Home
Class 9
MATHS
Prove that: (i)\ sqrt(1/4)+\ (0. 01)^(-1...

Prove that: `(i)\ sqrt(1/4)+\ (0. 01)^(-1/2)-\ (27)^(2/3)=3/2` `(ii)\ (2^n+\ 2^(n-1))/(2^(n+1)-2^n)=3/2`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COORDINATE GEOMETRY

    RD SHARMA ENGLISH|Exercise All Questions|23 Videos

  • FACTORIZATION OF ALGEBRAIC EXPRESSIONS

    RD SHARMA ENGLISH|Exercise All Questions|226 Videos

Similar Questions

Explore conceptually related problems

Prove that (2n!)/( n!) = 1,3,5 ….( 2n-1) 2^(n)

Prove that .^(n)C_(0) + (.^(n)C_(1))/(2) + (.^(n)C_(2))/(3) + "……" +(. ^(n)C_(n))/(n+1) = (2^(n+1)-1)/(n+1) .

Prove that 1/(n+1)=(.^n C_1)/2-(2(.^n C_2))/3+(3(.^n C_3))/4- . . . +(-1^(n+1))(n*(.^n C_n))/(n+1) .

Prove that : 1+2+3++n=(n(n+1))/2

Using mathematical induction, prove that (1)/(1.3.5) + (2)/(3.5.7) +….+(n)/((2n-1)( 2n+1) ( 2n+3)) =( n(n+1))/( 2(2n+1) (2n+3))

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n)," prove that " 1^(2)*C_(1) + 2^(2) *C_(2) + 3^(2) *C_(3) + …+ n^(2) *C_(n) = n(n+1)* 2^(n-2) .

Prove that: \ ^(2n)C_n=(2^n[1. 3. 5 (2n-1)])/(n !)

Prove that .^(n)C_(1) - (1+1/2) .^(n)C_(2) + (1+1/2+1/3) .^(n)C_(3) + "…" + (-1)^(n-1) (1+1/2+1/3 + "…." + 1/n) .^(n)C_(n) = 1/n

Prove that 1+1* ""^(1)P_(1)+2* ""^(2)P_(2)+3* ""^(3)P_(3) + … +n* ""^(n)P_(n)=""^(n+1)P_(n+1).

Prove by the principal of mathematcal induction that for all n in N . 1^(2) + 3^(2) + 5^(2) + …… + (2n - 1)^(2) = (n(2n - 1) (2n + 1))/(3)

RD SHARMA ENGLISH-EXPONENTS OF REAL NUMBER-All Questions
  1. Prove that: (1/4)^(-2)-3\ xx\ 8^(2/3)\xx\ 4^0+\ (9/(16))^(-1/2)=(16)/3

    Text Solution

    |

  2. Prove that: (2^(1/2)\ xx\ 3^(1/3)\ xx\ 4^(1/4))/(10^(-1/5)\ xx\ 5^(3/5...

    Text Solution

    |

  3. Prove that: (i)\ sqrt(1/4)+\ (0. 01)^(-1/2)-\ (27)^(2/3)=3/2 (ii)\...

    Text Solution

    |

  4. Prove that: ((64)/(125))^(-2/3)+1/(((256)/(625))^(1/4))+\ ((sqrt(25))/...

    Text Solution

    |

  5. Prove that: (3^(-3)\ xx\ 6^2xx\ sqrt(98))/(5^2\ xx\ root(3)(1/(25))\ x...

    Text Solution

    |

  6. Prove that: ((0. 6)^0-\ (0. 1)^(-1))/((3/8)^(-1)\ (3/2)^3+\ (-1/3)^(-1...

    Text Solution

    |

  7. Solve: 1/(1+x^(a-b))+1/(1+x^(b-a))=?

    Text Solution

    |

  8. Show that : (x^(a(b-c)))/(x^(b(a-c)))÷((x^b)/(x^a))^c=1 ((x^(a+b))^2...

    Text Solution

    |

  9. Solve the following equation - (i) 2^(x+1)=8

    Text Solution

    |

  10. Show that: (i)\ (x^(a-b))^(a+b)\ (x^(b-c))^(b+c)\ (x^(c-a))^(c+a)=1 ...

    Text Solution

    |

  11. Show that: ((a^(x+1))/(a^(y+1)))^(x+y)\ ((a^(y+2))/(a^(z+2)))^(y+z)\ (...

    Text Solution

    |

  12. Show that: ((3^a)/(3^b))^(a+b)\ ((3^b)/(3^c))^(b+c)\ ((3^c)/(3^a))^(c+...

    Text Solution

    |

  13. If 2^x = 3^y =12^z show that 1/z= 1/y+2/x

    Text Solution

    |

  14. If 2^x=3^y=6^(-z) prove that 1/x+1/y+1/z=0

    Text Solution

    |

  15. If a^x=b^y=c^z and b^2=a c , then show that y=(2z x)/(z+x)

    Text Solution

    |

  16. If 3^x=5^y=(75)^z show that z=(xy)/(2x+y

    Text Solution

    |

  17. If 27^x=9/(3^x), find xdot

    Text Solution

    |

  18. Find the values of x in each of the following : (i)2^(5x)-:2^x=2^(20/...

    Text Solution

    |

  19. Find the value of x in each of the following: (i)\ (3/5)^x\ (5/3)^(2x)...

    Text Solution

    |

  20. Find the value of x in each of the following: 2^(x-7)\ xx\ 5^(x-4)=125...

    Text Solution

    |