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This mock test of Test: Engineering Mathematics & General Aptitude- 2 for GATE helps you for every GATE entrance exam.
This contains 25 Multiple Choice Questions for GATE Test: Engineering Mathematics & General Aptitude- 2 (mcq) to study with solutions a complete question bank.
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*Answer can only contain numeric values

QUESTION: 1

Determine the minimum number of vertices to be removed from a complete graph K_{10} to make the graph disconnected.

Solution:

QUESTION: 2

Which of the following propositions is/are a contingency?

Solution:

A contingency is a proposition that is neither a tautology nor a contradiction.

QUESTION: 3

The number of one-one (injective) functions from a set of 7 elements to a set of 5 elements is

Solution:

QUESTION: 4

**Direction :** This question consists of a word or a phrase that is underline. It is followed by four words or phrases. Select the word or phrase that is most closely opposite in meaning to the underline word or phrases

**Q. **

**The teachers have been.observing his impertinent behaviour.**

Solution:

QUESTION: 5

**Direction :** In the given below sentence, each sentence has three parts, indicated by (a), (b), (c). Read sentence to find out whether there is any error. If you find any error in any one part (a, b, c) indicate your response by blackening the letter related to the part in the answer sheet provided. If a sentence has no error, indicate this by blackening (d) which stands for ‘no error'.

Q.

He goes / (a) to college / (b) by foot everyday / (c) No error (d)

Solution:

QUESTION: 6

**Direction :** In the following question, sentence is given with blank to be filled with an appropriate word(s). Four alternatives are suggested, choose the correct alternative

**Q. **

**However honest he____________________ I do nottrust him.**

Solution:

QUESTION: 7

In this question a related pair of word of followed by four pair of words. Select the pair that best expresses a relationship similar to the expressed in original pair.

**MARATHON : STAMINA**

Solution:

QUESTION: 8

A shopkeeper gives 12% additional discount on the discounted price, after giving an initial discount of 20% on the labelled price of a radio. If the final sale price of the radio is Rs. 704, then what is its labelled price?

Solution:

Let the marked price be Rs. 100.

Successive discounts of 20% and 12% were given.

Sale price = 100*80100*88100=Rs.704/10

If the sale price is Rs.704/10, the marked price is Rs.100

If the sale price is Rs.704, the marked price is

= 100*10*704/704= Rs.1000

QUESTION: 9

Find the odd man out

385, 462, 572, 396. 427, 671,264

Solution:

*Answer can only contain numeric values

QUESTION: 10

25 persons are in a room. 15 of them play hockey, 17 of them play football and 10 of them play both hockey and football. Then the number of persons playing neither hockey nor football is

Solution:

QUESTION: 11

In a factory, a radioactive source emits 2 particles (on an average) per second. The probability that 2 or more particles will be emitted in an interval of 5 seconds is

Solution:

X = 2.0

The number of particles emitted in the interval of 5 seconds is Poisson distributed with parameter = 5λ = 10

The required probability is, P(x __>__ 2) = 1-P(x < 2) = 1 - P(x = 0) -P (x = 1) = 1 - e^{-10} -10e^{-10} = 1-11e^{-10}

QUESTION: 12

Consider the set of all integers (Z) with the operation defined as m*n = m + n + 2, m,ne Z

**Q. **

**If (z, *) forms a group, then determine the left identity element.**

Solution:

(Z, *) forms a group. Let e ∈ z be the left identity element.

Then e * m = m

QUESTION: 13

Consider the set of all integers (Z) with the operation defined as m*n = m + n + 2, m,ne Z

**Q. **

**Determine the left inverse of element (-4)**

Solution:

Let m ∈ z and m' ∈ zbe the left inverse of element m

Then m’* m = e m’+ m + 2 = -2 ⇒ m` = -m- 4

Here m = (-4) ∴ m` = 0

and m'* m = 0*(-4) = 0-4 +2 =-2 = e

QUESTION: 14

Consider the following probability distribution table of a discrete random variable X

**Q. **

**Find the value of K**

Solution:

⇒ K+0.1 +2K +0.2 +3K +0.1 = 1 ⇒ 6K + 0.4 = 1 ⇒ 6K = 0.6 => K = 0.1

QUESTION: 15

Consider the following probability distribution table of a discrete random variable X

**Q. **

**Calculate the Variance (V)**

Solution:

QUESTION: 16

If DEER = 12215 and HIGH = 5645. how will you code HEEL?

Solution:

QUESTION: 17

In a competitive examination in State A, 6% candidates got selected from the tota appeared candidates. State B had an equa number of candidates appeared and 7% candidates got selected with 80 mom candidates got selected than A. What was the number of candidates appeared from each State?

Solution:

QUESTION: 18

A sum of money is borrowed and paid back in two annual instalments of Rs. 882 each allowing 5% compound interest. The sum borrowed was

Solution:

QUESTION: 19

A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other at:

Solution:

QUESTION: 20

Five friends A, B, C, D and E are standing in a row facing South but not necessarily in the same order. Only B is between A and E, C is immediate right to E and D is immediate left to A. On the basis of above information, which of the following statements is definitely true?

Solution:

QUESTION: 21

Five children were administered psychological tests to know their intellectual levels. In the report, psychologist pointed out that the child A is less intelligent than the child B. The child C is less intelligent than the child D. The child B is less intelligent than the child C and Child A is more intelligent than the child E. Which child is the most intelligent?

Solution:

QUESTION: 22

Production of fertilizers by a Company (in 10000 tonnes) over the Years given in following bar graph:

In which year was the percentage increase in production as compared to the previous year the maximum?

Solution:

*Answer can only contain numeric values

QUESTION: 23

These questions are to be answered on the basic ot the following pie chart which gives marks scored by a student in different subjects-English, Hindi, Mathematics, Science and Social Science in an examination. Assuming that the total marks obtained for the examination are 540 answer the following questions:

The aggregate marks obtained by the students averaged over the 5 subjects is

Solution:

QUESTION: 24

The following pie-chart shows the percentage of Literate and Illiterate-males and females in a city

What is the difference between the number of Literate Males and Literate Females?

Solution:

QUESTION: 25

Read the following instruction carefully and answer the question given below:

“P is son of Q, R, Q’s sister has a sons and daughter T. U is the maternal uncle of S. How is T related to U?

Solution:

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