Islamic University of Technology ইসলামিক ইউনিভার্সিটি অব টেকনোলজি ভর্তি পরীক্ষা ২০২৩-২০২৪

Bangladesh will launch a geo-stationary satellite of mass 3500 kg at an orbital distance h from the earth surface as shown in the following figure with given condition. $\mathrm{E}=$ Earth, $\mathrm{S}=$ Geo-stationary satellite, time period =24 =24 Hours. $R=6.4 \times$ $10^{6} \mathrm{~m}, \mathrm{M}=6 \times 10^{24} \mathrm{~kg}, \mathrm{G}=6.7 \times$ $10^{-11} \mathrm{Nm}^{2} \mathrm{~kg}^{-1}$ . What will the height of the satellite to be launched?

An ice piece of 200 grams has been dropped from a certain height. For this reason, ice melts 10% 10 % due to falling by created heat. Here, total mechanical energy is converted to heat energy. The specific latent heat of fusion of ice is 336000 $\mathrm{Jkg}^{-1}$ and specific heat of water is $4200 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}$ Find the height from where the ice piece was dropped? Assume $\mathrm{g}=9.81 \mathrm{~ms}^{-2}$ .

If a mass of 5 kg is hung at lower end of a spring, the spring elongates by 1 cm . If another 2 kg mass is attached to the lower end of the spring, then calculate the further increase of length of the spring.

A simple harmonic wave is moving through air along +X axis and its amplitude is 4 cm , velocity is $40 \mathrm{~ms}^{-1}$ and frequency is 400 Hz . What will be the displacement of the progressive wave at 10 m distance from origin after 6 sec ?

In how many dB, $10^5$ watt sound intensity is stronger than 10 watt sound intensity?

A pendulum with effective length 10 cm has mass of the bob 50 gm. By pulling the bob in one side, the thread is made horizontal and then released. When the thread made an angle of 30 $\degree$ with the horizontal line, then what is the kinetic energy of the bob?

Which is not a fundamental postulates of gas molecules?

On a foggy morning, two approaching bus drivers spot each other at 80 m distance. The speeds of the two buses are $72 \mathrm{kmh}^{-1}$ and $60 \mathrm{kmh}^{-1}$, respectively. The drivers press their respective brake pedals immediately after spotting each other. If the retardation of each bus is $5 \mathrm{~ms}^{-2}$ . What is the total distance covered by the two buses before coming to rest?

Three masses are placed at the corners of an equilateral triangle as shown below. Find the center of mass of the system.

An airplane passenger has $100 \mathrm{~cm}^{3}$ of air in his stomach just before the plane takes off from a sealevel airport. What volume will the air have at cruising altitude if cabin pressure drops to $7.50 \times$ $10^{4} \mathrm{Nm}^{-2}$?

A balloon partially filled with helium has a volume of $30 \mathrm{~m}^{3}$ at the earth's surface where pressure is 76 cm Hg and temperature is $27^{\circ} \mathrm{C}$ . What will be the increase in volume of gas if balloon rises to a height, where pressure is 7.6 cm Hg and temperature is $-54^{\circ} \mathrm{C}$?

What is the force acting on proton that is in a $4.0 \times 10^{4} \mathrm{Vm}^{-1}$ uniform electric field?

Which of the following does show the change in electric current (I) with the change in potential difference (V) of two ends of a constant resistance?

In closed circuit ABDA which equation is correct according to Kirchhoff's voltage law?

Refer to the following figure, what is the correct stored energy in the circuit?

Radii of curvature of a double convex lens of refractive index in air are 6 cm and 12 cm respectively Refractive index of lens is $\frac{3}{2}$ . What is the focal length of the lens?

A wire of resistance $10 \Omega$ is stretched 50% 50 % . If the volume remains constant, find the new resistance.

If an electron moves at velocity of $10^{6} \mathrm{~ms}^{-1}$ in a uniform magnetic field of $10^{5}$ gauss making an angle of $30^{\circ}$ with the field, find the force acting on the electron.

Focal lengths of the objective and eye piece of an astronomical telescope are respectively 40 cm and 10 cm . Calculate the ratio of the length of the instrument and magnification by it for focusing in the least distance of distinct vision.

An astronaut went in a rocket at velocity $1.5 \times 10^{8} \mathrm{~ms}^{-1}$ to $\mathrm{KN}-1$ planet. Length of the rocket on earth was 100 m . What will be the length of the moving rocket measured from the earth?

After 6000 years if a radioactive material becomes $\frac{1}{64}$ th part, then what is its half-life?

In a common emitter configuration, a transistor has $\beta=100$ and input resistance is $5 \mathrm{k} \Omega$ . If the peak value of ac input voltage is 0.1 volt, what is the peak value of collector current?

The electron and proton of an atom are separated by $8.5 \times 10^{-10} \mathrm{~m}$ . Find the ratio between the electric force and the gravitational force between the two particles. [Electron charge $=-1.6 \times$ $10^{-19} \mathrm{C}$, Electron mass $=9.11 \times 10^{-31} \mathrm{~kg}$, Proton mass $=1.67 \times 10^{-27} \mathrm{~kg}$, Gravitational Constant $\mathrm{G}=6.67 \times 10^{-11} \mathrm{Nm}^{2} \mathrm{~kg}^{-2}$ ]

For the circuit shown in the figure, the switch $S$ is initially open, and the capacitor voltage is 70 V. The switch is then closed at time $\mathrm{t}=0 \mathrm{~s}$ . Calculate the time required by the circuit for having a current of $5 \mu \mathrm{~A}$ .

A ray of light, emitted beneath the surface of an unknown liquid with air above it, undergoes total internal reflection as shown in the figure below. What is the index of refraction for the liquid?

Refer to the following figure, what is the value of $V_{0}$ across the diode?

At what net rate does heat radiate from a $275 \mathrm{~m}^{2}$ black roof on a night when the roof's temperature is $30.0^{\circ} \mathrm{C}$, and the surrounding temperature is $15.0^{\circ} \mathrm{C}$? The emissivity of the roof is 0.90 [Stefan-Boltzamann Constant $=5.67 \times$ $10^{8} \mathrm{Js}^{-1} \mathrm{~m}^{-2} \mathrm{~K}^{-4} \mathrm{]}$ .

UV radiation having a 300 nm wavelength falls on uranium metal, ejecting 0.5 eV electrons. What is the binding energy of electrons to uranium metal? [Planck's constant $=6.63 \times 10^{-34} \mathrm{kgm}^{2} \mathrm{~s}^{-1}$ ]

Find out the expression of y y for the following logic circuit.

In a single slit diffraction experiment, a slit of width 'd' is illuminated by red light of wavelength 650 nm . For what value of ' $d$ ' will the first maximum fall at an angle of diffraction of $30^{\circ}$?

In a heat engine, the temperature of the source and sink are 500 K and 375 K . If the engine consumes $25 \times 10^{5} \mathrm{~J}$ per cycle, find the heat rejected to the sink per cycle.

If the pH of a solution is changed from 1 to 3 with the addition of an antacid, what percentage of $\left[\mathrm{H}^{+}\right]$ has been neutralized?

Calculate the wavelength of the first line in the Lyman series of the hydrogen spectrum $\left(\mathrm{R}_{\mathrm{H}}=\right.$ $109677 \mathrm{~cm}^{-1}$ )

At a certain temperature, 0.10 mole of $\mathrm{H}_{2}$ and 0.10 mole of $\mathrm{I}_{2}$ were placed in a 1.0 L flask. The purple colour of iodine vapor was used to monitor the reaction. After the equilibrium was established. It was found that the concentration of $\mathrm{I}_{2}$ decreased to $0.02 \mathrm{~mole} / \mathrm{L}$ . Calculate the value of $\mathrm{K}_{\mathrm{c}}$ for the reaction at the given temperature.

Calculate the pH of $0.2 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}$ $\left(\mathrm{K}_{\mathrm{a}}=1.85 \times 10^{-5}\right)$

Calculate the time required to complete 75% 75 % of a first order reaction whose half-life value is 50 sec.

The solubility product of $\mathrm{Mg}(\mathrm{OH})_{2}$ is $2.00 \times$ $10^{-11} \mathrm{~mol}^{3} \mathrm{dm}^{-9}$ at 298 K . Calculate the solubility.

What is the principle underlying HPLC (High Performance Liquid Chromatography)?

How many moles of electrons are required to reduce 2.93 grams of nickel ions from $\mathrm{NiCl}_{2}$ (Molar Mass of $\mathrm{Ni}=58.7 \mathrm{~g} / \mathrm{mol}$ )

When 190 grams of $\mathrm{MgCl}_{2}$ are dissolved in water and the resulting solution is 500 mL in volume. What is the molar concentration of $\mathrm{MgCl}_{2}$ in the solution?

$2 \mathrm{Al}+6 \mathrm{HCl} \rightarrow 2 \mathrm{AlCl}_{3}+3 \mathrm{H}_{2}$ If 2 moles of Al and 6 moles of HCl react according to the above equation, then how many moles of electrons are transferred during the redox reaction?

How much bromine is present in 500 mL of 0.1 M NaBr solution?

$\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} \rightarrow 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}+2 \mathrm{CO}_{2}$ Which type of reaction does the above equation represent?

Which two compounds are not isomers of each other?

Which one of the following is present at the position of letter B, $\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{Br} \xrightarrow[\text{Alcohol}]{\mathrm{KOH}} \mathrm{A} \xrightarrow{\mathrm{H}_{2} / \mathrm{Pt}} \mathrm{B}$ .

Find the compounds in the place of $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and D .