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.
| 51. |
If \[a\,{{\cos }^{3}}\alpha +3a\,\cos \alpha \,{{\sin }^{2}}\alpha =m\] and\[a\,{{\sin }^{3}}\alpha +3a\,{{\cos }^{2}}\alpha \sin \alpha =n,\] then \[{{(m+n)}^{2/3}}+{{(m-n)}^{2/3}}\] is equal to |
| A. | \[2{{a}^{2}}\] |
| B. | \[2{{a}^{1/3}}\] |
| C. | \[2{{a}^{2/3}}\] |
| D. | \[2{{a}^{3}}\] |
| Answer» D. \[2{{a}^{3}}\] | |
| 52. |
The locus of the midpoint of the line segment joining the focus to a moving point on the parabola \[{{y}^{2}}=4ax\] is another parabola with the directrix [IIT Screening 2002] |
| A. | \[x=-a\] |
| B. | \[x=-\frac{a}{2}\] |
| C. | \[x=0\] |
| D. | \[x=\frac{a}{2}\] |
| Answer» D. \[x=\frac{a}{2}\] | |
| 53. |
If \[{{z}^{2}}+z|z|+|z{{|}^{2}}=0\], then the locus of \[z\] is |
| A. | A circle |
| B. | A straight line |
| C. | A pair of straight lines |
| D. | None of these |
| Answer» D. None of these | |
| 54. |
If A lies in the third quadrant and \[3\,\tan A-4=0,\] then \[5\,\sin 2A+3\,\sin A+4\,\cos A=\] [EAMCET 1994] |
| A. | 0 |
| B. | \[\frac{-24}{5}\] |
| C. | \[\frac{24}{5}\] |
| D. | \[\frac{48}{5}\] |
| Answer» B. \[\frac{-24}{5}\] | |
| 55. |
If z, iz and \[z+iz\] are the vertices of a triangle whose area is 2 units, then the value of \[|z|\] is [RPET 2000] |
| A. | -2 |
| B. | 2 |
| C. | 4 |
| D. | 8 |
| Answer» B. 2 | |
| 56. |
The harmonic mean of two numbers is 4 and the arithmetic and geometric means satisfy the relation \[2A+{{G}^{2}}=27\], the numbers are [MNR 1987; UPSEAT 1999, 2000] |
| A. | \[6,\,3\] |
| B. | 5, 4 |
| C. | \[5,\ -2.5\] |
| D. | \[-3,\ 1\] |
| Answer» B. 5, 4 | |
| 57. |
The locus of the poles of normal chords of an ellipse is given by [UPSEAT 2001] |
| A. | \[\frac{{{a}^{6}}}{{{x}^{2}}}+\frac{{{b}^{6}}}{{{y}^{2}}}={{({{a}^{2}}-{{b}^{2}})}^{2}}\] |
| B. | \[\frac{{{a}^{3}}}{{{x}^{2}}}+\frac{{{b}^{3}}}{{{y}^{2}}}={{({{a}^{2}}-{{b}^{2}})}^{2}}\] |
| C. | \[\frac{{{a}^{6}}}{{{x}^{2}}}+\frac{{{b}^{6}}}{{{y}^{2}}}={{({{a}^{2}}+{{b}^{2}})}^{2}}\] |
| D. | \[\frac{{{a}^{3}}}{{{x}^{2}}}+\frac{{{b}^{3}}}{{{y}^{2}}}={{({{a}^{2}}+{{b}^{2}})}^{2}}\] |
| Answer» B. \[\frac{{{a}^{3}}}{{{x}^{2}}}+\frac{{{b}^{3}}}{{{y}^{2}}}={{({{a}^{2}}-{{b}^{2}})}^{2}}\] | |
| 58. |
If at least one value of the complex number \[z=x+iy\] satisfy the condition \[|z+\sqrt{2}|={{a}^{2}}-3a+2\] and the inequality \[|z+i\sqrt{2}| |
| A. | \[a>2\] |
| B. | \[a=2\] |
| C. | \[a<2\] |
| D. | None of these |
| Answer» B. \[a=2\] | |
| 59. |
If \[{{A}_{1}},\ {{A}_{2}};{{G}_{1}},\ {{G}_{2}}\] and \[{{H}_{1}},\ {{H}_{2}}\] be \[AM's,\ GM's\] and \[HM's\] between two quantities, then the value of \[\frac{{{G}_{1}}{{G}_{2}}}{{{H}_{1}}{{H}_{2}}}\] is [Roorkee 1983; AMU 2000] |
| A. | \[\frac{{{A}_{1}}+{{A}_{2}}}{{{H}_{1}}+{{H}_{2}}}\] |
| B. | \[\frac{{{A}_{1}}-{{A}_{2}}}{{{H}_{1}}+{{H}_{2}}}\] |
| C. | \[\frac{{{A}_{1}}+{{A}_{2}}}{{{H}_{1}}-{{H}_{2}}}\] |
| D. | \[\frac{{{A}_{1}}-{{A}_{2}}}{{{H}_{1}}-{{H}_{2}}}\] |
| Answer» B. \[\frac{{{A}_{1}}-{{A}_{2}}}{{{H}_{1}}+{{H}_{2}}}\] | |
| 60. |
\[\left( 1+\cos \frac{\pi }{8} \right)\,\left( 1+\cos \frac{3\pi }{8} \right)\,\left( 1+\cos \frac{5\pi }{8} \right)\,\left( 1+\cos \frac{7\pi }{8} \right)=\] [IIT 1984; WB JEE 1992] |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{1}{4}\] |
| C. | \[\frac{1}{8}\] |
| D. | \[\frac{1}{16}\] |
| Answer» D. \[\frac{1}{16}\] | |
| 61. |
If the normal at any point P on the ellipse cuts the major and minor axes in G and g respectively and C be the centre of the ellipse, then [Kurukshetra CEE 1998] |
| A. | \[{{a}^{2}}{{(CG)}^{2}}+{{b}^{2}}{{(Cg)}^{2}}={{({{a}^{2}}-{{b}^{2}})}^{2}}\] |
| B. | \[{{a}^{2}}{{(CG)}^{2}}-{{b}^{2}}{{(Cg)}^{2}}={{({{a}^{2}}-{{b}^{2}})}^{2}}\] |
| C. | \[{{a}^{2}}{{(CG)}^{2}}-{{b}^{2}}{{(Cg)}^{2}}={{({{a}^{2}}+{{b}^{2}})}^{2}}\] |
| D. | None of these |
| Answer» B. \[{{a}^{2}}{{(CG)}^{2}}-{{b}^{2}}{{(Cg)}^{2}}={{({{a}^{2}}-{{b}^{2}})}^{2}}\] | |
| 62. |
If the complex number \[{{z}_{1}},{{z}_{2}}\] the origin form an equilateral triangle then \[z_{1}^{2}+z_{2}^{2}=\] [IIT 1983] |
| A. | \[{{z}_{1}}\,{{z}_{2}}\] |
| B. | \[{{z}_{1}}\,\overline{{{z}_{2}}}\] |
| C. | \[\overline{{{z}_{2}}}\,{{z}_{1}}\] |
| D. | \[|{{z}_{1}}{{|}^{2}}=|{{z}_{2}}{{|}^{2}}\] |
| Answer» B. \[{{z}_{1}}\,\overline{{{z}_{2}}}\] | |
| 63. |
If \[a,\ b,\ c\] are in G.P. and \[\log a-\log 2b,\ \log 2b-\log 3c\]and \[\log 3c-\log a\] are in A.P., then \[a,\ b,\ c\] are the length of the sides of a triangle which is |
| A. | Acute angled |
| B. | Obtuse angled |
| C. | Right angled |
| D. | Equilateral |
| Answer» C. Right angled | |
| 64. |
For the equation \[3{{x}^{2}}+px+3=0,\,p>0\] if one of the root is square of the other, then p is equal to [IIT Screening 2000] |
| A. | \[\frac{1}{3}\] |
| B. | 1 |
| C. | 3 |
| D. | \[\frac{2}{3}\] |
| Answer» D. \[\frac{2}{3}\] | |
| 65. |
\[{{\sin }^{4}}\frac{\pi }{4}+{{\sin }^{4}}\frac{3\pi }{8}+{{\sin }^{4}}\frac{5\pi }{8}+{{\sin }^{4}}\frac{7\pi }{8}=\] [Roorkee 1980] |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{1}{4}\] |
| C. | \[\frac{3}{2}\] |
| D. | \[\frac{3}{4}\] |
| Answer» D. \[\frac{3}{4}\] | |
| 66. |
The locus of the middle point of the intercept of the tangents drawn from an external point to the ellipse \[{{x}^{2}}+2{{y}^{2}}=2\] between the co-ordinates axes, is [IIT Screening 2004] |
| A. | \[\frac{1}{{{x}^{2}}}+\frac{1}{2{{y}^{2}}}=1\] |
| B. | \[\frac{1}{4{{x}^{2}}}+\frac{1}{2{{y}^{2}}}=1\] |
| C. | \[\frac{1}{2{{x}^{2}}}+\frac{1}{4{{y}^{2}}}=1\] |
| D. | \[\frac{1}{2{{x}^{2}}}+\frac{1}{{{y}^{2}}}=1\] |
| Answer» D. \[\frac{1}{2{{x}^{2}}}+\frac{1}{{{y}^{2}}}=1\] | |
| 67. |
Suppose \[{{z}_{1}},\,{{z}_{2}},\,{{z}_{3}}\] are the vertices of an equilateral triangle inscribed in the circle \[|z|\,=2\]. If \[{{z}_{1}}=1+i\sqrt{3},\] then values of \[{{z}_{3}}\] and \[{{z}_{2}}\] are respectively [IIT 1994] |
| A. | \[-2,\,1-i\sqrt{3}\] |
| B. | \[2,\,1+i\sqrt{3}\] |
| C. | \[1+i\sqrt{3},-2\] |
| D. | None of these |
| Answer» B. \[2,\,1+i\sqrt{3}\] | |
| 68. |
In a G.P. the sum of three numbers is 14, if 1 is added to first two numbers and subtracted from third number, the series becomes A.P., then the greatest number is [Roorkee 1973] |
| A. | 8 |
| B. | 4 |
| C. | 24 |
| D. | 16 |
| Answer» B. 4 | |
| 69. |
For what value of \[\lambda \]the sum of the squares of the roots of \[{{x}^{2}}+(2+\lambda )\,x-\frac{1}{2}(1+\lambda )=0\] is minimum [AMU 1999] |
| A. | 44230 |
| B. | 1 |
| C. | 44228 |
| D. | 44297 |
| Answer» D. 44297 | |
| 70. |
If \[\sin 6\theta =32{{\cos }^{5}}\theta \sin \theta -32{{\cos }^{3}}\theta \sin \theta +3x,\] then \[x=\] [EAMCET 2003] |
| A. | \[\cos \theta \] |
| B. | \[\cos 2\theta \] |
| C. | \[\sin \theta \] |
| D. | \[\sin 2\theta \] |
| Answer» E. | |
| 71. |
Tangent is drawn to ellipse \[\frac{{{x}^{2}}}{27}+{{y}^{2}}=1\] at \[(3\sqrt{3}\cos \theta ,\ \sin \theta )\] where \[\theta \in (0,\ \pi /2)\]. Then the value of \[\theta \] such that sum of intercepts on axes made by this tangent is minimum, is [IIT Screening 2003] |
| A. | \[\pi /3\] |
| B. | \[\pi /6\] |
| C. | \[\pi /8\] |
| D. | \[\pi /4\] |
| Answer» C. \[\pi /8\] | |
| 72. |
If \[a,b,c\] and\[u,v,w\] are complex numbers representing the vertices of two triangles such that \[c=(1-r)a+rb\] and \[w=(1-r)u+rv\], where r is a complex number, then the two triangles |
| A. | Have the same area |
| B. | Are similar |
| C. | Are congruent |
| D. | None of these |
| Answer» C. Are congruent | |
| 73. |
If \[a,\ b,\ c\] are the positive integers, then \[(a+b)(b+c)(c+a)\]is [DCE 2000] |
| A. | \[<8abc\] |
| B. | \[>8abc\] |
| C. | \[=8abc\] |
| D. | None of these |
| Answer» C. \[=8abc\] | |
| 74. |
If \[\frac{x}{\cos \theta }=\frac{y}{\cos \left( \theta -\frac{2\pi }{3} \right)}=\frac{z}{\cos \left( \theta +\frac{2\pi }{3} \right)},\]then \[x+y+z=\] |
| A. | \[1\] |
| B. | \[0\] |
| C. | \[-1\] |
| D. | None of these |
| Answer» C. \[-1\] | |
| 75. |
The value of \[\sum\limits_{r=1}^{8}{\left( \sin \frac{2r\pi }{9}+i\cos \frac{2r\pi }{9} \right)}\]is |
| A. | \[-1\] |
| B. | 1 |
| C. | \[i\] |
| D. | \[-i\] |
| Answer» E. | |
| 76. |
If \[a,\ b,\ c,\ d\] be in H.P., then |
| A. | \[{{a}^{2}}+{{c}^{2}}>{{b}^{2}}+{{d}^{2}}\] |
| B. | \[{{a}^{2}}+{{d}^{2}}>{{b}^{2}}+{{c}^{2}}\] |
| C. | \[ac+bd>{{b}^{2}}+{{c}^{2}}\] |
| D. | \[ac+bd>{{b}^{2}}+{{d}^{2}}\] |
| Answer» D. \[ac+bd>{{b}^{2}}+{{d}^{2}}\] | |
| 77. |
The value of ?\[c\]?for which \[|{{\alpha }^{2}}-{{\beta }^{2}}|=\frac{7}{4}\], where \[\alpha \] and \[\beta \] are the roots of \[2{{x}^{2}}+7x+c=0\], is |
| A. | 4 |
| B. | 0 |
| C. | 6 |
| D. | 2 |
| Answer» D. 2 | |
| 78. |
On the ellipse \[4{{x}^{2}}+9{{y}^{2}}=1\], the points at which the tangents are parallel to the line \[8x=9y\] are [IIT 1999] |
| A. | \[\left( \frac{2}{5},\ \frac{1}{5} \right)\] |
| B. | \[\left( -\frac{2}{5},\ \frac{1}{5} \right)\] |
| C. | \[\left( -\frac{2}{5},\ -\frac{1}{5} \right)\] |
| D. | \[\left( \frac{2}{5},\ -\frac{1}{5} \right)\] |
| Answer» C. \[\left( -\frac{2}{5},\ -\frac{1}{5} \right)\] | |
| 79. |
A boy goes to school from his home at a speed of x km/hour and comes back at a speed of y km/hour, then the average speed is given by [DCE 2002] |
| A. | A.M. |
| B. | G.M. |
| C. | H.M. |
| D. | None of these |
| Answer» D. None of these | |
| 80. |
If \[\alpha ,\beta \]are the roots of \[{{x}^{2}}-ax+b=0\] and if \[{{\alpha }^{n}}+{{\beta }^{n}}={{V}_{n}}\], then [RPET 1995; Karnataka CET 2000; Pb. CET 2002] |
| A. | \[{{V}_{n+1}}=a{{V}_{n}}+b{{V}_{n-1}}\] |
| B. | \[{{V}_{n+1}}=a{{V}_{n}}+a{{V}_{n-1}}\] |
| C. | \[{{V}_{n+1}}=a{{V}_{n}}-b{{V}_{n-1}}\] |
| D. | \[{{V}_{n+1}}=a{{V}_{n-1}}-b{{V}_{n}}\] |
| Answer» D. \[{{V}_{n+1}}=a{{V}_{n-1}}-b{{V}_{n}}\] | |
| 81. |
The angle of intersection of ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] and circle \[{{x}^{2}}+{{y}^{2}}=ab\], is |
| A. | \[{{\tan }^{-1}}\left( \frac{a-b}{ab} \right)\] |
| B. | \[{{\tan }^{-1}}\left( \frac{a+b}{ab} \right)\] |
| C. | \[{{\tan }^{-1}}\left( \frac{a+b}{\sqrt{ab}} \right)\] |
| D. | \[{{\tan }^{-1}}\left( \frac{a-b}{\sqrt{ab}} \right)\] |
| Answer» E. | |
| 82. |
The set of values of \[x\] which satisfy \[5x+2 |
| A. | \[(2,\,3)\] |
| B. | \[(-\infty ,\,1)\cup (2,\,3)\] |
| C. | \[(-\infty ,\,1)\] |
| D. | \[(1,\,3)\] |
| Answer» C. \[(-\infty ,\,1)\] | |
| 83. |
If \[a{{\sin }^{2}}x+b{{\cos }^{2}}x=c,\,\,\]\[b\,{{\sin }^{2}}y+a\,{{\cos }^{2}}y=d\] and \[a\,\tan x=b\,\tan y,\]then \[\frac{{{a}^{2}}}{{{b}^{2}}}\] is equal to |
| A. | \[\frac{(b-c)\,\,(d-b)}{(a-d)\,\,(c-a)}\] |
| B. | \[\frac{(a-d)\,\,(c-a)}{(b-c)\,\,(d-b)}\] |
| C. | \[\frac{(d-a)\,\,(c-a)}{(b-c)\,\,(d-b)}\] |
| D. | \[\frac{(b-c)\,\,(b-d)}{(a-c)\,\,(a-d)}\] |
| Answer» C. \[\frac{(d-a)\,\,(c-a)}{(b-c)\,\,(d-b)}\] | |
| 84. |
The line \[x\cos \alpha +y\sin \alpha =p\] will be a tangent to the conic \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\], if [Roorkee 1978] |
| A. | \[{{p}^{2}}={{a}^{2}}{{\sin }^{2}}\alpha +{{b}^{2}}{{\cos }^{2}}\alpha \] |
| B. | \[{{p}^{2}}={{a}^{2}}+{{b}^{2}}\] |
| C. | \[{{p}^{2}}={{b}^{2}}{{\sin }^{2}}\alpha +{{a}^{2}}{{\cos }^{2}}\alpha \] |
| D. | None of these |
| Answer» D. None of these | |
| 85. |
If \[a,\ b,\ c\] are in H.P., then the value of \[\left( \frac{1}{b}+\frac{1}{c}-\frac{1}{a} \right)\,\left( \frac{1}{c}+\frac{1}{a}-\frac{1}{b} \right)\], is [MP PET 1998; Pb. CET 2000] |
| A. | \[\frac{2}{bc}+\frac{1}{{{b}^{2}}}\] |
| B. | \[\frac{3}{{{c}^{2}}}+\frac{2}{ca}\] |
| C. | \[\frac{3}{{{b}^{2}}}-\frac{2}{ab}\] |
| D. | None of these |
| Answer» D. None of these | |
| 86. |
If 8, 2 are the roots of \[{{x}^{2}}+ax+\beta =0\] and 3, 3 are the roots of \[{{x}^{2}}+\alpha \,x+b=0\], then the roots of \[{{x}^{2}}+ax+b=0\] are [EAMCET 1987] |
| A. | \[8,\,-1\] |
| B. | - 9, 2 |
| C. | \[-8,-2\] |
| D. | 9, 1 |
| Answer» E. | |
| 87. |
Given that the equation \[{{z}^{2}}+(p+iq)z+r+i\,s=0,\] where \[p,q,r,s\] are real and non-zero has a real root, then |
| A. | \[pqr={{r}^{2}}+{{p}^{2}}s\] |
| B. | \[prs={{q}^{2}}+{{r}^{2}}p\] |
| C. | \[qrs={{p}^{2}}+{{s}^{2}}q\] |
| D. | \[pqs={{s}^{2}}+{{q}^{2}}r\] |
| Answer» E. | |
| 88. |
If \[p,\ q,\ r\] are in A.P. and are positive, the roots of the quadratic equation \[p{{x}^{2}}+qx+r=0\] are all real for [IIT 1995] |
| A. | \[\left| \,\frac{r}{p}-7\ \right|\ \ge 4\sqrt{3}\] |
| B. | \[\left| \ \frac{p}{r}-7\ \right|\ <4\sqrt{3}\] |
| C. | All \[p\]and \[r\] |
| D. | No \[p\] and \[r\] |
| Answer» B. \[\left| \ \frac{p}{r}-7\ \right|\ <4\sqrt{3}\] | |
| 89. |
In the expansion of \[\frac{1+x}{1\,!}+\frac{{{(1+x)}^{2}}}{2\,!}+\frac{{{(1+x)}^{3}}}{3\,!}+.....,\] the coefficient of \[{{x}^{n}}\] will be |
| A. | \[\frac{1}{n\,!}\] |
| B. | \[\frac{1}{n\,!}+\frac{1}{(n+1)\,!}\] |
| C. | \[\frac{e}{n\,!}\] |
| D. | \[e\,\left[ \frac{1}{n\,!}+\frac{1}{(n+1)\,!} \right]\] |
| Answer» D. \[e\,\left[ \frac{1}{n\,!}+\frac{1}{(n+1)\,!} \right]\] | |
| 90. |
If \[\frac{3\pi }{4} |
| A. | \[1+\cot \alpha \] |
| B. | \[1-\cot \alpha \] |
| C. | \[-1-\cot \alpha \] |
| D. | \[-1+\cot \alpha \] |
| Answer» D. \[-1+\cot \alpha \] | |
| 91. |
If \[{{z}_{1}},{{z}_{2}}\] and \[{{z}_{3}},{{z}_{4}}\] are two pairs of conjugate complex numbers, then \[arg\left( \frac{{{z}_{1}}}{{{z}_{4}}} \right)+arg\left( \frac{{{z}_{2}}}{{{z}_{3}}} \right)\] equals |
| A. | 0 |
| B. | \[\frac{\pi }{2}\] |
| C. | \[\frac{3\pi }{2}\] |
| D. | \[\pi \] |
| Answer» B. \[\frac{\pi }{2}\] | |
| 92. |
If \[x,\,y,z\] are three consecutive positive integers, then \[\frac{1}{2}{{\log }_{e}}x+\frac{1}{2}{{\log }_{e}}z+\frac{1}{2xz+1}+\frac{1}{3}{{\left( \frac{1}{2xz+1} \right)}^{3}}+....=\] |
| A. | \[{{\log }_{e}}x\] |
| B. | \[{{\log }_{e}}y\] |
| C. | \[{{\log }_{e}}z\] |
| D. | None of these |
| Answer» C. \[{{\log }_{e}}z\] | |
| 93. |
If \[\text{cosec}\theta =\frac{p+q}{p-q},\] then \[\cot \,\left( \frac{\pi }{4}+\frac{\theta }{2} \right)=\] [EAMCET 2001] |
| A. | \[\sqrt{\frac{p}{q}}\] |
| B. | \[\sqrt{\frac{q}{p}}\] |
| C. | \[\sqrt{pq}\] |
| D. | \[pq\] |
| Answer» C. \[\sqrt{pq}\] | |
| 94. |
If \[|z-25i|\le 15\], then \[|\max .amp(z)-\min .amp(z)|=\] |
| A. | \[{{\cos }^{-1}}\left( \frac{3}{5} \right)\] |
| B. | \[\pi -2{{\cos }^{-1}}\left( \frac{3}{5} \right)\] |
| C. | \[\frac{\pi }{2}+{{\cos }^{-1}}\left( \frac{3}{5} \right)\] |
| D. | \[{{\sin }^{-1}}\left( \frac{3}{5} \right)-{{\cos }^{-1}}\left( \frac{3}{5} \right)\] |
| Answer» C. \[\frac{\pi }{2}+{{\cos }^{-1}}\left( \frac{3}{5} \right)\] | |
| 95. |
If \[1+\cos \alpha +{{\cos }^{2}}\alpha +.......\,\infty =2-\sqrt{2,}\] then \[\alpha ,\] \[(0 |
| A. | \[\pi /8\] |
| B. | \[\pi /6\] |
| C. | \[\pi /4\] |
| D. | \[3\pi /4\] |
| Answer» E. | |
| 96. |
In a triangle \[ABC\] the value of \[\angle A\] is given by \[5\cos A+3=0\], then the equation whose roots are \[\sin A\] and \[\tan A\] will be [Roorkee 1972] |
| A. | \[15{{x}^{2}}-8x+16=0\] |
| B. | \[15{{x}^{2}}+8x-16=0\] |
| C. | \[15{{x}^{2}}-8\sqrt{2}x+16=0\] |
| D. | \[15{{x}^{2}}-8x-16=0\] |
| Answer» C. \[15{{x}^{2}}-8\sqrt{2}x+16=0\] | |
| 97. |
If \[y=2{{x}^{2}}-1\], then \[\left[ \frac{1}{y}+\frac{1}{3{{y}^{3}}}+\frac{1}{5{{y}^{5}}}+.... \right]\] is equal to |
| A. | \[\frac{1}{2}\left[ \frac{1}{{{x}^{2}}}-\frac{1}{2{{x}^{4}}}+\frac{1}{3{{x}^{6}}}-..... \right]\] |
| B. | \[\frac{1}{2}\left[ \frac{1}{{{x}^{2}}}+\frac{1}{2{{x}^{4}}}+\frac{1}{3{{x}^{6}}}+..... \right]\] |
| C. | \[\frac{1}{2}\left[ \frac{1}{{{x}^{2}}}+\frac{1}{3{{x}^{6}}}+\frac{1}{5{{x}^{10}}}+..... \right]\] |
| D. | \[\frac{1}{2}\left[ \frac{1}{{{x}^{2}}}-\frac{1}{3{{x}^{6}}}+\frac{1}{5{{x}^{10}}}-..... \right]\] |
| Answer» C. \[\frac{1}{2}\left[ \frac{1}{{{x}^{2}}}+\frac{1}{3{{x}^{6}}}+\frac{1}{5{{x}^{10}}}+..... \right]\] | |
| 98. |
If \[\tan x=\frac{2b}{a-c}(a\ne c),\]\[y=a\,{{\cos }^{2}}x+2b\,\sin x\cos x+c\,{{\sin }^{2}}x\]and \[z=a{{\sin }^{2}}x-2b\sin x\cos x+c{{\cos }^{2}}x,\] then |
| A. | \[y=z\] |
| B. | \[y+z=a+c\] |
| C. | \[y-z=a+c\] |
| D. | \[y-z={{(a-c)}^{2}}+4{{b}^{2}}\] |
| Answer» C. \[y-z=a+c\] | |
| 99. |
Let \[z\] and \[w\] be the two non-zero complex numbers such that \[|z|\,=\,|w|\] and \[arg\,z+arg\,w=\pi \]. Then \[z\] is equal to [IIT 1995; AIEEE 2002] |
| A. | \[w\] |
| B. | \[-w\] |
| C. | \[\overline{w}\] |
| D. | \[-\overline{w}\] |
| Answer» E. | |
| 100. |
\[2.\overset{\bullet \,\,\bullet \,\,\bullet }{\mathop{357}}\,=\] [IIT 1983; RPET 1995] |
| A. | \[\frac{2355}{1001}\] |
| B. | \[\frac{2370}{997}\] |
| C. | \[\frac{2355}{999}\] |
| D. | None of these |
| Answer» D. None of these | |