Home
Class 12
MATHS
Evaluate |{:(.^(x)C(1),,.^(x)C(2),,.^(x)...

Evaluate `|{:(.^(x)C_(1),,.^(x)C_(2),,.^(x)C_(3)),(.^(y)C_(1),,.^(y)C_(2),,.^(y)C_(3)),(.^(x)C_(1),,.^(z)C_(2),,.^(z)C_(3)):}|`

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(12)xyz(x-y)(y-z)(z-x)`
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    ARIHANT MATHS ENGLISH|Exercise Determinants Exercise 7:|3 Videos

  • DETERMINANTS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

  • DETERMINANTS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Statement I And Ii Type Questions)|7 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

  • DIFFERENTIAL EQUATION

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

Similar Questions

Explore conceptually related problems

|{:(.^(x)C_(r),,.^(x)C_(r+1),,.^(x)C_(r+2)),(.^(y)C_(r),,.^(y)C_(r+1),,.^(y)C_(r+2)),(.^(z)C_(r),,.^(z)C_(r+1),,.^(z)C_(r+2)):}| is equal to

if x,y and z are not all zero and connected by the equations a_(1)x+b_(1)y+c_(1)z=0,a_(z)x+b_(2)y+c_(2)z=0 and (p_(1)+lambdaq_(1))x+(p_(2)+lambdaq_(2))y+(p_(3)+lambdaq_(3))z=0 show that lambda =-|{:(a_(1),,b_(1),,c_(1)),(a_(2) ,,b_(2),,c_(2)),(p_(1) ,, p_(2),,p_(3)):}|-:|{:(a_(1),,b_(1),,c_(1)),(a_(2) ,,b_(2),,c_(2)),(q_(1) ,, q_(2),,q_(3)):}|

Show that |[""^xC_r, ""^x C_(r+1),""^x C_(r+2)],[""^y C_r,""^y C_(r+1),""^y C_(r+2)],[""^z C_r,""^z C_(r+1),""^z C_(r+2)]|=|[""^(x)C_r, ""^(x+1) C_(r+1),""^(x+2) C_(r+2)],[""^y C_r,""^(y+1) C_(r+1),""^(y+2) C_(r+2)],[""^z C_r,""^(z+1) C_(r+1),""^(z+2) C_(r+2)]|

STATEMENT-1: If three points (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)) are collinear, then |{:(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1):}|=0 STATEMENT-2: If |{:(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1):}|=0 then the points (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)) will be collinear. STATEMENT-3: If lines a_(1)x+b_(1)y+c_(1)=0,a_(2)=0and a_(3)x+b_(3)y+c_(3)=0 are concurrent then |{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}|=0

Show that |^x C_r^x C_(r+1)^x C_(r+2)^y C_r^y C_(r+1)^y C_(r+2)^z C_r^z C_(r+1)^z C_(r+1)|=|^x C_r^(x+1)C_(r+1)^(x+2)C_(r+2)^y C_r^(y+1)C_(r+1)^(y+2)C_(r+2)^z C_r^(z+1)C_(r+1)^(z+2)C_(r+1)| .

Let a=xhati+12hatj-hatk,b=2hati+2xhatj+hatk and c=hati+hatk . If b,c,a in that order form a left handed system, then find the value of x. [x_(1)a+y_(1)b+z_(1)c,x_(2)a+y_(2)b+z_(2)c,x_(3)a+y_(3)b+z_(3)c] =|(x_(1),y_(1),z_(1)),(x_(2),y_(2),z_(2)),(x_(3),y_(3),z_(3))|[abc] .

If x, y and r are positive integers, then ""^(x)C_(r)+""^(x)C_(r-1)+""^(y)C_(1)+""^(x)C_(r-2)""^(y)C_(2)+......+""^(y)C_(r)=

If n gt 3 , then xyz^(n)C_(0)-(x-1)(y-1)(z-1)""^(n)C_(1)+(x-2)(y-2)(z-2)""^(n)C_(2)- (x-3)(y-3)(z-3)""^(n)C_(3)+…..+(-1)^(n)(x-n)(y-n)(z-n)""^(n)C_(n) equals :

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 (1+x)^(n)=C_(0)+C_(1).x+C_(2).x^(2)+C_(3).x^(3)+......+C_(n).x^(n), then prove that C_(0)+2C_(1)+4C_(2)+6C_(3)+...+2n.C_(n)=1+n*2^(n)

ARIHANT MATHS ENGLISH-DETERMINANTS -Exercise (Subjective Type Questions)
  1. Prove that |{:(b+c,c,b),(c,c+a,a),(b,a,a+b):}| = 4 abc

    Text Solution

    |

  2. Prove: |[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]|=(a+b+c)^3

    Text Solution

    |

  3. Find the value of determinant |[sqrt((13))+sqrt(3),2sqrt(5),sqrt(5)],[...

    Text Solution

    |

  4. Find the value of the determinant |(bc,ca, ab),( p, q, r),(1, 1, 1)|,w...

    Text Solution

    |

  5. Without expanding the determinant at any stage prove that |{:(-5,3+5i...

    Text Solution

    |

  6. Prove without expansion that |a h+bgga b+c h bf+b afh b+b c af+b cc bg...

    Text Solution

    |

  7. In a triangleABC, if |(1,1,1),(1+sinA,1+sinB,1+sinC),(sinA+sin^2A,sinB...

    Text Solution

    |

  8. The value of |{:(betagamma,betagamma'+beta'gamma,beta'gamma'),(gammaal...

    Text Solution

    |

  9. If y=(u)/(v), where u & v are functions of 'x' show that v^(3)(d^(2)y)...

    Text Solution

    |

  10. Show that the determinant Delta(x) given by Delta(x) = |{:(sin(x+al...

    Text Solution

    |

  11. Evaluate |{:(.^(x)C(1),,.^(x)C(2),,.^(x)C(3)),(.^(y)C(1),,.^(y)C(2),,....

    Text Solution

    |

  12. (i) Find maximum value of f(x)=|{:(1+sin^(2)x,cos^(2)x,4sin2x),(sin...

    Text Solution

    |

  13. If f(x) = |[x^2-4x+6,2x^2+4x+10,3x^2-2x+16],[x-2,2x+2,3x-1],[1,2,3]| t...

    Text Solution

    |

  14. If |A| = 2 and A = | (2x, 6) , (5x, 1)| then find the value of x

    Text Solution

    |

  15. Show that in general there are three values of t for which the followi...

    Text Solution

    |

  16. Find dy/dx if y=13x-y^2

    Text Solution

    |

  17. If x, y, z are not all zero & if ax + by + cz=0, bx+ cy + az=0 & cx ...

    Text Solution

    |