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GATE Questions

A) 225 | B) 425 |

C) 525 | D) 625 |

Explanation:

The relationship is ${x}^{y}:{\left(x+1\right)}^{\left(y+1\right)}$

Now , $64={4}^{3}$

So, required number = ${\left(4+1\right)}^{\left(3+1\right)}$ = ${5}^{4}$ = 625

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) 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) 5:3 | B) 1:4 |

C) 4:1 | D) 9:1 |

Explanation:

Milk = 3/5 x 20 = 12 liters, water = 8 liters

If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters.

Remaining milk = 12 - 6 = 6 liters

Remaining water = 8 - 4 = 4 liters

10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters.

The ratio of milk and water in the new mixture = 16:4 = 4:1

If the process is repeated one more time and 10 liters of the mixture are removed,

then amount of milk removed = 4/5 x 10 = 8 liters.

Amount of water removed = 2 liters.

Remaining milk = (16 - 8) = 8 liters.

Remaining water = (4 -2) = 2 liters.

Now 10 lts milk is added => total milk = 18 lts

The required ratio of milk and water in the final mixture obtained

= (8 + 10):2 = 18:2 = 9:1.

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) 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,

Then, ^{7}C_{1 }x ^{6}C_{2 }x ^{4}C_{4 }

_{= 7 x 15 x 1 = 105}

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 |

A) 7 lts | B) 14 lts |

C) 98 lts | D) 42 lts |

Explanation:

To know the the measuring cylinder that can fill all the given capacities , they must be divisible by the required number.

98,182,266 all are divisible by 14

So 14 litres is the largest cylinder that can fill all the given cylinders.

(or)

The other method is take HCF of all given capacities i.e 98, 182 and 266.