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

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE ENGLISH|Exercise Multiple Correct Answer|5 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

The sum of 1+n(1-1/x)+(n(n+1))/(2!)(1-1/x)^2+oo will be a. x^n b. x^(-n) c. (1-1/x)^n d. none of these

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)!

If f(x)=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)f^(x)-xy(x)= 1 (b) -1 (c) 0 (d) none of these

cos^(-1)((1-x^(2n))/(1+x^(2n)))

If f(x)=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)f^(x)-xf(x)= (a)1 (b) -1 (c) 0 (d) none of these

The value of (lim)_(x->oo)(n !)/((n+1)!-(n)!) is a. 1 b . -1 c. 0 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 f(x+1)+f(x-1)=2f(x)a n df(0),=0, then f(n),n in N , is nf(1) (b) {f(1)}^n (c) 0 (d) none of these

The value of lim_(xrarr1){(x^n-1)/(n(x-1))}^((1)/(x-1)) , is

The value of the determinants |{:(1,a,a^(2)),(cos(n-1)x,cos nx , cos(n+1)x),(sin(n-1)x , sin nx , sin(n+1)x):}| is zero if

CENGAGE ENGLISH-DETERMINANTS-All Questions
  1. If a,b,c are positive and are the pth, qth rth terms respectively 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 =|[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

    |

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

    Text Solution

    |

  7. Show that the determinant |a^2+b^2+c^2b c+c a+a bb c+c a+a bb c+c a+a ...

    Text Solution

    |

  8. 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

    |

  9. 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

    |

  10. Prove that |2alpha+beta+gamma+deltaalphabeta+gammadelta alpha+beta+g...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. 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)x1+b^2x(1+c...

    Text Solution

    |

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

    Text Solution

    |

  16. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. If sum(n=1)^nalphan=a n^2+b n ,w h e r ea ,b are constants and alp...

    Text Solution

    |