Home
Class 12
MATHS
Let g(x)=int0^x(3t^(2)+2t+9)dt and f(x) ...

Let `g(x)=int_0^x(3t^(2)+2t+9)dt and f(x) ` be a decreasing function `forallxge0` such that `AB=f(x)hat(i)+g(x)hat(j) and AC=g(x)hat(i)+f(x)hat(j)` are the two smallest sides of a triangle ABC whose circumcentre lies outside the triangle `forall cgto.` Q. Which of the following is true (for `xgeo)`

A

`0`

B

`1`

C

e

D

does not exist

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • PRODUCT OF VECTORS

    ARIHANT MATHS ENGLISH|Exercise Product of Vectors Exercise 5 : Matching Type Questions|2 Videos

  • PRODUCT OF VECTORS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Single Integer Answer Type Questions)|15 Videos

  • PRODUCT OF VECTORS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Statement I And Ii Type Questions)|12 Videos

  • PROBABILITY

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|54 Videos

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|21 Videos

Similar Questions

Explore conceptually related problems

Let g(x)=int_0^x(3t^(2)+2t+9)dt and f(x) be a decreasing function forallxge0 such that AB=f(x)hat(i)+g(x)hat(j) and AC=g(x)hat(i)+f(x)hat(j) are the two smallest sides of a triangle ABC whose circumcentre lies outside the triangle forall cgt 0. Q. Which of the following is true (for xgeo)

If the vectors vec(A) B = 3 hat(i)+4 hat (k) and vec(AC) = 5 hat(i)-2 hat(j)+4hat(k) are the sides of a triangle ABC, then the length of the median through A is

Let g(x)=int_0^(e^x) (f\'(t)dt)/(1+t^2) . Which of the following is true?

Let f(x) and g(x) be differentiable functions such that f(x)+ int_(0)^(x) g(t)dt= sin x(cos x- sin x) and (f'(x))^(2)+(g(x))^(2) = 1,"then" f(x) and g (x) respectively , can be

If vec(A) = 4hat(i) - 2hat(j) + 6hat(k) and B = hat(i) - 2hat(j) - 3hat(k) the angle which the vec(A) vec(B) makes with x-axis is :

If the vectors hat(i) - 2x hat(j) + 3 y hat(k) and hat(i) +2x hat(j) - y hat(k) are perpendicular, then the locus of (x,y) is

If f(x)= int_(0)^(x)(f(t))^(2) dt, f:R rarr R be differentiable function and f(g(x)) is differentiable at x=a , then

If f(x)= int_(0)^(x)(f(t))^(2) dt, f:R rarr R be differentiable function and f(g(x)) is differentiable at x=a , then

If vec(A)=-hat(i)+ x hat(j) - 3 hat(k) and vec(B) = 2hat(i) - hat(k) then the value(s) of x for which the dot product of bar(A) & bar(B) is equal to unity :

Given two vectors vec(A) = -hat(i) + 2hat(j) - 3hat(k) and vec(B) = 4hat(i) - 2hat(j) + 6hat(k) . The angle made by (A+B) with x-axis is :

ARIHANT MATHS ENGLISH-PRODUCT OF VECTORS-Exercise (Passage Based Questions)
  1. Consider three vectors p=hat(i)+hat(j)+hat(k), q=2hat(i)+4hat(j)-hat(k...

    Text Solution

    |

  2. Consider three vectors p=hat(i)+hat(j)+hat(k), q=2hat(i)+4hat(j)-hat(k...

    Text Solution

    |

  3. Consider the three vectors p, q, r such that p=hat(i)+hat(j)+hat(k) an...

    Text Solution

    |

  4. Consider the three vectors p, q, r such that p=hat(i)+hat(j)+hat(k) an...

    Text Solution

    |

  5. Consider the three vectors p, q, r such that p=hat(i)+hat(j)+hat(k) an...

    Text Solution

    |

  6. Let P, Q are two points on the curve y = log(1/2) (x-0.5)+log2 sqrt(4x...

    Text Solution

    |

  7. Let P and Q are two points on the curve y=log((1)/(2))(x-0.5)+log2sqrt...

    Text Solution

    |

  8. Let P, Q are two points on the curve y = log(1/2) (x-0.5)+log2 sqrt(4x...

    Text Solution

    |

  9. If a, b, c are three given non-coplanar vectors and any arbitratry vec...

    Text Solution

    |

  10. If a, b, c are three given non-coplanar vectors and any arbitratry vec...

    Text Solution

    |

  11. If a, b, c are three given non-coplanar vectors and any arbitratry vec...

    Text Solution

    |

  12. If a, b, c are three given non-coplanar vectors and any arbitratry vec...

    Text Solution

    |

  13. Let g(x)=int0^x(3t^(2)+2t+9)dt and f(x) be a decreasing function fora...

    Text Solution

    |

  14. Let g(x)=int0^x(3t^(2)+2t+9)dt and f(x) be a decreasing function fora...

    Text Solution

    |

  15. Let x, y, z be the vector, such that |x|=|y|=|z|=sqrt(2) and x, y, z m...

    Text Solution

    |

  16. Let x,y,z be the vector, such that |x|=|y|=|z| =sqrt(2) and x,y,z make...

    Text Solution

    |

  17. Let x, y, z be the vector, such that |x|=|y|=|z|=sqrt(2) and x, y, z m...

    Text Solution

    |

  18. Let a, b, c are non-zero unit vectors inclined pairwise with the same ...

    Text Solution

    |

  19. Let a, b, c are non-zero unit vectors inclined pairwise with the same ...

    Text Solution

    |

  20. a, b, c are non-zero unit vectors inclined pairwise with the same angl...

    Text Solution

    |