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</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</p> Signup and view all the answers

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

    <p>0</p> Signup and view all the answers

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

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

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

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

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

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

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

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

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

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

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

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

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

    <p>No</p> Signup and view all the answers

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

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

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

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

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

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

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

    <p>2 J - s</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</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$^{-1}$</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>$12.5g$</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$</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>$16$</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</p> Signup and view all the answers

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

    <p>Carbon</p> Signup and view all the answers

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

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

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