MTH201 Quiz 1

Q1. Which of the following is the representation of spherical coordinates

1. $$(r, ,z)$$
2. $$( , , )$$
3. $$( , ,z)$$
4. $$(x, y, z)$$

Correct answer: $$( , , )$$

Q2. In rectangular coordinate system the point (-2,-2) is in

1. third quadrant
2. first quadrant
3. second quadrant
4. fourth quadrant

Correct answer: third quadrant

Q3. $$Face~~ of~~ the~~ parabola~~ y = a{x^2} + bx + c ~~ is~~ opening~~ upward~~ when$$

1. a < 0
2. b < 0
3. a > 0
4. b > 0

Correct answer: a > 0

$${\text{The}}\,\,{\text{partial}}\,\,{\text{derivative}}\,\,{\text{with}}\,\,{\text{respect}}\,\,{\text{to}}\,\,x\,\,{\text = \frac{x}{y}\,\,{\text{is}}\,\_\_\_\_\_\_\_\_\_.$$ A. $$1$$ B. $$x$$ C. $$- {x}{{{y^2}}}$$

D. $${1}{y}$$

Q5. $${\text{If }} ~y = x + t,~ x = {e^u} ~{\text{and}}~ t= sin u, {\text{then by chain rule, }}\frac{{dy}}{{du}} =$$

1. $${e^u} - u$$
2. $$- {e^u} - u$$
3. $$- {e^u} + u$$
4. $${e^u} + u$$

Correct answer: $${e^u} + u$$

Q6. A zero vector has magnitude equal to zero and ---------- direction.

1. Upward
2. Arbitrary
3. Downward
4. No

Correct answer: No

Q7. Which of the following function is not the function of one variable

1. z= g(n) + 2
2. y = f( x, y)
3. m = g(s) + constant
4. y = f(x)

Correct answer: y = f( x, y)

Q8. If the partial derivative (w.r.t ‘x’ or ‘y’) at any point on the surface: “z=f(x,y)” is zero, then tangent plane at that point will be--------to XY-plane.

1. Perpendicular
2. Parallel

Correct answer: Parallel

Q9. $${\text{Value}}\,\,{\text{of}}\,\,{\text{the}}\,\,{\text{function}}\,\,{\text{ }}f(x,{\text{ }}y) = {x^3}y\,\,{\text{at}}\,\,{\text{the}}\,\,{\text{point}}\,({x^2},\,{x^3})\,\,{\text{is}}\,\,\,\_\_\_\_\_\_\_\_\_.$$

1. $${x^6}$$
2. $${x^9}$$
3. $${x^2}.\,{x^3}$$
4. $${x^2}.\,{x^6}$$

Correct answer: $${x^2}.\,{x^3}$$

Q10. $${\text{The}}\,\,{\text{partial}}\,\,{\text{derivative}}\,\,{\text{of}}\,\,f(x,y) = {x^2}{e^{ - y}}\,\,{\text{with}}\,\,{\text{respect}}\,\,{\text{to}}\,\,x\,\,{\text{is _________}}{\text{.}}$$

1. $${x^2}\,{e^{ - y}}$$
2. $$- {x^2}\,{e^{ - y}}$$
3. $${x^2}\,{e^{ - y}}$$
4. $$2x\,{e^{ - y}}$$

Correct answer: $$2x\,{e^{ - y}}$$