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GATE Questions

**Stack:**

- Stack is a ordered collection of items

- Stack is a dynamic object whose size is constantly changing as items are pushed and popped .

- Stack may contain different data types

**Array:**

- Array is an ordered collection of items

- Array is a static object i.e. no of item is fixed and is assigned by the declaration of the array

- It contains same data types.

A) 101 | B) 102 |

C) 103 | D) 104 |

Explanation:

Here the series of the form is $x2-1,x2-2,x2-3,...$

53 x 2 - 4 = 106 - 4 = 102

A) 23/42 | B) 19/42 |

C) 7/32 | D) 16/39 |

Explanation:

A red ball can be drawn in two mutually exclusive ways

(i) Selecting bag I and then drawing a red ball from it.

(ii) Selecting bag II and then drawing a red ball from it.

Let E1, E2 and A denote the events defined as follows:

E1 = selecting bag I,

E2 = selecting bag II

A = drawing a red ball

Since one of the two bags is selected randomly, therefore

P(E1) = 1/2 and P(E2) = 1/2

Now, $P\left(\frac{A}{{E}_{1}}\right)$ = Probability of drawing a red ball when the first bag has been selected = 4/7

$P\left(\frac{A}{{E}_{2}}\right)$ = Probability of drawing a red ball when the second bag has been selected = 2/6

Using the law of total probability, we have

P(red ball) = P(A) = $P\left({E}_{1}\right)\times P\left(\frac{A}{{E}_{1}}\right)+P\left({E}_{2}\right)\times P\left(\frac{A}{{E}_{2}}\right)$

= $\frac{1}{2}\times \frac{4}{7}+\frac{1}{2}\times \frac{2}{6}=\frac{19}{42}$

A) 4% | B) 5% |

C) 6% | D) 8% |

Explanation:

SP of first article = Rs.1000

Profit = 20%

$CP=SPx\frac{100}{100+P\%}=Rs.\frac{2500}{3}$

SP of Second Article = Rs.1000

Loss = 20%

$CP=SPx\frac{100}{100-L\%}=Rs.1250$

So, Total SP = Rs.2000; Total CP = Rs.6250/3

As the CP is more than SP, he makes a loss.

Loss = CP - SP = (6250/3) - 2000 = Rs.(250/3)

So, Loss Percent = Lossx100/CP = 4%

A) 60% | B) 40% |

C) 50% | D) 30% |

Explanation:

Lets say shyam sells at 100,

Since Ram sells 25% cheaper than Shyam,

Therefor Ram sells at less than 25% of100 or 75 rs.

Ram sells 25% dearer than Bram or 125% of Ram =100% of Bram or

125% of x (say x price of bram )=75rs.

or 100% of x =60rs.

hence price of bram is 60rs.

now Bram's good is cheaper than Shyam's as (100-60)x100/100% or 40%.

Hence Brams Good is 40% cheaper than that of Shyam's good.

A) Johannesburg | B) Paris |

C) Dubai | D) Saudi |

A) 14 | B) 16 |

C) 18 | D) 20 |

Explanation:

Let the third proportion to 9 & 12 be 'x'.

=> 9:12 = 12 :p

=> p = 12x12/9 = 16.

A) increase by 2% | B) decrease by 3% |

C) decrease by 4% | D) increase by 5% |

Explanation:

Here, x = 20 and y = - 20

Therefore, the net % change in value

=**$x+y+\frac{xy}{100}$ %**

= $\mathbf{20}\mathbf{}\mathbf{+}\mathbf{}\left(\mathbf{-}\mathbf{20}\right)\mathbf{}\mathbf{+}\mathbf{}\frac{\mathbf{20}\mathbf{}\mathbf{\times}\mathbf{}\mathbf{-}\mathbf{20}}{\mathbf{100}}$% or - 4%

Since the sign is negative, there is a decrease in value by 4%.