MCQOPTIONS
Saved Bookmarks
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.
| 1. |
If \[z\] is a complex number, then the minimum value of \[|z|+|z-1|\] is [Roorkee 1992] |
| A. | 1 |
| B. | 0 |
| C. | 44228 |
| D. | None of these |
| Answer» B. 0 | |
| 2. |
If \[{{S}_{1}},\ {{S}_{2}},\ {{S}_{3}},...........{{S}_{m}}\] are the sums of \[n\] terms of \[m\] A.P.'s whose first terms are \[1,\ 2,\ 3,\ ...............,m\] and common differences are \[1,\ 3,\ 5,\ ...........2m-1\] respectively, then \[{{S}_{1}}+{{S}_{2}}+{{S}_{3}}+.......{{S}_{m}}=\] |
| A. | \[\frac{1}{2}mn(mn+1)\] |
| B. | \[mn(m+1)\] |
| C. | \[\frac{1}{4}mn(mn-1)\] |
| D. | None of the above |
| Answer» B. \[mn(m+1)\] | |
| 3. |
If the roots of the equation \[q{{x}^{2}}+px+q=0\]where p, q are real, be complex, then the roots of the equation \[{{x}^{2}}-4qx+{{p}^{2}}=0\] are |
| A. | Real and unequal |
| B. | Real and equal |
| C. | Imaginary |
| D. | None of these |
| Answer» B. Real and equal | |
| 4. |
The sum of the series\[\frac{4}{1\,!}+\frac{11}{2\,!}+\frac{22}{3\,!}+\frac{37}{4\,!}+\frac{56}{5\,!}+...\]is [Kurukshetra CEE 2002] |
| A. | 6 e |
| B. | 6 e ? 1 |
| C. | 5 e |
| D. | 5 e + 1 |
| Answer» C. 5 e | |
| 5. |
The centre of the circle passing through the point (0, 1) and touching the curve \[y={{x}^{2}}\]at (2, 4) is [IIT 1983] |
| A. | \[\left( \frac{-16}{5},\ \frac{27}{10} \right)\] |
| B. | \[\left( \frac{-16}{7},\ \frac{5}{10} \right)\] |
| C. | \[\left( \frac{-16}{5},\ \frac{53}{10} \right)\] |
| D. | None of these |
| Answer» D. None of these | |
| 6. |
If \[(1+i)(1+2i)(1+3i).....(1+ni)=a+ib\], then 2.5.10....\[(1+{{n}^{2}})\] is equal to [Karnataka CET 2002; Kerala (Engg.) 2002] |
| A. | \[{{a}^{2}}-{{b}^{2}}\] |
| B. | \[{{a}^{2}}+{{b}^{2}}\] |
| C. | \[\sqrt{{{a}^{2}}+{{b}^{2}}}\] |
| D. | \[\sqrt{{{a}^{2}}-{{b}^{2}}}\] |
| Answer» C. \[\sqrt{{{a}^{2}}+{{b}^{2}}}\] | |
| 7. |
Let \[{{S}_{1}},\ {{S}_{2}},.......\]be squares such that for each \[n\ge 1\], the length of a side of \[{{S}_{n}}\] equals the length of a diagonal of \[{{S}_{n+1}}\]. If the length of a side of \[{{S}_{1}}\]is\[10cm\], then for which of the following values of \[n\] is the area of \[{{S}_{n}}\] less then \[1\ sq\ cm\] [IIT 1999] |
| A. | 7 |
| B. | 8 |
| C. | 9 |
| D. | 10 |
| Answer» D. 10 | |
| 8. |
If \[a |
| A. | Real and distinct |
| B. | Real and equal |
| C. | Imaginary |
| D. | None of these |
| Answer» B. Real and equal | |
| 9. |
If \[S=\sum\limits_{n=0}^{\infty }{\frac{{{(\log x)}^{2n}}}{(2n)\,!},}\] then \[S\] = |
| A. | \[x+{{x}^{-1}}\] |
| B. | \[x-{{x}^{-1}}\] |
| C. | \[\frac{1}{2}(x+{{x}^{-1}})\] |
| D. | None of these |
| Answer» D. None of these | |
| 10. |
If \[x\]is real and \[k=\frac{{{x}^{2}}-x+1}{{{x}^{2}}+x+1},\] then [MNR 1992; RPET 1997] |
| A. | \[\frac{1}{3}\le k\le 3\] |
| B. | \[k\ge 5\] |
| C. | \[k\le 0\] |
| D. | None of these |
| Answer» B. \[k\ge 5\] | |
| 11. |
If\[\cos \,(\theta -\alpha )=a,\,\,\sin \,(\theta -\beta )=b,\,\,\]then \[{{\cos }^{2}}(\alpha -\beta )+2ab\,\sin \,(\alpha -\beta )\] is equal to |
| A. | \[4{{a}^{2}}{{b}^{2}}\] |
| B. | \[{{a}^{2}}-{{b}^{2}}\] |
| C. | \[{{a}^{2}}+{{b}^{2}}\] |
| D. | \[-{{a}^{2}}{{b}^{2}}\] |
| Answer» D. \[-{{a}^{2}}{{b}^{2}}\] | |
| 12. |
The length of the latus-rectum of the parabola whose focus is \[\left( \frac{{{u}^{2}}}{2g}\sin 2\alpha ,\ -\frac{{{u}^{2}}}{2g}\cos 2\alpha \right)\] and directrix is \[y=\frac{{{u}^{2}}}{2g}\], is |
| A. | \[\frac{{{u}^{2}}}{g}{{\cos }^{2}}\alpha \] |
| B. | \[\frac{{{u}^{2}}}{g}\cos 2\alpha \] |
| C. | \[\frac{2{{u}^{2}}}{g}{{\cos }^{2}}2\alpha \] |
| D. | \[\frac{2{{u}^{2}}}{g}{{\cos }^{2}}\alpha \] |
| Answer» E. | |
| 13. |
The sum of the series \[\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+...+\frac{1}{\sqrt{{{n}^{2}}-1}+\sqrt{{{n}^{2}}}}\]equals [AMU 2002] |
| A. | \[\frac{(2n+1)}{\sqrt{n}}\] |
| B. | \[\frac{\sqrt{n}+1}{\sqrt{n}+\sqrt{n-1}}\] |
| C. | \[\frac{(n+\sqrt{{{n}^{2}}-1})}{2\sqrt{n}}\] |
| D. | \[n-1\] |
| Answer» E. | |
| 14. |
\[{{n}^{th}}\] term of the series\[\frac{{{1}^{3}}}{1}+\frac{{{1}^{3}}+{{2}^{3}}}{1+3}+\frac{{{1}^{3}}+{{2}^{3}}+{{3}^{3}}}{1+3+5}+......\] will be [Pb. CET 2000] |
| A. | \[{{n}^{2}}+2n+1\] |
| B. | \[\frac{{{n}^{2}}+2n+1}{8}\] |
| C. | \[\frac{{{n}^{2}}+2n+1}{4}\] |
| D. | \[\frac{{{n}^{2}}-2n+1}{4}\] |
| Answer» D. \[\frac{{{n}^{2}}-2n+1}{4}\] | |
| 15. |
The sum of n terms of the series \[\frac{1}{1+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{7}}+.........\] is [UPSEAT 2002] |
| A. | \[\sqrt{2n+1}\] |
| B. | \[\frac{1}{2}\sqrt{2n+1}\] |
| C. | \[\sqrt{2n+1}-1\] |
| D. | \[\frac{1}{2}(\sqrt{2n+1}-1)\] |
| Answer» E. | |
| 16. |
For any odd integer \[n\ge 1\],\[{{n}^{3}}-{{(n-1)}^{3}}+...........+{{(-1)}^{n-1}}{{1}^{3}}=\] [IIT 1996] |
| A. | \[\frac{1}{2}{{(n-1)}^{2}}(2n-1)\] |
| B. | \[\frac{1}{4}{{(n-1)}^{2}}(2n-1)\] |
| C. | \[\frac{1}{2}{{(n+1)}^{2}}(2n-1)\] |
| D. | \[\frac{1}{4}{{(n+1)}^{2}}(2n-1)\] |
| Answer» E. | |
| 17. |
If the equation \[{{x}^{2}}+\lambda x+\mu =0\] has equal roots and one root of the equation \[{{x}^{2}}+\lambda x-12=0\]is 2, then \[(\lambda ,\mu )\]= |
| A. | (4, 4) |
| B. | (-4,4) |
| C. | \[(4,-4)\] |
| D. | \[(-4,-4)\] |
| Answer» B. (-4,4) | |
| 18. |
On the parabola \[y={{x}^{2}}\], the point least distance from the straight line \[y=2x-4\] is [AMU 2001] |
| A. | (1, 1) |
| B. | (1, 0) |
| C. | (1, ?1) |
| D. | (0, 0) |
| Answer» B. (1, 0) | |
| 19. |
\[\omega \] is an imaginary cube root of unity. If \[{{(1+{{\omega }^{2}})}^{m}}=\] \[{{(1+{{\omega }^{4}})}^{m}},\] then least positive integral value of m is [IIT Screening 2004] |
| A. | 6 |
| B. | 5 |
| C. | 4 |
| D. | 3 |
| Answer» E. | |
| 20. |
The two roots of an equation \[{{x}^{3}}-9{{x}^{2}}+14x+24=0\] are in the ratio 3 : 2. The roots will be [UPSEAT 1999] |
| A. | 6, 4, - 1 |
| B. | 6, 4, 1 |
| C. | - 6, 4, 1 |
| D. | - 6, - 4, 1 |
| Answer» B. 6, 4, 1 | |
| 21. |
The equation of common tangents to the parabola \[{{y}^{2}}=8x\] and hyperbola \[3{{x}^{2}}-{{y}^{2}}=3\], is |
| A. | \[2x\pm y+1=0\] |
| B. | \[2x\pm y-1=0\] |
| C. | \[x\pm 2y+1=0\] |
| D. | \[x\pm 2y-1=0\] |
| Answer» B. \[2x\pm y-1=0\] | |
| 22. |
Let \[\omega \] is an imaginary cube roots of unity then the value of\[2(\omega +1)({{\omega }^{2}}+1)+3(2\omega +1)(2{{\omega }^{2}}+1)+.....\]\[+(n+1)(n\omega +1)(n{{\omega }^{2}}+1)\] is [Orissa JEE 2002] |
| A. | \[{{\left[ \frac{n(n+1)}{2} \right]}^{2}}+n\] |
| B. | \[{{\left[ \frac{n(n+1)}{2} \right]}^{2}}\] |
| C. | \[{{\left[ \frac{n(n+1)}{2} \right]}^{2}}-n\] |
| D. | None of these |
| Answer» B. \[{{\left[ \frac{n(n+1)}{2} \right]}^{2}}\] | |
| 23. |
Suppose \[a,\,b,\,c\] are in A.P. and \[{{a}^{2}},{{b}^{2}},{{c}^{2}}\] are in G.P. If a < b < c and \[a+b+c=\frac{3}{2}\], then the value of a is [IIT Screening 2002] |
| A. | \[\frac{1}{2\sqrt{2}}\] |
| B. | \[\frac{1}{2\sqrt{3}}\] |
| C. | \[\frac{1}{2}-\frac{1}{\sqrt{3}}\] |
| D. | \[\frac{1}{2}-\frac{1}{\sqrt{2}}\] |
| Answer» E. | |
| 24. |
If \[a0\] has the solution represented by [AMU 2001] |
| A. | \[\frac{1+\sqrt{1-4a}}{a}>x>\frac{1-\sqrt{1-4a}}{a}\] |
| B. | \[x<\frac{1-\sqrt{1-4a}}{a}\] |
| C. | x < 2 |
| D. | \[2>x>\frac{1+\sqrt{1-4a}}{a}\] |
| Answer» B. \[x<\frac{1-\sqrt{1-4a}}{a}\] | |
| 25. |
If a circle cuts a rectangular hyperbola \[xy={{c}^{2}}\] in A, B, C, D and the parameters of these four points be \[{{t}_{1}},\ {{t}_{2}},\ {{t}_{3}}\] and \[{{t}_{4}}\] respectively. Then [Kurukshetra CEE 1998] |
| A. | \[{{t}_{1}}{{t}_{2}}={{t}_{3}}{{t}_{4}}\] |
| B. | \[{{t}_{1}}{{t}_{2}}{{t}_{3}}{{t}_{4}}=1\] |
| C. | \[{{t}_{1}}={{t}_{2}}\] |
| D. | \[{{t}_{3}}={{t}_{4}}\] |
| Answer» C. \[{{t}_{1}}={{t}_{2}}\] | |
| 26. |
An ellipse has eccentricity \[\frac{1}{2}\] and one focus at the point\[P\left( \frac{1}{2},\ 1 \right)\]. Its one directrix is the common tangent nearer to the point P, to the circle \[{{x}^{2}}+{{y}^{2}}=1\] and the hyperbola\[{{x}^{2}}-{{y}^{2}}=1\]. The equation of the ellipse in the standard form, is [IIT 1996] |
| A. | \[\frac{{{(x-1/3)}^{2}}}{1/9}+\frac{{{(y-1)}^{2}}}{1/12}=1\] |
| B. | \[\frac{{{(x-1/3)}^{2}}}{1/9}+\frac{{{(y+1)}^{2}}}{1/12}=1\] |
| C. | \[\frac{{{(x-1/3)}^{2}}}{1/9}-\frac{{{(y-1)}^{2}}}{1/12}=1\] |
| D. | \[\frac{{{(x-1/3)}^{2}}}{1/9}-\frac{{{(y+1)}^{2}}}{1/12}=1\] |
| Answer» B. \[\frac{{{(x-1/3)}^{2}}}{1/9}+\frac{{{(y+1)}^{2}}}{1/12}=1\] | |
| 27. |
Let \[{{z}_{1}}\] and \[{{z}_{2}}\] be nth roots of unity which are ends of a line segment that subtend a right angle at the origin. Then n must be of the form [IIT Screening 2001; Karnataka 2002] |
| A. | 4k + 1 |
| B. | 4k + 2 |
| C. | 4k + 3 |
| D. | 4k |
| Answer» E. | |
| 28. |
If \[\frac{2x}{2{{x}^{2}}+5x+2}\]>\[\frac{1}{x+1}\], then [IIT 1987] |
| A. | \[-2>x>-1\] |
| B. | \[-2\ge x\ge -1\] |
| C. | \[-2<x<-1\] |
| D. | \[-2<x\le -1\] |
| Answer» D. \[-2<x\le -1\] | |
| 29. |
Let A, B and C are the angles of a plain triangle and \[\tan \frac{A}{2}=\frac{1}{3},\,\,\tan \frac{B}{2}=\frac{2}{3}\]. Then \[\tan \frac{C}{2}\] is equal to [Orissa JEE 2003] |
| A. | 44446 |
| B. | 44441 |
| C. | 44256 |
| D. | 44257 |
| Answer» B. 44441 | |
| 30. |
If a, b, g are roots of equation \[{{x}^{3}}+a{{x}^{2}}+bx+c=0\], then \[{{\alpha }^{-1}}+{{\beta }^{-1}}+{{\gamma }^{-1}}=\] [EAMCET 2002] |
| A. | a/c |
| B. | - b/c |
| C. | b/a |
| D. | c/a |
| Answer» C. b/a | |
| 31. |
The combined equation of the asymptotes of the hyperbola \[2{{x}^{2}}+5xy+2{{y}^{2}}+4x+5y=0\] [Karnataka CET 2002] |
| A. | \[2{{x}^{2}}+5xy+2{{y}^{2}}=0\] |
| B. | \[2{{x}^{2}}+5xy+2{{y}^{2}}-4x+5y+2=0\] |
| C. | \[2{{x}^{2}}+5xy+2{{y}^{2}}+4x+5y-2=0\] |
| D. | \[2{{x}^{2}}+5xy+2{{y}^{2}}+4x+5y+2=0\] |
| Answer» E. | |
| 32. |
If \[i=\sqrt{-1},\] then \[4+5{{\left( -\frac{1}{2}+\frac{i\sqrt{3}}{2} \right)}^{334}}\] \[+3{{\left( -\frac{1}{2}+\frac{i\sqrt{3}}{2} \right)}^{365}}\]is equal to [IIT 1999] |
| A. | \[1-i\sqrt{3}\] |
| B. | \[-1+i\sqrt{3}\] |
| C. | \[i\sqrt{3}\] |
| D. | \[-i\sqrt{3}\] |
| Answer» D. \[-i\sqrt{3}\] | |
| 33. |
\[\cos \,\,2\theta +2\,\,\cos \theta \] is always |
| A. | Greater than \[-\frac{3}{2}\] |
| B. | Less than or equal to \[\frac{3}{2}\] |
| C. | Greater than or equal to \[-\frac{3}{2}\] and less than or equal to 3 |
| D. | None of these |
| Answer» D. None of these | |
| 34. |
Let \[P(a\sec \theta ,\ b\tan \theta )\] and \[Q(a\sec \varphi ,\ b\tan \varphi )\], where \[\theta +\varphi =\frac{\pi }{2}\], be two points on the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\]. If (h, k) is the point of intersection of the normals at P and Q, then k is equal to [IIT 1999; MP PET 2002] |
| A. | \[\frac{{{a}^{2}}+{{b}^{2}}}{a}\] |
| B. | \[-\left( \frac{{{a}^{2}}+{{b}^{2}}}{a} \right)\] |
| C. | \[\frac{{{a}^{2}}+{{b}^{2}}}{b}\] |
| D. | \[-\left( \frac{{{a}^{2}}+{{b}^{2}}}{b} \right)\] |
| Answer» E. | |
| 35. |
The value of the expression \[1.(2-\omega )(2-{{\omega }^{2}})+2.(3-\omega )(3-{{\omega }^{2}})+.......\]\[....+(n-1).(n-\omega )(n-{{\omega }^{2}}),\]where \[\omega \] is an imaginary cube root of unity, is [IIT 1996] |
| A. | \[\frac{1}{2}(n-1)n({{n}^{2}}+3n+4)\] |
| B. | \[\frac{1}{4}(n-1)n({{n}^{2}}+3n+4)\] |
| C. | \[\frac{1}{2}(n+1)n({{n}^{2}}+3n+4)\] |
| D. | \[\frac{1}{4}(n+1)n({{n}^{2}}+3n+4)\] |
| Answer» C. \[\frac{1}{2}(n+1)n({{n}^{2}}+3n+4)\] | |
| 36. |
If \[x>1,\ y>1,z>1\] are in G.P., then \[\frac{1}{1+\text{In}\,x},\ \frac{1}{1+\text{In}\,y},\] \[\ \frac{1}{1+\text{In}\,z}\] are in [IIT 1998; UPSEAT 2001] |
| A. | A.P. |
| B. | H.P. |
| C. | G.P. |
| D. | None of these |
| Answer» C. G.P. | |
| 37. |
If \[x=9\] is the chord of contact of the hyperbola \[{{x}^{2}}-{{y}^{2}}=9\], then the equation of the corresponding pair of tangents is [IIT 1999] |
| A. | \[9{{x}^{2}}-8{{y}^{2}}+18x-9=0\] |
| B. | \[9{{x}^{2}}-8{{y}^{2}}-18x+9=0\] |
| C. | \[9{{x}^{2}}-8{{y}^{2}}-18x-9=0\] |
| D. | \[9{{x}^{2}}-8{{y}^{2}}+18x+9=0\] |
| Answer» C. \[9{{x}^{2}}-8{{y}^{2}}-18x-9=0\] | |
| 38. |
If \[1,\omega ,{{\omega }^{2}},{{\omega }^{3}}.......,{{\omega }^{n-1}}\] are the \[n,{{n}^{th}}\] roots of unity, then \[(1-\omega )(1-{{\omega }^{2}}).....(1-{{\omega }^{n-1}})\] equals [MNR 1992; IIT 1984; DCE 2001; MP PET 2004] |
| A. | 0 |
| B. | 1 |
| C. | \[n\] |
| D. | \[{{n}^{2}}\] |
| Answer» D. \[{{n}^{2}}\] | |
| 39. |
Three numbers form a G.P. If the \[{{3}^{rd}}\] term is decreased by 64, then the three numbers thus obtained will constitute an A.P. If the second term of this A.P. is decreased by 8, a G.P. will be formed again, then the numbers will be |
| A. | 4, 20, 36 |
| B. | 4, 12, 36 |
| C. | 4, 20, 100 |
| D. | None of the above |
| Answer» D. None of the above | |
| 40. |
If \[f(x)={{\cos }^{2}}x+{{\sec }^{2}}x,\] then [MNR 1986] |
| A. | \[f(x)<1\] |
| B. | \[f(x)=1\] |
| C. | \[1<f(x)<2\] |
| D. | \[f(x)\ge 2\] |
| Answer» E. | |
| 41. |
If the cube roots of unity be \[1,\omega ,{{\omega }^{2}},\] then the roots of the equation \[{{(x-1)}^{3}}+8=0\]are [IIT 1979; MNR 1986; DCE 2000; AIEEE 2005] |
| A. | \[-1,\,1+2\omega ,\,1+2{{\omega }^{2}}\] |
| B. | \[-1,\,1-2\omega ,\,1-2{{\omega }^{2}}\] |
| C. | \[-1,\,-1,\,-1\] |
| D. | None of these |
| Answer» C. \[-1,\,-1,\,-1\] | |
| 42. |
If \[(x+1)\] is a factor of\[{{x}^{4}}-(p-3){{x}^{3}}-(3p-5){{x}^{2}}\] \[+(2p-7)x+6\], then \[p=\] [IIT 1975] |
| A. | 4 |
| B. | 2 |
| C. | 1 |
| D. | None of these |
| Answer» B. 2 | |
| 43. |
If \[{{z}_{r}}=\cos \frac{r\alpha }{{{n}^{2}}}+i\sin \frac{r\alpha }{{{n}^{2}}},\] where r = 1, 2, 3,?.,n, then \[\underset{n\to \infty }{\mathop{\lim }}\,\,\,{{z}_{1}}{{z}_{2}}{{z}_{3}}...{{z}_{n}}\] is equal to [UPSEAT 2001] |
| A. | \[\cos \alpha +i\,\sin \alpha \] |
| B. | \[\cos (\alpha /2)-i\sin (\alpha /2)\] |
| C. | \[{{e}^{i\alpha /2}}\] |
| D. | \[\sqrt[3]{{{e}^{i\alpha }}}\] |
| Answer» D. \[\sqrt[3]{{{e}^{i\alpha }}}\] | |
| 44. |
The value of 'a' for which the equations \[{{x}^{2}}-3x+a=0\] and \[{{x}^{2}}+ax-3=0\] have a common root is [Pb. CET 1999] |
| A. | 3 |
| B. | 1 |
| C. | -2 |
| D. | 2 |
| Answer» E. | |
| 45. |
Equation \[\frac{1}{r}=\frac{1}{8}+\frac{3}{8}\cos \theta \] represents [EAMCET 2002] |
| A. | A rectangular hyperbola |
| B. | A hyperbola |
| C. | An ellipse |
| D. | A parabola |
| Answer» C. An ellipse | |
| 46. |
If \[\cos \alpha +\cos \beta +\cos \gamma =\sin \alpha +\sin \beta +\sin \gamma =0\] then \[\cos 3\alpha +\cos 3\beta +\cos 3\gamma \] equals to [Karnataka CET 2000] |
| A. | 0 |
| B. | \[\cos (\alpha +\beta +\gamma )\] |
| C. | \[3\cos (\alpha +\beta +\gamma )\] |
| D. | \[3\sin (\alpha +\beta +\gamma )\] |
| Answer» D. \[3\sin (\alpha +\beta +\gamma )\] | |
| 47. |
If \[\theta \] and \[\varphi \] are eccentric angles of the ends of a pair of conjugate diameters of the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\], then \[\theta -\varphi \] is equal to |
| A. | \[\pm \frac{\pi }{2}\] |
| B. | \[\pm \pi \] |
| C. | 0 |
| D. | None of thesew |
| Answer» B. \[\pm \pi \] | |
| 48. |
If PQ is a double ordinate of hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] such that OPQ is an equilateral triangle, O being the centre of the hyperbola. Then the eccentricity e of the hyperbola satisfies [EAMCET 1999] |
| A. | \[1<e<2/\sqrt{3}\] |
| B. | \[e=2/\sqrt{3}\] |
| C. | \[e=\sqrt{3}/2\] |
| D. | \[e>2/\sqrt{3}\] |
| Answer» E. | |
| 49. |
If \[x=-5+2\sqrt{-4},\] then the value of the expression \[{{x}^{4}}+9{{x}^{3}}+35{{x}^{2}}-x+4\] is [IIT 1972] |
| A. | 160 |
| B. | \[-160\] |
| C. | 60 |
| D. | \[-60\] |
| Answer» C. 60 | |
| 50. |
If \[n\] is even, then in the expansion of \[{{\left( 1+\frac{{{x}^{2}}}{2\,!}+\frac{{{x}^{4}}}{4\,!}+...... \right)}^{2}}\], the coefficient of \[{{x}^{n}}\] is |
| A. | \[\frac{{{2}^{n}}}{n\,!}\] |
| B. | \[\frac{{{2}^{n}}-2}{n\,\,!}\] |
| C. | \[\frac{{{2}^{n-1}}-1}{n\,!}\] |
| D. | \[\frac{{{2}^{n-1}}}{n\,!}\] |
| Answer» E. | |