MCQOPTIONS
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MCQOPTIONS
This section includes 8 Mcqs, each offering curated multiple-choice questions to sharpen your Curve Tracing knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Which of the following is not correct regarding signs of derivatives? |
| A. | If \(\frac{dy}{dx}>0,\) then the curve is increasing in [a, b] |
| B. | If \(\frac{dy}{dx}<0,\) then the curve is increasing in [a, b] |
| C. | If \(\frac{d^2 x}{dy^2}>0, \) then curve is convex and concave upward (holds water) |
| D. | If \(\frac{d^2 x}{dy^2}>0, \) then curve is concave downward (spills water) |
| Answer» C. If \(\frac{d^2 x}{dy^2}>0, \) then curve is convex and concave upward (holds water) | |
| 2. |
At the point where \(\frac{dy}{dx}=0,\) the tangent is parallel to y axis. |
| A. | False |
| B. | True |
| Answer» B. True | |
| 3. |
What are the tangents to the curve x3+ y3=3axy at the origin? |
| A. | x=0 |
| B. | x=0, y=0 |
| C. | y=0 |
| D. | x=y |
| Answer» C. y=0 | |
| 4. |
Which of the following graphs represent symmetric about the origin? |
| A. | y2=4ax |
| B. | x5+y5=5a2x2y |
| C. | x2=4ay |
| D. | x2+y2=a2 |
| Answer» C. x2=4ay | |
| 5. |
Which of the following is not an example for curve symmetric about y axis? |
| A. | x2=4ay |
| B. | x2=ay |
| C. | y2=4ax |
| D. | x2=2ay |
| Answer» D. x2=2ay | |
| 6. |
If f(x,y)=ayn+(bx+c) yn-1+(dx2+ex+f) yn-2+⋯+un(x)=0…(1), is the algebraic curve of nth order then, what is the condition for the curve to be symmetric about x-axis? |
| A. | Only even powers of x appear in (1) |
| B. | Only odd powers of x appear in (1) |
| C. | yn-1+(dx2+ex+f) yn-2+⋯+un(x)=0…(1), is the algebraic curve of nth order then, what is the condition for the curve to be symmetric about x-axis?a) Only even powers of x appear in (1)b) Only odd powers of x appear in (1)c) Only odd powers of y appear in (1) |
| D. | Only even powers of y appear in (1) |
| Answer» E. | |
| 7. |
Which of the following is the representation of a plane algebraic curve of nth degree? |
| A. | f(x,y)=ayn+(bx+c) yn-1+(dx2+ex+f) yn-2+⋯+un (x)=0 |
| B. | f(x,y)=ayn-1+(bx+c) yn-2+(dx2+ex+f) yn-3+⋯+un (x)=0c) f(x,y)=ayn+byn-1+cyn-2+⋯+un (x)=0d) f(x,y)=ayn+(bx+ |
| C. | yn-1+(dx2+ex+f) yn-2+⋯+un (x)=0b) f(x,y)=ayn-1+(bx+c) yn-2+(dx2+ex+f) yn-3+⋯+un (x)=0c) f(x,y)=ayn+byn-1+cyn-2+⋯+un (x)=0 |
| D. | f(x,y)=ayn+(bx+c) yn+(dx2+ex+f) yn+⋯+un (x)=0 |
| Answer» B. f(x,y)=ayn-1+(bx+c) yn-2+(dx2+ex+f) yn-3+⋯+un (x)=0c) f(x,y)=ayn+byn-1+cyn-2+⋯+un (x)=0d) f(x,y)=ayn+(bx+ | |
| 8. |
Which of the following characteristic is not included in the study of general procedure for tracing the algebraic curve? |
| A. | Symmetry |
| B. | Region or Extent |
| C. | Orthogonality |
| D. | Tangents to the Curve at the origin |
| Answer» D. Tangents to the Curve at the origin | |