Islamic University of Technology ইসলামিক ইউনিভার্সিটি অব টেকনোলজি ভর্তি পরীক্ষা ২০২১-২০২২

A number of scientific theories that are____ today, were once treated with______by the scientific establishment.

I am impressed at the length he has gone through to create this detailed report in which he_______the text at several places.

While filling up the survey, he was very open____ an in revealing his feelings about the organization's compensation program.

INDOMITABLE

DIVULGE

ACUMEN ( synonym).

In ancient times wealth was measured and exchanged in things that could be touched: food, tools, and precious metals and stones. Then the barter system was replaced by coins, which still had real value since they were pieces of rare metal. Coins were followed by fiat money, paper notes that have value only because everyone agrees to accept them.Today electronic monetary systems are gradually being introduced that will transform money into even less tangible forms, reducing it to a series of "bits and bytes", or units of computerized information, going between machines at the speed of light. Already. electronic fund transfer allows money to be instantly sent and received by different banks, companies, and countries through computers and telecommunications devices.According to the passage, which of the following was the earliest kind of exchange of wealth?

A drug having higher efficacy in treating many types of infection can, at present, be obtained only from the bark of the ibora, a tree that is very rare. It takes the bark of 500 trees to make 100 gram of the drug. It follows, therefore, that continued production of the drug must lead to the ibora's extinction from the planet. Which of the following, if true, most seriously weakens the argument above?[IUT : 2021-22]

Like people living near an active volcano, many of us are             about the possibility of atomic warfare and its attendant destruction.

If a thin light-ray falls upon the X-axis along the line 5x+5y=3 and gets fully reflected, what will be equation of the line of the reflected  ray?

A line intersect another perpendicular line at (2, 4) that goes through the origin. Find The equation of the first line.

$\lim_{x \to 0} \frac{1 - \cos x}{\sin^2 2x}$ - এর মান কোনটি?

If A+B+C =π/2 and sinBsinC = -sinA then what is the value of cotA+ cotB+cotC ? [M-1.7, IUT : 2021-22]

If y = ( m - x) -1, the evaluate yn = dny / dnx .

Find the inverse of $A = \left [ \begin{matrix} 4 & 5 & 0 & 0 \\ 3 & 4 & 0 & 0 \\ 0 & 0 & 3 & 2 \\ 0 & 0 & 4 & 3 \end{matrix} \right ]$

Given the matrix, $A = \left [ \begin{matrix} 1 & n \\ 0 & 1 \end{matrix} \right ]$, what is the resultant of matrix An?

The determinants of the reverse identity matrices are defined as follow:∣$\left|J_{1}\right|=|1|=+1,\left|J_{2}\right|=\left|\begin{array}{ll} 0 & 1 \\ 1 & 0 \end{array}\right|=-1,\left|J_{3}\right|=$ ∣$\left|\begin{array}{lll}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{array}\right|=-1$, $\cdots$ Find the determinant of $\mathrm{J}_{100}$ .

Given $A = \left [ \begin{matrix} x + y & - 6 \\ a b & 7 \end{matrix} \right ] \quad\text{and}\quad B = \left [ \begin{matrix} - 3 & a + b \\ - 9 & x + y \end{matrix} \right ]$, where AT+BT=I. What are the values of a and b?

Partial fraction of $\frac{5 x^{2} - 4}{x^{2} \left ( x - 2 \right )} i s -$

Suppose you want to build a 1125ft3 swimming pool with a square base of x ft on each side and having y ft depth. If the cost of construction is defined as c = 5x2 + 30 xy, the what values of x amd y will minimize the cost?

The volume of a cone-shaped metallic object is increasing at a rate of 20 ft³/min. Both the base-diameter and height of the object are always equal. How fast is the height of the object increasing when it is 10 ft tall?

Find the equation of the tangent of the curve xy = 3 at the point (4,¾).

What is the area of the shaded region of the following figure?

$\int_{0}^{1} \sqrt{\frac{1-\mathrm{x}}{1+\mathrm{x}}} \mathrm{dx}$ এর মান কোনটি?

Suppose a pyramid has a square base of length 3 m in each side and a height of 5 m. What is the volume of that pyramid?

The sum of all angels of a polygon is 1080. How many  sides does  the polygon have?

Given cos-1x/ sin-1x  < 1, find the most appropriate value of x.

The roots of equation  x3 + px2 + qx + r = 0 are a, b and c. Evaluate ∑(a+b)2 .

Find the cubic equation whose roots are 2 and 1+2i. [M-2.3, IUT : 2021-22]

For the ellipse 5x2 + 4y2 = 20, find the equation of the directrix.

The equation of an ellipse is $4x^2\ +\ 9y^2\ =\ 36$. The area ( in square unit) bounded by ellipse is-

$\cos^{-1}\left(\cos\left(\frac{4\pi}{3}\right)\right)$ is equal to-

If the roots of the equation $6x^2\ -\ 5x\ \ +1\ =\ 0$ are a and b; then the equation with roots 1/a  and 1/b is-

A bag contains 10 blue and 15 red balls. If a boy draws 2 balls at random consecutively, which one is the probability of both be of same color?

Two men are carrying a straight uniform bar of length 8 m and weight 60 kg. One man supports it at a distance of 2 m from one end and the other man at a distance 3 m from the other end. What weight does each man bear?

For which value of x, the 21 and 22nd terms are equal in the expansion of (1 + x)⁴⁴?[M-2.5, IUT : 2021-22]

A force $\vec{F} = \left ( 40 \hat{i} + 30 \hat{j} \right ) N$   is acting an object of mess 10kg. What is the megnitude of acceleration of the object? assume other forces are involved.

When 7500kg diesel engine pull a 25000 kg train along straight and level rails,it produces of acceleration of 2.5ms-2. What will be the acceleration of engine when the mass of the train becames 45000 kg. (neglect the friction)

An 80W electric fan is rotating at 300rpm. How much torque is being produced by the electric motor of the fan?

A flywheel is being driven from rest by an electric motor with a constant torque of 25 Nm.The moment of inertia of the fly wheel is 5kgm2. What is the kinetic energy of the flywheel after 10 second?

In a construction site a lifting machine on the ground is used to lift bricks to the $8^{\text{th}}$ floor which is 25m high. At a time the machine can lift a 2000kg load is 1min.The power satellite to the engine of the lift is 15HP.what is the efficiency of the lifting machine?[P-1.5, IUT : 2021-22]

To measure the spring constant of a hookean spring constant a 500g mess is hooked up at its end and length of the stretched spring is measured. Then the mass is increased to 550g and observed that the spring is stretched 10cm more. What is the spring constant?

The mass of a metallic sphere is 6g, it is fastened at one end of a thread of length of 3m and it rotated 4 times per second.what is its angular momentum ?

A car of mass 480 kg moving at a speed of 54 kmph, is stopped in 10 s. Calculate the force applied by the brakes.

An engine pumps 1000kg of water per minute from a well of depth of 100m.if the 24% efficiency of the engine is lost, find the horsepower of the engine.

A body is allowed to fall freely from a higher of 30m.from the ground where will it's kinetic energy be twice the potential energy?

In an experiment the value of $\frac{L}{\left ( T \right )^{2}}$ at a place was found 0.25 $m s^{- 2}$ calculate the value of g at that place?

Two pendulum having 2 sec time period,one is on the earth and the other is on the moon having the length ratio of 81:16 .if the value of g on the earth surface 9.81 $m s^{- 2}$ find the value of g on the moon's surface.

Density of the carbon dioxide gas is 1.98 $k g{m}^{- 3}$ at 0°C temperature and 1.0×105Nm-2 pressure.calculate the root mean square of velocity of the molecules of that gas at 30°C temperature and at the same pressure.

From when height a priece of ice is allowed to fall due to the action of gravity so that 10% of ice will be melt by the heat produce?conceder that all the mechanical of energy has been converted into heat.