InterviewSolution
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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
If `a_(1)` and `a_(2)` are two values of a for which the unit vector `aveci + bvecj +1/2veck` is linearly dependent with `veci+2vecj` and `vecj-2veck`, then `1/a_(1)+1/a_(2)` is equal toA. 1B. `1/8`C. `-16/11`D. `-11/16` |
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Answer» Correct Answer - C `ahati+bhatj+1/2hatk=l(hati+2hatj)+m(hatj-2hatk)` `rArr a=l, b=2l+m` and `m=-1/4` `ahati+bhatj+1/2hatk` is unit vector `therefore a^(2)+b^(2)=3/4` `rArr 5a^(2)-a-11/16=0` `a_(1)` and `a_(2)` are roots of above equation `rArr 1/a_(1)+1/a_(2)=(a_(1)+a_(2))/(a_(1)a_(2))=-16/11` |
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| 2. |
The number of integral values of p for which `(p+1) hati-3hatj+phatk, phati + (p+1)hatj-3hatk` and `-3hati+phatj+(p+1)hatk` are linearly dependent vectors is q |
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Answer» Correct Answer - B The vectors are linearly dependent `rArr |{:(p+1,-3,p),(p,p+1,-3),(-3,p,p+1):}|=0` `rArr (2p-2)|{:(1,-3,p),(1,p+1,-3),(1,p,p+1):}|=0` `rArr 2(p-1)|{:(1,-3,p),(0,p+4,-3-p),(0,p+3,1):}|=0` `rArr 2(p-1)(p+4)+(p+3)^(2)=0` `rArr (p-1)(p^(2)+7p+13)=0` Roots of `p^(2)+7p+13=0` are (imaginary) `therefore p=1` Only integral value of p is 1. |
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| 3. |
The number of distinct real values of `lamda` for which the vectors `veca=lamda^(3)hati+hatk, vecb=hati-lamda^(3)hatj` and `vecc=hati+(2lamda-sin lamda)hati-lamdahatk` are coplanar is |
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Answer» Correct Answer - A Put `Delta=0` `rArr lambda^(7)+lambda^(3)-sinlambda=0` Let `f(lambda)=(7lambda^(6)+3lambda^(2)+2-coslambda) gt 0` in R `therefore f(lambda)=0` has only one real solution `lambda=0` |
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