Partial Derivatives
Curriculum and historical examination lineage for Partial Derivatives under Unit 2 (Functions of Several Variables) of Calculus And Linear Algebra (21MAB101T) at SRMIST.
Historical appearance distribution across SRMIST Formative Tests (CT1, CT2) and University End Semester examinations.
Factual marks weightage of questions asked on this topic in historical examinations.
Question templates that recur across multiple examination cycles with similar conceptual stems.
“If $u$ and $v$ are functionally dependent then their Jacobian value is _________ (A) $0$ (B) $1$...”
“The locus of center of curvature is called (A) Involute (B) Evolute (C) Radius of curvature (D)...”
“The radius of curvature of y = e^x at x = 0 is (A) 2\sqrt{2} (B) \frac{2}{\sqrt{2}} (C)...”
“A curve which touches each member of a family of curves is called _________ (A) Evolute (B)...”
“(a) Find the radius of curvature for the curve $x = a(\cos t + t \sin t), y = a(\sin t - t \cos...”
Representative historical questions extracted directly from SRMIST examination papers.
If x = r \cos \theta, y = r \sin \theta verify that \frac{\partial(x, y)}{\partial(r, \theta)} \frac{\partial(r, \theta)}{\partial(x, y)} = 1.
Find $\frac{dy}{dx}$ and Jacobian $\frac{\partial(x,y)}{\partial(u,v)}$.
Find the derivative using partial differentiation. (a) Find $\frac{dz}{dt}$ for given functions. (b) Find Jacobian $\frac{\partial(u,v)}{\partial(x,y)}$.
(a) Find the radius of curvature for the curve $x = a(\cos t + t \sin t), y = a(\sin t - t \cos t)$. --- OR --- 24. Find the envelope of the family of lines $y = mx - am^3$. (b)...
Find the envelope of the family of lines $y = mx - am^3$. (b) Find the envelope of the family of lines $y = mx - am^3$.
Examinations where questions for Partial Derivatives have appeared.
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