GATE CE branch:ce PYQs & Answers — Page 34

Questions 331–340 of 1300. Imported answers require independent review unless marked reviewed.

What are the eigenvalues of the matrix

Your answerChoose one option.

1, 2, 5

1, 3, 4

−5, 1, 2

−5, −1, 2

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In a sample of 100 heart patients, each patient has 80% chance of having a heart attack without medicine X. It is clinically known that medicine X reduces the probability of having a heart attack by 50%. Medicine X is taken by 50 of these 100 patients. The probability that a randomly selected patient, out of the 100 patients, takes medicine X and has a heart attack is

Your answerChoose one option.

40%

60%

20%

30%

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A vector field

and a scalar field

are given by

Consider the statements P and Q.

P: Curl of the gradient of the scalar field

is a null vector.

Q: Divergence of curl of the vector field

is zero.

Which one of the following options is CORRECT?

Your answerChoose one option.

Both P and Q are FALSE

P is TRUE and Q is FALSE

P is FALSE and Q is TRUE

Both P and Q are TRUE

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A linearly elastic beam of length 2l with flexural rigidity EI has negligible mass. A massless spring with a spring constant k and a rigid block of mass m are attached to the beam as shown in the figure. The natural frequency of this system is

Diagram for Civil Engineering question 37

Your answerChoose one option.

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Find the correct match between the plane stress states and the Mohr’s circles.

Plane stress states P, Q, R and S and Mohr’s circles I, II, III and IV are shown in the figures.

Diagram for Civil Engineering question 38

Your answerChoose one option.

(P)-(III); (Q)-(IV); (R)-(I); (S)-(II)

(P)-(III); (Q)-(II); (R)-(I); (S)-(IV)

(P)-(I); (Q)-(IV); (R)-(III); (S)-(II)

(P)-(I); (Q)-(II); (R)-(III); (S)-(IV)

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A critical activity in a project is estimated to take 15 days to complete at a cost of Rs. 30,000. The activity can be expedited to complete in 12 days by spending a total amount of Rs. 54,000. Consider the statements P and Q.

P: It is economically advisable to complete the activity early by crashing, if the indirect cost of the project is Rs. 8,500 per day.

Q: It is economically advisable to complete the activity early by crashing, if the indirect cost of the project is Rs. 10,000 per day.

Which one of the following options is CORRECT?

Your answerChoose one option.

Both P and Q are TRUE

P is TRUE and Q is FALSE

Both P and Q are FALSE

P is FALSE and Q is TRUE

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The beam shown in the figure is subjected to a uniformly distributed downward load of intensity

between supports A and B.

Diagram for Civil Engineering question 39

Considering the upward reactions as positive, the support reactions are

Your answerChoose one option.

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A homogeneous, prismatic, linearly elastic steel bar fixed at both the ends has a slenderness ratio (l/r) of 105, where l is the bar length and r is the radius of gyration. The coefficient of thermal expansion of steel is 12 × 10⁻⁶/°C. Consider the effective length of the steel bar as 0.5l and neglect the self-weight of the bar.

The differential increase in temperature (rounded off to the nearest integer) at which the bar buckles is

Your answerChoose one option.

28 °C

85 °C

400 °C

250 °C

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A homogeneous shaft PQ with fixed supports at both ends is subjected to a torsional moment T at point Q, as shown in the figure.

Diagram for Civil Engineering question 40

The polar moments of inertia of the portions PQ and QR of the shaft with circular cross-sections are

and

, respectively. The torsional moment reactions at the supports P and R are

and

, respectively.

and

, the ratio of the lengths

Your answerChoose one option.

0.50

0.25

4.00

2.00

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Consider the statements P and Q related to the analysis/design of retaining walls.

P: When a rough retaining wall moves toward the backfill, the wall friction force/resistance mobilizes in upward direction along the wall.

Q: Most of the earth pressure theories calculate the earth pressure due to surcharge by neglecting the actual distribution of stresses due to surcharge.

Which one of the following options is CORRECT?

Your answerChoose one option.

Both P and Q are TRUE

P is TRUE and Q is FALSE

Both P and Q are FALSE

P is FALSE and Q is TRUE

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GATE CE branch:ce PYQs

Question 36

Question 36

Question 37

Question 37

Question 38

Question 38

Question 39

Question 39

Question 40

Question 40