Home
Class 12
MATHS
If int2^xg(t)dt=(x^2)/2+intx^2t^2g(t)dt ...

If `int_2^xg(t)dt=(x^2)/2+int_x^2t^2g(t)dt ,` then equation `g(x)=lambda` has 2 solution if `|lambda|+<1/2` 2 solution if `|lambda|<1/2&lambda!=0` 1 solution if `lambda=-1/2` No solution if `|lambda|>1/2`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP ENGLISH|Exercise All Questions|15 Videos

  • MATRICES

    RESONANCE DPP ENGLISH|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

If int_0^xf(t) dt=x+int_x^1 tf(t)dt, then the value of f(1)

If int_(0)^(x)f(t)dt = x^(2)-int_(0)^(x^(2))(f(t))/(t)dt then find f(1) .

If int_(0)^(x)f(t)dt=e^(x)-ae^(2x)int_(0)^(1)f(t)e^(-t)dt , then

If f(x)=x^(2)int_(0)^(1)f(t)dt+2 , then

If f(x)=int_0^x tf(t)dt+2, then

If int_(0)^(x^(2)) sqrt(1+t^(2)) dt, then f'(x)n equals

Let f(x)=1/x^2 int_4^x (4t^2-2f'(t))dt then find 9f'(4)

Let f(x) = int_(-2)^(x)|t + 1|dt , then

If f(x)=int_(x^2)^(x^2+1)e^(-t^2)dt , then f(x) increases in

y=f(x) satisfies the relation int_(2)^(x)f(t)dt=(x^(2))/2+int_(x)^(2)t^(2)f(t)dt The value of x for which f(x) is increasing is

RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. The area bounded by y = x |sinx| and x - axis between x = 0, x = 2pi i...

    Text Solution

    |

  2. The area bounded by the curve a^2y=x^2(x+a) and the x-axis is (a^2)/3s...

    Text Solution

    |

  3. If int2^xg(t)dt=(x^2)/2+intx^2t^2g(t)dt , then equation g(x)=lambda ha...

    Text Solution

    |

  4. If vec a= hat i+ hat j+ hat k , vec c= hat j- hat k , vec adot vec b...

    Text Solution

    |

  5. The number of ordered quadruples (a1,a2,a3,a4) of positive odd integer...

    Text Solution

    |

  6. Find the value of lambda so that the four points, A, B, C and D wit...

    Text Solution

    |

  7. If vec a , vec b ,a n d vec c are three non-coplanar non-zero vec...

    Text Solution

    |

  8. A six-faced dice is so biased that it is twice as likely to show an ev...

    Text Solution

    |

  9. If the planes x-cy-bz=0, cx-y+az=0 and bx+ay-z=0 pass through a line, ...

    Text Solution

    |

  10. In a multiple choice question, there are four alternative answers of w...

    Text Solution

    |

  11. Find the sum of integers from 1 to 100 that are divisible by 2 or 5...

    Text Solution

    |

  12. The equation |{:((1+x)^(2),(1-x)^(2),-(2+x^(2))),(2x+1,3x,1-5x),(x+1,2...

    Text Solution

    |

  13. The equation of tangent drawn to the curve y^(2)-2x^(3)-4y+8=0 from th...

    Text Solution

    |

  14. If A and B are two sets, then A nn (A uu B) equals (A-B)uu(B-A)uu(AnnB...

    Text Solution

    |

  15. Let P be any point on the curve x^(2//3)+y^(2//3)=a^(2//3). Then the...

    Text Solution

    |

  16. Let R be a relation defined on the set of natural numbers N as R={...

    Text Solution

    |

  17. A lamp of negligible height is placed on the ground l1 away from a wal...

    Text Solution

    |

  18. If sinx+sin^2x=1," then the value of "cos^12x+3cos^10x+3cos^8x+cos^6x-...

    Text Solution

    |

  19. Value of (1-(cos61^0)/(cos1^0))*(1-(cos62^0)/(cos2^0))*(1-(cos63^0)/(c...

    Text Solution

    |

  20. e^(2x)-(a-1)e^x-a ge 0 AA x in R then the value of a will satisfy

    Text Solution

    |