Differential Equations Test

Result

Differential Equations Test - 4

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Score
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Question 1/10
1 / -0

Correct

Wrong

Skipped
A
y/x

Correct

Wrong

Skipped
B
x/y

Correct

Wrong

Skipped
C
x²/y²

Correct

Wrong

Skipped
D
y²/x²

Solutions
Question 2/10
1 / -0

Correct

Wrong

Skipped
A
decreases on (-∞, ∞)

Correct

Wrong

Skipped
B
decreases on (0, ∞)

Correct

Wrong

Skipped
C
neither decreases nor increases on (0, ∞)

Correct

Wrong

Skipped
D
increases on (-∞, ∞)

Solutions
Question 3/10
1 / -0

Let f(x) = sin x + cos x. Then,

Correct

Wrong

Skipped
A
x = 17π/4 is a point of minima

Correct

Wrong

Skipped
B
x = 13π/4 is a point of maxima

Correct

Wrong

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C
x = 21π/4 is a point of minima

Correct

Wrong

Skipped
D
x = 29π/4 is a point of maxima

Solutions
Question 4/10
1 / -0

The sides of the rectangle of the greatest area, that can be inscribed in the ellipse x² + 2y² = 8, are given by

Correct

Wrong

Skipped
A
4√2,4

Correct

Wrong

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B
4,2√2

Correct

Wrong

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C
2,√2

Correct

Wrong

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D
2√2,2

Solutions
Question 5/10
1 / -0

Directions For Questions

(1) f(x) has one point of inflexion.

(2) g(x) has one point of inflexion.

(3) f(x) has one point of local minima.

(4) g(x) has one point of local maxima.

...view full instructions

Which one of the following is correct regarding the above statements?

Correct

Wrong

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A
(1) is true. (2) is false.

Correct

Wrong

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B
(1) is false. (2) is true.

Correct

Wrong

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C
(3) and (4) both are true.

Correct

Wrong

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D
(1) and (2) both are true.

Solutions
Question 6/10
1 / -0

Correct

Wrong

Skipped
A
ad – bc < 0

Correct

Wrong

Skipped
B
ad – bc > 0

Correct

Wrong

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C
ab – cd > 0

Correct

Wrong

Skipped
D
ab – cd < 0

Solutions
Question 7/10
1 / -0

If f(x) = x e^{x(1 – x)}, then f(x) is

Correct

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Skipped
A
increasing on [– 1/2, 1]

Correct

Wrong

Skipped
B
decreasing on R

Correct

Wrong

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C
increasing on R

Correct

Wrong

Skipped
D
decreasing on [– 1/2, 1]

Solutions
Question 8/10
1 / -0

Correct

Wrong

Skipped
A
16

Correct

Wrong

Skipped
B
28

Correct

Wrong

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C
30

Correct

Wrong

Skipped
D
31

Solutions
Question 9/10
1 / -0

An equation of the circle that is tangent to y = x³ at (1, 1) and has the same second derivative is

Correct

Wrong

Skipped
A
x² + y² + 24x – 28y + 2 = 0

Correct

Wrong

Skipped
B
2(x² + y²) + 12x – 8y – 8 = 0

Correct

Wrong

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C
3(x² + y²) – 24x + 10y + 8 = 0

Correct

Wrong

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D
None of these

Solutions
Question 10/10
1 / -0

An approximate value of cos 40° is

Correct

Wrong

Skipped
A
0.7688

Correct

Wrong

Skipped
B
0.7071

Correct

Wrong

Skipped
C
0.7117

Correct

Wrong

Skipped
D
0.7

Solutions

Question 1/10

y/x

x/y

x2/y2

y2/x2

Question 2/10

decreases on (-∞, ∞)

decreases on (0, ∞)

neither decreases nor increases on (0, ∞)

increases on (-∞, ∞)

Question 3/10

x = 17π/4 is a point of minima

x = 13π/4 is a point of maxima

x = 21π/4 is a point of minima

x = 29π/4 is a point of maxima

Question 4/10

4√2,4

4,2√2

2,√2

2√2,2

Question 5/10

(1) is true. (2) is false.

(1) is false. (2) is true.

(3) and (4) both are true.

(1) and (2) both are true.

Question 6/10

ad – bc < 0

ad – bc > 0

ab – cd > 0

ab – cd < 0

Question 7/10

increasing on [– 1/2, 1]

decreasing on R

increasing on R

decreasing on [– 1/2, 1]

Question 8/10

16

28

30

31

Question 9/10

x2 + y2 + 24x – 28y + 2 = 0

2(x2 + y2) + 12x – 8y – 8 = 0

3(x2 + y2) – 24x + 10y + 8 = 0

None of these

Question 10/10

0.7688

0.7071

0.7117

0.7

x²/y²

y²/x²

x² + y² + 24x – 28y + 2 = 0

2(x² + y²) + 12x – 8y – 8 = 0

3(x² + y²) – 24x + 10y + 8 = 0