IUT ইসলামিক ইউনিভার্সিটি অব টেকনোলজি ভর্তি পরীক্ষা ২০২১-২০২২

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]

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.

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

INDOMITABLE

DIVULGE

ACUMEN ( synonym).

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.

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.

lim⁡x→01−cos⁡xsin⁡22x\lim_{x \to 0} \frac{1 - \cos x}{\sin^2 2x} - এর মান কোনটি?

The equation of an ellipse is 4x2 + 9y2 = 364x^2\ +\ 9y^2\ =\ 36. The area ( in square unit) bounded by ellipse is-

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=[4500340000320043] A = \left [ \begin{matrix} 4 & 5 & 0 & 0 \ 3 & 4 & 0 & 0 \ 0 & 0 & 3 & 2 \ 0 & 0 & 4 & 3 \end{matrix} \right ]

cos⁡−1(cos⁡(4π3))\cos^{-1}\left(\cos\left(\frac{4\pi}{3}\right)\right)is equal to-

Given the matrix, A=[1n01] A = \left [ \begin{matrix} 1 & n \ 0 & 1 \end{matrix} \right ] , what is the resultant of matrix An?

If the roots of the equation6x2 − 5x  +1 = 06x^2\ -\ 5x\ \ +1\ =\ 0 are a and b; then the equation with roots 1/a  and 1/b is-

The determinants of the reverse identity matrices are defined as follow:∣J1∣=∣1∣=+1,∣J2∣=∣0110∣=−1,∣J3∣= \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|= ∣001010100∣=−1,⋯ \left|\begin{array}{lll}0 & 0 & 1 \ 0 & 1 & 0 \ 1 & 0 & 0\end{array}\right|=-1, \cdots Find the determinant of J100 \mathrm{J}_{100} .

Given A=[x+y−6ab7]andB=[−3a+b−9x+y], 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 5x2−4x2(x−2)is− \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?

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?

∫011−x1+xdx \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?

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   F⃗=(40i^+30j^)N \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?

A 12V and 50W lamp is connected 12 volt battery with internal resistance 0.1ohm. what is the actual voltage applied to the lamp terminals?

In a construction site a lifting machine on the ground is used to lift bricks to the  8^(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?

A coal fired power plant that operate that an efficiency of 38% generates 750MW of electric power. How much heat does the plant discharge to the environment in one day.

An old battery with an emf of 9V has terminal voltage of 8.2V when it is supplying a current of 2 mA. What is the internal resistance of the battery?

A thermometer is made using a carbon resistor having a temperature coefficient of resistivity  of -0.00050Ω° C−1 C^{- 1} .the variation of resistance with temperature in the linear reason is used to measure the temperature. On a cold winter day when the temperature is 8°C,the resistance is 216.8Ω. what is the temperature on a summer day when the resistance is 213.5Ω?

Suppose that NASA wants to explore a distance solar system 200 light years away from the earth. What will be the again of the astronauts travelling in a spaceship with a speed of 0.99c as measures from the spaceships frame of reference, where c is the speed of light in vacuum?

An npn transistor in CE configuration has ɑ=0.995. what is the base current if the collector current is 4mA?

An automobile battery is charged by a constant current of 2 A for 10 hours. The Terminal voltage of the battery is V=(11+0.5t)V for t ≥0 \ge 0 where time t is in hours. What is the total energy delivered to the battery during this time?

In one cycle a heat engine absorb 500j from a high temperature reservoir and expels 300 j to a low temperature reservoir.if the efficiency of the engine is 60% of the efficiency of carnot engine, what is the ratio of the low temperature to the high temperature in the Carnot engine?[P-2.1, IUT : 2021-22]