# GATE Questions

Q:

A problem is given to three students whose chances of solving it are 1/2, 1/3 and 1/4 respectively. What is the probability that the problem will be solved?

 A) 1/4 B) 1/2 C) 3/4 D) 7/12

Explanation:

Let A, B, C be the respective events of solving the problem and  be the respective events of not solving the problem. Then A, B, C are independent event

are independent events

Now,  P(A) = 1/2 , P(B) = 1/3 and P(C)=1/4

$\therefore$ P( none  solves the problem) = P(not A) and (not B) and (not C)

= $P\left(\overline{)A}\cap \overline{)B}\cap \overline{)C}\right)$

= $P\left(\overline{)A}\right)P\left(\overline{)B}\right)P\left(\overline{)C}\right)$

=  $\frac{1}{2}×\frac{2}{3}×\frac{3}{4}$

= $\frac{1}{4}$

Hence, P(the problem will be solved) = 1 - P(none solves the problem)

= $1-\frac{1}{4}$= 3/4

79 31977
Q:

A milkman purchases the milk at Rs. x per litre and sells it at Rs. 2x per litre still he mixes 2 litres water with every 6 litres of pure milk. What is the profit percentage?

 A) 116% B) 166.66% C) 60% D) 100%

Explanation:

Let the cost price of 1-liter pure milk be Re.1, then

8 litre mixture  =>

SP =>  8 x 2 = Rs. 16

Profit % =

152 22938
Q:

What was the day of the week on 17th June, 1998 ?

 A) Monday B) Tuesday C) Wednesday D) Friday

Explanation:

17th June, 1998 = (1997 years + Period from 1.1.1998 to 17.6.1998)
Odd days in 1600 years = 0
Odd days in 300 years = 1
97 years has 24 leap years + 73 ordinary years.
Number of odd days in 97 years ( 24 x 2 + 73) = 121 = 2 odd days.
Jan. Feb. March. April. May. June.
(31 + 28 + 31 + 30 + 31 + 17) = 168 days
168 days = 24 weeks = 0 odd day.
Total number of odd days = (0 + 1 + 2 + 0) = 3.
Given day is Wednesday.

18 7924
Q:

Study the given bar graph and pie chart to answer the following questions.

The bar graph shows the production (in thousand tonnes) of Wheat, Rice and Maize in different states.

The pie-chart shows the percentage of agricultural land in the given six states.

Productivity = $\inline \dpi{100} \frac{Total\: Production}{Area\: of\: agricultural\: land}$

1.The productivity of which state is the maximum ?

1. Bihar       2. Haryana     3. Punjab     4. UP       5. MP

2.The production of which state is the maximum ?

1. Bihar       2. MP         3. Haryana       4. UP       5. Punjab

3.The prodution of wheat in punjab is what per cent more than the production of Maize in odisha ?

1. 350%       2. 250%       3. 300%       4. 200%       5. 400%

4.What is the ratio of the production of Rice in Bihar to the production of Wheat in Haryana ?

1. 2:3           2. 3:2           3. 2:1           4. 1:1             5. 1:2

5.If MP exports 40% of Rice at the rate of Rs.30 per kg and UP exports 30% of Rice at the rate of Rs.32 per kg, then what is the ratio of the income from the exports ?

1. 65:48       2. 31:42       3. 43:54       4. 57:62       5. 1:2

Explanation : Productivity = Total production/area of Agr.land

Productivity of UP = 35000+30000+25000/(30/100) = 300000

Productivity of MP = 30000+37500+27500/(25/100) = 380000

Productivity of Bihar = 22500+27500+25000/(20/100) = 375000

Productivity of Odisha = 22500+15000+10000/5/100 = 950000

Productivity of Haryana = 30000+25000+35000/(8/100) = 1125000

Productivity of Punjab = 40000+35000+30000/(12/100) = 875000

The Productivity of Haryana is the maximum.

Explanation : Production of Punjab is maximum = 105000 tonnes

Explanation : Production of Wheat in Punjab = 40000 tones

Production of Maize in Odisha = 10000 tones

Required % = 40000 - 10000/100 = 300%

Explanation : The ratio of prodution of Rice in Bihar to the production of Wheat in Haryana = 25000 tonnes : 25000 tonnes = 1 : 1

Explanation : Income of MP from export of 40% of Rice at the rate of Rs.30 per kg = Rs.39 crore

Income of UP from export of 30% of Rice at the rate of Rs.32 per kg = Rs.28.8 crore

Required ratio = 39 : 28.8 = 390 : 288 = 65 : 48

7527
Q:

What is the difference between stack and array?

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.

Subject: C++ - Technology Exam Prep: GATE

7028
Q:

8, 15, 28, 53, ?, 199

 A) 101 B) 102 C) 103 D) 104

Explanation:

Here the series of the form is

53 x 2 - 4 = 106 - 4 = 102

Filed Under: Series - Verbal Reasoning - Mental Ability
Exam Prep: AIEEE , Bank Exams , CAT , GATE
Job Role: Bank Clerk , Bank PO

59 5793
Q:

A bag contains 4 red and 3 black balls. A second bag contains 2 red and 4 black balls. One bag is selected at random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is red.

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

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

18 5727
Q:

A Shopkeeper sells two articles at Rs.1000 each, making a profit of 20% on the first article and a loss of 20% on the second article. Find the net Profit or loss that he makes?

 A) 4% B) 5% C) 6% D) 8%

Explanation:

SP of first article = Rs.1000

Profit = 20%

SP of Second Article = Rs.1000

Loss = 20%

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%