November 15, 2017

| No Comments

**Answer the questions independently of each other.**

## Mathematics Tests-23

Start the test!

Start

Congratulations - you have completed *Mathematics Tests-23*.

You scored %%SCORE%% out of %%TOTAL%%.

Your performance has been rated as %%RATING%%

Your answers are highlighted below.

Question 1 |

A | The two curves intersect once |

B | The two curves do not intersect |

C | The two curves intersect thrice |

D | The two curves intersect twice |

Question 1 Explanation:

When we substitute two values of x in the above curves, at x = –2 we get y = –8 + 4 + 5 = 1 y = 4 – 2 + 5 = 7 Hence at x = –2 the curves do not intersect. At x = 2, y = 17 and y = 11 At x = –1, y = 5 and 5 When x = 0, y = 5 and y = 5 And at x = 1, y = 7 and y = 7 Therefore, the two curves meet thrice when x = –1, 0 and 1.

Question 2 |

A | 10 |

B | 11 |

C | 9 |

D | 12 |

Question 2 Explanation:

Let us say there are only 3 questions. Thus there are 23–1 = 4 students who have done 1 or more questions wrongly, 23–2 = 2 students who have done 2 or more questions wrongly and 23–3 = 1 student who must have done all 3 wrongly. Thus total number of wrong answers = 4 + 2 + 1 = 7 = 23 – 1 = 2n – 1. In our question, the total number of wrong answers = 4095 = 212 – 1. Thus n = 12.

Question 3 |

**The number of positive integers n in the range 12 ? n? 40 such that the product (n – 1) (n – 2)…3.2.1 is not divisible by n is ...**

A | 5 |

B | 7 |

C | 13 |

D | 14 |

Question 3 Explanation:

From 12 to 40, there are 7 prime number, i.e. 13, 17, 19, 23, 29, 31, 37, which is not divisible by (n– 1)!

Question 5 |

**A graph may be defined as a set of points connected by lines called edges. Every edge connects a pair of points. Thus, a triangle is a graph with 3 edges and 3 points. The degree of a point is the number of edges connected to it. For example, a triangle is a graph with three points of degree 2 each. Consider a graph with 12 points. It is possible to reach any point from any other point through a sequence of edges. The number of edges, e, in the graph must satisfy the condition...**

A | 11? e? 65 |

B | 0? e? 11 |

C | 11? e? 66 |

D | 10? e? 66 |

Question 5 Explanation:

The least number of edges will be when one point is connected to each of the other 11 lines, giving a total of 11 lines. One can move from any point to any other point via the common point. The maximum edges will be when a line exists between any two points. Two points can be selected from 12 points in 12C2 i.e. 66 lines.

Question 6 |

**Let T be the set of integers {3, 11, 19, 27,…451, 459, 467} and S be a subset of T such that the sum of no two elements of S is 470. The maximum possible number of elements in S is...**

A | 32 |

B | 29 |

C | 28 |

D | 30 |

Question 6 Explanation:

Tn = a + (n – 1)d 467 = 3 + (n – 1)8 n = 59 Half of n = 29 terms 29th term is 227 and 30th term is 243 and when these two terms are added the sum is more than 470. Hence the maximum possible values the set S can have are 30.

Question 7 |

**There are 6 boxes numbered 1, 2, …6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is...**

A | 33 |

B | 21 |

C | 60 |

D | 5 |

Question 7 Explanation:

GRRRRR, RGRRRR, RRGRRR, RRRGRR, RRRRGR, RRRRRG GGRRRR, RGGRRR, RRGGRR, RRRGGR, RRRRGG GGGRRR, RGGGRR, RRGGGR, RRRGGG GGGGRR, RGGGGR, RRGGGG GGGGGR, RGGGGG GGGGGG Hence 21 ways.

Once you are finished, click the button below. Any items you have not completed will be marked incorrect.
Get Results

There are 7 questions to complete.

You have completed

questions

question

Your score is

Correct

Wrong

Partial-Credit

You have not finished your quiz. If you leave this page, your progress will be lost.

Correct Answer

You Selected

Not Attempted

Final Score on Quiz

Attempted Questions Correct

Attempted Questions Wrong

Questions Not Attempted

Total Questions on Quiz

Question Details

Results

Date

Score

Hint

Time allowed

minutes

seconds

Time used

Answer Choice(s) Selected

Question Text

All done

Need more practice!

Keep trying!

Not bad!

Good work!

Perfect!