Home
Class 11
MATHS
Statement 1: The number of ways in which...

Statement 1: The number of ways in which three distinct numbers can be selected from the set `{3^1,3^2,3^3, ,3^(100),3^(101)}` so that they form a G.P. is 2500.
Statement 2: if `a ,b ,c` are in A.P., then `3^a ,3^b ,3^c` are in G.P.
(a) Statement 1 and Statement 2, both are correct. Statement 2 is the correct explanation for Statement 1
(b) Statement 1 and Statement 2, both are correct. Statement 2 is not the correct explanation for Statement 1
(c) Statement 1 is correct but Statement 2 is not correct.
(d) Both Statement 1 and Statement 2 are not correct.

Promotional Banner

Topper's Solved these Questions

  • LOGARITHM

    CENGAGE PUBLICATION|Exercise All Questions|177 Videos

  • PROBABILITY

    CENGAGE PUBLICATION|Exercise All Questions|1 Videos

Similar Questions

Explore conceptually related problems

Statement 1: Number of terms in the expansion of (x+y+z+w)^(50) is ""^(53)C_3 Statement 2: Number of non-negative solution of the equation p+q+r+s=50 is ""^(53)C_3 (a) Statement 1 and Statement 2, both are correct. Statement 2 is the correct explanation for Statement 1 (b) Statement 1 and Statement 2, both are correct. Statement 2 is not the correct explanation for Statement 1 (c) Statement 1 is correct but Statement 2 is not correct. (d) Both Statement 1 and Statement 2 are not correct.

Statement 1: Through (lambda,lambda+1) , there cannot be more than one normal to the parabola y^2=4x , if lambda (a) Statement 1 and Statement 2 , both are correct. Statement 2 is correct explanation for Statement 1. (b) Statement 1 and Statement 2 , both are correct. Statement 2 is not the correct explanation for Statement 1. (c) Statement 1 is correct but Statement 2 is not correct. (d) Statement 2 is correct but Statement 1 is not correct.

Statement 1: Number of ways in which Indian team (11 players) can bat, if Yuvraj wants to bat before Dhoni and Pathan wants to bat after Dhoni is 11!/3! . Statement 2: Yuvraj, Dhoni, and Pathan can be arranged in batting order in 3! ways. (a) Statement 1 and Statement 2, both are correct. Statement 2 is the correct explanation for Statement 1 (b) Statement 1 and Statement 2, both are correct. Statement 2 is not the correct explanation for Statement 1 (c) Statement 1 is correct but Statement 2 is not correct. (d) Both Statement 1 and Statement 2 are not correct.

Statement 1: Total number of five-digit numbers having all different digit divisible by 4 can be formed using the digits {1,3,2,6,8,9} is 192. Statement 2: A number is divisible by 4, if the last two digits of the number are divisible by 4. (a) Statement 1 and Statement 2, both are correct. Statement 2 is the correct explanation for Statement 1 (b) Statement 1 and Statement 2, both are correct. Statement 2 is not the correct explanation for Statement 1 (c) Statement 1 is correct but Statement 2 is not correct. (d) Both Statement 1 and Statement 2 are not correct.

If N is the number of ways in which 3 distinct numbers canbe selected from the set {3^1,3^2,3^3, ,3^(10)} so that they form a G.P. then the value of N//5 is ______.

Statement 1: In the expansion of (1+x)^(41)(1-x+x^2)^(40), the coefficient of x^(85) is zero. Statement 2: In the expansion of (1+x)^(41)a n d(1-x+x^2)^(40), x^(85) term does not occur. (a) Statement 1 and Statement 2, both are correct. Statement 2 is the correct explanation for Statement 1 (b) Statement 1 and Statement 2, both are correct. Statement 2 is not the correct explanation for Statement 1 (c) Statement 1 is correct but Statement 2 is not correct. (d) Both Statement 1 and Statement 2 are not correct.

Statement 1: The number of positive integral solutions of a b c=30 is 27. Statement 2: Number of ways in which three prizes can be distributed among three persons is 3^3 (a) Statement 1 and Statement 2 , both are correct. Statement 2 is correct explanation for Statement 1. (b) Statement 1 and Statement 2 , both are correct. Statement 2 is not the correct explanation for Statement 1. (c) Statement 1 is correct but Statement 2 is not correct. (d) Statement 2 is correct but Statement 1 is not correct.

Statement 1: the number of ways of writing 1400 as a product of two positive integers is 12. Statement 2: 1400 is divisible by exactly three prime factors. (a) Statement 1 and Statement 2 , both are correct. Statement 2 is correct explanation for Statement 1. (b) Statement 1 and Statement 2 , both are correct. Statement 2 is not the correct explanation for Statement 1. (c) Statement 1 is correct but Statement 2 is not correct. (d) Statement 2 is correct but Statement 1 is not correct.

Statement 1: let E={1,2,3,4}a n dF={a ,b} Then the number of onto functions from EtoF is 14. Statement 2: Number of ways in which four distinct objects can be distributed into two different boxes is 14 if no box remains empty. (a) Statement 1 and Statement 2, both are correct. Statement 2 is the correct explanation for Statement 1 (b) Statement 1 and Statement 2, both are correct. Statement 2 is not the correct explanation for Statement 1 (c) Statement 1 is correct but Statement 2 is not correct. (d) Both Statement 1 and Statement 2 are not correct.

Statement 1: For f(x)=sinx ,f^(prime)(pi)=f^(prime)(3pi) Statement 2: For f(x)=sinx ,f(pi)=f(3pi)dot a. Statement 1 and Statement 2, both are correct and Statement 2 is the correct explanation for Statement 1 b. Statement 1 and Statement 2, both are correct and Statement 2 is not the correct explanation for Statement 1 c. Statement 1 is correct but Statement 2 is wrong. d. Statement 2 is correct but Statement 1 is wrong.

CENGAGE PUBLICATION-PERMUTATIONS AND COMBINATIONS-All Questions
  1. Find the equation of the line passing through the point (2, – 5) and m...

    Text Solution

    |

  2. n different toys have to be distributed among n children. Find the num...

    Text Solution

    |

  3. Statement 1: The number of ways in which three distinct numbers can ...

    Text Solution

    |

  4. Statement 1: Total number of five-digit numbers having all different...

    Text Solution

    |

  5. Find the number of ways of dividing 52 cards among four players equ...

    Text Solution

    |

  6. Find the number of ways in which the number 300300 can be split into ...

    Text Solution

    |

  7. The number of words of four letters that can be formed from the let...

    Text Solution

    |

  8. Find the number of ways in which 8 non-identical apples can be dist...

    Text Solution

    |

  9. The number of ways in which the letters of the word PERSON can plac...

    Text Solution

    |

  10. Find the number of ways to give 16 different things to three persons A...

    Text Solution

    |

  11. There are two bags can each of which contains n balls. A man has to se...

    Text Solution

    |

  12. Find the total number of proper factors of the number 35700. Also find...

    Text Solution

    |

  13. In how many ways can a team of 6 horses be selected out of a stud o...

    Text Solution

    |

  14. There are 3 books of mathematics, 4 of science, and 5 of literature. ...

    Text Solution

    |

  15. Number of ways in which a lawn-tennis mixed double be made from sev...

    Text Solution

    |

  16. Find the number of divisors of the number N=2^3 .3^5 .5^7 .7^9 which a...

    Text Solution

    |

  17. Find the equation of a line, which has the y-intercept 4, and is paral...

    Text Solution

    |

  18. Find the number of ways in which the number 94864 can be resolved as a...

    Text Solution

    |

  19. A class contains three girls and four boys. Every Saturday, five go...

    Text Solution

    |

  20. Show that 1!+2!+3!++n ! cannot be a perfect square for any n in N ,ng...

    Text Solution

    |