#
GATE Questions

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) Rs. 1800 | B) Rs. 2000 |

C) Rs. 1400 | D) Rs. 1250 |

Explanation:

2500 in 5th year and 3000 in 7th year

So in between 2 years Rs. 500 is increased => for a year 500/2 = 250

So, per year it is increasing Rs.250 then in 5 years => 250 x 5 = 1250

Hence, the initial amount must be 2500 - 1250 = Rs. 1250

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) 31/25 | B) 15/17 |

C) 14/25 | D) 11/16 |

Explanation:

The original fraction is $\frac{25}{51}\times \left(\frac{350+100}{150+100}\right)$ = 15/17.

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) 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) 193 : 122 | B) 97 : 102 |

C) 115 : 201 | D) 147 : 185 |

Explanation:

Given the three mixtures ratio as (1:2),(2:3),(3:4)

(1+2),(2+3),(3+4)

Total content = 3,5,7

Given equal quantities of the three mixtures are mixed, then LCM of 3, 5, 7 = 105

105/3 = 35 , 105/5 = 21 , 105/7 = 15

Now, the individual equal quantity ratios are (35x1, 35x2), (21x2, 21x3), (15x3, 15x4)

i.e (35,70), (42,63), (45,60)

So overall mixture ratio of milk and water is

35+42+45 : 70+63+60

122:193

But in the question asked the ratio of water to milk = 193 : 122

A) 129780 | B) 1587600 |

C) 35600 | D) None of these |

Explanation:

H L C N T A U I O

L N A I

There are total 131 letters out of which 7 are consonants and 6 are vowels. Also ther are 2L's , 2N's, 2A's and 2I's.

If all the consonants are together then the numberof arrangements = $\frac{\mathbf{7}\mathbf{!}}{\mathbf{2}\mathbf{!}}$x 1/2! .

But the 7 consonants can be arranged themselves in $\frac{\mathbf{7}\mathbf{!}}{\mathbf{2}\mathbf{!}}$ x 1/2! ways.

Hence the required number of ways = ${\left(\frac{{\displaystyle 7!}}{{\displaystyle 2!2!}}\right)}^{2}$ = 1587600