If A + B = A - B then vector B must be
(A) zero vector
(B) unit vector
(C) Non zero vector
(D) equal to vector A
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If in a system unit of mass is 5kg, unit of length is 10m and unit of time as 5sec, then what will be the value of 1 unit energy in new system.
`[E]=[ML^(2)T^(-2)]=(5)` `=(10)^(2)(5)^(2)=20` joules
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If `veca,vecb and vecc` are three mutually perpendicular unit vectors and `vecd` is a unit vector which makes equal angal with `veca,vecb and vecc`, t
`|veca+vecb+vecc+vecd|^(2)=sum|veca|^(2)+2sumveca.vecb=4+2vecd.(veca+vecb+vecc) " " (veca,vecb,vecc "are mutually perpendicular")` `Let vecd=lambdaveca+muvecb+v vecc. Then vecd.veca=vecd.vecb=vecd.vecc=costheta`Therefore, `lambda=mu=v=costheta` ` lambda^(2)+mu^(2)+v^(2)=1Rightarrow3cos^(2)theta=1costheta=1/sqrt3` `|veca+vecb+vecc+vecd|^(2)=4+-(2.3)/sqrt3=4+-2sqrt3`
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If `veca,vecb and vecc` are non coplnar and non zero vectors and `vecr` is any vector in space then`[vecc vecr vecb]veca+pveca vecr vecc] vecb+[vecb v
`Let" " vecr=x_(1)veca+x_(2)vecb+x_(3)veccRightarrow vecr.(vecbxxvecc)=x_(1)veca.(vecbxxvecc)or x_(1)=([vecr vecb vecc])/([veca vecb vecc])`. `Also, " " vecr.(veccxxveca)=x_(2)vecb.(veccxxveca)orx_(2)=([vecrveccveca])/([vecavecbvecc])` `and vecr.(vecaxxvecb)=x_(3)vecc. (vecaxxvecb)or x_(3)=([vecr vecavecb])/([veca vecbvecc])` `Rightarrow vecr=([vecrvecb vecc])/([vecavecbvecc])veca+([vecrveccveca])/([vecavecbvecc])vecb+([vecrvecavecb])/([vecavecb vecc])vecc` `or [vecbveccvecr]veca+[veccvecavecr]vecb+[vecavecbvecr]vecr=[vecavecbvecc]vecr`
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If `veca, vecb and vecc` are three non-coplanar non-zero vectors, then prove that `(veca.veca) vecb xx vecc + (veca.vecb) vecc xx veca + (veca.vecc)ve
As `veca ,vecb and vecc` are non- coplanar, `vecb xx veca,veccxxveca and vecaxxvecb` are also non-coplanar, So, any vector con be expressend as a linear combination of these vectors. `veca=lambdavecbxxvecc+mu...
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For `a`, `b`,`c` non-zero, real distinct, the equation, `(a^(2)+b^(2))x^(2)-2b(a+c)x+b^(2)+c^(2)=0` has non-zero real roots. One of these roots is als
Correct Answer - C `(c )` ` (a^(2)+b^(2))x^(2)-2b(a+c)x+b^(2)+c^(2)=0` `D=4b^(2)(a+c)^(2)-4(a^(2)+b^(2))(b^(2)+c^(2))` `=-4(b^(4)-2b^(2)ac+a^(2)c^(2))` `=-(n^(2)-ac)^(2)` For real roots, `D ge 0` `implies -4(b^(2)-ac)^(2) ge 0` `implies b^(2)-ac=0` `implies` Roots are real and equal. `:.` Roots...
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The number of words that can be formed using all the letters of the word REGULATIONS such that `G` must come after `R`, `L` must come after `A`, and `
Correct Answer - A `(a)` The other five letters (other than `G`, `R`, `L`, `A`, `S`, `N`) in `11` places can be arranged in `"^(11)P_(5)` ways. Then three remains six places....
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Find the number of ways of arranging 15 students `A_1,A_2,........A_15` in a row such that (i) `A_2`, must be seated after `A_1 and A_2`, must come af
Correct Answer - A `(a)` First arrange `12` persons `A_(4),A_(5),….A_(15)` in `"^(15)P_(12)` ways There remains `3` places. Keep `A_(1)` in the first place and arrange `A_(2)`, `A_(3)` in the remaining two...
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If `a , b , c` are non-zero, then the system of equations `(alpha+a)x+alphay+alphaz=0,alphax+(alpha+b)y+alphaz=0,alphax+alphay+(alpha+c)z=0` has a non
Correct Answer - D `(d)` The given system of equations will have a non-trivial solution if `|{:(alpha+a,alpha,alpha),(alpha,alpha+b,alpha),(alpha,alpha,alpha+c):}|=0` Operate `R_(2)toR_(2)-R_(1)` , `R_(3)-R_(3)-R_(1)`, then `|{:(alpha+a,alpha,alpha),(-a,b,0),(-a,0,c):}|=0` `impliesalpha(bc+ca+ab)+abc=0` Since, `a,b,c ne 0` `:.(1)/(alpha)=-((1)/(a)+(1)/(b)+(1)/(c ))`
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i. Minimum four Committee Meetings must be held in a year. ii. Creditors Meeting must be held once a year.
i. Minimum four Directors Meetings must be held in a year. ii. Annual General Meeting must be held once a year. iii. Annual General Meeting must be held every year. iv. The Meeting of all Directors is...
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The expression 1/√2 (i + j) is a (A) unit vector (B) null vector (C) vector of magnitude (D) scalar
Correct option is: (A) unit vector
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