Integration and Symmetry Quiz
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Questions and Answers

What is the value of 'z' in the given equation?

  • 398 (correct)
  • 3980
  • 39.8
  • 39800

What is the local minimum of the function f'(x) = 3k (x^2 - 2x)?

  • 3
  • 0
  • 1 (correct)
  • -1

What is the distance between the horizontal tangents of the function f(x) = x^3 - 3x^2 - 9x + 5?

  • 32 (correct)
  • 16
  • 10
  • 26

What is the variance of the given data set?

<p>80 (D)</p> Signup and view all the answers

What is the value of 'k' in the function f(x) = x^3 - 3x^2 - 9x + 5?

<p>1 (D)</p> Signup and view all the answers

How many points are there where the given function is not continuous?

<p>0 (C)</p> Signup and view all the answers

What is the value of the expression $d$ in the context of the given function?

<p>$3$ (B)</p> Signup and view all the answers

Which property ensures that the sum or difference of continuous functions results in a continuous function?

<p>Property of Continuity (D)</p> Signup and view all the answers

What is the value of $a + b + c$ in the context of the given function?

<p>$1$ (A)</p> Signup and view all the answers

Which type of functions are known to be continuous within their domain?

<p>Trigonometric Functions (B)</p> Signup and view all the answers

How many distinct functions are summed up to create the given function?

<p>$3$ (A)</p> Signup and view all the answers

What is the result of $\int_0^1 e^{t} dt$?

<p>$e$ (C)</p> Signup and view all the answers

In the context provided, what does the variable $t$ represent?

<p>A dummy variable in an integral (B)</p> Signup and view all the answers

Based on the given text, is the relation R symmetric?

<p>No (A)</p> Signup and view all the answers

What is the value of $\gcd(a, c)$ if $b = 3$?

<p>$3$ (D)</p> Signup and view all the answers

What type of function is ${x}$ based on the information provided?

<p>Periodic function (C)</p> Signup and view all the answers

In the context of the circle described, what are the coordinates of point A?

<p>(5,0) (B)</p> Signup and view all the answers

What is the angular momentum transferred by the bullet to the door?

<p>2 J - s (C)</p> Signup and view all the answers

What is the moment of inertia of the door about the vertical axis at one of its ends?

<p>4 kg - m^2 (A)</p> Signup and view all the answers

What is the value of angular velocity (ω) when the angular momentum is 4 J - s?

<p>$0.5$ rads$^{-1}$ (B)</p> Signup and view all the answers

What is the total height (in terms of 'g') reached when an object travels for 5 seconds under gravity?

<p>$12.5g$ (A)</p> Signup and view all the answers

What is the acceleration (a) when a force of 20 N acts on an object at an angle of 37 degrees with the horizontal?

<p>$20$ m/s^2$ (B)</p> Signup and view all the answers

If the ratio of angular momentum (L) to angular velocity (ω) is given as $100: \tan 45°$, what is the value of R in terms of L?

<p>$16$ (D)</p> Signup and view all the answers

What is done to detect halogens, nitrogen, and sulfur in an organic compound?

<p>Fusing with sodium metal (D)</p> Signup and view all the answers

Which element is oxidized to carbon dioxide when heating an organic compound with CuO?

<p>Carbon (C)</p> Signup and view all the answers

Which ion will have the highest fourth ionization enthalpy according to the text?

<p>La4+ (D)</p> Signup and view all the answers

What is the purpose of the silver nitrate test mentioned in the text?

<p>Detect type of halogen in haloalkane (D)</p> Signup and view all the answers

Why is it easier to remove an electron from an orbital with lower energy according to the text?

<p>It requires less energy input (B)</p> Signup and view all the answers

How are carbon and hydrogen detected in an organic compound according to the text?

<p>Heating with CuO (C)</p> Signup and view all the answers

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