Home
Class 12
MATHS
Let alpha=(2kpi)/(2025),beta=(2mpi)/(202...

Let `alpha=(2kpi)/(2025),beta=(2mpi)/(2026)"and " gamma=(2kpi)/(2027)` where k,m,n `in` Z.
`A=((cosalpha,-sinalpha),(sinalpha,cosalpha)),`
`B= ((cosbeta,-sinbeta),(sinbeta,cosgamma))`
`C=((sin gamma, -sin gamma),(sin gamma, cos gamma))`
then det `(A^(2025)+B^(2026)+C^(2027))` is equal to _______

Text Solution

Verified by Experts

The correct Answer is:
9
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    MCGROW HILL PUBLICATION|Exercise EXERCISE (Concept - based) (Single Correct Answer Type Questions)|10 Videos

  • MATRICES

    MCGROW HILL PUBLICATION|Exercise EXERCISE ( LEVEL -1) (Single Correct Answer Type Questions)|43 Videos

  • MATRICES

    MCGROW HILL PUBLICATION|Exercise SOLVED EXAMPLES ( LEVEL 2 ( Straight Objective Type Questions ) )|11 Videos

  • MATHEMATICAL REASONING

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B. ARCHITECTURE ENTRANCE EXAMINATION PAPERS|11 Videos

  • PARABOLA

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B-ARCHITECTRE ENTRANCE EXAMINATION PAPERS|9 Videos

Similar Questions

Explore conceptually related problems

|(sin alpha, cosalpha,sin(alpha+delta)),(sinbeta, cos beta,sin(beta+delta)),(singamma,cosgamma,sin(gamma+delta))|=

Prove that: |(sinalpha, cosalpha, 1),(sinbeta, cosbeta, 1),(singamma, cosgamma, 1)|=sin(alpha-beta)+sin(beta-gamma)+sin(gamma-alpha)

Prove that det [[sin alpha, cos alpha, sin (alpha + delta) sin beta, cos beta, sin (beta + delta) sin gamma, cos gamma, sin (gamma + delta)]] = 0

Show that |[sinalpha, cosalpha, cos(alpha+delta)],[sinbeta, cosbeta, cos(beta+delta)],[singamma, cosgamma, cos(gamma+delta)]|=0

If (0,0) is orthocentre of triangle formed by A(cos alpha,sin alpha),B(cos beta,sin beta),C(cos gamma,sin gamma) then /_BAC=

If 0

The value of the determinant Delta = |(sin 2 alpha,sin (alpha + beta),sin (alpha + gamma)),(sin (beta + gamma),sin 2 beta,sin (gamma + beta)),((sin gamma + alpha),sin (gamma + beta),sin 2 gamma)| , is

If (0,0) is orthocentre of triangle formed by A(cos alpha,sin alpha),B(cos beta,sin beta),C(cos gamma,sin gamma) then /_BAC is

If cosalpha+cosbeta=0=sinalpha+sinbeta , then cos2alpha+cos2beta=?

Find the area of the triangle whose vertices are : (a cos alpha, b sin alpha), (a cos beta, b sin beta), (a cos gamma, b sin gamma)

MCGROW HILL PUBLICATION-MATRICES-SOLVED EXAMPLES ( LEVEL 2 (Numercial Answer Type Questions))
  1. Let A = [(7,5),(4,8)] ,B= [(2,3),(3,5)] and C= [(5,-3),(-3,2)] then su...

    Text Solution

    |

  2. If x =alpha, y=beta, z = gamma is a solution of the system of equation...

    Text Solution

    |

  3. Suppose p,q,r in R and and pqr = 2.5 . Let A = [(p,q,r),(r,p,q),(q,r,...

    Text Solution

    |

  4. Suppose A and B are two 3xx3 non singular matrices such that tr (AB) =...

    Text Solution

    |

  5. Suppose k is a root of x^(2)-6.1x+5.1=0 such that A=[(1,2,1),(3,2,3),(...

    Text Solution

    |

  6. Let A = ((2.1,2.7,1.3),(3.1,3.2,1.7),(2.1,2.5,2.9)). The sum of values...

    Text Solution

    |

  7. If the system of linear equations ax+(a+1)y+(a-1)z=0 (a-1)x+(a+2)y...

    Text Solution

    |

  8. Let A = [(3,-1),(0,2)] . Suppose A satisfies the equation x^(2)+ax+b=0...

    Text Solution

    |

  9. Let A = [(5.1,-3.1,0),(-3.1,5.1,0),(0,0,2.2)] X be a non zero 3xx1 mat...

    Text Solution

    |

  10. A solution set of the equations x+2y+z=1, x+3y+4z=k, x+5y+10z=k^(2) is

    Text Solution

    |

  11. Let alpha=(2kpi)/(2025),beta=(2mpi)/(2026)"and " gamma=(2kpi)/(2027) ...

    Text Solution

    |

  12. Let A = ((1,2,3),(0,0,0),(3,2,1)) and A^(n)=((a(n),b(n),c(n)),(0,0,0),...

    Text Solution

    |

  13. Let A and B be two 3xx3 real matrices such that AB ne BA AB-B^(2)...

    Text Solution

    |

  14. Let A and B be two 3xx3 matrices with integer entries . If 6AB +2A+3B=...

    Text Solution

    |

  15. Let A = ((1,1,3),(5,2,6),(-2,-1,-3)) and let n be the smallest value o...

    Text Solution

    |

  16. Suppose a,b,c in R - {0} and a+b+c =0 Let alpha =(1)/(5) (a^(5)+b^(5)+...

    Text Solution

    |

  17. Let m = the number of values of a for which the system of equations ...

    Text Solution

    |

  18. If A = [(2,52,152),(4 , 106,358),(6,162,620)] then det (adj ((1)/(2) A...

    Text Solution

    |