Home
Class 12
MATHS
Let |(a,l,m),(l,b,n),(m,n,c)||(bc-n^2,mn...

Let `|(a,l,m),(l,b,n),(m,n,c)||(bc-n^2,mn-lc,ln-bm),(mn-lc,ac-m^2,ml-an),(ln-bm,lm-an,ab-l^2)|=64.` If the value of `|(2a+3l,3l+5m,5m+4a),(2l+3b,3b+5n,5n+4l),(2m+3n,3n+5c,5c+4m)|=lambda` then `[lambda/2]` equals

A

`180`

B

`240`

C

`360`

D

`480`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `DeltaDelta^(2)=64`
`impliesDelta^(3)=64impliesDelta=4`
`|{:(2a+3l,3l+5m,5m+4a),(2l+3b,3b+5n,5n+4l),(2m+3n,3n+5c,5c+4m):}|`
`=[(2xx3xx5)+(3xx5xx4)]Delta`
`=(30+60)Delta`
`=90(4)`
`=360`
Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|5 Videos

  • DETERMINANT

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|5 Videos

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise JEE ADVANCED|38 Videos

  • DETERMINANTS

    CENGAGE PUBLICATION|Exercise All Questions|262 Videos

Similar Questions

Explore conceptually related problems

Write the values of n, l and m for 3p-subshell.

If x/(lm - n^2) = y/(mn - l^2) = z/(nl - m^2) the value of lx + my +nz will be

Let ** be a binary on NN defined by a**b=L.C.M. (a,b) (for all a,bin NN) . 2**4=lambda then lambda will be---

m^(3)-n^(3)-m(m^(2)-n^(2))+n(m-n)^(2)

Let's write the value of (m^2 + n^2) (m^3 + n^3) by calculation if m + n = 5 and mn = 6.

If x/(lm-n^2)=y/(mn-l^2)=z/(nl-m^2) , then show that lx+my+nz=0

If y=|(f(x),g(x),h(x)),(l,m,n),(a, b,c)| , prove that, (dy)/(dx)=|(f'(x),g'(x),h'(x)),(l,m,n),(a, b,c)|

If l,m and n are real numbers such that l^2+m^2+n^2=0 , then show that |{:(1+l^2,lm,ln),(lm,1+m^2,mn),(ln,mn,1+n^2):}|=1

Given A=|[a,b,2c],[d,e,2f],[l,m,2n]|,B=|[f,2d,e],[2n,4l,2m],[c,2a,b]| , then the value of B//A is ___________.

Let's find value of : a (m + n) + b ( n + l) + c(l + m) if a = lx + my +n, b = mx + ny +l, c = nx + ly +m

CENGAGE PUBLICATION-DETERMINANT-Single correct Answer
  1. |[1/c,1/c,-(a+b)/c^2],[-(b+c)/a^2,1/a,1/a],[(-b(b+c))/(a^2c),(a+2b+c)/...

    Text Solution

    |

  2. The equation |((1+x)^2,(1-x)^2,-(2+x^2)),(2x+1,3x,1-5x),(x+1,2x,2-3x)...

    Text Solution

    |

  3. Let Delta(1)=|{:(ap^(2),2ap,1),(aq^(2),2aq,1),(ar^(2),2ar,1):}| and De...

    Text Solution

    |

  4. Area of triangle whose vertices are (a,a^2),(b,b^2),(c,c^2) is 1/2 . a...

    Text Solution

    |

  5. Prove that |{:(betagamma,betagamma'+beta'gamma,beta'gamma'),(gammaalph...

    Text Solution

    |

  6. If |{:(a,b,1),(b,c,1),(c,a,1):}|=2010 and if |{:(c-a,c-b,ab),(a-b,a-c,...

    Text Solution

    |

  7. Let |(a,l,m),(l,b,n),(m,n,c)||(bc-n^2,mn-lc,ln-bm),(mn-lc,ac-m^2,ml-an...

    Text Solution

    |

  8. The value of |{:(x^(2)+y^(2),ax+by,x+y),(ax+by,a^(2)+b^(2),a+b),(x+y,a...

    Text Solution

    |

  9. If u=ax+by+cz, v=ay+bz+cx, w=az+bx+cy, then the value of |{:(a,b,c),(b...

    Text Solution

    |

  10. If the number of positive integral solutions of u+v+w=n be denoted by ...

    Text Solution

    |

  11. If f(x), h(x) are polynomials of degree 4 and |(f(x), g(x),h(x)),(a, b...

    Text Solution

    |

  12. If f(x)=|[x-2, (x-1)^2, x^3] , [(x-1), x^2, (x+1)^3] , [x,(x+1)^2, (x+...

    Text Solution

    |

  13. If f(x)=|{:(sinx,cosx,tanx),(x^(3),x^(2),x),(2x,1,x):}|, then lim(xto0...

    Text Solution

    |

  14. If the system of linear equations x+2ay +az =0,x+3by+bz =0 and x+4cy ...

    Text Solution

    |

  15. Find all values of lambda for which the (lambda-1)x+(3lambda+1)y+2lamb...

    Text Solution

    |

  16. The system of homogenous equations tx+(t+1)y+(t-1)z=0, (t+1)x+ty+(t+...

    Text Solution

    |

  17. If a , b , c are non-zero, then the system of equations (alpha+a)x+alp...

    Text Solution

    |

  18. The values of theta, lambda for which the following equations sintheta...

    Text Solution

    |

  19. If the system of equation {:(,x-2y+z=a),(2x+y-2z=b),and,(x+3y-3z=c):} ...

    Text Solution

    |

  20. If A,B,C are the angles of a triangle, the system of equations (sinA...

    Text Solution

    |