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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.
| 5251. |
If \[\left| \,\begin{matrix} y+z & x & y \\ z+x & z & x \\ x+y & y & z \\ \end{matrix}\, \right|=k(x+y+z){{(x-z)}^{2}}\], then \[k=\] |
| A. | \[2xyz\] |
| B. | 1 |
| C. | \[xyz\] |
| D. | \[{{x}^{2}}{{y}^{2}}{{z}^{2}}\] |
| Answer» C. \[xyz\] | |
| 5252. |
If \[\omega \]is a cube root of unity, then \[\left| \,\begin{matrix} x+1 & \omega & {{\omega }^{2}} \\ \omega & x+{{\omega }^{2}} & 1 \\ {{\omega }^{2}} & 1 & x+\omega \\ \end{matrix}\, \right|=\] [MNR 1990; MP PET 1999] |
| A. | \[{{x}^{3}}+1\] |
| B. | \[{{x}^{3}}+\omega \] |
| C. | \[{{x}^{3}}+{{\omega }^{2}}\] |
| D. | \[{{x}^{3}}\] |
| Answer» E. | |
| 5253. |
\[\left| \,\begin{matrix} 1+x & 1 & 1 \\ 1 & 1+y & 1 \\ 1 & 1 & 1+z \\ \end{matrix}\, \right|=\] [RPET 1992; Kerala (Engg.) 2002] |
| A. | \[xyz\left( 1+\frac{1}{x}+\frac{1}{y}+\frac{1}{z} \right)\] |
| B. | \[xyz\] |
| C. | \[1+\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\] |
| D. | \[\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\] |
| Answer» B. \[xyz\] | |
| 5254. |
\[\left| \,\begin{matrix} {{b}^{2}}+{{c}^{2}} & {{a}^{2}} & {{a}^{2}} \\ {{b}^{2}} & {{c}^{2}}+{{a}^{2}} & {{b}^{2}} \\ {{c}^{2}} & {{c}^{2}} & {{a}^{2}}+{{b}^{2}} \\ \end{matrix}\, \right|=\] [IIT 1980] |
| A. | \[abc\] |
| B. | \[4abc\] |
| C. | \[4{{a}^{2}}{{b}^{2}}{{c}^{2}}\] |
| D. | \[{{a}^{2}}{{b}^{2}}{{c}^{2}}\] |
| Answer» D. \[{{a}^{2}}{{b}^{2}}{{c}^{2}}\] | |
| 5255. |
\[\left| \,\begin{matrix} 1/a & {{a}^{2}} & bc \\ 1/b & {{b}^{2}} & ca \\ 1/c & {{c}^{2}} & ab \\ \end{matrix}\, \right|=\] [RPET 1990, 99] |
| A. | \[abc\] |
| B. | \[1/abc\] |
| C. | \[ab+bc+ca\] |
| D. | 0 |
| Answer» E. | |
| 5256. |
\[\left| \,\begin{matrix} {{b}^{2}}-ab & b-c & bc-ac \\ ab-{{a}^{2}} & a-b & {{b}^{2}}-ab \\ bc-ac & c-a & ab-{{a}^{2}} \\ \end{matrix}\, \right|=\] [MNR 1988] |
| A. | \[abc(a+b+c)\] |
| B. | \[3{{a}^{2}}{{b}^{2}}{{c}^{2}}\] |
| C. | 0 |
| D. | None of these |
| Answer» D. None of these | |
| 5257. |
\[\left| \,\begin{matrix} a & b & c \\ b & c & a \\ c & a & b \\ \end{matrix}\, \right|=\] [MP PET 1991] |
| A. | \[3abc+{{a}^{3}}+{{b}^{3}}+{{c}^{3}}\] |
| B. | \[3abc-{{a}^{3}}-{{b}^{3}}-{{c}^{3}}\] |
| C. | \[abc-{{a}^{3}}+{{b}^{3}}+{{c}^{3}}\] |
| D. | \[abc+{{a}^{3}}-{{b}^{3}}-{{c}^{3}}\] |
| Answer» C. \[abc-{{a}^{3}}+{{b}^{3}}+{{c}^{3}}\] | |
| 5258. |
\[\left| \begin{matrix} 0 & a & -b \\ -a & 0 & c \\ b & -c & 0 \\ \end{matrix} \right|=\] [MP PET 1992] |
| A. | \[-2abc\] |
| B. | \[abc\] |
| C. | 0 |
| D. | \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}\] |
| Answer» D. \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}\] | |
| 5259. |
\[\left| \,\begin{matrix} 1 & 1 & 1 \\ a & b & c \\ {{a}^{3}} & {{b}^{3}} & {{c}^{3}} \\ \end{matrix}\, \right|=\] [AMU 1979; RPET 1990; DCE 1999] |
| A. | \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}-3abc\] |
| B. | \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}+3abc\] |
| C. | \[(a+b+c)(a-b)(b-c)(c-a)\] |
| D. | None of these |
| Answer» D. None of these | |
| 5260. |
\[\left| \,\begin{matrix} 1 & a & {{a}^{2}}-bc \\ 1 & b & {{b}^{2}}-ac \\ 1 & c & {{c}^{2}}-ab \\ \end{matrix}\, \right|=\] [IIT 1988; MP PET 1990, 91; RPET 2002] |
| A. | 0 |
| B. | \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}-3abc\] |
| C. | \[3abc\] |
| D. | \[{{(a+b+c)}^{3}}\] |
| Answer» B. \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}-3abc\] | |
| 5261. |
\[\left| \,\begin{matrix} 1 & a & b \\ -a & 1 & c \\ -b & -c & 1 \\ \end{matrix}\, \right|=\] [MP PET 1991] |
| A. | \[1+{{a}^{2}}+{{b}^{2}}+{{c}^{2}}\] |
| B. | \[1-{{a}^{2}}+{{b}^{2}}+{{c}^{2}}\] |
| C. | \[1+{{a}^{2}}+{{b}^{2}}-{{c}^{2}}\] |
| D. | \[1+{{a}^{2}}-{{b}^{2}}+{{c}^{2}}\] |
| Answer» B. \[1-{{a}^{2}}+{{b}^{2}}+{{c}^{2}}\] | |
| 5262. |
\[\left| \,\begin{matrix} x+1 & x+2 & x+4 \\ x+3 & x+5 & x+8 \\ x+7 & x+10 & x+14 \\ \end{matrix}\, \right|=\] [MNR 1985; UPSEAT 2000] |
| A. | 2 |
| B. | -2 |
| C. | \[{{x}^{2}}-2\] |
| D. | None of these |
| Answer» C. \[{{x}^{2}}-2\] | |
| 5263. |
One of the roots of the given equation \[\left| \,\begin{matrix} x+a & b & c \\ b & x+c & a \\ c & a & x+b \\ \end{matrix}\, \right|=0\] is [MP PET 1988, 2002; RPET 1996] |
| A. | \[-(a+b)\] |
| B. | \[-(b+c)\] |
| C. | \[-a\] |
| D. | \[-(a+b+c)\] |
| Answer» E. | |
| 5264. |
\[\left| \,\begin{matrix} b+c & a & a \\ b & c+a & b \\ c & c & a+b \\ \end{matrix}\, \right|=\] [Roorkee 1980; RPET 1997, 99; KCET 1999; MP PET 2001] |
| A. | \[abc\] |
| B. | \[2abc\] |
| C. | \[3abc\] |
| D. | \[4abc\] |
| Answer» E. | |
| 5265. |
\[\left| \,\begin{matrix} a+b & a+2b & a+3b \\ a+2b & a+3b & a+4b \\ a+4b & a+5b & a+6b \\ \end{matrix}\, \right|=\] [IIT 1986; MNR 1985; MP PET 1998; Pb. CET 2003] |
| A. | \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}-3abc\] |
| B. | \[3ab\] |
| C. | \[3a+5b\] |
| D. | 0 |
| Answer» E. | |
| 5266. |
\[\left| \,\begin{matrix} a-b-c & 2a & 2a \\ 2b & b-c-a & 2b \\ 2c & 2c & c-a-b \\ \end{matrix}\, \right|=\] [RPET 1990, 95] |
| A. | \[{{(a+b+c)}^{2}}\] |
| B. | \[{{(a+b+c)}^{3}}\] |
| C. | \[(a+b+c)(ab+bc+ca)\] |
| D. | None of these |
| Answer» C. \[(a+b+c)(ab+bc+ca)\] | |
| 5267. |
If \[\left| \,\begin{matrix} y+z & x-z & x-y \\ y-z & z-x & y-x \\ z-y & z-x & x+y \\ \end{matrix}\, \right|=k\,xyz\], then the value of k is [AMU 2005] |
| A. | 2 |
| B. | 4 |
| C. | 6 |
| D. | 8 |
| Answer» E. | |
| 5268. |
\[\left| \begin{matrix} 1+{{\sin }^{2}}\theta & {{\sin }^{2}}\theta & {{\sin }^{2}}\theta \\ {{\cos }^{2}}\theta & 1+{{\cos }^{2}}\theta & {{\cos }^{2}}\theta \\ 4\sin 4\theta & 4\sin 4\theta & 1+4\sin 4\theta \\ \end{matrix} \right|=0\] then \[\sin 4\theta \]equal to [Orissa JEE 2005] |
| A. | 44228 |
| B. | 1 |
| C. | -0.5 |
| D. | -1 |
| Answer» D. -1 | |
| 5269. |
The solutions of the equation \[\left| \,\begin{matrix} x & 2 & -1 \\ 2 & 5 & x \\ -1 & 2 & x \\ \end{matrix}\, \right|=0\] are [Karnataka CET 2005] |
| A. | \[3,\,\,-1\] |
| B. | \[-3,\,\,1\] |
| C. | 3, 1 |
| D. | \[-3,\,\,-1\] |
| Answer» B. \[-3,\,\,1\] | |
| 5270. |
The value of the determinant \[\left| \,\begin{matrix} 0 & {{b}^{3}}-{{a}^{3}} & {{c}^{3}}-{{a}^{3}} \\ {{a}^{3}}-{{b}^{3}} & 0 & {{c}^{3}}-{{b}^{3}} \\ {{a}^{3}}-{{c}^{3}} & {{b}^{3}}-{{c}^{3}} & 0 \\ \end{matrix}\, \right|\] is equal to is equal to [J & K 2005] |
| A. | \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}\] |
| B. | \[{{a}^{3}}-{{b}^{3}}-{{c}^{3}}\] |
| C. | 0 |
| D. | \[-{{a}^{3}}+{{b}^{3}}+{{c}^{3}}\] |
| Answer» D. \[-{{a}^{3}}+{{b}^{3}}+{{c}^{3}}\] | |
| 5271. |
If \[\left| \,\begin{matrix} x+1 & 3 & 5 \\ 2 & x+2 & 5 \\ 2 & 3 & x+4 \\ \end{matrix}\, \right|=0\], then x = [MP PET 1991] |
| A. | 1, 9 |
| B. | -1, 9 |
| C. | -1, -9 |
| D. | 1, -9 |
| Answer» E. | |
| 5272. |
The determinant \[\left| \,\begin{matrix} 4+{{x}^{2}} & -6 & -2 \\ -6 & 9+{{x}^{2}} & 3 \\ -2 & 3 & 1+{{x}^{2}} \\ \end{matrix}\, \right|\] is not divisible by [J & K 2005] |
| A. | x |
| B. | \[{{x}^{3}}\] |
| C. | \[14+{{x}^{2}}\] |
| D. | \[{{x}^{5}}\] |
| Answer» D. \[{{x}^{5}}\] | |
| 5273. |
If \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=-2\]and \[f(x)=\left| \begin{matrix} 1+{{a}^{2}}x & (1+{{b}^{2}})x & (1+{{c}^{2}})x \\ (1+{{a}^{2}})x & 1+{{b}^{2}}x & (1+{{c}^{2}})x \\ (1+{{a}^{2}})x & (1+{{b}^{2}})x & 1+{{c}^{2}}x \\ \end{matrix} \right|\] then f(x) is a polynomial of degree [AIEEE 2005] |
| A. | 3 |
| B. | 2 |
| C. | 1 |
| D. | 0 |
| Answer» C. 1 | |
| 5274. |
If a, b, c are all different and \[\left| \,\begin{matrix} a & {{a}^{3}} & {{a}^{4}}-1 \\ b & {{b}^{3}} & {{b}^{4}}-1 \\ c & {{c}^{3}} & {{c}^{4}}-1 \\ \end{matrix}\, \right|\] = 0 , then the value of \[abc(ab+bc+ca)\]is [Kurukshetra CEE 2002] |
| A. | \[a+b+c\] |
| B. | 0 |
| C. | \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}\] |
| D. | \[{{a}^{2}}-{{b}^{2}}+{{c}^{2}}\] |
| Answer» B. 0 | |
| 5275. |
The value of \[\left| \,\begin{matrix} 441 & 442 & 443 \\ 445 & 446 & 447 \\ 449 & 450 & 451 \\ \end{matrix}\, \right|\] is [Karnataka CET 2004] |
| A. | \[441\times 446\times 451\] |
| B. | 0 |
| C. | -1 |
| D. | 1 |
| Answer» C. -1 | |
| 5276. |
The value of \[\left| \,\begin{matrix} 1 & 1 & 1 \\ bc & ca & ab \\ b+c & c+a & a+b \\ \end{matrix}\, \right|\]is [Karnataka CET 2004] |
| A. | 1 |
| B. | 0 |
| C. | \[(a-b)(b-c)(c-a)\] |
| D. | \[(a+b)(b+c)(c+a)\] |
| Answer» D. \[(a+b)(b+c)(c+a)\] | |
| 5277. |
If \[\omega \] is an imaginary root of unity, then the value of \[\left| \,\begin{matrix} a & b{{\omega }^{2}} & a\omega \\ b\omega & c & b{{\omega }^{2}} \\ c{{\omega }^{2}} & a\omega & c \\ \end{matrix}\, \right|\] is [MP PET 2004] |
| A. | \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}-3abc\] |
| B. | \[{{a}^{2}}b-{{b}^{2}}c\] |
| C. | 0 |
| D. | \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}\] |
| Answer» D. \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}\] | |
| 5278. |
\[\left| \,\begin{matrix} 5 & 3 & -1 \\ -7 & x & -3 \\ 9 & 6 & -2 \\ \end{matrix}\, \right|=0\], then x is equal to [Pb. CET 2002] |
| A. | 3 |
| B. | 5 |
| C. | 7 |
| D. | 9 |
| Answer» E. | |
| 5279. |
The value of \[x,\]if \[\left| \,\begin{matrix} -x & 1 & 0 \\ 1 & -x & 1 \\ 0 & 1 & -x \\ \end{matrix}\, \right|=0\]is equal to [Pb. CET 2002] |
| A. | \[\pm \sqrt{6}\] |
| B. | \[\pm \sqrt{2}\] |
| C. | \[\pm \sqrt{3}\] |
| D. | \[\sqrt{2},\sqrt{3}\] |
| Answer» C. \[\pm \sqrt{3}\] | |
| 5280. |
The roots of the equation \[\left| \,\begin{matrix} x & 0 & 8 \\ 4 & 1 & 3 \\ 2 & 0 & x \\ \end{matrix}\, \right|=0\]are equal to [Pb. CET 2000] |
| A. | \[(-4,\,4)\] |
| B. | \[(2,\,-4)\] |
| C. | \[(2,\,4)\] |
| D. | \[(2,\,8)\] |
| Answer» B. \[(2,\,-4)\] | |
| 5281. |
If \[\left| \,\begin{matrix} x-1 & 3 & 0 \\ 2 & x-3 & 4 \\ 3 & 5 & 6 \\ \end{matrix}\, \right|=0\], then x = [RPET 2003] |
| A. | 0 |
| B. | 2 |
| C. | 3 |
| D. | 1 |
| Answer» E. | |
| 5282. |
The values of x in the following determinant equation, \[\left| \,\begin{matrix} a+x & a-x & a-x \\ a-x & a+x & a-x \\ a-x & a-x & a+x \\ \end{matrix}\, \right|=0\] are [MP PET 2003] |
| A. | \[x=0,x=4a\] |
| B. | \[x=0,x=a\] |
| C. | \[x=0,x=2a\] |
| D. | \[x=0,x=3a\] |
| Answer» E. | |
| 5283. |
The value of \[\left| \,\begin{matrix} {{1}^{2}} & {{2}^{2}} & {{3}^{2}} \\ {{2}^{2}} & {{3}^{2}} & {{4}^{2}} \\ {{3}^{2}} & {{4}^{2}} & {{5}^{2}} \\ \end{matrix}\, \right|\]is [Kerala (Engg.) 2001] |
| A. | 8 |
| B. | -8 |
| C. | 400 |
| D. | 1 |
| Answer» C. 400 | |
| 5284. |
The values of the determinant \[\left| \,\begin{matrix} 1 & \cos (\alpha -\beta ) & \cos \alpha \\ \cos (\alpha -\beta ) & 1 & \cos \beta \\ \cos \alpha & \cos \beta & 1 \\ \end{matrix}\, \right|\] is [UPSEAT 2003] |
| A. | \[{{\alpha }^{2}}+{{\beta }^{2}}\] |
| B. | \[{{\alpha }^{2}}-{{\beta }^{2}}\] |
| C. | 1 |
| D. | 0 |
| Answer» E. | |
| 5285. |
Solution of the equation \[\left| \,\begin{matrix} 1 & 1 & x \\ p+1 & p+1 & p+x \\ 3 & x+1 & x+2 \\ \end{matrix}\, \right|=0\]are [AMU 2002] |
| A. | \[x=1,\,2\] |
| B. | \[x=2,\,3\] |
| C. | \[x=1,\,p,\,2\] |
| D. | \[x=1,\,2,\,-p\] |
| Answer» B. \[x=2,\,3\] | |
| 5286. |
If \[\left| \,\begin{matrix} x+1 & 1 & 1 \\ 2 & x+2 & 2 \\ 3 & 3 & x+3 \\ \end{matrix}\, \right|=0,\]then x is [Kerala (Engg.) 2002] |
| A. | 0, - 6 |
| B. | 0, 6 |
| C. | 6 |
| D. | -6 |
| Answer» B. 0, 6 | |
| 5287. |
The determinant \[\left| \,\begin{matrix} a & b & a-b \\ b & c & b-c \\ 2 & 1 & 0 \\ \end{matrix}\, \right|\] is equal to zero if \[a,b,c\]are in [UPSEAT 2002] |
| A. | G. P. |
| B. | A. P. |
| C. | H. P. |
| D. | None of these |
| Answer» B. A. P. | |
| 5288. |
\[\left| \,\begin{matrix} {{({{a}^{x}}+{{a}^{-x}})}^{2}} & {{({{a}^{x}}-{{a}^{-x}})}^{2}} & 1 \\ {{({{b}^{x}}+{{b}^{-x}})}^{2}} & {{({{b}^{x}}-{{b}^{-x}})}^{2}} & 1 \\ {{({{c}^{x}}+{{c}^{-x}})}^{2}} & {{({{c}^{x}}-{{c}^{-x}})}^{2}} & 1 \\ \end{matrix}\, \right|=\][UPSEAT 2002; AMU 2005] |
| A. | 0 |
| B. | \[2abc\] |
| C. | \[{{a}^{2}}{{b}^{2}}{{c}^{2}}\] |
| D. | None of these |
| Answer» B. \[2abc\] | |
| 5289. |
\[\left| \,\begin{matrix} 1/a & 1 & bc \\ 1/b & 1 & ca \\ 1/c & 1 & ab \\ \end{matrix}\, \right|=\] [RPET 2002] |
| A. | 0 |
| B. | abc |
| C. | 1/abc |
| D. | None of these |
| Answer» B. abc | |
| 5290. |
\[\left| \,\begin{matrix} 1 & 1 & 1 \\ 1 & {{\omega }^{2}} & \omega \\ 1 & \omega & {{\omega }^{2}} \\ \end{matrix}\, \right|=\] [RPET 2002] |
| A. | \[3\sqrt{3}i\] |
| B. | \[-3\sqrt{3}i\] |
| C. | \[i\sqrt{3}\] |
| D. | 3 |
| Answer» B. \[-3\sqrt{3}i\] | |
| 5291. |
If A, B, C be the angles of a triangle, then \[\left| \,\begin{matrix} -1 & \cos C & \cos B \\ \cos C & -1 & \cos A \\ \cos B & \cos A & -1 \\ \end{matrix}\, \right|=\] [Karnataka CET 2002] |
| A. | 1 |
| B. | 0 |
| C. | \[\cos A\cos B\cos C\] |
| D. | \[\cos A+\cos B\cos C\] |
| Answer» C. \[\cos A\cos B\cos C\] | |
| 5292. |
If \[a+b+c=0\], then the solution of the equation \[\left| \,\begin{matrix} a-x & c & b \\ c & b-x & a \\ b & a & c-x \\ \end{matrix}\, \right|=0\] is [UPSEAT 2001] |
| A. | 0 |
| B. | \[\pm \frac{3}{2}({{a}^{2}}+{{b}^{2}}+{{c}^{2}})\] |
| C. | \[0,\,\pm \sqrt{\frac{3}{2}({{a}^{2}}+{{b}^{2}}+{{c}^{2}})}\] |
| D. | \[0,\,\,\pm \sqrt{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}\] |
| Answer» D. \[0,\,\,\pm \sqrt{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}\] | |
| 5293. |
\[\left| \,\begin{matrix} a-b & b-c & c-a \\ x-y & y-z & z-x \\ p-q & q-r & r-p \\ \end{matrix}\, \right|=\] [MNR 1987] |
| A. | \[a(x+y+z)+b(p+q+r)+c\] |
| B. | 0 |
| C. | \[abc+xyz+pqr\] |
| D. | None of these |
| Answer» C. \[abc+xyz+pqr\] | |
| 5294. |
\[{{(1+x)}^{n}}-nx-1\] divisible (where \[n\in N\]) |
| A. | by \[2x\] |
| B. | by \[{{x}^{2}}\] |
| C. | by \[2{{x}^{3}}\] |
| D. | All of these |
| Answer» C. by \[2{{x}^{3}}\] | |
| 5295. |
In the expansion of the following expression\[1+(1+x)+\]\[{{(1+x)}^{2}}+.....+{{(1+x)}^{n}}\]the coefficient of \[{{x}^{k}}(0\le k\le n)\] is [RPET 2000] |
| A. | \[^{n+1}{{C}_{k+1}}\] |
| B. | \[^{n}{{C}_{k}}\] |
| C. | \[^{n}{{C}_{n-k-1}}\] |
| D. | None of these |
| Answer» B. \[^{n}{{C}_{k}}\] | |
| 5296. |
The value of \[{{(\sqrt{5}+1)}^{5}}-{{(\sqrt{5}-1)}^{5}}\]is [MP PET 1985] |
| A. | 252 |
| B. | 352 |
| C. | 452 |
| D. | 532 |
| Answer» C. 452 | |
| 5297. |
\[\frac{1}{\sqrt{5+4x}}\]can be expanded by binomial theorem, if |
| A. | \[x<1\] |
| B. | \[|x|<1\] |
| C. | \[|x|\,\,<\frac{5}{4}\] |
| D. | \[|x|<\frac{4}{5}\] |
| Answer» D. \[|x|<\frac{4}{5}\] | |
| 5298. |
The total number of terms in the expansion of \[{{(x+a)}^{100}}+{{(x-a)}^{100}}\] after simplification will be [Pb. CET 1990] |
| A. | 202 |
| B. | 51 |
| C. | 50 |
| D. | None of these |
| Answer» C. 50 | |
| 5299. |
The formulae\[{{(a+b)}^{m}}={{a}^{m}}+m{{a}^{m-1}}b\]\[+\frac{m(m-1)}{1.2}{{a}^{m-2}}{{b}^{2}}+....\] holds when |
| A. | \[b<a\] |
| B. | \[a<b\] |
| C. | \[|a|\,<\,|b|\] |
| D. | \[|b|\,<\,|a|\] |
| Answer» E. | |
| 5300. |
\[{{x}^{5}}+10{{x}^{4}}a+40{{x}^{3}}{{a}^{2}}+80{{x}^{2}}{{a}^{3}}\]\[+80x{{a}^{4}}+32{{a}^{5}}=\] |
| A. | \[{{(x+a)}^{5}}\] |
| B. | \[{{(3x+a)}^{5}}\] |
| C. | \[{{(x+2a)}^{5}}\] |
| D. | \[{{(x+2a)}^{3}}\] |
| Answer» D. \[{{(x+2a)}^{3}}\] | |