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

Monjur Alahi

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-trivial solution if `alpha^(-1)=-(a^(-1)+b^(-1)+c^(-1))` b. `alpha^(-1)=a+b+c` c.`alpha+a+b+c=1` d. none of these
A. `2alpha=a+b+c`
B. `alpha^(-1)=a+b+c`
C. `alpha+a+b+c=1`
D. `alpha^(-1)=-(a^(-1)+b^(-1)+c^(-1))`


0 like 0 dislike
1 views
Share with your friends

1 Answers

Salim Ahmed Kawsar

Call

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 ))`

0 like 0 dislike
1 views
Talk Doctor Online in Bissoy App
A travelling wave on a string is given by `y = A sin [alphax + betat + (pi)/(6)]`. If `alpha = 0.56 //cm, beta = 12//sec, A = 7.5 cm`, then find the p

Correct Answer - B Put `alpha, beta, A, x` and `t` in the equation `(2pi)/(lambda) = 0.56 cm^(-1)` `2pif = 2 sec^(-1)` `alphabeta + betat + (pi)/(6) = (12.56 xx 180)/(3.14)...

2 Answers 8 views
If a variable takes the discrete values `alpha-4`, `alpha -(7)/(2), alpha-(5)/(2), alpha-2,alpha+(1)/(2), alpha-(1)/(2), alpha+5(alpha gt 0)`, then th

Correct Answer - A Arrange the data as follows : `alpha-(7)/(2), alpha-3, alpha-(5)/(2),alpha-2, alpha-(1)/(2),alpha+(1)/(2),alpha+4,alpha+5` Median `=(1)/(2)` [value of 4th item+value of 5th item] `therefore " Median"=(alpha-2+alpha-(1)/(2))/(2)=(2alpha-(5)/(2))/(2)=alpha-(5)/(4)`

2 Answers 1 views
Prove that `tan alpha+2 tan 2 alpha+2^(2)tan^(2)alpha+..............+2^(n-1)tan2^(n-1)alpha+2^(@)cot2^(@)alpha=cotalpha`

We know `tan theta=cot theta-2 cot 2 theta`. Putting `theta=alpha,2alpha,2^(2)alpha,....................` in (i), we get `tan alpha=(cot alpha-2 cot 2alpha)` `2(tan2alpha)=2(cot 2 alpha-2 cot 2 ^(2)alpha)` `2^(2)(tan2^(2)alpha)=2^(2)(cot2^(2)alpha-2cot2^(3)alpha)` `2^(n-1)(tan2^(n-1)alpha)=2^(n-1)(cot2^(n-1)alpha-2cos2^(n)alpha)` Adding, `tan alpha+2tan...

2 Answers 1 views
If `A(alpha, beta)=[("cos" alpha,sin alpha,0),(-sin alpha,cos alpha,0),(0,0,e^(beta))]`, then `A(alpha, beta)^(-1)` is equal to

Correct Answer - A We have, `A(alpha, beta)^(-1)=1/e^(beta) [(e^(beta) cos alpha,-e^(beta) sin alpha,0),(e^(beta) sin alpha,e^(beta) cos alpha,0),(0,0,1)]` `=A(-alpha, -beta)`

2 Answers 2 views
If `f(x)=x^(11)+x^9-x^7+x^3+1` and `f(sin^(-1)(sin8)=alpha,alpha` is constant, then `f(tan^(-1)(t a n8)` is equal to `alpha` (b) `alpha-2` (c) `alpha+

Correct Answer - D `f(x) + f(-x) = 2` Now `(sin^(-1) (sin 8)) = 3pi - 8 = y` And `(tan^(-1) (tan 8)) = (8 - 3pi) = -y` Hence, `f(y)...

2 Answers 1 views
The coefficient of the middle term in the binomial expansion in powers of `x` of`(1+alphax)^4` and of`(1-alphax)^6` is the same, if `alpha` equals

Correct Answer - C Middle term of `(1+alphax)^(4)` is `T_(3)`. Its coefficient is `.^(4)C_(2)(alpha)^(2)=6alpha^(2)`. Middle term of `(1-alphax)^(6)` is `T_(4)`. Its coefficient is `.^(6)C_(3) (-alpha)^(3) = -20alpha^(3)`. According to question. `6alpha^(2)...

2 Answers 3 views
If `2sec^2 alpha- sec^4 alpha-2 cosec^2 alpha+cosec^4 alpha=15/4` then `tan alpha=`

Correct Answer - A::D `2sec^2alpha-sec^4alpha-2cosec^2alpha+cosec^4alpha=15/4` `or 2(sec^2alpha-cosec^2alpha)+(cosec^2alpha+sec^2alpha)xx(cosec^2alpha-sec^2alpha-sec^2alpha)=15/4` `or (cosec^2alpha-sec^2alpha)[cosec^2alpha+sec^2alpha-2]=15/4` `or 4(cot^2alpha-tan^2alpha)[cosec^2alpha+sec^2alpha)=15` `or4(cot^4alpha-tan^4alpha)=15` `or 4(1-tan^8alpha)=15tan^4alpha` `or 4tan^8alpha+15tan^4alpha` `or 4tan^8alpha+154tan^4alpha-4=0` `or (4tan^4alpha-1)(tan^4alpha+4)=0` `or tan^4alpha=1/4ot tan^4alpha=-4` `or tan^2alpha=pm1/2` `or tan^2alpha=+1/2` `or tanalpha=pm1/sqrt2`

2 Answers 1 views
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...

2 Answers 1 views
There are two sets of parallel lines, their equations being `x cos alpha+y sin alpha=p` and `x sin alpha- y cos alpha=p` , `p=1,2,3,….n` and `alpha in

Correct Answer - C `(c )` `"^(n)C_(2)*^(n)C_(2)=225impliesn=6`

2 Answers 1 views
If the system of linear equations `x+2ay +az =0,x+3by+bz =0 and x+4cy + cz =0` has a non-zero solution, then `a, b, c`

Correct Answer - C `(c )` The system of linear equation has a non zero solution. `Delta=|{:(1,2a,a),(1,3b,b),(1,4c,c):}|=0` `:.(3bc-4bc)-(2ac-4ac)+(2ab-3ab)=0` `:.bc+ab=2ac` `:. (1)/(a)+(1)/(c )=(2)/(b)` `impliesa,b,c` are in `H.P.`

2 Answers 1 views
X