^{2}}={{b}^{2}}+{{c}^{2}}\] |
| C. | \[{{a}^{2}}+{{b}^{2}}-2ac=0\] |
| D. | \[{{a}^{2}}+{{b}^{2}}+2ac=0\] |
| Answer» B. \[{{(a-c)}^{2}}={{b}^{2}}+{{c}^{2}}\] | |
| 118. |
In the expansion of \[{{\log }_{e}}\frac{1}{1-x-{{x}^{2}}+{{x}^{3}}}\], the coefficient of \[x\] is |
| A. | 0 |
| B. | 1 |
| C. | ? 1 |
| D. | 44228 |
| Answer» C. ? 1 | |
| 119. |
If \[a\ne 0\] and the line \[2bx+3cy+4d=0\] passes through the points of intersection of the parabolas \[{{y}^{2}}=4ax\] and \[{{x}^{2}}=4ay\], then [AIEEE 2004] |
| A. | \[{{d}^{2}}+{{(3b-2c)}^{2}}=0\] |
| B. | \[{{d}^{2}}+{{(3b+2c)}^{2}}=0\] |
| C. | \[{{d}^{2}}+{{(2b-3c)}^{2}}=0\] |
| D. | \[{{d}^{2}}+{{(2b+3c)}^{2}}=0\] |
| Answer» E. | |
| 120. |
If one root of the quadratic equation \[a{{x}^{2}}+bx+c=0\] is equal to the nth power of the other root, then the value of \[{{(a{{c}^{n}})}^{\frac{1}{n+1}}}+{{({{a}^{n}}c)}^{\frac{1}{n+1}}}=\] [IIT 1983] |
| A. | \[b\] |
| B. | |
| C. | \[{{b}^{\frac{1}{n+1}}}\] |
| D. | \[-{{b}^{\frac{1}{n+1}}}\] |
| Answer» C. \[{{b}^{\frac{1}{n+1}}}\] | |
| 121. |
If \[|x| |
| A. | 44228 |
| B. | 44287 |
| C. | 43831 |
| D. | 44470 |
| Answer» D. 44470 | |
| 122. |
\[\tan \alpha +2\tan 2\alpha +4\tan 4\alpha +8\cot \,8\alpha =\] [IIT 1988; MP PET 1991] |
| A. | \[\tan \alpha \] |
| B. | \[\tan 2\alpha \] |
| C. | \[\cot \,\alpha \] |
| D. | \[\cot \,2\alpha \] |
| Answer» D. \[\cot \,2\alpha \] | |
| 123. |
The equation of the common tangent to the curves \[{{y}^{2}}=8x\] and \[xy=-1\] is [IIT Screening 2002] |
| A. | \[3y=9x+2\] |
| B. | \[y=2x+1\] |
| C. | \[2y=x+8\] |
| D. | \[y=x+2\] |
| Answer» E. | |
| 124. |
Let\[z\]and \[w\] be two complex numbers such that \[|z|\,\le 1,\] \[|w|\,\le 1\]and\[|z+iw|\,=\,|z-i\overline{w}|=2\]. Then \[z\] is equal to [IIT 1995] |
| A. | 1 or \[i\] |
| B. | \[i\] or \[-i\] |
| C. | 1 or - 1 |
| D. | \[i\]or -1 |
| Answer» D. \[i\]or -1 | |
| 125. |
The value of\[\sin \frac{\pi }{14}\sin \frac{3\pi }{14}\sin \frac{5\pi }{14}\sin \frac{7\pi }{14}\sin \frac{9\pi }{14}\sin \frac{11\pi }{14}\sin \frac{13\pi }{14}\] is equal to [IIT 1991; MNR 1992] |
| A. | \[\frac{1}{8}\] |
| B. | \[\frac{1}{16}\] |
| C. | \[\frac{1}{32}\] |
| D. | \[\frac{1}{64}\] |
| Answer» E. | |
| 126. |
For any two complex numbers \[{{z}_{1}}\]and\[{{z}_{2}}\] and any real numbers a and b; \[|(a{{z}_{1}}-b{{z}_{2}}){{|}^{2}}+|(b{{z}_{1}}+a{{z}_{2}}){{|}^{2}}=\] [IIT 1988] |
| A. | \[({{a}^{2}}+{{b}^{2}})(|{{z}_{1}}|+|{{z}_{2}}|)\] |
| B. | \[({{a}^{2}}+{{b}^{2}})(|{{z}_{1}}{{|}^{2}}+|{{z}_{2}}{{|}^{2}})\] |
| C. | \[({{a}^{2}}+{{b}^{2}})(|{{z}_{1}}{{|}^{2}}-|{{z}_{2}}{{|}^{2}})\] |
| D. | None of these |
| Answer» C. \[({{a}^{2}}+{{b}^{2}})(|{{z}_{1}}{{|}^{2}}-|{{z}_{2}}{{|}^{2}})\] | |
| 127. |
If \[{{z}_{1}}=a+ib\] and \[{{z}_{2}}=c+id\] are complex numbers such that \[|{{z}_{1}}|\,=\,|{{z}_{2}}|=1\] and \[R({{z}_{1}}\overline{{{z}_{2}}})=0,\] then the pair of complex numbers \[{{w}_{1}}=a+ic\] and \[{{w}_{2}}=b+id\] satisfies [IIT 1985] |
| A. | \[|{{w}_{1}}|=1\] |
| B. | \[|{{w}_{2}}|=1\] |
| C. | \[R({{w}_{1}}\overline{{{w}_{2}}})=0,\] |
| D. | All the above |
| Answer» E. | |
| 128. |
The locus of \[z\]satisfying the inequality \[{{\log }_{1/3}}|z+1|\,>\] \[{{\log }_{1/3}}|z-1|\] is |
| A. | \[R\,(z)<0\] |
| B. | \[R\,(z)>0\] |
| C. | \[I\,(z)<0\] |
| D. | None of these |
| Answer» B. \[R\,(z)>0\] | |
| 129. |
If the first term of a G.P. \[{{a}_{1}},\ {{a}_{2}},\ {{a}_{3}},..........\]is unity such that \[4{{a}_{2}}+5{{a}_{3}}\] is least, then the common ratio of G.P. is |
| A. | \[-\frac{2}{5}\] |
| B. | \[-\frac{3}{5}\] |
| C. | \[\frac{2}{5}\] |
| D. | None of these |
| Answer» B. \[-\frac{3}{5}\] | |
| 130. |
If \[{{a}_{1}},\ {{a}_{2}},\,{{a}_{3}},......{{a}_{24}}\] are in arithmetic progression and \[{{a}_{1}}+{{a}_{5}}+{{a}_{10}}+{{a}_{15}}+{{a}_{20}}+{{a}_{24}}=225\], then \[{{a}_{1}}+{{a}_{2}}+{{a}_{3}}+........+{{a}_{23}}+{{a}_{24}}=\] [MP PET 1999; AMU 1997] |
| A. | 909 |
| B. | 75 |
| C. | 750 |
| D. | 900 |
| Answer» E. | |
| 131. |
If the roots of the equation \[{{x}^{3}}-12{{x}^{2}}+39x-28=0\] are in A.P., then their common difference will be [UPSEAT 1994, 99, 2001; RPET 2001] |
| A. | \[\pm 1\] |
| B. | \[\pm 2\] |
| C. | \[\pm 3\] |
| D. | \[\pm 4\] |
| Answer» D. \[\pm 4\] | |
| 132. |
The coefficient of \[x\] in the equation \[{{x}^{2}}+px+q=0\]was taken as 17 in place of 13, its roots were found to be -2 and -15, The roots of the original equation are [IIT 1977, 79] |
| A. | 3, 10 |
| B. | - 3, - 10 |
| C. | - 5, - 18 |
| D. | None of these |
| Answer» C. - 5, - 18 | |
| 133. |
The values of \['a'\] for which \[({{a}^{2}}-1){{x}^{2}}+2(a-1)x+2\] is positive for any \[x\] are [UPSEAT 2001] |
| A. | \[a\ge 1\] |
| B. | \[a\le 1\] |
| C. | \[a>-3\] |
| D. | \[a<-3\]or \[a>1\] |
| Answer» E. | |
| 134. |
If \[m,\,n\] are the roots of the equation \[{{x}^{2}}-x-1=0\], then the value of \[\frac{\left( 1+m{{\log }_{e}}3+\frac{{{(m{{\log }_{e}}3)}^{2}}}{2\,!\,}+...\infty \right)\,\,\left( 1+n{{\log }_{e}}3+\frac{{{(n{{\log }_{e}}3)}^{2}}}{2\,!\,}+..\infty \right)\,}{\left( 1+mn{{\log }_{e}}3+\frac{{{(mn{{\log }_{e}}3)}^{2}}}{2\,!}+.....\infty \right)}\] |
| A. | 9 |
| B. | 3 |
| C. | 0 |
| D. | 1 |
| Answer» B. 3 | |
| 135. |
In the expansion of \[\frac{a+bx+c{{x}^{2}}}{{{e}^{x}}}\], the coefficient of \[{{x}^{n}}\] will be |
| A. | \[\frac{a\,{{(-1)}^{n}}}{n\,!}+\frac{b{{(-1)}^{n-1}}}{(n-1)\,!}+\frac{c{{(-1)}^{n-2}}}{(n-2)\,!}\] |
| B. | \[\frac{a}{n\,!}+\frac{b}{(n-1)\,!}+\frac{c}{(n-2)\,!}\] |
| C. | \[\frac{\,{{(-1)}^{n}}}{n\,!}+\frac{{{(-1)}^{n-1}}}{(n-1)\,!}+\frac{{{(-1)}^{n-2}}}{(n-2)\,!}\] |
| D. | None of these |
| Answer» B. \[\frac{a}{n\,!}+\frac{b}{(n-1)\,!}+\frac{c}{(n-2)\,!}\] | |
| 136. |
\[\sin {{20}^{o}}\,\sin {{40}^{o}}\,\sin {{60}^{o}}\,\sin {{80}^{o}}=\] [MNR 1976, 81] |
| A. | \[-3/16\] |
| B. | \[5/16\] |
| C. | \[3/16\] |
| D. | \[-5/16\] |
| Answer» D. \[-5/16\] | |
| 137. |
If \[{{\cos }^{6}}\alpha +{{\sin }^{6}}\alpha +K\,{{\sin }^{2}}2\alpha =1,\] then K = |
| A. | \[\frac{4}{3}\] |
| B. | \[\frac{3}{4}\] |
| C. | \[\frac{1}{2}\] |
| D. | 2 |
| Answer» C. \[\frac{1}{2}\] | |
| 138. |
If \[\tan \theta =\frac{\sin \alpha -\cos \alpha }{\sin \alpha +\cos \alpha },\]then \[\sin \alpha +\cos \alpha \] and \[\sin \alpha -\cos \alpha \] must be equal to [WB JEE 1971] |
| A. | \[\sqrt{2}\cos \theta ,\,\,\sqrt{2}\sin \theta \] |
| B. | \[\sqrt{2}\sin \theta ,\,\,\sqrt{2}\cos \theta \] |
| C. | \[\sqrt{2}\sin \theta ,\,\,\sqrt{2}\sin \theta \] |
| D. | \[\sqrt{2}\,\cos \theta ,\,\,\sqrt{2}\,\cos \theta \] |
| Answer» B. \[\sqrt{2}\sin \theta ,\,\,\sqrt{2}\cos \theta \] | |
| 139. |
The angle of intersection of the curves \[{{y}^{2}}=2x/\pi \] and \[y=\sin x\], is [Roorkee 1998] |
| A. | \[{{\cot }^{-1}}(-1/\pi )\] |
| B. | \[{{\cot }^{-1}}\pi \] |
| C. | \[{{\cot }^{-1}}(-\pi )\] |
| D. | \[{{\cot }^{-1}}(1/\pi )\] |
| Answer» C. \[{{\cot }^{-1}}(-\pi )\] | |
| 140. |
Which one of the following curves cuts the parabola \[{{y}^{2}}=4ax\] at right angles [IIT 1994] |
| A. | \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\] |
| B. | \[y={{e}^{-x/2a}}\] |
| C. | \[y=ax\] |
| D. | \[{{x}^{2}}=4ay\] |
| Answer» C. \[y=ax\] | |
| 141. |
Consider a circle with its centre lying on the focus of the parabola \[{{y}^{2}}=2px\] such that it touches the directrix of the parabola. Then, a point of intersection of the circle and the parabola is [IIT 1995] |
| A. | \[\left( \frac{p}{2},\ p \right)\] |
| B. | \[\left( \frac{p}{2},\ -p \right)\] |
| C. | \[\left( \frac{-p}{2},\ p \right)\] |
| D. | \[\left( \frac{-p}{2},\ -p \right)\] |
| Answer» C. \[\left( \frac{-p}{2},\ p \right)\] | |
| 142. |
If the sum of first \[n\] terms of an A.P. be equal to the sum of its first \[m\] terms, \[(m\ne n)\], then the sum of its first \[(m+n)\] terms will be [MP PET 1984] |
| A. | 0 |
| B. | \[n\] |
| C. | \[m\] |
| D. | \[m+n\] |
| Answer» B. \[n\] | |
| 143. |
If the angles of a quadrilateral are in A.P. whose common difference is\[{{10}^{o}}\], then the angles of the quadrilateral are |
| A. | \[{{65}^{o}},\,{{85}^{o}},\,{{95}^{o}},\,{{105}^{o}}\] |
| B. | \[{{75}^{o}},\,{{85}^{o}},\,{{95}^{o}},\,{{105}^{o}}\] |
| C. | \[{{65}^{o}},\,{{75}^{o}},\,{{85}^{o}},\,{{95}^{o}}\] |
| D. | \[{{65}^{o}},\,{{95}^{o}},\,{{105}^{o}},\,{{115}^{o}}\] |
| Answer» C. \[{{65}^{o}},\,{{75}^{o}},\,{{85}^{o}},\,{{95}^{o}}\] | |
| 144. |
If \[x=\sqrt{1+\sqrt{1+\sqrt{1+.......\text{to infinity}}}},\]then x = |
| A. | \[\frac{1+\sqrt{5}}{2}\] |
| B. | \[\frac{1-\sqrt{5}}{2}\] |
| C. | \[\frac{1\pm \sqrt{5}}{2}\] |
| D. | None of these |
| Answer» B. \[\frac{1-\sqrt{5}}{2}\] | |
| 145. |
\[\frac{1}{1\,!}+\frac{4}{2\,!}+\frac{7}{3\,!}+\frac{10}{4\,!}+.....\infty =\] |
| A. | \[e+4\] |
| B. | \[2+e\] |
| C. | \[3+e\] |
| D. | \[e\] |
| Answer» C. \[3+e\] | |
| 146. |
The value of \[{{\sin }^{2}}{{5}^{o}}+{{\sin }^{2}}{{10}^{o}}+{{\sin }^{2}}{{15}^{o}}+...+\] \[{{\sin }^{2}}{{85}^{o}}+{{\sin }^{2}}{{90}^{o}}\] is equal to [Karnataka CET 1999] |
| A. | 7 |
| B. | 8 |
| C. | 9 |
| D. | \[9\frac{1}{2}\] |
| Answer» E. | |
| 147. |
\[\frac{\frac{1}{2\,!}+\frac{1}{4\,!}+\frac{1}{6\,!}+.....\infty }{1+\frac{1}{3\,!}+\frac{1}{5\,!}+\frac{1}{7\,!}+.....\infty }=\] |
| A. | \[\frac{e+1}{e-1}\] |
| B. | \[\frac{e-1}{e+1}\] |
| C. | \[\frac{{{e}^{2}}+1}{{{e}^{2}}-1}\] |
| D. | \[\frac{{{e}^{2}}-1}{{{e}^{2}}+1}\] |
| Answer» C. \[\frac{{{e}^{2}}+1}{{{e}^{2}}-1}\] | |
| 148. |
The circular wire of diameter 10cm is cut and placed along the circumference of a circle of diameter 1 metre. The angle subtended by the wire at the centre of the circle is equal to [MNR 1974] |
| A. | \[\frac{\pi }{4}radian\] |
| B. | \[\frac{\pi }{3}radian\] |
| C. | \[\frac{\pi }{5}radian\] |
| D. | \[\frac{\pi }{10}radian\] |
| Answer» D. \[\frac{\pi }{10}radian\] | |
| 149. |
The number of points of intersection of the two curves\[y=2\sin x\] and \[y=5{{x}^{2}}+2x+3\] is [IIT 1994] |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | \[\infty \] |
| Answer» B. 1 | |
| 150. |
The equation of \[2{{x}^{2}}+3{{y}^{2}}-8x-18y+35=k\] represents [IIT 1994] |
| A. | No locus if \[k>0\] |
| B. | An ellipse, if \[k<0\] |
| C. | A point if,\[k=0\] |
| D. | A hyperbola, if \[k>0\] |
| Answer» D. A hyperbola, if \[k>0\] | |