Home
Class 12
MATHS
If the system of equtions 2x-y+z=0,x-2...

If the system of equtions 2x-y+z=0,x-2y+z=0, tx-y+2z=0 has infinitely many solution and f(x) be a continuous function such that f(5+x)+f(x)=2, then `f_(0)^(-2t)` f(x) dx is equal to

A

0

B

`-2t`

C

5

D

t

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|15 Videos
  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|21 Videos
  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise For Session 4|10 Videos
  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos
  • DIFFERENTIAL EQUATION

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

Similar Questions

Explore conceptually related problems

If the system of equations 2x-y+z=0,x-2y+z=0,tx-y+2z=0 has infinitely many solutions and f(x) be a continuous function,such that f(5+x)+f(x)=2 then int_(0)^(-2t)f(x)dx is equal to

The system of equations 2x-y+z=0,x-2y+z=0 and lambda x-y+2z=0 has infinite number of non-trivial solution for

The system of equations lambda x + y + 3z = 0, 2x + mu y - z = 0, 5x + 7y + z = 0 has infinitely many solutions in R. Then,

If f is continuously differentiable function then int_(0)^(2.5) [x^2] f'(x) dx is equal to

If f(x) is a continuous function in [0,pi] such that f(0)=f(x)=0, then the value of int_(0)^(pi//2) {f(2x)-f''(2x)}sin x cos x dx is equal to

If f:R rarr R be a function such that f(x+2y)=f(x)+f(2y)+4xy, AA x,y and f(2) = 4 then, f(1)-f(0) is equal to

Let f(x) be a continuous function in R such that f(x)+f(y)=f(x+y) , then int_-2^2 f(x)dx= (A) 2int_0^2 f(x)dx (B) 0 (C) 2f(2) (D) none of these

ARIHANT MATHS-DETERMINANTS -Exercise (Single Option Correct Type Questions)
  1. If A,B and C are angle of a triangle of a triangle ,the value of |{:(...

    Text Solution

    |

  2. If |{:(x^(n),x^(n+2),x^(2n)),(1,x^(a),a),(x^(n+5),x^(a+6),x^(2n+5)):}|...

    Text Solution

    |

  3. If x,y and z are the integers in AP lying between 1 and 9 and x 51, ...

    Text Solution

    |

  4. If a(1),b(1),c(1),a(2),b(2),c(2) "and" a(3),b(3),c(3) are three digit ...

    Text Solution

    |

  5. If a,b,and c are sides of Delta ABC such that |{:(c,bcosB+alphabeta,ac...

    Text Solution

    |

  6. If x(1),x(2) "and" y(1),y(2) are the roots of the equations 3x^(2) ...

    Text Solution

    |

  7. The value of |(.^(10)C(4).^(10)C(5).^(11)C(m)),(.^(11)C(6).^(11)C(7).^...

    Text Solution

    |

  8. The value of the determinant |{:(1,sin(alpha-beta)theta,cos (alpha-be...

    Text Solution

    |

  9. If f(x), h(x) are polynomials of degree 4 and |(f(x), g(x),h(x)),(a, b...

    Text Solution

    |

  10. If f(x) =|{:(cos (x+alpha),cos(x+beta),cos(x+gamma)),(sin (x+alpha),si...

    Text Solution

    |

  11. If |(1,1,1),(a,b,c),(a^(3),b^(3),c^(3))|= (a -b) (b -c) (c -a) (a + b+...

    Text Solution

    |

  12. Let a ,b , c in R such that no two of them are equal and satisfy |2a ...

    Text Solution

    |

  13. The number of positive integral solutions of the equation |(x^3+1,x^2y...

    Text Solution

    |

  14. If f(x)=ax^(2)+bx+c,a,b,c in R and eqation f(x)-x=0 has imaginary roo...

    Text Solution

    |

  15. If the system of equtions 2x-y+z=0,x-2y+z=0, tx-y+2z=0 has infinitel...

    Text Solution

    |

  16. if (1+ax+bx^(2))^(4)=a(0) +a(1)x+a(2)x^(2)+…..+a(8)x^(8), where a,b,a(...

    Text Solution

    |

  17. Given (f(x) =log(10) x and g(x) = e^(piix) . phi (x) =|{:(f(x).g(x),...

    Text Solution

    |

  18. The value of the determinant |(1,(alpha^(2x)-alpha^(-2x))^2,(alpha^(2...

    Text Solution

    |

  19. If a,b and c are non-zero real numbers and if the equation (a-1)x=y+z,...

    Text Solution

    |

  20. the set of equations lambdax-y+(cos 0) z=0,3x+y+2z=0 (cos 0) x+y+2z...

    Text Solution

    |