Geometry Regions Quiz

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What is the distance between L and M2?

20 cm

Where is the point object S placed?

At the mid-point between L and M2

When does one of the images coincide with S?

When the distance between L and M1 is $n/7$ cm

In the experiment to determine the focal length of a thin convex lens, what are the given values?

<p>Object distance = 10 ± 0.1 cm, image distance = 20 ± 0.2 cm</p> Signup and view all the answers

What is the composition of the gas mixture in the closed container?

<p>2 moles of an ideal monatomic gas and 1 mole of an ideal diatomic gas</p> Signup and view all the answers

What is the height of the person and the lamp post?

<p>Person: 1.6 m, Lamp post: 4 m</p> Signup and view all the answers

At 𝑡 = 0.2 s, what is the magnitude of the induced emf in Volts?

<p>0.07</p> Signup and view all the answers

What is the magnitude of the magnetic force in Newton at 𝑡 = 0.2 s?

<p>0.14</p> Signup and view all the answers

At 𝑡 = 0.2 s, how much power is dissipated as heat in Watts?

<p>1.20</p> Signup and view all the answers

What is the magnitude of the terminal velocity of the rod in m s−1?

<p>0.12</p> Signup and view all the answers

Which list correctly matches the values at 𝑡 = 0.2 s to their corresponding parameters?

<p>𝑃 → 4, 𝑄 → 3, 𝑅 → 1, 𝑆 → 2</p> Signup and view all the answers

According to the given information, what is the value of 𝑒 −1?

<p>0.4</p> Signup and view all the answers

What is the number of real solutions to the equation $2 \cos(2x) - 3 \tan^{-1}(\tan x) = 1$ in the set $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$?

<p>4</p> Signup and view all the answers

What is the maximum value of the function $f(x)$ defined in the question, if the area of the region bounded by the curves $x = 0$, $x = 1$, $y = 0$, and $y = f(x)$ is 4?

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

What is the value of $x$ in the expression $\frac{\pi}{2} + \tan^{-1}(x) = \frac{3\pi}{4}$?

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

What is the value of $x$ in the expression $\frac{\pi}{2} + \tan^{-1}(x) = \frac{3\pi}{4}$?

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

What is the value of $\cos(2x)$ in the equation $2 \cos(2x) - 3 \tan^{-1}(\tan x) = 1$?

<p>$\frac{1}{2}$</p> Signup and view all the answers

What is the value of $\int_0^1 g(x) dx$?

<p>$\frac{1}{2}$</p> Signup and view all the answers

If $f(x) = x^2$ for all $x \in (0, 1)$, then $\int_0^1 f(x) g(x) dx$ is equal to

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

If $g(x) = \frac{1}{x^2}$ for all $x \in (0, 1)$, then $\int_0^1 g(x) dx$ is equal to

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

If $f(x) = \frac{1}{x}$ for all $x \in (0, 1)$, then $\int_0^1 f(x) g(x) dx$ is equal to

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

If $g(x) = \frac{1}{x^3}$ for all $x \in (0, 1)$, then $\int_0^1 g(x) dx$ is equal to

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

If $f(x) = x^3$ for all $x \in (0, 1)$, then $\int_0^1 f(x) g(x) dx$ is equal to

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

What is the resonant angular frequency of the LCR circuit?

<p>$105 \text{ rad s}^{-1}$</p> Signup and view all the answers

What is the current amplitude at resonance, $I_0$, in mA?

<p>44.4</p> Signup and view all the answers

What is the quality factor of the LCR circuit?

<p>18</p> Signup and view all the answers

What is the bandwidth of the LCR circuit in rad s^-1?

<p>2250</p> Signup and view all the answers

What is the peak power dissipated at resonance in Watts?

<p>400</p> Signup and view all the answers

What is the value of the inductance $L$ in the LCR circuit?

<p>50 mH</p> Signup and view all the answers

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