Islamic University of Technology ইসলামিক ইউনিভার্সিটি অব টেকনোলজি ভর্তি পরীক্ষা ২০১৯-২০২০

Subversive (Synonym).

Antonym of Unequivocal?

What is the synonym of “Diatribe”?

Epigram

Chose the word or phrase which is most nearly similar of the meaning of the given word. [question 96-100]
“Auspicious”-

What is the synonym of the word “Destitute”?

Prodigious

On which side of the line 4x-3y-10= 0, does the point (3.-2) lie?

At x=0, the function f(e-x2 )= is:

A rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a single-strand electric fence. With 800 m of wire at your disposal, what is the largest area you can enclose and what are its dimensions?

Find the area of the region between the x -axis and the graph of $f(x)=x^{3}-x^{2}-2 x,-1 \leq x \leq 2$ .

If regular polygon with n sides has any of its angle represented in both radian and degree representations,then the difference between those two values will be:

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

During midnight, a car is traveling south at the speed of 8km/hour for 30 minutes and then turns west. A flashlight located at the point of departure has been tracking the car. How fast is the flashlight rotating I hour after departure?

If A+B+C=(2n+1)π/2 for n  then value of tan A tan B + tan B tan C + tan C tan A is-

If the circle x²+ y²+8x+2ky+c=0 touches both the axes then possible valued of k and C are.

$\lim_{n → ∞} \frac{1}{n^{4}} ∑_{r = 1}^{n} r^{3}$ = ?

Differentiation of $\left ( x √ \left ( x √ \left ( x √ x \ldots ∞ \right ) \right ) \right ) i s -$

If tan x=b/a, then value of (a2+ b²) sin 2x is-

If the sum of two numbers is 8, then what is the maximum value of its product?

Find the domain of the function $f{\left ( x \right )} = \sqrt{x^{2} - 4 x + 3}$

The isosceles right triangle has a side AC of length 5 cm and PQ shows the arc of a circle centered at A. Find the area of the shaded region given below.

Seven IUTian boys and seven IUTian girls together all meet up for a meal. To commemorate the occasion. they arranged for a photograph to be taken of all 14 of them standing in a line. How many different arrangements are there if the 7 boys all stand together and 7 girls all stand together?

$\frac{1}{3} i$  এর বর্গমূল কোনটি?

If the roots of the equation (4-k)x²+26kx+5= 0 are inverse of each other then find the  value of k?

The ratio of the ordinates of a point and its corresponding point is $\frac { 2 \sqrt { 2 } } { 3 }$ then eccentricity is ____________________.

A bird flies against the wind blowing at 5 kmh-1 for a distance of 10 km and then flies back in the direction of wind. If the whole flight time is 2 hours, find the bird's flying speed in still air.

Two buses of length 15m and 25m have started their journey from Board Bazar towards Dhaka at the speed of 5.2 km/h and 5 km/h, respectively. When will they cross each other?

In the triangle ABC, AB = 5 cm, BC = 6 cm and area of triangle is 11.25 cm². What is the value of angle ∠ABC?

Straight line y = 6 intersects the line x = 5 at A and the curve y²=6(x-7) at B. What is the length of AB?

Ordinate of a point P on the parabola y2= 9x is 12. What is the focal distance of the point P?

Equation of asymptote of the hyperbola, $\frac{y^2}{3}-\ \frac{x^2}{4}=\ 0$ is-

If 1+√2i is a root of quadratic equation, which one is that equation?

If f(x)=|x-2|+1/3, then the lowest value of f(x)=?

Suppose in a room there are five doors. One Bangladeshi, one Canadian, one Japanese and one Australian want to enter into that room. Find the probability of their entering through different doors.

The probability that a person going to a hospital will have his blood group checked is 0.12; the probability that he will check his blood pressure is 0.29 and the probability that he will ask to have both of them checked is 0.07. Find the probability that a person who will check his blood pressure, will also have his blood group checked.

The co-ordinates of a moving particale at any time t are given by x= $\alpha$ t3 and y= $\beta$ t3.The speed to the particle at time t is given by -----

A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring, and the spring reads 49 N when the lift is stationary. If the lift moves downward with an acceleration of 5m/s2 , the reading of the spring balance will be-

A ball of mass 0.2 kg is thrown vertically upwards by hand. If the hand moves 0.2 m which applying the force and the ball goes up to 2 m height further, find the magnitude of the force.[Consider g = 10 ms-2]

When a rubber -band is stretched by a distance x,it exerts a restoring force of magnitude $F= ax + bx^2$ where a and b are constants. the work done is stretching the unstretched rubber band by L is : ;

At time t=0s a particle starts moving along the x axis. If the kinetic energy increases uniformly with time 't', the net force acting on it must be proportional to

The height at which the acceleration due to gravity becomes $\frac{g}{9}$   (where g = the acceleration due to gravity on the surface of the earth) in terms of R, the radius of the earth, is-

Two bodies of masses m and 4m are placed at a distance r. The gravitational potential at A point on the line joining them, where the gravitational field is zero, is

A particle performs simple harmonic motion with amplitude A. Its angular speed is tripled at the instant that it is at a distance from equilibrium position. ($x = \frac{2A}{3}$)The new amplitude of the motion is:

The length of a simple pendulum executing simple harmonic motion is increased by 21%. The percentage increase in the time period of the pendulum of increased length is

The temperature of an open room of volume 30 m³ increases from 17°C to 27°C due to the sunshine. The atmospheric pressure in the room remains 1 x 105 Pa. If n, and n, are the number of molecules in the room before and after heating, then ni , nf will be:

The muzzle velocity of a 3.30 g bullet fired from a rifle is 965 ms-1 just as it leaves the 45.0 cm barrel. Assume that the barrel is frictionless and a constant horizontal acceleration of the bullet in the barrel. What is the force exerted by the rifle on the bullet while it is in the barrel?

A marathon runner with mass 60.0 kg runs up the stairs to the tallest building of the world Burj Khalifa of height 828 m in 30.0 minutes. What is his average power output in horsepower?

An armature shooter holds a 4.50 kg rifle loosely ,allowing it to recoil freely when fired,and fires a bullet of mass 4.20 g horizontally with a speed of 900 ms-1.What is the recoil speed of the rifle?

A slab of ice floates on a freshwater lake .What minimum volume must the slab have for a 55.0 kg woman to be able to stand on it without getting her feet wet?Density of ice is 0.92 times of that of water.