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Advance Math Quiz
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Question 1 of 10
1. Question
1 pointsLet a and b be non – zero real numbers. Then, the equation \(\left( {a{x^2} + b{y^2} + c} \right)\left( {{x^2} – 5xy + 6{y^2}} \right) = 0\)
represents
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Question 2 of 10
2. Question
1 pointsThe total number of local maxima and local minima of the function \(f\left( x \right) = \left\{ {\frac{{{{\left( {2 + x} \right)}^3},–3 < x \le –1}}{{{x^{2\beta }},–1 < x < 2}}} \right.\) is
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Question 3 of 10
3. Question
1 pointsLet \(g\left( x \right) = \frac{{{{\left( {x – 1} \right)}^n}}}{{\log {{\cos }^m}\left( {x – 1} \right)}};0 < x < 2\) m and n are integers, \(m \ne 0,n > 0\)
and let p be the Left hand derivative of \(\left {x – 1} \right{\rm{ at}}\,x = 1\) If \(\mathop {\lim }\limits_{x \to {1^ + }} g\left( x \right) = p\) then
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Question 4 of 10
4. Question
1 pointsIf \(0 < x < 1\) then \({\left[ {{{\left\{ {x\cos \left( {{{\cot }^{ – 1}}x} \right) + \sin \left( {{{\cot }^{ – 1}}x} \right)} \right\}}^2} – 1} \right)^{1/2}}\)
is equal to
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Question 5 of 10
5. Question
1 pointsLet f(x) be a continuous function such that f(x) does not vanish for all If \(\int_2^3 {f(x)dx} = \int_{ – 2}^3 {f(x)dx} \) then f(x), \(x \in R,\)
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Question 6 of 10
6. Question
1 pointsA company’s profit P (in dollars) from selling x units of a product can be modeled by \(P = 500x – \frac{{{x^2}}}{4}\) The sales are deceasing at a rate of 10 units per day. The rate of change in the profit (in dollars per day) when 500 units have been sold is
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Question 7 of 10
7. Question
1 pointsFind the area of the region bounded by the graphs of \(f\left( x \right) = 3{x^3} – {x^2} – 10x\) and \(g\left( x \right) = – {x^2} + 2x\)
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Question 8 of 10
8. Question
1 pointsA soft ball league has 13 teams, if every team must play with a every other team, once in the first round of league play, how many games must be scheduled?
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Question 9 of 10
9. Question
1 pointsSolve the differential equation \({\left( {xdx + ydy + xdz} \right)^2}z = \left( {{z^2} – {x^2} – {y^2}} \right)\left( {xdx + ydy + zdz} \right)dz\)
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Question 10 of 10
10. Question
1 pointsThe rate of change of y is proportional to y. When t = 0, y = 2 and when t = 2, y = 4 What is the value of y when t = 3?
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