GATE ME format:mcq PYQs & Answers — Page 48

Questions 471–480 of 599. Imported answers require independent review unless marked reviewed.

Topic practice 599 questionsPage 48 of 60

Consider the following three statements: (i) Some roses are red. (ii) All red flowers fade quickly. (iii) Some roses fade quickly.

Which of the following statements can be logically inferred from the above statements?

Your answerChoose one option.

If (i) is true and (ii) is false, then (iii) is false.

If (i) is true and (ii) is false, then (iii) is true.

If (i) and (ii) are true, then (iii) is true.

If (i) and (ii) are false, then (iii) is false.

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An unbiased coin is tossed six times in a row and four different such trials are conducted. One trial implies six tosses of the coin. If H stands for head and T stands for tail, the following are the observations from the four trials: (1) HTHTT (2) TTHHT (3) HTHTT (4) HHT___.

Which statement describing the last two coin tosses of the fourth trial has the highest probability of being correct?

Your answerChoose one option.

Two T will occur.

One H and one T will occur.

Two H will occur.

One H will be followed by one T.

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Four red balls, four green balls and four blue balls are put in a box. Three balls are pulled out of the box at random one after another without replacement. The probability that all three balls are red is

Your answerChoose one option.

1/72

1/55

1/36

1/27

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The Fourier cosine series for an even function

is given by

The value of the coefficient

for the function

Your answerChoose one option.

−0.5

0.0

0.5

1.0

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The rank of the matrix

Your answerChoose one option.

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The divergence of the vector field

Your answerChoose one option.

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According to the Mean Value Theorem, for a continuous function f (x) in the interval [a, b], there exists a value ξ in this interval such that

Your answerChoose one option.

f (ξ)(b − a)

f (b)(ξ − a)

f (a)(b − ξ)

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Consider a function

which depends on position

and time

. The partial differential equation

is known as the

Your answerChoose one option.

Wave equation

Heat equation

Laplace’s equation

Elasticity equation

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F (z) is a function of the complex variable z = x + iy given by

For what value of k will F (z) satisfy the Cauchy-Riemann equations?

Your answerChoose one option.

−1

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is the solution of the differential equation

, the value of

Your answerChoose one option.

−2

−1

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GATE ME format:mcq PYQs

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