Islamic University of Technology ইসলামিক ইউনিভার্সিটি অব টেকনোলজি ভর্তি পরীক্ষা ২০২২-২০২৩

The masses of the blocks and the velocities before and after a collision are (directions are indicated by the arrows)In this situation, the collision is:

Two bodies of masses 40 kg and 60 kg collide with each other when coming from opposite sides with velocities of $10\ {\rm ms}^{-1}$ and $5\ {\rm ms}^{-1}$ respectively and then get stuck and move together. What will be the velocity of the two bodies after collision?

A particle moves with simple harmonic motion in a straight line. In first $\tau \mathrm{s}$, after starting from rest it travels a distance a, and in next $\tau$ s it travels 2 a , in same direction, then:

When a foice $\vec{i}=(\hat{i}-3 \hat{j}+2 \hat{k}) N$ acts on a particle its displacement occurs $\overrightarrow{\mathrm{d}}=\left(2 \hat{\mathrm{i}}+\mathrm{d}_{y} \hat{\mathrm{j}}- k\right)$. $m$ . For what value of $d_{y}$, the work done would be zero?

A body was at rest. A force of 16 N acted upon it for 5 s and stopped. After that, the body travelled 52 m distance in 6 s . What is the mass of the body?

The mass of a cylinder is 50 kg and its radius is 0.20 m. The moment of inertia of the cylinder about its axis is $1.0 \mathrm{kgm}^{2}$ . What is the total kinetic energy of the cylinder when it rolls at a horizontal velocity $2 \mathrm{~ms}^{-1}$?

The ratio of the radii of the orbits around the sun of venus and earth is 54:75 54: 75 . If 365 days make a year in the earth, how many days will make a year in the venus?

The Young's modulus of the material of the wire of diameter $5.0 \times 10^{-4} \mathrm{~m}$ is $9.0 \times 10^{10} \mathrm{Nm}^{-2}$ . To increase its length by 5% 5 % , how much force needs to apply?

A rocket is launched vertically. In the first 2 seconds after launching, the rocket loses $\frac{1}{60}$ of its weight. The velocity of the gas released from the rocket is $3600 \mathrm{~ms}^{-1}$ . Determine the net acceleration of the rocket. (Assume $\mathrm{g}=$ $9.8 \mathrm{~ms}^{-2}$ )

Two bodies A and B have masses 2 kg and 4 kg respectively, and they are separated by 2 m . On their connecting line, a body C of mass 1 kg is placed so that the gravitational force on C is zero. Determine the distance of C from A . (Ignore gravitational forces with everything else)

A sphere of 10 gm is placed at a height of 1.2 m from the ground. It falls from there (with initial zero velocity) along a slanted piece of wood and its velocity is $4 \mathrm{~ms}^{-1}$ when it reaches the ground. Determine the work done by friction as it falls.

A well is filled in with water. Its diameter is 4 m and its depth is 12 m . A pump can evacuate all the water from the well in 20 minutes. Determine the power of the pump.

An object is tied to the end of a spring and it is undergoing simple harmonic motion with an amplitude of 12 cm and a period of 1.7 sec . Determine the maximum acceleration.

A spring has the property that it changes its length by 10 cm if 100 N force is applied to the spring. This spring is used in a test. In this test, an object of 1.5 kg is tied to the spring and it is undergoing a simple harmonic motion. Determine the frequency of the motion in the test.

A piece of wood from a recently cut tree shows 20 decays per minute. A wooden piece of same size in a museum (obtained from a tree cut years back) shows 2 decay per minute. If the half-life of $\mathrm{C}^{14}$ is 5730 years, then the age of the wooden piece placed in the museum is approximately:

An electron was accelerated from rest through a potential difference of 990 V . What is its speed? (Use the mass of an electron $=9.11 \times 10^{-31} \mathrm{~kg}$ . the mass of proton $=1.67 \times 10^{-27} \mathrm{~kg}$ and the charge of an electron $=1.6 \times 10^{-19} \mathrm{C}$ ).

A charged particle is observed travelling in a circular path in a uniform magnetic field. If the particle had been travelling twice as fast, the radius of the circular path would be:

Two identical wires A and B, each of length ' $l$ ', carry the same current I. Wire A is bent into a circle of radius R and wire B is bent to form a square of side ' $a$ '. If $B_{A}$ and $B_{B}$ are the values of magnetic field at the centers of the circle and square respectively, then the ratio $\frac{\mathrm{B}_{\mathrm{A}}}{\mathrm{B}_{\mathrm{B}}}$ is:

The resistances of a resistance thermometer at $0^{\circ} \mathrm{C}$ and $100^{\circ} \mathrm{C}$ be respectively $10 \Omega$ and $25 \Omega$ . When the thermometer is placed in an oven, the resistance becomes $38 \Omega$ . Find the temperature of the oven.

$8.4 \times 10^{4} \mathrm{~J}$ heat energy is supplied to a Carnot engine working between $27^{\circ} \mathrm{C}$ and $160^{\circ} \mathrm{C}$ . How much heat energy will be converted into work by the engine?

What is the electric potential at the mid-point of the line connecting two charges of magnitudes $+1.00 \mu \mathrm{C}$ and $-5.00 \mu \mathrm{C}$ and separated by a distance of 1 m ?

The emf and internal resistance of a cell are 2 V and $0.5 \Omega$ respectively. It is arranged with $1 \Omega$, $2 \Omega$, and $4 \Omega$ resistance in a parallel combination, Find the potential difference of the two ends of middle resistance.

An immersion heater of 100 W can raise the temperature of 1 liter of water from $30^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C}$ in 7 minutes. Determine the value of the mechanical equivalent of heat.

The refractive indices of water and diamond are respectively 1.33 and 2.4 . Find the velocity of light in diamond. The velocity of light in water is $2.28 \times 10^{8} \mathrm{~ms}^{-1}$ .

At the age of 25 years an astronaut went to space travel in a spaceship moving with velocity $1.8 \times$ $10^{8} \mathrm{~ms}^{-1}$ and he returns to earth after 30 years according to the calendar of the earth. What is his age now?

A piece of radium becomes one-fifth part on radiating radioactive radiation for 5000 years. Find the decay constant of radium.

A uniform hole in a brass plate has a diameter of 1.2 cm at $25^{\circ} \mathrm{C}$ . What is the diameter of the hole when the plate is heated to $475^{\circ} \mathrm{C}$? (Use the coefficient of linear thermal expansion for brass = = $19 \times 10^{-6} \mathrm{~K}^{-1}$ )

The volume of a gas is $1.8 \mathrm{~m}^{3}$ at a pressure of $10^{5}$ Pa and temperature of $25^{\circ} \mathrm{C}$ . It is compressed in an isothermal process to get a pressure of $5 \times 10^{5} \mathrm{~Pa}$ . Determine the amount of heat released. (Gas constant $\mathrm{R}=8.134 \mathrm{JK}^{-1} \mathrm{~mole}^{-1}$ )

The charges Q Q and 4O 4 O are placed with a distance of 1 m between them. From the charge O O , determine the distance of the point on the connecting line where the electric field intensity is zero.

Two capacitors are connected in series. Their capacitances are $4 \mu \mathrm{~F}$ and $5 \mu \mathrm{~F}$ . If they are connected to a source of 900 volts, determine the stored energy.

Determine the logic gate equivalent to the following combination.

Determine the current through $5 \Omega$ resistor

Find the current through $12 \Omega$ resistor.

A 2 V battery is connected between A and B . If the positive terminal is connected to A , the current through the battery is $I_{1}$ . If the negative terminal is connected to A , the current through the battery is $\mathrm{I}_{2}$, Determine the difference between the values of $\mathrm{I}_{1}$ and $\mathrm{I}_{2}$ . (Assume diodes are ideal)

200 mL 0.2 M KOH and $50 \mathrm{~mL} 0.3 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}$ were mixed in a vessel. Calculate the pH of the mixture.

The solubility product of AgCl is $1.0 \times 10^{-10}$ at $25^{\circ} \mathrm{C}$ . What will be its solubility in 0.1 M NaCl solution at this temperature?

Nitrogen reacts with hydrogen to form ammonia.$\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g})=2 \mathrm{NH}_{3}(\mathrm{~g})$ The pressure exerted by this mixture of hydrogen, nitrogen and ammonia at constant temperature is $2.000 \times 10^{7} \mathrm{~Pa}$ . Under these conditions, the partial pressure of nitrogen is $1.490 \times 10^{7} \mathrm{~Pa}$, and the partial pressure of hydrogen is $0.400 \times$ $10^{7} \mathrm{~Pa}$ . Calculate the value of $\mathrm{K}_{\mathrm{p}}$ for this reaction.

Which of the following elements has the same number of neutrons as Nickel-58?

According to the following figure:(i) Gas A has a molecular mass of $82.0 \mathrm{~g} / \mathrm{mol}$ .(ii) Gas B has a molecular mass of $72.84 \mathrm{~g} / \mathrm{mol}$ .(iii) Gas B has a higher diffusion rate than Gas A .Which of the following is correct?

Which of the following statements is correct?

Which of the following reactions is wrong?

In the reaction $4 \mathrm{Fe}+3 \mathrm{O}_{2} \rightarrow 4 \mathrm{Fe}^{3+}+60^{2-}$ which one of the following statements is incorrect?

When 0.75 A electricity passed through a metal salt solution for 45 min , then 0.6662 gm of cathode increased. If the valency of metal is 2.0 then what is the atomic mass of that metal?

When chlorine and hot concentrated aqueous sodium hydroxide are mixed the following reaction take place: $3 \mathrm{Cl}_{2}(\mathrm{aq})+6 \mathrm{NaOH}(\mathrm{aq}) \rightarrow$ $5 \mathrm{NaCl}(\mathrm{aq})+\mathrm{NaClO}_{3}(\mathrm{aq})+3 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})$ The name of the above rection is:

What volume of 0.1 M hydrochlonic acid ( HCl ) is needed to react with 25 mL of 0.2 M sodiom hydroxide ( NaOH )?

$\mathrm{R}-\mathrm{OH}+\mathrm{HCl} \xrightarrow{\mathrm{ZnCl}_{2}} \mathrm{X}+\mathrm{H}_{2} \mathrm{O}$ ; $X$ compound is(i) Volatile(ii) Liquid at room temperature(iii) Harmful to bodyWhich of the following is correct?

Which of the following is the product of the following reaction: $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}+\mathrm{H}_{2} \mathrm{SO}_{4}$?

How many moles of $\mathrm{CO}_{2}$ are produced when 2 moles of $\mathrm{C}_{3} \mathrm{H}_{8}$ react with excess $\mathrm{O}_{2}$ in the following reaction? $\mathrm{C}_{3} \mathrm{H}_{8}+5 \mathrm{O}_{2} \rightarrow 3 \mathrm{CO}_{2}+4 \mathrm{H}_{2} \mathrm{O}$

In a nickel-cadmium battery, which of the following reactions occurs at the anode during discharge?