Home
Class 12
MATHS
if A[{:(5,-3),(111,336):}] and det(-3A^(...

if `A[{:(5,-3),(111,336):}]` and det`(-3A^(2013)+A^(2014))=alpha^(alpha)+beta^(2)(1+gamma+gamma^(2))` where `alpha,beta,gamma` are natural numbers and `(alphagtgammagtbeta)` then

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP|Exercise All Questions|15 Videos
  • MATRICES

    RESONANCE DPP|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

The minimum value of the expression sin alpha+sin beta+sin gamma, where alpha,beta,gamma are real numbers satisfying alpha+beta+gamma=pi is

|[1,alpha,alpha^3],[1,beta,beta^3],[1,gamma,gamma^3]|=(alpha-beta)(beta-gamma)(gamma-alpha)(alpha+ beta+gamma)

Show that |(1,alpha,alpha^3),(1,beta,beta^3),(1,gamma,gamma^3)|=(alpha-beta)(beta-gamma)(gamma-alpha)( alpha+beta+gamma)

If alpha, beta, gamma are the cube roots of 8 , then |(alpha,beta,gamma),(beta,gamma,alpha),(gamma,alpha,beta)|=

If cos^(-1)alpha+cos^(-1)beta+cos^(-1)gamma=3 pi then alpha beta+beta gamma+gamma alpha equals

If alpha beta gamma are the roots of x^3+x^2-5x-1=0 then alpha+beta+gamma is equal to

If alpha beta gamma are roots of x^(3)+x^(2)-5x-1=0 then alpha + beta + gamma is equal to

If cos^(-1) alpha + cos^(-1) beta + cos^(-1) gamma = 3pi , then alpha (beta + gamma) + beta(gamma + alpha) + gamma(alpha + beta) equal to

RESONANCE DPP-JEE MAINS-All Questions
  1. If the point P(4, -2) is the one end of the focal chord PQ of the para...

    Text Solution

    |

  2. Let f(x)=(sin {pi[x-pi]})/(1-[x^(2)]), where [.] stands for the greate...

    Text Solution

    |

  3. if A[{:(5,-3),(111,336):}] and det(-3A^(2013)+A^(2014))=alpha^(alpha)+...

    Text Solution

    |

  4. If x^2+a x-3x-(a+2)=0 has real and distinct roots, then the minimum va...

    Text Solution

    |

  5. If a and b are the solutions of equation log5(log(64)(|x|)-1/2+25^x)=2...

    Text Solution

    |

  6. Tangents are drawn to the circle x^2+y^2=50 from a point "P lying on ...

    Text Solution

    |

  7. The value of int(-pi/2)^(pi/2)1/(e^(sin x)+1) dx equal to

    Text Solution

    |

  8. Show that the function f(x)=3x+ 2 is one-one and onto

    Text Solution

    |

  9. The total number of ordered pairs (x, y) satisfying |y|=cosx and y=si...

    Text Solution

    |

  10. Locus of a point that is equidistant from the lines x+y-2=0a n dx+y-1=...

    Text Solution

    |

  11. If the ellipse x^2/4 + y^2 =1 meets the ellipse x^2 + y^2/a^2 =1 in fo...

    Text Solution

    |

  12. If A is a square matrix such that A(a d j\ A)=[5 0 0 0 5 0 0 0 5] ,...

    Text Solution

    |

  13. A variable circle passes through the fixed point (2, 0) and touches y-...

    Text Solution

    |

  14. If ("lim")(xrarr0)({(a-n)n x-tanx}sinn x)/(x^2)=0, where n is no...

    Text Solution

    |

  15. If a matrix A is such that 3A^3 +2A^2+5A+I= 0, then A^(-1) is equal to

    Text Solution

    |

  16. From point P(4,0) tangents PA and PB are drawn to the circle S: x^2+y^...

    Text Solution

    |

  17. The coordinates of the point on the curve x^(3)=y(x-a)^(2) where the o...

    Text Solution

    |

  18. Value of [log(e^3)5^8 - log(e^3)2^8] equals to

    Text Solution

    |

  19. Let P1 denote the equation of a plane to which the vector ( hat i+...

    Text Solution

    |

  20. Find the name of the conic represented by sqrt((x/a))+sqrt((y/b))=1.

    Text Solution

    |