Home
Class 12
MATHS
The base of prism is equilateral triangl...

The base of prism is equilateral triangle. The distance from the centre of one base to one of the vertices of the other base is `ldot` Then altitude of the prism for which the volume is greatest is (a)`l/2` (b) `l/(sqrt(3))` (c) `l/3` (d) `l/4`

Promotional Banner

Topper's Solved these Questions

  • 3D COORDINATION SYSTEM

    CENGAGE PUBLICATION|Exercise DPP 3.1|11 Videos
  • APPLICATION OF INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|143 Videos

Similar Questions

Explore conceptually related problems

The base of prism. Is triangular in shape with sides 3cm , 4cm , and 5cm , Find the volume of the prism if its height is 10 cm .

The equation of an altitude of an equilateral triangle is sqrt3x + y = 2sqrt3 and one of its vertices is (3,sqrt3) then the possible number of triangles is

The equation of an altitude of an equilateral triangle is sqrt3x + y = 2sqrt3 and one of its vertices is (3,sqrt3) then the possible number of triangles is

A B C is an isosceles triangle. If the coordinates of the base are B(1,3) and C(-2,7) , the coordinates of vertex A

In an equilateral triangle, three coins of radii 1 unit each are kept so that they touch each other and also the sides of the triangle. The area of the triangle is 2sqrt(3) (b) 6+4sqrt(3) 12+(7sqrt(3))/4 (d) 3+(7sqrt(3))/4

The equation to the base of an equilateral triangle is 4x-3y+10=0 and its vertex is at (-2,-1), find the length of a side of the triangle.

A ray of light incident on an equilateral glass prism propagates parallel to the base line of the prism inside it. Find the angle of incidence of this ray. Given refractive index of material of glass prism is sqrt(3) .

An electron is in one of the 3d orbitals. Give the possible values on n, l and m_(l) for this electron.

If one of the vertices of a square is (3,2) and one of the diagonalls is along the line 3x+4y+8=0, then find the centre of the square and other vertices.

Average distance of the Earth from the Sun is L_(1) . If one year of the Earth= D days, one year of another planet whose average distance from the Sun is L_(2) will be

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. The vertices of a triangle are (0,0), (x ,cosx), and (sin^3x ,0),w h ...

    Text Solution

    |

  2. Assertion Let f:R→R,f(x)=x^3+x^2+3x+sinx f(x) is one-one. Reason f(x) ...

    Text Solution

    |

  3. The base of prism is equilateral triangle. The distance from the centr...

    Text Solution

    |

  4. Let f(x)=2x-sinx and g(x)=3sqrtx . Then

    Text Solution

    |

  5. Let f(x)=x^4-4x^3+6x^2-4x+1. Then, (a) f increase on [1,oo] (b) f dec...

    Text Solution

    |

  6. The set of all x for which log(1+ x) le x is equal to …… .

    Text Solution

    |

  7. The maximum value of the function f(x)=2x^3-15 x^2+36 x-48 on the set ...

    Text Solution

    |

  8. Let f(x)={x e^(a x),x lt=0;x+a x^2-x^3,x >0 where a is a positive con...

    Text Solution

    |

  9. Suppose f(x) is a function satisfying the following conditions : ...

    Text Solution

    |

  10. It is given that equation 4x^3-3x-p=0 has a unique root in the interva...

    Text Solution

    |

  11. Using the relation 2(1−cosx)<x^2 ,x=0 or prove that sin(tanx)≥x,∀ϵ[0,...

    Text Solution

    |

  12. If P(1)=0a n d(d P(x))/(dx)gtP(x), for all xge1. Prove that P(x)&gt;0...

    Text Solution

    |

  13. If p(x) is a polynomial of degree 3 satisfying p(-1)=10 , p(1) =-6 a...

    Text Solution

    |

  14. The larger of cos[log(theta)] and log(costheta) if e^(-pi/2) < theta <...

    Text Solution

    |

  15. The function y=2x^2-log(x) is monotonically increasing for values of x...

    Text Solution

    |

  16. The volume of the greatest cylinder which can be inscribed in a cone o...

    Text Solution

    |

  17. Use the function f(x)=x^(1//x),xgt0 to determine the bigger of the two...

    Text Solution

    |

  18. For all x in (0,1) (a) e^x<1+x (b) (log)e (1+x) < x (c) sin x > x ...

    Text Solution

    |

  19. Let A(p^2,-p),B(q^2, q),C(r^2,-r) be the vertices of triangle ABC. A p...

    Text Solution

    |

  20. If the function f(x)=(Ksinx+2cosx)/(sinx+cosx) is strictly increasing ...

    Text Solution

    |