A) 525 | B) 535 |

C) 545 | D) 555 |

Explanation:

The number of points of intersection of 37 lines is . But 13 straight lines out of the given 37 straight lines pass through the same point A. Therefore instead of getting points, we get only one point A. Similarly 11 straight lines out of the given 37 straight lines intersect at point B. Therefore instead of getting points, we get only one point B.

Hence the number of intersection points of the lines is = 535

A) 5040 | B) 2525 |

C) 2052 | D) 4521 |

Explanation:

The Word LOGARITHMS contains 10 letters.

To find how many 4 letter words we can form from that = 10p4 =10x9x8x7 = 5040.

A) 1000 | B) 625 |

C) 525 | D) 125 |

Explanation:

Methods for selecting 4 questions out of 5 in the first section = 5x4x3x2x1/4x3x2x1 = 5

similarly for other 2 sections also i.e 5 and 5

so total methods = 5 x 5 x 5 = 125.

A) 51/1221 | B) 42/221 |

C) 1/221 | D) 52/1245 |

Explanation:

Total Combination of getting a card from 52 cards = 52C1

Because there is no replacement, so number of cards after getting first card= 51

Now, Combination of getting an another card= 51C1

Total combination of getting 2 cards from 52 cards without replacement= (52C1)x(51C1)

There are total 4 Ace in stack. Combination of getting 1 Ace is = 4C1

Because there is no replacement, So number of cards after getting first Ace = 3

Combination of getting an another Ace = 3C1

Total Combination of getting 2 Ace without replacement=(4C1)x(3C1)

Now,Probability of getting 2 cards which are Ace = (4C1)x(3C1)/(52C1)x(51C1) = 1/221.

A) 142 | B) 175 |

C) 212 | D) 253 |

Explanation:

The first person shakes hands with 22 different people, the second person also shakes hands with 22 different people, but one of those handshakes was counted in the 22 for the first person, so the second person actually shakes hands with 21 new people. The third person, 20 people, and so on...

So,

22 + 21 + 20 + 19 + 18 + 17 + 16 + 15 + 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1

= n(n+1)/2 = 22 x 23 /2 = 11 x 23 = 253.

A) 105 | B) 7! x 6! |

C) 7!/5! | D) 420 |

Explanation:

Choose 1 person for the single room & from the remaining choose 2 for the double room & from the remaining choose 4 people for the four person room,

^{7}C

_{1 }x

^{6}C

_{2 }x

^{4}C

_{4 }

_{ = 7 x x 1 }

_{ = 7 x 15 = 105.}