Home
Class 12
MATHS
Value of |{:(1+x(1),,1+x(1)x,,1+x(1)x^(2...

Value of `|{:(1+x_(1),,1+x_(1)x,,1+x_(1)x^(2)),(1+x_(2),,1+x_(2)x,,1+x_(2)x^(2)),(1+x_(3),,1+x_(3)x,,1+x_(3)x^(2)):}|` depends upon

A

x only

B

`x_(1)`only

C

`x_(2)`only

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
`|{:(1+x_(1),,1+x_(1)x,,1+x_(1)x^(2)),(1+x_(2),,1+x_(2)x,,1+x_(2)x^(2)),(1+x_(3),,1+x_(3)x,,1+x_(3)x^(2)):}|`
`=|{:(1,,x_(1),,0),(1,,x_(2),,0),(1,,x_(3),,0):}||{:(1,,1,,0),(1,,x,,0),(1,,x^(2),,0):}|`
Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos

Similar Questions

Explore conceptually related problems

Value of |1+x_1 1+x_1x1+x_1x^2 1+x_2 1+x_2x1+x_2x^2 1+x_3 1+x_3x1+x_3x^2| depends upon "xo n l y" b. "x"_1"o n l y" c. "x"_2on l y d. none of these

it x_(1)^(2) +2y_(1)^(2)+3z_(1)^(2)=x_(2)^(2)+2y_(2)^(2)+3z_(2)^(2)=x_(3)^(2)+2y_(3)^(2)+3z_(3)^(2)=2 " and " x_(2)x_(3) +2y_(2)y_(3)+3z_(2)z_(3)=x_(3)x_(1)+2y_(3)y_(1)+3z_(3)z_(1)=x_(1)x_(2)+2y_(1)y_(2)+3z_(1)z_(2)=1 Then find the value of |{:(x_(1),,y_(1),,z_(1)),(x_(2),,y_(2),,z_(2)),(x_(3),,y_(3),,z_(3)):}|

Show that if x_(1),x_(2),x_(3) ne 0 |{:(x_(1) +a_(1)b_(1),,a_(1)b_(2),,a_(1)b_(3)),(a_(2)b_(1),,x_(2)+a_(2)b_(2),,a_(2)b_(3)),(a_(3)b_(1),,a_(3)b_(2),,x_(3)+a_(3)b_(3)):}| =x_(1)x_(2)x_(3) (1+(a_(1)b_(1))/(x_(1))+(a_(2)b_(2))/(x_(2))+(a_(3)b_(3))/(x_(3)))

Given the sequence of numbers x_(1),x_(2),x_(3),x_(4),….,x_(2005) , (x_(1))/(x_(1)+1)=(x_(2))/(x_(2)+3)=(x_(3))/(x_(3)+5)=...=(x_(2005))/(x_(2005)+4009) , the nature of the sequence is

A triangle has vertices A_(i) (x_(i),y_(i)) for i= 1,2,3,. If the orthocenter of triangle is (0,0) then prove that |{:(x_(2)-x_(3),,y_(2)-y_(3),,y_(1)(y_(2)-y_(3))+x_(1)(x_(2)-x_(3))),(x_(3)-x_(1) ,,y_(3)-y_(1),,y_(2)(y_(3)-y_(1))+x_(2)(x_(3)-x_(1))),( x_(1)-x_(2),,y_(1)-y_(2),,y_(3)(y_(1)-y_(2))+x_(3)(x_(1)-x_(2))):}|=0

if (x_(1),x_(2))^(2)+(y_(1)-y_(2))^(2)=a^(2), (x_(2)-x_(3))^(2)+(y_(2)-y_(3))^(2)=b^(2) (x_(3)-x_(1))^(2)+(y_(3)-y_(1))^(2)=c^(2). where a,b,c are positive then prove that 4 |{:(x_(1),,y_(1),,1),(x_(2) ,,y_(2),,1),( x_(3),, y_(3),,1):}| = (a+b+c) (b+c-a) (c+a-b)(a+b-c)

If p_(1)^(x_(1))timesp_(2)^(x_(2))timesp_(3)^(x_(3))timesp_(4)^(x_(4))=11340 where p_(1), p_(2), p_(3), p_(4) are primes in ascending order and x_(1), x_(2), x_(3), x_(4) are integers, find the value of p_(1), p_(2), p_(3), p_(4) and x_(1), x_(2), x_(3), x_(4) .

Consider the quantities such that x_(1),x_(2),….x_(10),-1 lex_(1),x_(2)….,x_(10)le 1 and x_(1)^(3)+x_(2)^(3)+…+x_(10)^(3)=0 , then the maximum value of x_(1)+x_(2)+….+x_(10) is

Let the equation x^(5) + x^(3) + x^(2) + 2 = 0 has roots x_(1), x_(2), x_(3), x_(4) and x_(5), then find the value of (x_(1)^(2) - 1)(x_(2)^(2) - 1)(x_(3)^(2) - 1)(x_(4)^(2) - 1)(x_(5)^(2) - 1).

If x_(1) , x_(2) and x_(3) are the positive roots of the equation x^(3)-6x^(2)+3px-2p=0 , pinR , then the value of sin^(-1)((1)/(x_(1))+(1)/(x_(2)))+cos^(-1)((1)/(x_(2))+(1)/(x_(3)))-tan^(-1)((1)/(x_(3))+(1)/(x_(1))) is equal to

CENGAGE-DETERMINANTS-All Questions
  1. Value of |{:(1+x(1),,1+x(1)x,,1+x(1)x^(2)),(1+x(2),,1+x(2)x,,1+x(2)x^(...

    Text Solution

    |

  2. Statement 1: If b c+q r=c a+r p=a b+p q=-1, t h e n|a p a p b q b q c...

    Text Solution

    |

  3. If f(theta)=|sinthetacosthetasintheta costhetasinthetacostheta costhet...

    Text Solution

    |

  4. If f(theta)=|[sin^2A,cot A,1],[sin^2B,cosB,1],[sin^2C,cosC,1]| , then...

    Text Solution

    |

  5. The roots of the equation |^x Cr^(n-1)Cr^(n-1)C(r-1)^(x+1)Cr^n Cr^n C(...

    Text Solution

    |

  6. Let Delta(x)=|[3,3x,3x^2+2a^2] , [3x, 3x^2+2a^2, 3x^3+6a^2x] , [3x^2+2...

    Text Solution

    |

  7. The determinant "Delta"=|(a^2+x) ab ac ab (b^2+x) bc ac bc (c^2+...

    Text Solution

    |

  8. If f(x)=|[a,-1, 0],[a x, a,-1],[a x^2,a x, a]|,t h e nf(2x)-f(x) is d...

    Text Solution

    |

  9. If g(x)-(f(x))/((x-a)(x-b)(x-c)),w h e r ef(x) is a polynomial of d...

    Text Solution

    |

  10. If (x)= |x^2+4x-3 2x+4 13 ...

    Text Solution

    |

  11. If |y z-x^2z x-y^2x y-z^2x z-y^2x y-z^2y z-x^2x y-z^2y z-x^2z x-y^2|=|...

    Text Solution

    |

  12. Let f (n) = |{:(n,,n+1,,n+2),(.^(n)P(n),,.^(n+1)P(n+1),,.^(n+2)P(n+2)...

    Text Solution

    |

  13. If |x^n x^(n+2)x^(2n)1x^a a x^(n+5)x^(a+6)x^(2n+5)|=0,AAx in R ,w h e...

    Text Solution

    |

  14. Let x<1, then value of [[x^2+2, 2x+1 ,1],[ 2x+1,x+2, 1],[ 3, 3 ,1]...

    Text Solution

    |

  15. If f (x) = |(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0)|then

    Text Solution

    |

  16. Value of [[x+y, z,z ],[x, y+z, x],[y, y, z+x]], where x ,y ,z are non...

    Text Solution

    |

  17. Which of the following is not the root of the equation |[x,-6,-1],[ 2,...

    Text Solution

    |

  18. If A,B,C are the angles of a non right angled triangle ABC. Then find ...

    Text Solution

    |

  19. If f(x)=|x a a a x a a a x|=0, then f^(prime)(x)=0a n df^(x)=0 has com...

    Text Solution

    |

  20. Evaluate {:[( cos alpha cos beta , cos alpha sin beta , -sin alpha ),...

    Text Solution

    |

  21. Roots of the equation |x m n1a x n1a b x1a b c1|=0 are independent of ...

    Text Solution

    |