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GATE Questions

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) 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) 38 | B) 39 |

C) 40 | D) 41 |

Explanation:

Given M.P=45,S.P=42, Profit = 0.05

Let C.P=x , Then

Profit = (42-x)/x = 0.05

=> x = 40.

A) 215 | B) 268 |

C) 254 | D) 216 |

Explanation:

Since each ring consists of six different letters, the total number of attempts possible with the three rings is = 6 x 6 x 6 = 216. Of these attempts, one of them is a successful attempt.

Maximum number of unsuccessful attempts = 216 - 1 = 215.

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) 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

A) 215 | B) 315 |

C) 415 | D) 115 |

Explanation:

Hence, the given problem can be considered as selecting pairs of lines from the given 2 sets of parallel lines.

Therefore, the total number of parallelograms formed =

^{7}C

_{2}x

^{6}C

_{2}= 315

A) Saturday | B) Sunday |

C) Friday | D) Monday |

Explanation:

We know that,

After every 400 years, the same day occurs.

Thus, if 9th August 2016 is Saturday, before 400 years i.e., on 9th August 1616 has to be Saturday.