Home
Class 12
MATHS
Let a, lambda , mu in R.Consider the sy...

Let `a, lambda , mu in R`.Consider the system of linear equations
`ax+2y=lambda`
`3x-2y=mu`
Which of the following statement(s) is (are) correct ?

A

If `a=-3`, then the system has infinitely many solutions for all values of ` lambda` and `mu`

B

If `a ne -3 ` , then the system has a unique solution for all values of `lambda "and" mu`

C

If `lambda+mu` =0 , then the system has infinitely many solutions for `a=-3`

D

If `lambda+mu ne `0 then the system has no solution for `a =-3`

Text Solution

Verified by Experts

The correct Answer is:
B, C, D
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    ARIHANT MATHS|Exercise Determinants Exercise 7:|3 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|37 Videos

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|26 Videos

Similar Questions

Explore conceptually related problems

Solve system of linear equations, using matrix method: 5x+2y=3, 3x+2y=5

Solve system of linear equations, using matrix method: 2x-y=-2, 3x+4y=3

The following system of linear equations has x+ 2y + 3z=1,2x + y + 3z = 2, 5x+ 5y + 9z = 4

Solve the system of linear-equations : 2x + 3y + 3z = 5, x - 2y + z = - 4, 3x - y - 2z = 3 Using matrix method.

Find the value of lambda the equation is 2x+3y+lambda where x=2 and y=1

For what value of 'k', the system of linear equations : x+y+z=2,2x+y-z=3 and 3x+2y+kz=4 has a unique solution.

Find the value of lambda the equation is 5x+y+lambda=0 where x=1 and y=5

Using Cramer's Rule, solve the following linear equations: 3x-2y=5,x-3y=-3

If the system of equations ax+y=1,x+2y=3,2x+3y=5 are consistent, then a is given by

ARIHANT MATHS-DETERMINANTS -Exercise (Questions Asked In Previous 13 Years Exam)
  1. If a^2+b^2+c^2=-2, and f(x)= |{:(1+a^2x,(1+b^2)x,(1+c^2)x),((1+a^2)x,...

    Text Solution

    |

  2. The value of |alpha| for which the system of equation alphax+y+z=alpha...

    Text Solution

    |

  3. if a(1),a(2),…….a(n),……. form a G.P. and a(1) gt 0 , for all I ge 1 ...

    Text Solution

    |

  4. If D =|{:(1,1,1),(1,1+x,1),(1,1,1+y):}|"for" " "xne0,yne0 then D is

    Text Solution

    |

  5. Consider the system of equations x-2y+3z=-1 -x+y-2z=k x-3y+4z=1 ...

    Text Solution

    |

  6. Let a,b,c, be any real number. Suppose that there are real numbers x,y...

    Text Solution

    |

  7. Prove that |{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}| =abc (1+(1)/(a)+(1)/(...

    Text Solution

    |

  8. If f(theta)=|{:(1,tantheta,1),(-tantheta,1,tantheta),(-1,-tantheta,1):...

    Text Solution

    |

  9. The number of values of k for which the linear equations 4x+ky+2...

    Text Solution

    |

  10. If the trivial solution is the only solution of the system of equation...

    Text Solution

    |

  11. The number of values of k, for which the system of equations (k""+""...

    Text Solution

    |

  12. If f(n)=alpha^(n)+beta^(n) and |{:(3,1+f(1),1+f(2)),(1+f(1),1+f(2),1+f...

    Text Solution

    |

  13. The set of all values of lambda for which the system of linear equ...

    Text Solution

    |

  14. Which of the following values of alpha satisfying the equation |{:((1+...

    Text Solution

    |

  15. The system of linear equations x+y+z=2,2x+y-z=3, 3x+2y+kz=4 has a uniq...

    Text Solution

    |

  16. The total number of distinct x in R for which |{:(x,,x^(2),,...

    Text Solution

    |

  17. Let a, lambda , mu in R.Consider the system of linear equations ax...

    Text Solution

    |

  18. If S is the set of distinct values of 'b' for which the following ...

    Text Solution

    |