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GATE Questions

A) Hydrogen sulphide | B) Oxygen |

C) Nitrogen | D) Carbon dioxide |

A) 8/39 | B) 15/39 |

C) 12/13 | D) None of these |

Explanation:

P( selecting atleast one couple) = 1 - P(selecting none of the couples for the prize)

= $1-\left(\frac{{16}_{{C}_{1}}\times {14}_{{C}_{1}}\times {12}_{{C}_{1}}\times {10}_{{C}_{1}}}{{16}_{{C}_{4}}}\right)=\frac{15}{39}$

A) 2012 | B) 2014 |

C) 2016 | D) 2010 |

Explanation:

We already know that the calendar after a leap year repeats again after 28 years.

Here year 1988 is a Leap year, then the same calendar will be in the year = 1988 + 28 = 2016.

A) 2880 | B) 1440 |

C) 720 | D) 2020 |

Explanation:

There are total 9 places out of which 4 are even and rest 5 places are odd.

4 women can be arranged at 4 even places in 4! ways.

and 5 men can be placed in remaining 5 places in 5! ways.

Hence, the required number of permutations = 4! x 5! = 24 x 120 = 2880

A) 27 | B) 24 |

C) 21 | D) 42 |

Explanation:

Let the numbers be 3x, 3x + 3 and 3x + 6.

Then,

3x + (3x + 3) + (3x + 6) = 72

9x = 63

x = 7

Largest number = 3x + 6 = 27.

=> Second largest number = 27 - 3 = 24

A) 34 | B) 36 |

C) 38 | D) 40 |

Explanation:

M + Tu + W + Th = 4 x 48 = 192

Tu + W + Th + F = 4 x 46 = 184

M = 42

Tu + W + Th = 192 - 42 = 150

F = 184 – 150 = 34

A) 17 men | B) 14 men |

C) 13 men | D) 16 men |

Explanation:

M x T / W = Constant

where, M= Men (no. of men)

T= Time taken

W= Work load

So, here we apply

M1 x T1/ W1 = M2 x T2 / W2

Given that, M1 = 4 men, T1 = 7 hours ; T2 = 2 hours, we have to find M2 =?

Note that here, W1 = W2 = 1 road, ie. equal work load.

Clearly, substituting in the above equation we get, M2 = 14 men.

A) All frustrated people are drug addicts | B) Frustrated people are whimsical |

C) All drug addicts are artists | D) Some artists may be drug addicts |