Differential Equations - Online Test
Q1. Forming a differential equation representing the given family of curves by eliminating arbitrary constants a and b from y = (a cosx + b sinx) yields the differential equation
Answer : Option D
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Q2. Differential equation of the family of circles touching the y-axis at origin is
Answer : Option A
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Q3. Differential equation of the family of parabolas having vertex at origin and axis along positive y-axis is
Answer : Option B
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Q4. Differential equation of the family of ellipses having foci on y-axis and centre at origin is
Answer : Option A
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Q5. Find the equation of a curve passing through the point (0, 0) and whose differential equation is y′ = sin x.
Answer : Option A
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Q6. Find the equation of a curve passing through the point (0, –2) given that at any point (x, y) on the curve, the product of the slope of its tangent and y coordinate of the point is equal to the x coordinate of the point.
Answer : Option B
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Q7. At any point (x, y) of a curve, the slope of the tangent is twice the slope of the line segment joining the point of contact to the point (– 4, –3). Find the equation of the curve given that it passes through (–2, 1).
Answer : Option D
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Q8. Solution of is
Answer : Option C
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Q9. Variable separation method can be used to solveFirst Order, First Degree Differential Equations in which y’ is of the form.
Answer : Option B
Explaination / Solution:
y’ = h(x)g(y) since we can segregate functions of y with dy and x with dx.
Q10. Solution of is
Answer : Option D
Explaination / Solution:
