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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.
| 1351. |
If the roots of the equation \[a{{x}^{2}}-bx+c=0\] are \[\alpha ,\beta \] then the roots of the equation \[{{b}^{2}}c{{x}^{2}}-a{{b}^{2}}x+{{a}^{3}}=0\] are |
| A. | \[\frac{1}{{{\alpha }^{3}}+\alpha \beta },\frac{1}{{{\beta }^{3}}+\alpha \beta }\] |
| B. | \[\frac{1}{{{\alpha }^{2}}+\alpha \beta },\frac{1}{{{\beta }^{2}}+\alpha \beta }\] |
| C. | \[\frac{1}{{{\alpha }^{4}}+\alpha \beta },\frac{1}{{{\beta }^{4}}+\alpha \beta }\] |
| D. | None of these |
| Answer» C. \[\frac{1}{{{\alpha }^{4}}+\alpha \beta },\frac{1}{{{\beta }^{4}}+\alpha \beta }\] | |
| 1352. |
If z is a complex number such that \[z+|z|=8+12i,\] then the value of \[|{{z}^{2}}|\] is equal to |
| A. | 228 |
| B. | 144 |
| C. | 121 |
| D. | 169 |
| Answer» E. | |
| 1353. |
For the equation \[\left| {{x}^{2}} \right|+\left| x \right|-6=0,\] the roots are |
| A. | One and only one real number |
| B. | Real with sum one |
| C. | Real with sum zero |
| D. | Real with product zero |
| Answer» D. Real with product zero | |
| 1354. |
If \[{{z}_{1}},{{z}_{2}}\] and \[{{z}_{3}}\] are complex numbers such that \[\left| {{z}_{1}} \right|=\left| {{z}_{2}} \right|=\left| {{z}_{3}} \right|=\left| \frac{1}{{{z}_{1}}}+\frac{1}{{{z}_{2}}}+\frac{1}{{{z}_{3}}} \right|=1,\] then \[\left| {{z}_{1}}+{{z}_{2}}+{{z}_{3}} \right|\]is |
| A. | equal to 1 |
| B. | less than 1 |
| C. | greater than 3 |
| D. | equal to 3 |
| Answer» B. less than 1 | |
| 1355. |
Let \[z={{\log }_{2}}(1+i),\] then \[(z+\bar{z})+i(z-\bar{z})=\] |
| A. | \[\frac{\ln \,4+\pi }{\ln \,\,4}\] |
| B. | \[\frac{\pi -\ln \,4}{\ln \,\,2}\] |
| C. | \[\frac{\ln \,4-\pi }{\ln \,\,4}\] |
| D. | \[\frac{\pi +\ln \,\,4}{\ln \,\,2}\] |
| Answer» D. \[\frac{\pi +\ln \,\,4}{\ln \,\,2}\] | |
| 1356. |
If the roots of the equation \[{{x}^{2}}-ax+b=0\] are real and differ by a quantity which is less than \[c(c>0),\] then b lies between |
| A. | \[\frac{{{a}^{2}}-{{c}^{2}}}{4}\] and \[\frac{{{a}^{2}}}{4}\] |
| B. | \[\frac{{{a}^{2}}+{{c}^{2}}}{4}\] and \[\frac{{{a}^{2}}}{4}\] |
| C. | \[\frac{{{a}^{2}}-{{c}^{2}}}{2}\] and \[\frac{{{a}^{2}}}{4}\] |
| D. | None of these |
| Answer» B. \[\frac{{{a}^{2}}+{{c}^{2}}}{4}\] and \[\frac{{{a}^{2}}}{4}\] | |
| 1357. |
What is \[{{\left[ \frac{\sin \frac{\pi }{6}+i\left( 1-\cos \frac{\pi }{6} \right)}{\sin \frac{\pi }{6}-i\left( 1-\cos \frac{\pi }{6} \right)} \right]}^{3}}\] where \[i=\sqrt{-1},\] equal to? |
| A. | 1 |
| B. | \[-1\] |
| C. | \[i\] |
| D. | \[-i\] |
| Answer» D. \[-i\] | |
| 1358. |
The roots of the equation \[ab{{c}^{2}}{{x}^{2}}+3{{a}^{2}}cx+{{b}^{2}}cx-6{{a}^{2}}-ab+2{{b}^{2}}=0\] are |
| A. | non real |
| B. | rational if a, b, c are rational |
| C. | irrational if a, b, c are rational |
| D. | None of these |
| Answer» C. irrational if a, b, c are rational | |
| 1359. |
The value of \[Arg\left[ i\,\,\ln \left( \frac{a-ib}{a+ib} \right) \right],\] where a and b are real numbers, is |
| A. | \[0\] or \[\pi \] |
| B. | \[\frac{\pi }{2}\] |
| C. | not defined |
| D. | None of these |
| Answer» B. \[\frac{\pi }{2}\] | |
| 1360. |
If the roots of \[a{{x}^{2}}+bx+c=0\] are the reciprocals of those of \[\ell {{x}^{2}}+mx+n=0\] then \[a:b:c=\] |
| A. | \[n:m:\ell \] |
| B. | \[\ell :m:n\] |
| C. | \[m:n:\ell \] |
| D. | \[n:\ell :m\] |
| Answer» B. \[\ell :m:n\] | |
| 1361. |
If \[z=1+i\tan \alpha \,\left( -\pi |
| A. | \[\frac{1}{\cos \alpha }(\cos \alpha +i\sin \alpha )\] |
| B. | \[\frac{1}{-\cos \alpha }[\cos \,(\pi +\alpha )+i\sin (\pi +\alpha )\] |
| C. | \[\frac{1}{\cos \alpha }[\cos \,(2\pi +\alpha )+i\sin (2\pi +\alpha )]\] |
| D. | None of these |
| Answer» C. \[\frac{1}{\cos \alpha }[\cos \,(2\pi +\alpha )+i\sin (2\pi +\alpha )]\] | |
| 1362. |
If \[\alpha \] and \[\beta \] \[(\alpha |
| A. | \[0<\alpha <\beta \] |
| B. | \[\alpha <0<\beta <\,|\alpha |\] |
| C. | \[\alpha <\beta <0\] |
| D. | \[\alpha <0<\,|\alpha |\,<\beta \] |
| Answer» C. \[\alpha <\beta <0\] | |
| 1363. |
Suppose the quadratic equations \[{{x}^{2}}+px+q=0\] and \[{{x}^{2}}+rx+s=0\] are such that p, q, r, s are real and \[pr=2(q+s).\] Then |
| A. | Both the equations always have real roots |
| B. | At least one equation always has real roots |
| C. | Both the equation always have non real roots |
| D. | At least one equation always has real and equal roots |
| Answer» C. Both the equation always have non real roots | |
| 1364. |
If \[{{z}_{1}},{{z}_{2}}\] are the roots of the quadratic equation \[a{{z}^{2}}+bz+c=0\] such that \[\operatorname{Im}({{z}_{1}},{{z}_{2}})\ne 0\] then |
| A. | a, b, c are all real |
| B. | at least one of a, b, c is real |
| C. | at least one of a, b, c is imaginary |
| D. | all of a, b, c are imaginary |
| Answer» D. all of a, b, c are imaginary | |
| 1365. |
What is the real part of \[{{(\sin x+i\cos x)}^{3}}\]where\[i=\sqrt{-1}\] ? |
| A. | \[-\cos \,3x\] |
| B. | \[-\sin \,3x\] |
| C. | \[\sin \,3x\] |
| D. | \[\cos \,3x\] |
| Answer» C. \[\sin \,3x\] | |
| 1366. |
What is the argument of \[(1-\sin \theta )+i\cos \theta \]? |
| A. | \[\frac{\pi }{2}-\frac{\theta }{2}\] |
| B. | \[\frac{\pi }{2}+\frac{\theta }{2}\] |
| C. | \[\frac{\pi }{4}-\frac{\theta }{2}\] |
| D. | \[\frac{\pi }{4}+\frac{\theta }{2}\] |
| Answer» E. | |
| 1367. |
If \[\alpha ,\beta \] be the roots of the equation \[{{x}^{2}}-px+q=0\] and \[{{\alpha }_{1}},\,\,{{\beta }_{1}}\] the roots of the equation \[{{x}^{2}}-qx+p=0,\] then the equation whose roots are \[\frac{1}{{{\alpha }_{1}}\beta }+\frac{1}{\alpha {{\beta }_{1}}}\] and \[\frac{1}{\alpha {{\alpha }_{1}}}+\frac{1}{\beta {{\beta }_{1}}}\] is |
| A. | \[pq{{x}^{2}}-pqx+{{p}^{2}}+{{q}^{2}}+4pq=0\] |
| B. | \[{{p}^{2}}{{q}^{2}}{{x}^{2}}-{{p}^{2}}{{q}^{2}}x+{{p}^{3}}+{{q}^{3}}-4pq=0\] |
| C. | \[{{p}^{3}}{{q}^{3}}{{x}^{2}}-{{p}^{3}}{{q}^{3}}x+{{p}^{4}}+{{q}^{4}}-4{{p}^{2}}{{q}^{2}}=0\] |
| D. | \[(p+q){{x}^{2}}-(p+q)x+{{p}^{2}}+{{q}^{2}}+pq=0\] |
| Answer» C. \[{{p}^{3}}{{q}^{3}}{{x}^{2}}-{{p}^{3}}{{q}^{3}}x+{{p}^{4}}+{{q}^{4}}-4{{p}^{2}}{{q}^{2}}=0\] | |
| 1368. |
Let \[\lambda \in \mathbf{R}\] If the origin and the non-real roots of \[2{{z}^{2}}+2z+\lambda =0\] form the three vertices of an equilateral triangle in the arg and plane. Then \[\lambda \] is |
| A. | 1 |
| B. | \[\frac{2}{3}\] |
| C. | 2 |
| D. | \[-1\] |
| Answer» C. 2 | |
| 1369. |
If \[0 |
| A. | \[|\alpha =|\beta |\] |
| B. | \[|\alpha |\,>1\] |
| C. | \[|\beta |\,<1\] |
| D. | None of these |
| Answer» D. None of these | |
| 1370. |
If \[f({{x}_{1}})-f({{x}_{2}})=f\left( \frac{{{x}_{1}}-{{x}_{2}}}{1-{{x}_{1}}{{x}_{2}}} \right)\] for then what is \[f(x)\] equal to? |
| A. | \[\ln \left( \frac{1-x}{1+x} \right)\] |
| B. | \[\ln \left( \frac{2+x}{1-x} \right)\] |
| C. | \[{{\tan }^{-1}}\left( \frac{1-x}{1+x} \right)\] |
| D. | \[{{\tan }^{-1}}\left( \frac{1+x}{1-x} \right)\] |
| Answer» B. \[\ln \left( \frac{2+x}{1-x} \right)\] | |
| 1371. |
If z in any complex number satisfying then which of the following is correct? |
| A. | \[\arg \,(z-1)=2argz\] |
| B. | \[2\arg \,(z)=\frac{2}{3}arg({{z}^{2}}-z)\] |
| C. | \[\arg (z-1)=\arg (z+1)\] |
| D. | \[\arg z=2\arg (z+1)\] |
| Answer» B. \[2\arg \,(z)=\frac{2}{3}arg({{z}^{2}}-z)\] | |
| 1372. |
Consider \[f(x)={{x}^{2}}-3x+a+\frac{1}{a},\]\[a\in R-\{0\},\]such that \[f(3)>0\] and \[f(2)\le 0.\] If \[\alpha \] and \[\beta \] are the roots of equation \[f(x)=0\] then the value of \[{{\alpha }^{2}}+{{\beta }^{2}}\] is equal to |
| A. | greater than 11 |
| B. | less than 5 |
| C. | 5 |
| D. | depends upon a and a cannot be determined |
| Answer» D. depends upon a and a cannot be determined | |
| 1373. |
If \[\omega \] is a complex cube root of unity and \[x={{\omega }^{2}}-\omega -2,\] then what is the value of \[{{x}^{2}}+4x+7\]? |
| A. | \[-2\] |
| B. | \[-1\] |
| C. | \[0\] |
| D. | \[1\] |
| Answer» D. \[1\] | |
| 1374. |
Let \[\alpha ,\beta \] be the roots of \[{{x}^{2}}+x+1=0.\] Then the equation whose roots are \[{{\alpha }^{229}}\] and \[{{\alpha }^{1004}}\] is |
| A. | \[{{x}^{2}}-x-1=0\] |
| B. | \[{{x}^{2}}-x+1=0\] |
| C. | \[{{x}^{2}}+x-1=0\] |
| D. | \[{{x}^{2}}+x+1=0\] |
| Answer» E. | |
| 1375. |
If the roots of the equations \[p{{x}^{2}}+2qx+r=0\]and \[q{{x}^{2}}-2\sqrt{pr}x+q=0\] be real, then |
| A. | \[p=q\] |
| B. | \[{{q}^{2}}=pr\] |
| C. | \[{{p}^{2}}=qr\] |
| D. | \[{{r}^{2}}=pr\] |
| Answer» C. \[{{p}^{2}}=qr\] | |
| 1376. |
The greatest and the least value of \[|{{z}_{1}}+{{z}_{2}}|\] if \[{{z}_{1}}=24+7i\] and \[|{{z}_{2}}|=6\] respectively are |
| A. | \[25,\,\,19\] |
| B. | \[19,\,\,25\] |
| C. | \[-19,\,\,-25\] |
| D. | \[-25,\,\,-19\] |
| Answer» B. \[19,\,\,25\] | |
| 1377. |
The points \[{{z}_{1}},{{z}_{2}},{{z}_{3}},{{z}_{4}}\] in a complex plane are vertices of a parallelogram taken in order, then |
| A. | \[{{z}_{1}}+{{z}_{4}}={{z}_{2}}+{{z}_{3}}\] |
| B. | \[{{z}_{1}}+{{z}_{3}}={{z}_{2}}+{{z}_{4}}\] |
| C. | \[{{z}_{1}}+{{z}_{2}}={{z}_{3}}+{{z}_{4}}\] |
| D. | None of these |
| Answer» C. \[{{z}_{1}}+{{z}_{2}}={{z}_{3}}+{{z}_{4}}\] | |
| 1378. |
What is the value of \[{{\left( -\sqrt{-1} \right)}^{4n+3}}+{{\left( {{i}^{41}}+{{i}^{-257}} \right)}^{9}},\] where \[n\in N\]? |
| A. | 0 |
| B. | 1 |
| C. | i |
| D. | \[-i\] |
| Answer» D. \[-i\] | |
| 1379. |
If \[\alpha ,\beta \] are roots of \[a{{x}^{2}}+bx+b=0,\] then \[\sqrt{\frac{\alpha }{\beta }}+\sqrt{\frac{\beta }{\alpha }}+\sqrt{\frac{b}{a}}\] is (\[{{b}^{2}}\ge 4ab,\] a and b are of same sign) |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | \[2\sqrt{\frac{b}{a}}\] |
| Answer» E. | |
| 1380. |
If both the roots of the equation \[{{x}^{2}}-2kx+{{k}^{2}}-4=0\] lie between \[-3\] and 5, then which one of the following is correct? |
| A. | \[-2<k<2\] |
| B. | \[-5<k<3\] |
| C. | \[-3<k<5\] |
| D. | \[-1<k<3\] |
| Answer» E. | |
| 1381. |
The locus of a point in the Argand plane that moves satisfying the equation \[|z-1+i|-|z-2-i|=3:\] |
| A. | is a circle with radius 3 and centre at \[z=\frac{3}{2}\] |
| B. | is an ellipse with its foci at \[1-i\] and \[2+i\] and major axis \[=3\] |
| C. | is a hyperbola with its foci at \[1-i\] and \[2+i\]and its transverse axis \[=3\] |
| D. | None of the above |
| Answer» D. None of the above | |
| 1382. |
The real roots of the equation \[{{x}^{2}}+5|x|+4=0\] are |
| A. | \[\{-1,-4\}\] |
| B. | \[\{1,4\}\] |
| C. | \[\{-4,4\}\] |
| D. | None of these |
| Answer» E. | |
| 1383. |
If x be real and \[b |
| A. | \[(b,c)\] |
| B. | \[[b,c]\] |
| C. | \[(-\infty ,b]\cup [c,\infty )\] |
| D. | \[(-\infty ,b)\cup (c,\infty )\] |
| Answer» D. \[(-\infty ,b)\cup (c,\infty )\] | |
| 1384. |
\[A+iB\] form of \[\frac{(\cos x+i\sin x)(\cos y+i\sin y)}{(\cot u+i)(1+i\tan \,\,v)}\]is equal to: |
| A. | \[\sin u\,\,\cos v\,\,[\cos (x+y-u-v)+\]\[i\sin (x+y-u-v)]\] |
| B. | \[\sin \,u\,\cos \,v[\cos \,(x+y+u+v)+\]\[i\sin (x+y+u+v)]\] |
| C. | \[\sin \,\,u\,\,\,\cos \,\,v\,\,[\cos \,(x+y+u+v)-\]\[i\sin (x+y-u+v)]\] |
| D. | None of these |
| Answer» B. \[\sin \,u\,\cos \,v[\cos \,(x+y+u+v)+\]\[i\sin (x+y+u+v)]\] | |
| 1385. |
If \[{{z}^{2}}+z+1=0,\] where z is complex number, then the value of \[{{\left( z+\frac{1}{z} \right)}^{2}}+{{\left( {{z}^{2}}+\frac{1}{{{z}^{2}}} \right)}^{2}}+{{\left( {{z}^{3}}+\frac{1}{{{z}^{3}}} \right)}^{2}}\] \[+....+{{\left( {{z}^{6}}+\frac{1}{{{z}^{6}}} \right)}^{2}}\]is |
| A. | 18 |
| B. | 54 |
| C. | 6 |
| D. | 12 |
| Answer» E. | |
| 1386. |
If \[2x=3+5i,\] then what is the value of \[2{{x}^{3}}+2{{x}^{2}}-7x+72?\] |
| A. | 4 |
| B. | \[-4\] |
| C. | 8 |
| D. | \[-8\] |
| Answer» B. \[-4\] | |
| 1387. |
\[\sum\limits_{k=33}^{65}{\left( \sin \frac{2k\pi }{8}-i\cos \frac{2k\pi }{8} \right)}\] |
| A. | \[1+i\] |
| B. | \[1-i\] |
| C. | \[1+\frac{i}{\sqrt{2}}\] |
| D. | \[\frac{1-i}{\sqrt{2}}\] |
| Answer» E. | |
| 1388. |
If \[\operatorname{Re}\left( \frac{z-1}{z+1} \right)=0,\] where \[2=x+iy\] is a complex number, then which one of the following is correct? |
| A. | \[z=1+i\] |
| B. | \[\left| z \right|=2\] |
| C. | \[z=1-i\] |
| D. | \[\left| z \right|=1\] |
| Answer» E. | |
| 1389. |
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? |
| A. | \[3/2\] |
| B. | 1 |
| C. | \[1/2\] |
| D. | \[11/4\] |
| Answer» D. \[11/4\] | |
| 1390. |
If n is a positive integer grater than unity and z is a complex satisfying the equation \[{{z}^{n}}={{(z+1)}^{n}},\]then |
| A. | \[\operatorname{Re}(z)<2\] |
| B. | \[\operatorname{Re}(z)>0\] |
| C. | \[\operatorname{Re}(z)=0\] |
| D. | z lies on \[x=-\frac{1}{2}\] |
| Answer» E. | |
| 1391. |
Let Z and W be two complex numbers such that \[\left| Z \right|\le 1,\] \[\left| W \right|\le 1\] and \[\left| Z+i\,W \right|=\left| Z-i\overline{W} \right|=2.\] Then Z equals |
| A. | 1 or i |
| B. | i or \[-i\] |
| C. | 1 or \[-i\] |
| D. | i or \[-1\] |
| Answer» D. i or \[-1\] | |
| 1392. |
The set of all real numbers x for which \[{{x}^{2}}-[x+2]+x>0,\] is |
| A. | \[\left( -\infty ,-2 \right)\cup \left( 2,\infty \right)\] |
| B. | \[\left( -\infty ,-\sqrt{2} \right)\cup \left( \sqrt{2},\infty \right)\] |
| C. | \[\left( -\infty ,-1 \right)\cup \left( 1,\infty \right)\] |
| D. | \[\left( \sqrt{2},\infty \right)\] |
| Answer» C. \[\left( -\infty ,-1 \right)\cup \left( 1,\infty \right)\] | |
| 1393. |
Let \[a>0,\text{ }b>0\] and \[c>0\]. Then both the roots of the equation \[a{{x}^{2}}+bx+c=0\] |
| A. | are real and negative |
| B. | have negative real parts |
| C. | are rational numbers |
| D. | None of these |
| Answer» C. are rational numbers | |
| 1394. |
The value of \[{{(1+2\omega +{{\omega }^{2}})}^{3n}}-{{(1+\omega +2{{\omega }^{2}})}^{3n}}\] is: |
| A. | 0 |
| B. | 1 |
| C. | \[\omega \] |
| D. | \[{{\omega }^{2}}\] |
| Answer» B. 1 | |
| 1395. |
Number of solutions of the equation, \[{{z}^{3}}+\frac{3{{\left| z \right|}^{2}}}{z}=0,\] where z is a complex number and \[|z|=\sqrt{3}\] is |
| A. | 2 |
| B. | 3 |
| C. | 6 |
| D. | 4 |
| Answer» E. | |
| 1396. |
If \[z=\frac{-2\left( 1+2i \right)}{3+i}\] where \[i=\sqrt{-1},\] then argument \[\theta \,(-\pi |
| A. | \[\frac{3\pi }{4}\] |
| B. | \[\frac{\pi }{4}\] |
| C. | \[\frac{5\pi }{6}\] |
| D. | \[-\frac{3\pi }{4}\] |
| Answer» C. \[\frac{5\pi }{6}\] | |
| 1397. |
If \[\alpha ,\beta ,\gamma \] and a, b, c are complex numbers such that \[\frac{\alpha }{a}+\frac{\beta }{b}+\frac{\gamma }{c}=1+i\] and \[\frac{a}{\alpha }+\frac{b}{\beta }+\frac{c}{\gamma }=0,\] then the value of \[\frac{{{\alpha }^{2}}}{{{a}^{2}}}+\frac{{{\beta }^{2}}}{{{b}^{2}}}+\frac{{{\gamma }^{2}}}{{{c}^{2}}}\] is equal to |
| A. | \[0\] |
| B. | \[-1\] |
| C. | \[2i\] |
| D. | \[-2i\] |
| Answer» D. \[-2i\] | |
| 1398. |
The principle value of the \[\arg \,(z)\] and \[|z|\] of the complex number \[z=1+\cos \left( \frac{11\pi }{9} \right)+i\sin \left( \frac{11\pi }{9} \right)\] are respectively. |
| A. | \[\frac{11\pi }{8},\,2\cos \left( \frac{\pi }{18} \right)\] |
| B. | \[-\frac{7\pi }{18},-2\cos \left( \frac{11\pi }{18} \right)\] |
| C. | \[\frac{2\pi }{9},2\cos \left( \frac{7\pi }{18} \right)\] |
| D. | \[-\frac{\pi }{9},-2\cos \left( \frac{\pi }{18} \right)\] |
| Answer» C. \[\frac{2\pi }{9},2\cos \left( \frac{7\pi }{18} \right)\] | |
| 1399. |
If \[\omega \] is imaginary cube root of unity, then \[\sin \left\{ ({{\omega }^{13}}+{{\omega }^{2}})\pi +\frac{\pi }{4} \right\}\] is equal to |
| A. | \[-\frac{\sqrt{3}}{2}\] |
| B. | \[-\frac{1}{\sqrt{2}}\] |
| C. | \[\frac{1}{\sqrt{2}}\] |
| D. | \[\frac{\sqrt{3}}{2}\] |
| Answer» C. \[\frac{1}{\sqrt{2}}\] | |
| 1400. |
Let \[{{x}_{1}}\] and \[{{y}_{1}}\] be real numbers. If \[{{z}_{1}}\] and \[{{z}_{2}}\] are complex numbers such that \[|{{z}_{1}}|=|{{z}_{2}}|=4,\] then \[|{{x}_{1}}{{z}_{1}}-{{y}_{1}}{{z}_{2}}{{|}^{2}}+|{{y}_{1}}{{z}_{1}}+{{x}_{1}}{{z}_{2}}{{|}^{2}}=\] |
| A. | \[32({{x}_{1}}^{2}+{{y}_{1}}^{2})\] |
| B. | \[16({{x}_{1}}^{2}+{{y}_{1}}^{2})\] |
| C. | \[4({{x}_{1}}^{2}+{{y}_{1}}^{2})\] |
| D. | \[32({{x}_{1}}^{2}+{{y}_{1}}^{2})|{{z}_{1}}+{{z}_{2}}{{|}^{2}}\] |
| Answer» B. \[16({{x}_{1}}^{2}+{{y}_{1}}^{2})\] | |