Islamic University of Technology ইসলামিক ইউনিভার্সিটি অব টেকনোলজি ভর্তি পরীক্ষা ২০১৫-২০১৬

When having a problem, it is best to dissect the situation,then act. Dissect means–

The child apprised her father's authority and behaved herself in church. Apprised means

The helium-filled balloon______.

The scientist was able to evoke powerful emotions from her audience.Evoke means

The official exhibited a heedless attitude when dealing with the dignitaries. Heedless means

The general tried to instill the hope of victory in his troops. instill means

The winning team of the World Series often has a jovial attitude. Jovial means

Find the error:
The judge ‘The Tidy City contest’, we picked an uninterested party.

Arctic trees are.......  in milder climates.

If I __________, I would have delivered the package myself.

If he would have revised his first draft, he would have received a better grade.

These directions show you how to _____

When working on soft metals, you can___

For the following matrix multiplication, find the values of x,y,z and w $\left [ \begin{matrix} 5 & 10 \\ 2 & 7 \end{matrix} \right ] = \left [ \begin{matrix} x & 0 \\ y & z \end{matrix} \right ] \times \left [ \begin{matrix} 1 & w \\ 0 & 1 \end{matrix} \right ]$

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

Find the equation of a circle if the points P(1,2) and Q(3,8) are the endpoints of one of its diameters.

The area bounded by the curves $y\ =\ 2\ -\ x^2$ and y=x is?

The area of the region bounded by x=0, y=8 and y=x2 is:

The value of $\lim_{x \to 1} \frac{\sin{\left ( x - 1 \right )}}{x^{2} + 2 x - 3} i s -$

The equation of the tangent to the curve $y={ x }^{ 3 }-6x+5$ at (2,1)(2,1) is

If $y = \ln{\sqrt{\frac{1 - \cos{x}}{1 + \cos{x}}}}$, then dy/dx =?

Air is being pumped into a spherical balloon at a rate of 20 in3min-1. How fast is the radius of the balloon increasing when the radius is 6 in ? Volume of a sphere with radius r is $\frac{4}{3} \pi r^{3}$

Evaluate $\int_{3}^{7} x \sqrt{x - 3} dx$

The maximum area of a rectangle (shown in the figure below) inscribed in a circle of radius 10 m is:

Evaluated:$\int_{-\frac{3}{4}}^{\frac{3}{4}} \frac{\mathrm{dx}}{\sqrt{9-4 \mathrm{x}^{2}}}$ = ?

Suppose 4 mathematics books are selected from 6v different Mathematics books and 3 English books are chosen from 5 different English books. In how many ways can the seven books be arranged on a self if a math book is placed at the beginning and an English book in the middle of the shelf ?

A student has to answer 10 questions out of 13 questions, choosing at least 4 from each of Parts A and B. If there are 6 questions in Part A and 7 in Part B , in how many ways can the student choose 10 questions ?

A turtle and a rabbit engage in a footrace over a distance of 4.00 km. The rabbit runs 0.500 km and the stops for a 90.0 min nap. Upon awakening, he remembers the race and runs twice as fast. Finishing the course in a total time of 1.75 h, the rabbit wins the race. What was his average speed before he stopped for a nap!

Suppose the cause of produce x toys is c(x) = 80x + 150 and the revenue by selling x such toys is r(x) = -1.5x2 + 250x. Determine the number of toys needs to sell to make a positive profit.

The following figure $s how$ a scale with a capacity of only $250 \mathrm{~N}$ can be used to weight a heavier person. The density. It is free to pivot about he end (P) farthest from the scale. What is the weight of a person standing $1.2 \mathrm{~m}$ from the pivot end, if the scale reads $210 \mathrm{~N}$? Assume that the board remains nearly horizontal.

A cyclist, from 84m behind of a car, runs at a uniform velocity of 20 m/s toward the car. The car, at the same time, starts at a uniform acceleration of 2m/s in the same direction of the cyclist. After what shortest time, the cyclist will meet the car ?

If i2=-1 , and one root of the equation x2+px+q=0 is 2-i3, then find the value of p and q. (The complex roots of a quadratic equation are conjugate complex numbers.)

for what value of k the roots of the equation 3x2+(k-1)x-2=0 are equal and opposite ?

A whispering gallery is an elliptical- shaped room with a dome-shaped ceilling. If two people stand at the foci of the ellipse and whisper, they can hear each other, but others cannot. The maximum length and width of such a hall are 100m and 80m, respectively. Which of hte following equations models the  shape of the hall ?

When a ball is thrown or kicked, the path it travels is shaped like parabola. Suppose a football is kicked from ground level, reches a maximum height of 50m and hits the ground 200m from where it was kicked. Assume that the focus of the parabola is at the origin and is on the ground. Which of the following equations models flight of the ball ?

A hyperbolic mirror is used in some telescopes. Such a mirror has the property that light ray directed at one focus will be reflected to th eother focus as shown in the figure will below. Which of the following equations models the hyperbolic mirror's surface ?

If $\sin^{- 1}{x} + \cos^{- 1}{\left ( \frac{x}{2} \right )} = \frac{5 \pi}{6}$, then the value of x is-

In a chess tournament, your probability of winning a game is 0.3 against 50% of the player (say typel),0.4 against another 25% of the players (say type 2), and 0.5 against the remaining 25% of the players (say type 3). If you play against a randomly selected player and you win, what is the probability that you play against a Type 1 opponent?

The coefficient of $x^{n}$ in the expansion of $\dfrac{1}{(1-x)(1-2x)(1-3x)}$ is ;

Five coins are tossed simultaneously. Find the probability of the event that at least 1 head turns up?

A person in carrying a weight of W by hanging it from one end of a bar with length l and placing the bar on his shoulder. The person is maintaining the equilibrium by applying a force on the opposite end of the bar by his hand. Assume that the distance between his hand and shoulder is y. Which of the folowing values of y will produce the minimum force on hos shoulder ?

The average distance separating Earth and the Moon is 384000 km. What is the net gravitational force exerted by Earth and the Moon on a 3.00 x 104 kg spaceship located halfway between them? (Mass of earth-5.98 x 1024 kg and mass of moon=7.36 x 1022 kg)

A small ferryboat is 4.00 m wide and 6.00 m long. When a loaded truck pulls onto it, the boat sinks an additional 4.00.cm into the river. What is the weight of the truck?"

What is the force a 70.0 kg high jumper must exert on the ground to produce an upward acceleration 4.0 times the acceleration due to gravity?

A truck with 0.42 m radius tires travels at 32.0 ms-1 . What is the angular velocity of the rtating tires in rpm?

Using a small pendulum of length 0.171 m a geophysicist counts 72 complete swings in a time of 60 s.What is value of g at that location?

A 6500 kg freight car traveling at 2.5ms-1 collides with an 8000kg stationary freight car. If they interlock upon collision, what is their velocity?

What is the depth of water below the surface of a dam where the pressure is 1.00 atm?

A 60kg woman floats in the fresh water with 97% of her body volume submerged when her lungs are full of air.What is the average density of the woman?

If a ball rebounds two thirds as for as it falls , how far will it travel before coming to rest if it is dropped from a height of 30 meters ? ( Total distance it travels is the sum of a series)