Home
Class 12
MATHS
Statement-1: Number of rectangles on a c...

Statement-1: Number of rectangles on a chessboard is `.^(8)C_(2)xx.^(8)C_(2)`.
Statement-2: To form a rectangle, we have to select any two of the horizontal lines and any two of the vertical lines.

A

Statement-1 is true, statement-2 is true, statement-2 is a correct explanation for statement-1

B

Statement-1 is true, statement-2 is true, statement-2 is not a correct explanation for statement-1

C

Statement-1 is true, statement-2 is false

D

Statement-1 is false, statement-2 is true

Text Solution

Verified by Experts

The correct Answer is:
d
In a chessboard, there are 9 horizontal lines and 9 vertical lines.
`therefore`Number of rectangles of any size are `.^(9)C_(2)xx.^(9)C_(2)`.
Hence, statement-1 is fale and statement-2 is true.
Promotional Banner

Topper's Solved these Questions

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS|Exercise JEE Type Solved Examples: Single Matching Type Questions|1 Videos

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS|Exercise Exercise For Session 1|11 Videos

  • PARABOLA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|35 Videos

  • PROBABILITY

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|55 Videos

Similar Questions

Explore conceptually related problems

The largest area of a rectangle which has one side on the x-axis and the two vertices on the curve y=e^(-x^(2) is

Statement 1 : The number of circles passing through (1, 2), (4, 8) and (0, 0) is one. Statement 2 : Every triangle has one circumcircle

Statement-1: the number of even divisors of the number N=12600 is 54. Statement-2: 0,2,4,6,8, . . . Are even integers.

The points (1, 3) and (5, 1) are the opposite vertices of a rectangle. The other two vertices lie on the line y=2x+c. Find c and the remaining vertices.

Statement-1 If a set A has n elements, then the number of binary relations on A = n^(n^(2)) . Statement-2 Number of possible relations from A to A = 2^(n^(2)) . (a) Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for Statement-1 (b) Statement-1 is true, Statement-2 is true, Statement-2 is not a correct explanation for Statement-1 (c) Statement-1 is true, Statement-2 is false (d) Statement-1 is false, Statement-2 is true

Statement 1 : Let theta be the angle between the line (x-2)/(2)=(y-1)/(-3)= (z+2)/(-2) and the plane x+y-z=5 . Then theta= sin ^(-1)(1//sqrt(51)) . Statement 2 : The angle between a straight line and a plane is the complement of the angle between the line and the normal to the plane.

If centroid of a triangle be (1, 4) and the coordinates of its any two vertices are (4, -8) and (-9, 7), find the area of the triangle.

One side of a rectangle lies along the line 4x + 7y +5=0. Two of its vertices are (-3, 1) and (1, 1).Find the equations of the other three sides.

Find the distance between two Parallel lines : y=mx+c_1 and y=mx+c_2 .

ARIHANT MATHS-PERMUTATIONS AND COMBINATIONS -Exercise (Questions Asked In Previous 13 Years Exam)
  1. Statement-1: Number of rectangles on a chessboard is .^(8)C(2)xx.^(8)C...

    Text Solution

    |

  2. There is a rectangular sheet of dimension (2m-1)xx(2n-1), (where m > 0...

    Text Solution

    |

  3. If the letters of the word SACHIN are arranged in all possible ways ...

    Text Solution

    |

  4. lf r, s, t are prime numbers and p, q are the positive integers such t...

    Text Solution

    |

  5. At an election, a voter may vote for any number of candidates not grea...

    Text Solution

    |

  6. The letters of the word COCHIN are permuted and all the permutation...

    Text Solution

    |

  7. The set S""=""{1,""2,""3,""........ ,""12) is to be partitioned into...

    Text Solution

    |

  8. Consider all possible permutations of the letters of the word ENDEANOE...

    Text Solution

    |

  9. The number of words can be formed with the letters of the word 'MATHEM...

    Text Solution

    |

  10. In a shop, there are five types of ice-creams available. A child buys ...

    Text Solution

    |

  11. The number of seven digit integers, with sum of the digits equal to 10...

    Text Solution

    |

  12. Three boys and two girls stand in a queue. The probability that the nu...

    Text Solution

    |

  13. There are two urns. Urn A has 3 distinct red balls and urn B has 9 ...

    Text Solution

    |

  14. In how many ways 5 different balls can be distributed into 3 boxes so ...

    Text Solution

    |

  15. There are 10 points in a plane, out of these 6 are collinear. The numb...

    Text Solution

    |

  16. The total number of ways in which 5 balls of differert colours can be ...

    Text Solution

    |

  17. Let n denote the number of all n-digit positive integers formed by the...

    Text Solution

    |

  18. Let a(n) denote the number of all n-digit numbers formed by the digits...

    Text Solution

    |

  19. Assuming the balls to be identical except for difference in colours, t...

    Text Solution

    |

  20. Let Tn be the number of all possible triangles formed by joining ve...

    Text Solution

    |

  21. Consider the set of eight vector V={a hat i+b hat j+c hat k ; a ,bc in...

    Text Solution

    |