186. The velocity–position equation for a simple harmonic oscillator in SI units is $1 = V^2 + 250x^2 = \dfrac{25}{\pi^2}$. The oscillation frequency in hertz is?

(1) $\dfrac{1}{2}$ (2) $1$ (3) $2$ (4) $5$

187. A simple pendulum oscillates at a fixed location with a period of 2 seconds and completes N full oscillations in 2.6 minutes. By what percentage should we decrease or increase the length of the pendulum so that in the same time duration and at the same location, $18 - N$ full oscillations are completed?
(1) 69\% decrease (2) 69\% increase (3) 31\% decrease (4) 31\% increase

188. A loop with radius $20\,\text{cm}$ is placed in a uniform magnetic field perpendicular to the field lines on the surface of the loop. The electrical resistance of the loop is $0.3\,\Omega$. If the magnetic field changes harmonically with time, how many tesla per second must it change so that the current in the loop is $0.2\,\text{A}$? $(\pi = 3)$

(1) $0/2$ (2) $0/8$ (3) $2$ (4) $8$

189. A coil with 200 turns is placed in a uniform magnetic field $\mathbf{B} = 0.01\,\text{T}$ with a constant angular velocity. One of its diameters serves as the axis of rotation. The area of each turn is $50\,\text{cm}^2$ and the maximum induced EMF is 3 volts. The period of rotation of the coil in seconds is?

(1) $\dfrac{1}{150}$ (2) $\dfrac{\pi}{150}$ (3) $\dfrac{1}{300}$ (4) $\dfrac{\pi}{300}$

190. Two ends of a string are fixed at two points and a standing wave is formed on it. The wavelength is $16\,\text{cm}$. Which of the following measurements given in centimeters cannot be the length of this string?

(1) $24$ (2) $40$ (3) $60$ (4) $120$

191. The profile of a transverse wave on a string at moment $t = 0\,\text{s}$ is shown in the figure below. If $\dfrac{1}{300}\,\text{s}$ is the time for one full wavelength to pass, how many seconds does it take for point M to reach position $x = 2\,\text{cm}$ from point M?

[Figure: A transverse wave profile showing a sinusoidal wave. The y-axis is labeled $y\,(\text{cm})$ with amplitude 2, the x-axis is labeled $x\,(\text{cm})$. Points N and M are marked on the wave. The wave travels with velocity $V = 40\,\text{m/s}$ to the right. The wavelength appears to be $30\,\text{cm}$.]

(1) $\dfrac{1}{150}$ (2) $\dfrac{1}{60}$ (3) $\dfrac{7}{600}$ (4) $\dfrac{1}{120}$
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192. The speed of propagation of a transverse wave on a string is $100\,\dfrac{\text{m}}{\text{s}}$. This wave has a wavelength of $0.5$ meters and an amplitude of 2 millimeters on the string. If the $x$-axis is along the string and the wave propagates in the direction opposite to the $x$-axis, what is the wave function in SI units?

(1) $u_x = 2\times10^{-3}(120\pi t - 6\pi y)$ (2) $u_y = 2\times10^{-3}(400\pi t - 4\pi x)$
(3) $u_x = 2\times10^{-3}(120\pi t + 6\pi y)$ (4) $u_y = 2\times10^{-3}(400\pi t + 4\pi x)$

193. The frequency of a car horn is $900\,\text{Hz}$ and the car moves with a speed of $20\,\dfrac{\text{m}}{\text{s}}$ around a stationary listener and moves toward the rocky surface. If the sound frequency reaching the listener from the horn is $f_1$ and the sound frequency reaching the listener after reflection from the rock is $f_2$, then $f_1$ and $f_2$ are respectively how many hertz?
$$\left(V = 340\,\frac{\text{m}}{\text{s}}\right)$$
(1) $1012.5\ ,\ 956.25$ (2) $956.25\ ,\ 850$
(3) $1012.5\ ,\ 1012.5$ (4) $1012.5\ ,\ 850$

194. In the figure of a U-tube, the frequency is $680$ Hz and the cross-sectional area of the tube in each branch is one square centimeter. If the speed of sound propagation in the medium is $340\,\dfrac{\text{m}}{\text{s}}$, and resonance is to be achieved inside the tube, which of the following actions is appropriate?

[Figure: U-tube with two vertical branches, height labeled $65\,\text{cm}$, with water at the bottom]

(1) Pour $2.5$ cubic centimeters of water into one of the tubes.
(2) Pour $5$ cubic centimeters of water into one of the tubes.
(3) Remove $2.5$ cubic centimeters of water from the tube.
(4) Remove $5$ cubic centimeters of water from the tube.

195. In Young's experiment, if the distance between the two slits is $\dfrac{1}{2}$ and the distance of the screen from the two slits is $\dfrac{0.8}{1}$, but the wavelength of light does not change, the width of each fringe becomes how many times?

(1) $\dfrac{1}{2}$ (2) $\dfrac{2}{5}$ (3) $\dfrac{3}{4}$ (4) $\dfrac{4}{3}$
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196- Which photons related to electromagnetic waves have the most energy?
(1) Red light (2) Blue light (3) UHF radio waves (4) VHF radio waves

197- If in the hydrogen atom the electron transitions from $n = 2$ to $n = 4$, its speed becomes how many times?
(1) $2$ (2) $4$ (3) $\sqrt{2}$ (4) $\dfrac{1}{2}$

198- In a photoelectric experiment, the graph of stopping voltage versus frequency of incident light on two metals A and B is shown in the figure below. If light with frequency $10^{15}$ Hz is incident on both metals; the stopping voltage of metal A is $\dfrac{1}{2}$; what is the stopping voltage of metal B? $(h = 4\times10^{-15}\ \text{ev.s})$
[Figure: Graph of stopping voltage $V_0$ (vertical axis) vs. frequency $f(10^{15}\ \text{Hz})$ (horizontal axis), showing two lines A and B intersecting the horizontal axis at different points. Line A has a steeper slope. The vertical axis shows values $\frac{1}{2}$ and $\frac{1}{4}$, and the horizontal axis shows values $\frac{3}{4}$ and $1$.]
(1) $\dfrac{1}{2}$ (2) $\dfrac{3}{2}$ (3) $1$ (4) $2$

199- Which of the following statements about semiconductors is correct?

1. [(1)] Transistors exist only in P-type semiconductors.
2. [(2)] At very low temperatures, semiconductors act like insulators.
3. [(3)] At very low temperatures, semiconductors act like conductors.
4. [(4)] In semiconductors, as temperature increases, electrical resistivity also increases.

200- Which of the following statements about atomic nuclei is correct?

1. [(1)] Most isotopes are unstable and decay over time.
2. [(2)] Nuclear (strong) forces are very short-range compared to Coulomb forces.
3. [(3)] The mass of a nucleus equals the total mass of the nucleons forming it.
4. [(4)] The ratio of neutrons to protons is the same for all stable isotopes of an element.

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201- Chlorine in nature has two isotopes with atomic masses of 35 amu and 37 amu, and carbon has two isotopes with atomic masses of

202- The successive ionization energies of an element from period 2 are given below in $\text{kJ.mol}^{-1}$; the difference between the lowest and highest of these values is one unit, and in the valence shell of this atom there are several electrons with spin $+\dfrac{1}{2}$. (Choose the answer from right to left.)

$IE_1$	$IE_2$	$IE_3$	$IE_4$	$IE_5$	$IE_6$
1500	2850	4580	7480	9440	53270

(1) $3.0$ (2) $3.4$ (3) $4.8$ (4) $4.4$

203- All of the following statements are correct, except:

1. The sub-shell $p$ in the last shell of all metalloid elements is empty.
2. Some metalloid elements, like some main-group elements, have one type of valence electron.
3. In fifth-period transition elements, only in $_{48}\text{Cd}$, the total quantum spin number of electrons equals zero.
4. In metals of each period, as the atomic number increases, the number of electrons in the valence shell of the atom and also the metallic character increase.

204- Which statement about the third-period elements of the periodic table is correct?

1. The magnitude of the first ionization energy is stable in three groups of them as: $1A > 3A > 2A$.
2. As the atomic number increases, the shielding effect of inner electron layers and the effective nuclear charge on them increases.
3. Among them, two metalloid elements exist whose valence shell contains 4 and 5 electrons respectively.
4. The first ionization energy of them from their own group in period 2 is lower, and the most electronegative of them is $S_{16}$.

205- If one ton of gypsum (calcium sulfate dihydrate) with a purity of 85\% is heated to produce solid anhydrous product, how many kilograms of water are obtained? (Grams on kcal have no effect.)
$$(Ca = 40,\ S = 32,\ O = 16,\ H = 1 : \text{g.mol}^{-1})$$
(1) $911$ (2) $895$ (3) $872$ (4) $761$

206- If in the structure of the dichromate ion, around each atom, 8 electrons exist, how many pairs of bonding electrons are there? How many covalent bonds does one oxygen atom in it have?
(1) $2$ (2) $2.5$ (3) $3$ (4) $3.5$
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207- In which chemical bond do the non-bonding electron pairs have equal numbers?

• [(1)] ethanol, chloroatane (2) ethylene glycol, acetic acid
• [(3)] oxalic acid, formic acid (4) carbonate ion, sulfur dioxide

208- Considering the structural formula of glucose, how many C–C bonds exist in its molecule and how many atoms in it have four electrons?

• [(1)] $11\ ,\ 6$ (2) $12\ ,\ 6$ (3) $12\ ,\ 5$ (4) $11\ ,\ 5$

209- The intermolecular attractive force among the elements of group ............... is of type ............... periodic table and in group ............... decreases with increasing atomic mass of the elements, their melting and boiling points.

• [(1)] 1A, nonpolar dipole–dipole, $5A$ (2) 7A, dipole–dipole, $5A$
• [(3)] 7A, van der Waals, metallic bonds, dipole–dipole (4) 7A, van der Waals, dipole–dipole, metallic bonds

210- In which two compounds given below, the number of carbon isomers is equal?

• [(1)] benzaldehyde, 2-heptanone (2) ethyl butanoate, heptane
• [(3)] trimethylamine, 2-methylpropane (4) 2 and 5-dimethylhexane, naphthalene