Home
Class 12
MATHS
The value of the determinant of n^(t h) ...

The value of the determinant of `n^(t h)` order, being given by `|[x, 1, 1...], [1, x, 1...], [1, 1, x...],[... , ... , ...]|` is a. `(x-1)^(n-1)(x+n-1)` b. `(x-1)^n(x+n-1)` c. `(1-x)^(-1)(x+n-1)` d. none of these

Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|5 Videos
  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

(x^(2^(n-1))+y^(2^(n-1)))(x^(2^(n-1))-y^(2^(n-1)))=

The derivative of y=(1-x)(2-x)....(n-x) at x=1 is (a) 0 (b) (-1)(n-1)! (c) n !-1 (d) (-1)^(n-1)(n-1)!

ifint(dx)/(x^2(x^n+1)^(((n-1)/n))=-[f(x)]^(1/n)+c ,t h e nf(x)i s (1+x^n) (b) 1+x^(-1) x^n+x^(-n) (d) none of these

The coefficient of 1//x in the expansion of (1+x)^n(1+1//x)^n is (a). (n !)/((n-1)!(n+1)!) (b). ((2n)!)/((n-1)!(n+1)!) (c). ((2n)!)/((2n-1)!(2n+1)!) (d). none of these

If x is real, then x//(x^2-5x+9) lies between a. -1a n d-1//11 b. 1a n d-1//11 c. 1a n d1//11 d. none of these

ifint(dx)/(x^2(x^n+1)^(((n-1)/n)) )=-[f(x)]^(1/n)+c ,t h e nf(x)i s (a) (1+x^n) (b) 1+x^(-1) (c) x^n+x^(-n) (d) none of these

The coefficient of x^n in the expansion of (1+x)(1-x)^n is

The value of lim_(x rarr 1) (x+x^2+...+x^n-n)/(x-1) is

If |[ x^n ,x^(n+2) ,x^(2n)],[1 ,x^a , a ],[x^(n+5),x^(a+6),x^(2n+5)]|=0,AAx in R, where . n in N , then value of a is a. n b. n-1 c. n+1 d. none of these

Simplify : (1)/(1+x^(m-n)+x^(m-p))+(1)/(1+x^(n-p)+x^(n-m))+(1)/(1+x^(p-m)+x^(p-n)) .

CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. If a,b c(all positive)are the p th,q thand r th terms repectively of a...

    Text Solution

    |

  2. If the entries in a 3xx3 determinant are either 0 or 1, then the grea...

    Text Solution

    |

  3. The value of the determinant of n^(t h) order, being given by |[x, 1, ...

    Text Solution

    |

  4. Prove that a!=0,|[x+a, x,x],[x,x+a,x],[x,x,x+a^2]|=0 represents a stra...

    Text Solution

    |

  5. If a1b1c1,a2b2c2 and a3b3c3 are three digit even natural numbers and ...

    Text Solution

    |

  6. If =|[a b c, b^2c,c^2b],[ a b c,c^2a, c a^2],[a b c, a^2b,b^2a]|=0,(a ...

    Text Solution

    |

  7. The value of |[yz, z x,x y],[ p,2p,3r],[1, 1, 1]|,w h e r ex ,y ,z ar...

    Text Solution

    |

  8. Show that the determinant |a^2+b^2+c^2 bc+ca+ab bc+ca+ab bc+ca+ab a^2+...

    Text Solution

    |

  9. If x!=0,y!=0,z!=0 and |[1+x,1,1],[1+y,1+2y,1],[1+z,1+z,1+3z]|=0, then ...

    Text Solution

    |

  10. If x!=y!=za n d|[x,x^2, 1+x^3],[y ,y^2 ,1+y^3],[z, z^2, 1+z^3]|=0, th...

    Text Solution

    |

  11. Prove that |2 alpha+beta+gamma+delta alphabeta+gammadelta alpha+beta...

    Text Solution

    |

  12. Solve for x , |[x,-6,-1], [ 2,-3x,x-3], [-3, 2x, x+2]|=0.

    Text Solution

    |

  13. The value of the determinant |{:(1,,1,,1),(.^(m)C(1),,.^(m+1)C(1),...

    Text Solution

    |

  14. Solve the equation |[a-x, c, b], [ c, b-x, a], [b, a, c-x]|=0 where a...

    Text Solution

    |

  15. If a^2+b^2+c^2=-2a n df(x)= |[1+a^2x,(1+b^2)x,(1+c^2)x],[(1+a^2)x,1+b...

    Text Solution

    |

  16. Consider the set A of all determinants of order 3 with entries 0 or 1 ...

    Text Solution

    |

  17. Solve: |[x^2-1, x^2+2x+1, 2x^2+3x+1], [2x^2+x-1, 2x^2+5x-3, 2x^2+4x-3...

    Text Solution

    |

  18. If |[x,3, 6],[ 3, 6,x],[6,x,3]|=|[2,x,7],[x,7, 2],[ 7, 2,x]|=|[4, 5,x]...

    Text Solution

    |

  19. If A1B1C1 , A2B2C2 and A3B3C3 are three digit numbers, each of which ...

    Text Solution

    |

  20. If f^(prime)(x)=|[mx, mx-p, m x+p], [n, n+p, n-p], [mx+2n, m x+2n+p, m...

    Text Solution

    |