Explore topic-wise MCQs in Ordinary Differential Equations.

This section includes 5 Mcqs, each offering curated multiple-choice questions to sharpen your Ordinary Differential Equations knowledge and support exam preparation. Choose a topic below to get started.

1.

Which among the following is true for the curve rn = a sin⁡nθ?

A. Given family of curve is Self orthogonal
B. Orthogonal trajectory is rn=k cos⁡nθ where k is an constant
C. Orthogonal trajectory is rn=k cosec⁡nθ where k is an constant
D. Orthogonal trajectory is rn=k sin⁡nθ where k is an constant
Answer» C. Orthogonal trajectory is rn=k cosec⁡nθ where k is an constant
Discussion
2.

Find the orthogonal trajectories of the family r=a(1+sin θ).

A. r=k(sin θ)
B. r2=k(cos θ)2
C. r=k(1-cos θ)
D. r=k(1-sin θ)
Answer» E.
Discussion
3.

The Orthogonal DE for family of parabola y2=4a(x+a) is same as _______(where DE stands for Differential equation)a) DE of parabola y2=4a(x+a)b) DE of parabola y2=4axc) DE of parabola x2=4ayd) DE of parabola x2=4a(y+

A. is same as _______(where DE stands for Differential equation)a) DE of parabola y2=4a(x+a)
B. DE of parabola y2=4ax
C. DE of parabola x2=4ay
D. DE of parabola x2=4a(y+a)
Answer» B. DE of parabola y2=4ax
Discussion
4.

Find the orthogonal trajectories of the family of curves \(\frac{x^2}{a^2} + \frac{y^2}{b^2+k} = 1\) where k is the parameter.

A. x2-y2-3a2 log⁡x-k = 0
B. x2+2y2–\(\frac{a^2}{2}\) log⁡x-k = 0
C. x2+y2-2a2 log⁡x-k = 0
D. 2x2-y2–\(\frac{a^2}{3}\) log⁡x-k = 0
Answer» D. 2x2-y2–\(\frac{a^2}{3}\) log⁡x-k = 0
Discussion
5.

Find the orthogonal trajectories of the family of parabolas y2=4ax.

A. 2x2+y2=k
B. 2y2+x2=k
C. x2-2y2=k
D. 2x2-y2=k
Answer» B. 2y2+x2=k
Discussion