Home
Class 12
MATHS
Let M = 2^(30)-2^(15)+1, and M^(2) be ex...

Let `M = 2^(30)-2^(15)+1`, and `M^(2)` be expressed in base 2. The number of 1's in this base 2 representation of `M^(2)` is

A

29

B

30

C

59

D

60

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • QUESTION PAPER 2020

    KVPY PREVIOUS YEAR|Exercise PART-II(MATHEMATICS)|10 Videos
  • QUESTION PAPER 2020

    KVPY PREVIOUS YEAR|Exercise PART-II : MATHEMATICS|7 Videos
  • QUESTION PAPER 2013

    KVPY PREVIOUS YEAR|Exercise PART-II ( MATHEMATICS)|10 Videos
  • SOLVED PAPER 2018

    KVPY PREVIOUS YEAR|Exercise EXAMPLE|27 Videos

Similar Questions

Explore conceptually related problems

If m+ (1)/(m-2)=4 , find m^(2) + m+1 =?

If m+ (1)/(m+2)=-4 , find m^(2) + m+1 =?

1 m s^(-2) =_______ km h^(-2)

For the system shown in fig, there is no friction anywhere. Masses m_(1) and m_(2) can move up or down in the slots cut in mass M. Two non-zero horizontal force F_(1) and F_(2) are applied as shown. The pulleys are massles and frictionless. Given m_(1) != m_(2) Let F_(1) and F_(2) are applied in such a way that m_(1) and m_(2) do not move w.r.t. M. then what is the magnitude of the acceleration of M? Let m_(1) gt m_(2) .

Let T_(r) and S_(r) be the rth term and sum up to rth term of a series,respectively.If for an odd number n,S_(n)=n and T_(n)=(T_(n)-1)/(n^(2)), then T_(m)(m being even) is (2)/(1+m^(2)) b.(2m^(2))/(1+m^(2)) c.((m+1)^(2))/(2+(m+1)^(2))d(2(m+1)^(2))/(1+(m+1)^(2))

Water is filled in a container having square base (2m times2m) .Height of water in the container is h=2m . Now the container is tilted so that its base makes an angle of 30^(@) with the horizontal.The tilted container is accelerated to right with a horizontal acceleration of a=2m/s^(2) .Now the water surface makes an angle a with horizontal. If the value of alpha is tan^(-1)((1)/(x)) ,then what is the value of x( g=10m/s^(2) )?

when the quntum number n, l,m,s are represented by 3,3,2,=(1)/(2) the correct representation is:

Let z_(1) and Z_(2) be two complex numbers such that |z_(1)|=1 and |z_(2)|=10. If theta=arg((z_(1)-z_(2))/(z_(2))) then maximum value of tan^(2)theta can be expressed as (m)/(n) (where m and n are coprime ) .Find the value of (100m-n)

Let x, y be positive real numbers and m, n be positive integers, The maximum value of the expression (x^(m)y^(n))/((1+x^(2m))(1+y^(2n))) is

There are two sets M_1 and M_2 each of which consists of three numbers in arithmetic sequence whose sum is 15. Let d_1 and d_2 be the common differences such that d_1=1+d_2 and 8p_1=7p_2 where p_1 and p_2 are the product of the numbers respectively in M_1 and M_2. If d_2 gt 0 then find the value of (p_2-p_1)/(d_1+d_2)

KVPY PREVIOUS YEAR-QUESTION PAPER 2020-PART-I (MATHEMATICS)
  1. Consider the following statements : I. lim(n to oo) ( 2^n +(-2)^n)/...

    Text Solution

    |

  2. Consider a regular 10-gon with its vertices on the unit circle. With o...

    Text Solution

    |

  3. The value of the integral int(-pi//2)^(pi//2)(sin^(2)x)/(1+e^(x))dx ...

    Text Solution

    |

  4. Let RR be the set of all real numbers and f(x) = sin^(10) x ( cos^...

    Text Solution

    |

  5. A person standing on the top of a building of height 60sqrt(3) feel ob...

    Text Solution

    |

  6. Assume that 3.313 le pi le 3.15. The integer closest to the value of s...

    Text Solution

    |

  7. The maximum value of the function ƒ(x) = e^x + x ln x on the interval ...

    Text Solution

    |

  8. Let A be a 2 xx 2 matrix of the form A = [[a,b],[1,1]], where a, b are...

    Text Solution

    |

  9. Let A = (a(ij))(1 le I, j le 3) be a 3 xx 3 invertible matrix where ea...

    Text Solution

    |

  10. Let x, y be real numbers such that x gt 2y gt 0 and 2log (x-2y) = lo...

    Text Solution

    |

  11. Let (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1(b lt a). Be an ellipse with ...

    Text Solution

    |

  12. Let A denote the set of all real numbers x such that x^(3) - [x]^(3) =...

    Text Solution

    |

  13. S= lim(nrarroo) sum(k=0)^n 1/sqrt(n^2 + k ^2)

    Text Solution

    |

  14. Let RR be the set of all real numbers and ƒ : RR to RR be a contin...

    Text Solution

    |

  15. Let f(x) = {{:((x)/(sin x) ",",x in "(0,1)"),(1",",x=0):} Consider...

    Text Solution

    |

  16. The value of the integral int(1)^(3)((x-2)^(4)sin^(3)(x-2)+(x-2)^(20...

    Text Solution

    |

  17. In a regular 15-sided polygon with all its diagonals drawn, a diagonal...

    Text Solution

    |

  18. Let M = 2^(30)-2^(15)+1, and M^(2) be expressed in base 2. The number ...

    Text Solution

    |

  19. Let ABC be a triangle such that AB = 15 and AC = 9. The bisector of an...

    Text Solution

    |

  20. The figur in the complex plane given by 10zbar(z) - 3(z^(2)+bar(z)^(...

    Text Solution

    |