Home
Class 12
MATHS
Let for any three distinct consecutive t...

Let for any three distinct consecutive terms a, b, c of an A.P, the lines `ax + by + c = 0` be concurrent at the point P and Q `(alpha, beta)` be a point such that the system of equations
`x + y + z = 6`
`2x + 5y + alpha z = beta` and
`x + 2y + 3Z = 4`, has infinitely many solutions. Then `(PQ)^2` is equal to ________.

Text Solution

Verified by Experts

The correct Answer is:
113
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 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 fo equations x+y+z = 5 x + 2y + 3z = 9 x + 3y + alphaz = beta has infinitely many solution, then beta - alpha equals

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

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

If the system of equations x+y+z=7,x+2y+3z=10,x+3y+ alpha z= beta has infinitely many solutions, then beta+alpha equals (A) 18 (B)8 (C) 13 (D) 5

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 ____

JEE MAINS PREVIOUS YEAR-JEE MAIN 2024 ACTUAL PAPER-Question
  1. Let a unit vector hat u = x hat i + y hat j + z hat k make angles (pi)...

    Text Solution

    |

  2. Let alpha, beta be the roots of the equationx^2 - sqrt 6 x + 3 = 0 suc...

    Text Solution

    |

  3. Let for any three distinct consecutive terms a, b, c of an A.P, the li...

    Text Solution

    |

  4. Let P(alpha, beta) be a point on the parabola y^2= 4x. If P also lies ...

    Text Solution

    |

  5. If int(pi/6)^(pi/3) sqrt (1- sin 2x) dx = alpha + beta sqrt 2 + gamma ...

    Text Solution

    |

  6. Let the area of the region {(x, y): 0 le x le 3, 0 le y le min{x^2+ 2,...

    Text Solution

    |

  7. Let O be the origin, and M and N be the points on the lines frac{x-5}{...

    Text Solution

    |

  8. Let f(x) =sqrt ((lim(r-> x) {2r^2[f(r))^2 - f(x) f(r)]/(r^2-x^2)-r^3e^...

    Text Solution

    |

  9. Remainder when 64^(32^(32)is divided by 9 is equal to .

    Text Solution

    |

  10. Let the set C = {(x, y) | x^2- 2^y = 2023, x, y in }. Then sum((x,y) i...

    Text Solution

    |

  11. Let the slope of the line 45x + 5y + 3 = 0 be 27 r1 + (9r2)/ 2 for som...

    Text Solution

    |

  12. Let "P" be a point on the hyperbola H:(x^(2))/(9)-(y^(2))/(4)=1 ,in th...

    Text Solution

    |

  13. Let f(x)=(x+3)^(2)(x-2)^(3),x in[-4,4] .If "M" and "m" are the maximum...

    Text Solution

    |

  14. Let f(x)={(x^2+3x+a,xle1),(bx+2,xgt1)) is differentiable everywhere. T...

    Text Solution

    |

  15. Let "a" and "b" be be two distinct positive real numbers.Let 11^(" th ...

    Text Solution

    |

  16. Sum of common roots of the equations z^(3) + 2z^(2) + 2z + 1 =0 and z...

    Text Solution

    |

  17. Let vec a and vec b be two vectors such that |vec b|=1and |vec b times...

    Text Solution

    |

  18. Let R=([x,0,0],[0,y,0],[0,0,z]) be a non-zero 3times3 matrix,where x s...

    Text Solution

    |

  19. Let L(1):vec r=(hat i-hat j+2 hat k)+lambda(hat i-hat j+2 hat k),lambd...

    Text Solution

    |

  20. Consider the system of linear equations x+y+z=5, x+2y+lambda^(2)z=9,x+...

    Text Solution

    |