145. Which statement is correct?
(1) The set of points in space that are equidistant from two parallel lines lies in a finite number of planes.
(2) The set of points in space that are equidistant from two parallel lines lies on the perpendicular plane to both of them.
(3) The set of points in space that are equidistant from a point and a line that does not pass through that point lies on a parabolic surface.
(4) The set of points in space such that the distance from each point to two fixed points in space is equal lies on a circle.

147. A triangle has side lengths $13$, $14$, and $15$. What is the side length of the regular hexagon circumscribed about this triangle?
(1) $8$ (2) $\dfrac{8\sqrt{3}}{3}$ (3) $4$ (4) $\dfrac{4\sqrt{3}}{3}$

148. Angle $x\hat{O}y$ and point $M$ are inside the angle such that $2M\hat{O}y = x\hat{O}M$. From point $M$, perpendiculars $MN$ and $MP$ are drawn to the rays $Ox$ and $Oy$ respectively. What is the ratio $\dfrac{MN}{MP}$?
(1) $\dfrac{OP}{ON}$ (2) $\dfrac{OP}{OM}$ (3) $\dfrac{2OP}{ON}$ (4) $\dfrac{2OP}{OM}$

149. Rectangle $ABCD$ is given as shown in the figure below. What is the area of quadrilateral $MENF$?
[Figure: Rectangle $ABCD$ with vertices labeled, $A$ top-left, $B$ top-right, $C$ bottom-right, $D$ bottom-left; points $M$ on left side, $N$ on top side, $E$ on bottom side; dimensions $2$ and $4$ marked on left side, $1$ and $8$ marked on bottom.]
(1) $\dfrac{154}{9}$ (2) $13$ (3) $\dfrac{47}{3}$ (4) $16$

150. In a triangle with an angle of $138°$, what is the smallest angle (in degrees) between the two external bisectors?
(1) $21$ (2) $11.5$ (3) $33.5$ (4) $42$
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151. In the figure below, the radius of the circle is 3 units. What is the measure of arc $\widehat{EDC}$ in degrees?
[Figure: Circle with center O, points A, B, C, D, E on the circle, angle at B is $70°$]

• [(1)] $80°$
• [(2)] $90°$
• [(3)] $100°$
• [(4)] $120°$

156 -- Which of the following statements is correct?
A -- In $\beta^-$ decay, the emitted electron did not exist inside the nucleus, and furthermore it is not one of the atomic orbital electrons.
B -- In $\beta^+$ decay, the emitted particle from the nucleus has the same mass as the electron.
C -- Most nuclei after $\beta$ decay remain in a stable state.
D -- In $\beta^+$ decay, one of the neutrons inside the nucleus is converted into a proton and a positron.
(1) A and B (2) A and C (3) B and D (4) B and C

157 -- The figure below shows the velocity--time graph of a particle moving along the X-axis. The average velocity in the direction opposite to the direction of motion, in meters per second, is:
[Figure: velocity-time graph with $V(\frac{\text{m}}{\text{s}})$ on vertical axis and $t(\text{s})$ on horizontal axis. The graph starts at $V = 6$ m/s at $t = 0$, decreases linearly to $V = -12$ m/s, then increases back, crossing zero at $t = 20$ s.]

• [(1)] zero
• [(2)] 6
• [(3)] 8
• [(4)] 9

158 -- A particle moves along the X-axis with constant acceleration. If the velocity of the particle at $t = 0$ is in the positive X-direction, and the average velocity vector during the first 10 seconds of motion is $\vec{v}_{av} = (7.5\,\frac{\text{m}}{\text{s}})\,\hat{i}$ and the average velocity in this interval is $8.5\,\frac{\text{m}}{\text{s}}$, the distance traveled during the first 2 seconds of motion is how many meters?
(1) $5$ (2) $15$ (3) $25$ (4) $35$

159 -- The position--time graph of a particle moving with constant acceleration is shown below. The displacement during the time interval from $t_1 = 0\,\text{s}$ to $t_2 = 8\,\text{s}$ is how many meters?
[Figure: position-time graph $x(\text{m})$ vs $t(\text{s})$, showing a parabolic curve. The curve passes through $x = 3$ m at $t = 3$ s and reaches $t = 8$ s on the horizontal axis.]
$$\frac{5}{17} \quad (1)$$
$$\frac{5}{14} \quad (2)$$
$$\frac{8}{17} \quad (3)$$
$$\frac{9}{14} \quad (4)$$
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160- A particle moves with constant speed along the x-axis and passes through the origin at moments $t_1 = 3\,\text{s}$ and $t_2 = 5\,\text{s}$, and at the moment that it reaches the position $x = -1\,\text{m}$, the direction of motion reverses. The average speed of the particle from moment $t_1 = 0\,\text{s}$ to $t_2 = 5\,\text{s}$ is how many meters per second?
$$\frac{13}{5} \ (1) \qquad\qquad 3 \ (2) \qquad\qquad \frac{17}{5} \ (3) \qquad\qquad 6 \ (4)$$

161- The figure below shows the variation of the elastic force of three springs as a function of their elongation. If the elastic force $F_e = 30\,\text{N}$ elongates spring $S_2$ by 4 cm, by how many centimeters do the lengths of springs $S_1$ and $S_2$ increase, respectively?
[Figure: Graph of $F_e$ vs. $x$ showing three lines $S_1$, $S_2$, $S_3$ with increasing slopes]

• [(1)] 3 and 6
• [(2)] 6 and 2
• [(3)] 8 and 2
• [(4)] 9 and 3

162- A cube-shaped block of mass $5\,\text{kg}$ is tied to a string and placed on a horizontal surface with a constant horizontal force of $15\,\text{N}$. Starting from rest, after 2 seconds the string breaks. If the coefficient of kinetic friction is $0.2$, what is the total distance the block travels from the start of motion until it comes to rest? $\left(g = 10\,\dfrac{\text{m}}{\text{s}^2}\right)$
$$1.5 \ (1) \qquad\qquad 2 \ (2) \qquad\qquad 2.5 \ (3) \qquad\qquad 3 \ (4)$$

163- A light spring with constant $200\,\dfrac{\text{N}}{\text{m}}$ is attached to the ceiling of an elevator, and a mass $m = 5\,\text{kg}$ is hung from it. The elevator descends with acceleration $2\,\dfrac{\text{m}}{\text{s}^2}$ and the length of the spring is $L_1$. When the elevator descends with acceleration $1\,\dfrac{\text{m}}{\text{s}^2}$, the spring becomes $L_2$. What is the difference $L_2 - L_1$ in centimeters? $\left(g = 10\,\dfrac{\text{m}}{\text{s}^2}\right)$
$$15 \ (1) \qquad\qquad 7.5 \ (2) \qquad\qquad 5 \ (3) \qquad\qquad 2.5 \ (4)$$

164- A particle moves with constant speed $v = 10\pi\,\dfrac{\text{m}}{\text{s}}$ on a circular path of radius $20\,\text{m}$. The average centripetal acceleration of this particle in each second is how many times its centripetal acceleration?
$$\frac{3\sqrt{2}}{\pi} \ (1) \qquad\qquad \frac{5}{\pi} \ (2) \qquad\qquad 5\sqrt{2} \ (3) \qquad\qquad \sqrt{2} \ (4)$$
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165. The equation of oscillatory motion in SI units is $x = 0.02\cos\dfrac{\pi}{2}t$. The average velocity of the oscillator in the time interval $t_1 = \dfrac{1}{12}$ s to $t_2 = \dfrac{25}{12}$ s is how many centimeters per second?
(1) $1$ (2) $2$ (3) $4$ (4) $8$

166. The figure below shows a snapshot of a transverse wave on a string at moment $t_1$. At moment $t_2 = t_1 + \dfrac{9}{400}$ s, which of the following is correct?
[Figure: A transverse wave on a string moving with $v = 10\,\dfrac{\text{m}}{\text{s}}$ to the right; points A and B are marked on the wave; x-axis in cm with value 30 shown; y-axis shown.]

1. The velocity of point B is zero.
2. The velocity of point A is maximum.
3. Point A is moving in the negative direction.
4. Point B is moving in the negative direction.

167. The displacement–time graph of an oscillator with mass 50 grams is shown below. The mechanical energy of the oscillator is how many joules? $(\pi^2 = 10)$
[Figure: x(cm) vs t(s) graph; amplitude 4 cm, $t_1 = \dfrac{2}{15}$ s marked, minimum value $-4$ cm shown.]
(1) $\dfrac{1}{250}$ (2) $\dfrac{1}{25}$ (3) $\dfrac{2}{5}$ (4) $\dfrac{1}{50}$

168. A sound device with sound level $\beta_1 = 28\,\text{dB}$ and another sound device with sound level $\beta_2 = 92\,\text{dB}$ produce sound together. The intensities corresponding to these two levels are $I_1$ and $I_2$ respectively $\left(\dfrac{W}{m^2}\right)$. What is $\dfrac{I_2}{I_1}$? $(\log 2 = 0.3)$
(1) $2.5\times10^6$ (2) $2.5\times10^8$ (3) $4\times10^6$ (4) $4\times10^8$

169. The sum of the first two harmonics of a string fixed at both ends is 375 Hz. If the length of the string is 40 cm and its mass is 10 grams, the tension in the string is how many newtons?
(1) $180$ (2) $200$ (3) $360$ (4) $250$
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Download of Exam Questions and Answer Key from Riazisara Website
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170. According to the figure below, a light ray travels from air into a transparent medium and upon entering medium (2), it deviates $16^\circ$ from the initial direction and refracts. If the wavelength of light in medium 2 is $\frac{1}{\Lambda}\ \mu\text{m}$ of the wavelength of light in air, what is the frequency of that light?
[Figure: A light ray incident at $\Delta r^\circ$ from the normal, passing from air (medium 1) into medium (2)]
$$\left(\sin 53^\circ = 0.8,\quad v = 3\times10^8\ \frac{\text{m}}{\text{s}} = \text{speed of light in air}\right)$$

(1) $6\times10^{14}$

(2) $6\times10^{15}$

(3) $4.7\times10^{14}$

(4) $4.7\times10^{15}$

171. According to the figure below, a light ray enters a transparent medium from air and refracts. This ray travels from point A to point B in how many nanoseconds?
$$\left(c = 3\times10^8\ \frac{\text{m}}{\text{s}}\right)$$
[Figure: A ray incident at $45^\circ$ from the normal entering a medium with $n_1=1$ (air) and $n_2=\sqrt{2}$, with vertical distance $15\sqrt{3}$ cm between A and B]

(1) $\dfrac{\sqrt{2}}{2}$

(2) $1$

(3) $\sqrt{2}$

(4) $2$

172. In a photoelectric experiment, the threshold frequency of the metal is $\frac{5}{4}\times10^{15}$ Hz. If the energy of each photon incident on the metal is $4.125\times10^{-19}$ J, how many photoelectrons are produced per meter per second?
$$\left(h = 4\times10^{-15}\ \text{eV·s},\quad m_e = 9\times10^{-31}\ \text{kg},\quad c = 1.6\times10^{-19}\ \text{C}\right)$$

(1) $\dfrac{1}{6}\times10^5$

(2) $\dfrac{1}{6}\times10^6$

(3) $\dfrac{5}{7}\times10^4$

(4) $\dfrac{5}{7}\times10^5$

173. Which of the following cannot be explained for hydrogen atoms using the Bohr atomic model?
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174. In the hydrogen atom in the Balmer series ($n' = 2$), the longest wavelength of the emitted light is how many nanometers? $$\left[R = 0.01\ (\text{nm})^{-1}\right]$$

(1) $220$

(2) $330$

(3) $400$

(4) $500$