Home
Class 12
MATHS
If Delta=|(a,p,x),(b,q,y),(c,r,z)|=16 th...

If `Delta=|(a,p,x),(b,q,y),(c,r,z)|=16` then `Delta_(1)=|(p+x,a+x,a+p),(q+y,b+y,b+q),(r+z,c+z,c+r)|=32`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA ENGLISH|Exercise All Questions|168 Videos

  • DIFFERENTIABILITY

    RD SHARMA ENGLISH|Exercise All Questions|135 Videos

Similar Questions

Explore conceptually related problems

Delta=|{:(p,q,r),(p+2a,q+2b,r+2c),(a,b,c):}| then

If |[a, p, x],[ b, q, y], [c, r, z]|=16 , then the value of |[p+x, a+x, a+p], [q+y ,b+y, b+q],[ r+z, c+z, c+r]| is (a) 4 (b) 8 (c) 16 (d) 32

If A = |(a,b,c),(x,y,z),(p,q,r)| and B = |(q,-b,y),(-p,a,-x),(r,-c,z)| , then

If Delta_1=|[a, b, c],[ x, y, z],[ p, q, r]| and Delta_2=|[q,-b, y],[-p, a,-x],[ r,-c, z]|, without expanding or evaluating Delta_1 and Delta_2 , show that Delta_1+Delta_2=0

Prove that: |{:(a, b, c), (x, y, z), (p, q, r):}|=|{:(y, b, q), (x, a, p), (z, c, r):}|

If P=[(x,0, 0),( 0,y,0 ),(0, 0,z)] and Q=[(a,0 ,0 ),(0,b,0 ),(0, 0,c)] , prove that P Q=[(x a,0 ,0 ),(0,y b,0),( 0 ,0,z c)]=Q P

Using properties of determinants, prove that |(b+c,q+r,y+z),(c+a,r+p,z+x),(c+b,p+q,x+y)|=2|(a,p,x),(b,q,y),(c,r,z)|

a!=p , b!=q,c!=r and |(p,b,c),(a,q,c),(a,b,r)|=0 the value of p/(p-a)+q/(q-b)+r/(r-c)=

If A=[(a, b, c), (x, y, z), (p, q, r)], B=[(q,-b, y),(-p, a,-x),(r,-c, z)] and if A is invertible, then which of the following is not true? (a) |A|=|B| (b) |A|=-|B| (c) |adj A|=|adj B| (d) A is invertible if and only if B is invertible

If |{:(a-b,b-c,c-a),(x-y,y-z,z-x),(p-q,q-r,r-p):}|=m|{:(c,a,b),(z,x,y),(r,p,q):}|," then m"=

RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. If Ar=|(1,r,2^r),(2,n,n^2),(n,(n(n+1))/2 ,2^(n+1))| , then the value o...

    Text Solution

    |

  2. If a >0 and discriminant of a x^2+2b x+c is negative, then |[a,b,ax+b]...

    Text Solution

    |

  3. The value of |[5^2 ,5^3, 5^4], [5^3, 5^4, 5^5], [5^4, 5^5, 5^6]| is (a...

    Text Solution

    |

  4. |[(log)3 512,(log)4 3],[(log)3 8,(log)4 9]|xx|[(log)2 3,(log)8 3],[(lo...

    Text Solution

    |

  5. If a, b, c, are in A.P, then the determinant|[x+2,x+3,x+2a], [x+3,x+4,...

    Text Solution

    |

  6. If A+B+C=pi, then the value of |"sin"(A+B+C)sin(A+C)cosC-sinB0tanCcos...

    Text Solution

    |

  7. The number of distinct real roots of |{:(cosec x, secx, secx), (secx...

    Text Solution

    |

  8. Let A=|[1,sintheta,1],[-sintheta,1,sintheta],[-1,-sintheta,1]|, where ...

    Text Solution

    |

  9. If |[2x,5], [8,x]|=|[6,-2], [7, 3]| , then x= (a) 3 (b) +-3 (c) +-6 (...

    Text Solution

    |

  10. If f(x)=|[0,x-a, x-b], [x+a,0,x-c], [x+b, x+c,0]|,t h e n (a)f(a)=0 ...

    Text Solution

    |

  11. The value of the determinant |[a-b,b+c, a], [b-a, c+a, b], [c-a, a+b...

    Text Solution

    |

  12. If x , y , z are different from zero and |[1+x,1 ,1], [1, 1+y,1], [1, ...

    Text Solution

    |

  13. The determinant |{:(b^2-ab, b-c, bc-ac), (a b-a^2, a-b, b^2-ab) ,(b c-...

    Text Solution

    |

  14. If x , y in R , then the determinant =|[cosx,-sinx,1],[sinx,cosx,1],[...

    Text Solution

    |

  15. The maximum value of =|[1, 1, 1], [1, 1+sintheta,1], [1+costheta,1, 1]...

    Text Solution

    |

  16. The value of the determinant |[x,x+y, x+2y], [x+2y, x,x+y], [x+y, x+2y...

    Text Solution

    |

  17. Let f(x)=|[cosx, x, 1], [2sinx ,x,2x],[sinx, x, x]| , then (lim)(x->0)...

    Text Solution

    |

  18. If there are two values of a which makes determinant, Delta=|(1,-2,5...

    Text Solution

    |

  19. If Delta=|(a,p,x),(b,q,y),(c,r,z)|=16 then Delta(1)=|(p+x,a+x,a+p),(q+...

    Text Solution

    |

  20. The value of |[1, 1 ,1],[\ ^n C1,\ ^(n+2)C1,\ ^(n+4)C1],[\ ^n C2,\ ^(n...

    Text Solution

    |