Home
Class 12
MATHS
If the system of linear equations x-2y+z...

If the system of linear equations `x-2y+z=-4 ; 2x+alpha y+3z=5; 3x-y+beta z=3`,has infinitely many solutions, then `12 alpha+13 beta` is equal to

A

64

B

58

C

60

D

54

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • JEE MAIN 2024

    JEE MAINS PREVIOUS YEAR|Exercise Questions|18 Videos

  • JEE MAINS

    JEE MAINS PREVIOUS YEAR|Exercise Physics|30 Videos

Similar Questions

Explore conceptually related problems

If the system of linear equations {:(2x+y-z=3),(x-y-z=alpha),(3x+33y-betaz=3):} has infinitely many solution, then alpha+beta-alphabeta is equal to ______.

If the system of equation x - 2y + 5z = 3 2x - y + z = 1 and 11x - 7y + pz = q has infinitely many solution, then

If the system of equations 2x 3y – z = 5 x alpha y 3z = –4 3x – y beta z = 7 has infinitely many solutions, then 13 alpha beta is equal to

If the system of equations x+ y+z = 5 x+ 2y + 3z =9 x +3y + az = beta has infinitely many solutions, then beta-alpha equals

If the system of simultaneous linear equations x+y+z=a , x-y+bz=2 , 2x+3y-z=1 has infinitely many solutions,then b - 5a=

If the system fo equations x+y+z = 5 x + 2y + 3z = 9 x + 3y + alphaz = beta has infinitely many solution, then beta - alpha equals

For real numbers alpha and beta , consider the following system of linear equations: x+y-z=2, x+2y+alpha z=1, 2x- y+z= beta . If the system has infinite solutions, then alpha+beta is equal to ____

For a unique value of alpha and beta , then system of equations given by x+y+z=6,x+2y+3z=14 and 2x+5y+alphaz=beta ,has infinitely many solutions,then |alpha-beta| is

JEE MAINS PREVIOUS YEAR-JEE MAIN 2024 ACTUAL PAPER-Question
  1. If f(x)=|[x^(3),2x^(2)+1,1+3x],[3x^(2)+2,2x,x^(3)+6],[x^(3)-x,4,x^(2)-...

    Text Solution

    |

  2. If the foci of a hyperbola are same as that of the ellipse (x^(2))/(9)...

    Text Solution

    |

  3. If the system of linear equations x-2y+z=-4 ; 2x+alpha y+3z=5; 3x-y+be...

    Text Solution

    |

  4. The sum of series 1/(1-3.1^2+1^4)+2/(1-3.3^2+2^4)+3/(1-3.3^2+3^4)+.......

    Text Solution

    |

  5. Let alpha,beta,gamma,delta in Z and let A(alpha,beta),B(1,0),C(gamma,d...

    Text Solution

    |

  6. A={1,2,3,4} and R={(1,2),(2,3),(1,4)} be a relation on A .Let S be the...

    Text Solution

    |

  7. In the expansion of (1-x^2)(1+x)(1+3/x+3/x^2+1/x^3)^5 the sum of the c...

    Text Solution

    |

  8. If alpha denotes the number of solutions of |1-i|^(x)=2^(x) and beta=(...

    Text Solution

    |

  9. Let vec a and vec b be two vectors such that |vec a|=1,|vec b|=4 ,and ...

    Text Solution

    |

  10. The total number of words (with or without meaning) that can be formed...

    Text Solution

    |

  11. Let S=(-1,oo) and f:S rarr R be defined as f(x)=int(-1)^(x)(e^(t)-1)^(...

    Text Solution

    |

  12. If the integral 525int(0)^((pi)/(2))sin2x cos^((11)/(2))x(1+Cos^((5)/(...

    Text Solution

    |

  13. Let the foci and length of the latus rectum of an ellipse (x^(2))/(a^(...

    Text Solution

    |

  14. Let f:R to R be a function defined by f(x)=(4^x)/(4^x+2) and M=int(f(a...

    Text Solution

    |

  15. Let Q and R be the feet of perpendiculars from the point P(a,a,a) on t...

    Text Solution

    |

  16. If F :(- oo, -1] rightarrow (a, b] is defined as f(x) = e^(x^3-3x+1) s...

    Text Solution

    |

  17. The area of the region enclosed by the parabolas y=4x-x^(2) and 3y=(x-...

    Text Solution

    |

  18. Let A(a,b),B(3,4) and C(-6,-8) respectively denote the centroid,circum...

    Text Solution

    |

  19. Consider the function f:(0,oo)rarr R defined by f(x)=e^(-|log(e)x|) .I...

    Text Solution

    |

  20. Let z(1) and z(2) be two complex numbers such that z(1)+z(2)=5 and z(1...

    Text Solution

    |