# Engineering Mathematics [GATE (Graduate Aptitude Test in Engineering) Electronics]: Questions 63 - 68 of 71

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## Question 63

Appeared in Year: *2020*

### Question

MCQ▾The general solution of is

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## Question 64

Appeared in Year: *2021*

### Question

Numeric Answer▾If the vectors and in are linearly dependent the value of x is ________

## Question 65

Appeared in Year: *2021*

### Question

MCQ▾Consider the differential equation given below.

The integrating factor of the differential equation is

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## Question 66

Appeared in Year: *2020*

### Question

Numeric Answer▾The two sides of a fair coin are labelled as 0 and A. The coin is tossed two times independently. Let M and N denote the labels corresponding to the outcomes of those tosses. For a random variable X, defined as X = min (M, N) , the expected value E (X) (rounded off to two decimal places) is.

## Question 67

Appeared in Year: *2020*

### Question

MCQ▾Which one of the following options contains two solutions of the differential equation ?

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## Question 68

Appeared in Year: *2021*

### Question

MCQ▾A box contains the following three coins.

I. A fair coin with head on one face and tail on the other face.

II. A coin with heads on both the faces.

III. A coin with tails on both the faces.

A coin is picked randomly from the box and tossed. Out of the two remaining coins in the box, one coin is then picked randomly and tossed. If the first toss results in a head the probability of getting a head in the second toss is

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