IUT ইসলামিক ইউনিভার্সিটি অব টেকনোলজি ভর্তি পরীক্ষা ২০২০-২০২১

Newton’s surprising success at developing the laws of motion, as well as the development and refinement of other physical laws, led to the idea of scientific determinism. The first expression of this principle was in the beginning of the nineteenth century by Laplace, a French scientist. Laplace argued that if one knew the position and velocity of all the particles in the universe at a given time, the laws of physics would be able to predict the future state of the universe.
Scientific determinism held sway over a great many scientists until the early twentieth century, when the quantum mechanics revolution occurred. Quantum mechanics introduced the world to the idea of the uncertainty principle, which stated that it was impossible to accurately measure both the position and the velocity of a particle at one time. Because Laplace’s omniscience could never occur, even in theory, the principle of scientific determinism was thrown into doubt. However, quantum mechanics does allow for a reduced form of scientific determinism. Even though physicists are unable to know precisely where a particle is and what its velocity is, they can determine certain probabilities about its position and velocity. These probabilities are called wave functions. By use of a formula known as the Schrodinger equation, a scientist with the wave function of a particle at a given time can calculate the particle’s future wave function. These calculations can give the particle’s position or velocity, but not both. Thus, the physicist is in possession of exactly half of the information needed to satisfy Laplace’s view of determinism. Unfortunately, under modern physics theories, that is far as any researcher can go in predicting the future.The passage suggests that if scientific determinism were true-

What will be the appropriate word on the blank no. 8 of the following passage?

Select the word with similar denotation 'Colossal'.

Select the word with similar denotation 'Conducive' .

The antonym of the word ‘DISCREET’-

The antonym of the word ‘heinous’ is-

Antonym of eschew is:

The antonym of ‘Strand’

if  2[345x] + [1y01] = [70105] if\ \ 2\left[\begin{matrix}3&4\5&x\end{matrix}\right]\ +\ \left[\begin{matrix}1&y\0&1\end{matrix}\right]\ =\ \left[\begin{matrix}7&0\10&5\end{matrix}\right]\ then what is the value of (x-y)?

সর্বোত্তম অনুমানভিত্তিক উত্তর — আনুষ্ঠানিক উত্তর নয়: মূল তথ্য বা উত্তরে অস্পষ্টতা/অসম্পূর্ণতা রয়েছে। প্রদত্ত উত্তরটি নিশ্চিত নয়; যাচাই করে ব্যবহার করো।

The length of time, L hours, that a laptop will work before it needs charging is normally distributed with a mean of 100 hours and a standard deviation of 15 hours. Find the value of d such that P (L

Following figure shows the graph of y=f(x),  x€ℝ. The graph consists of two line segments that meet at the point P. The graph cut the y-axis at the point Q and the x-axis at the points (-3,0) and R. Find the coordinates of the point Q and R.

what is the value of x where,  32x=5x+1? 3^{2 x} = 5^{x + 1} ?

What is the value oflim⁡ x →∞ x2×1xx2(1+1x2)\lim\ _{x\ \rightarrow\infty}\ \frac{x^2\times\frac{1}{x}}{x^2\left(1+\frac{1}{x^2}\right)}?

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

ɑ and ẞ are two positive acute angles and cos 2ɑ=  3cos⁡2β−13−cos⁡2β \frac{3 \cos{2} β - 1}{3 - \cos{2} β}  Which of the following relation is correct?

If A is a 3 × 3 invertible matrix and det⁡A−1 = det⁡(A)k+2\det A^{-1}\ =\ \det\left(A\right)^{k+2} , then the value of k is-

If real part(2z + 1)(z+ 3i) when z = x + iy \frac{\left(2z\ +\ 1\right)}{\left(z+\ 3i\right)}\ when\ z\ =\ x\ +\ iy\ then  locus of z is-

If a complex number z satisfies [2z+10+10i|≤ 5√3-5 then the least principal argument of z is-

If tanx =ntany, n e R+, then the maximum value of sec2(x-y) is equal to-

The equation tan4 x-2 sec²x+a=0 will have at least one solution if-

The combined equation of straight lines that can be obtained by reflecting the lines y =|x-2| in the y- axis is -

The locus of the center of the circles such that the point (2, 3) is the midpoint of the chord: 5x+2y=16 is-

Alal and Dulal shopped at the same store. Alal bought 5kg of apples and 2kg of bananas and paid altogether BDT22. Dulal bought 4kg of apples and 6kg of bananas and paid together BDT 33. Find the cost of 1kg of bananas.

lim⁡x→∞e1x2−12tan⁡−1(x2)−π is equal to-\lim_{x \to \infty} \frac{e^{\frac{1}{x^{2}}} - 1}{2 \tan^{-1}(x^{2}) - \pi} \text{ is equal to-}

The resultant of two forces 8 N and Q acting at a point is 6 N, acting at right angle to the direction of Q. The value of Q is-

A hanging body weighing 12 kg is kept in a position by applying two forces P and Q on it. P is acting horizontally while Q is acting by making an angle of 45° with the horizontal. The magnitude of the Q is-

Let P, Q, R and S be the points on the plane with position vector  −2i^−j^,4i^,3i^+3j^and−3i^+2j^ - 2 \hat{i} - \hat{j} , 4 \hat{i} , 3 \hat{i} + 3 \hat{j} \quad\text{and}\quad - 3 \hat{i} + 2 \hat{j}  respectively. The quadrilateral PQRS must be a-

The period of cos⁡(sin⁡(nx))(tan⁡(xn) \frac{\cos{\left ( \sin{\left ( n x \right )} \right )}}{\left ( \tan{\left ( \frac{x}{n} \right )} \right.} ,n e N, Is 6π ,then n is equal to-

Equation of the plane containing the straight line x2=y3=z4 \frac{x}{2} = \frac{y}{3} = \frac{z}{4} and perpendicular to the plane containing the straight lines  x3=y4=z2 \frac{x}{3} = \frac{y}{4} = \frac{z}{2} and  x4=y2=z3is− \frac{x}{4} = \frac{y}{2} = \frac{z}{3} i s -

If in a triangle, (1−r1r2)(1−r1r3)=2 \left ( 1 - \frac{r_{1}}{r_{2}} \right ) \left ( 1 - \frac{r_{1}}{r_{3}} \right ) = 2  denote the radit of the escribed circles opposite to the angles A, B and C respectively), then the triangle is-

A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground in 45° . It flies off horizontally straight away from the point O. After 1 second, the elevation of the bird from O is reduced to 30°. The distance covered by the bird is-

Relative to a fixed origin 0, the point A has position vector   i^−3j^+2k^ \hat{i} - 3 \hat{j} + 2 \hat{k} and the point B has position vector  −2i^+2j^−k^ - 2 \hat{i} + 2 \hat{j} - \hat{k} The points A and B lie on a straight-line 1. The point C has position vector  2i^+pj^−4k^ 2 \hat{i} + p \hat{j} - 4 \hat{k}  with respect to O, where p is a constant. Given that AC is erpendicular to 1. Find the value of p.

The following figure represents a Venn diagram that shows the number of students in a class who read any of 3 popular magazines A, B and C. One of these students is selected at random. Find the probability the student reads more than one magazine.

IUT debate club consist of 10 boys and 5 girls. A team of 4 members have to select from this club including the selection of a captain (from the team members). If the team has to include at most one girl, the number of ways selecting the team is-

The sum of 1+n(1−1x)+nn−12!(1−1x)2+………..∞ 1 + n \left ( 1 - \frac{1}{x} \right ) + n \frac{n - 1}{2} ! \left ( 1 - \frac{1}{x} \right )^{2} + \ldots \ldots \ldots . . ∞ will be-

A natural number x is chosen at random from the first 100 natural numbers. The probability that x+100/x >50 is-

An experiment consists of selecting a ball from a bag and spinning a coin. The bag contains 5 red balls and 7 blue balls. A ball is selected at random from the bag, its color is noted and then the ball is returned to the bag. When a red ball is selected, a biased coin with probability 2/3 of landing heads is spun. When a blue ball is selected a fair coin is spun. Find the probability that she obtains a head.

A parachutist fell after releasing himself at 50 m down without any resistance. When the parachute was opened then the rate of decrease the acceleration was 2 m/s−2 2 \mathrm{~m} / \mathrm{s}^{-2} and he fell on the ground with velocity of 3 m/s 3 \mathrm{~m} / \mathrm{s} . At what height he was released?

At what angle a projectile is to be projected so that its horizontal range is equal to the maximum height it reaches?

The dimension of an examination hall is 20 m × 10 m × 5 m. How many kilograms of air is present in the room?The temperature of air in the room is 30oC and molecular weight of air is 29.

A jar test was conducted with alum and it was found that optimum alum dosage obtained when 50 mL alum solution containing 1.0gm/L is added into 2 L of water. The concentration of alum dosage was:

A particle A of mass 2 kg is moving along a straight horizontal line with speed 12 m/s. Another particle B of mass m kg is moving along the same straight line in the opposite direction to A, with speed 8 m/s. The particle collide. The direction of motion of A is unchanged by the collision. Immediately after the collision, A is moving with speed 3 m/s and B is moving with speed 4 m/s. Find the value of m.

Two particles A and B have masses 5 m and km respectively, where k < 5. The particles are connected by a light inextensible string which passes over a smooth light fixed pulley. The system is held at rest with the string taut, the hanging parts of the string vertical and with A and B at the same height above a horizontal plane, as shown in the following figure. The system is released from rest. After release, A descends with celeration (1/4)g Find the tension in the string as A descends.

Suppose, your swimming velocity is twice of current in a river. You wish to cross the river perpendicularly having the current. But you reached 300 m far from the opposite of your starting point. Then width of the river is-

Length of a simple pendulum (100.0±0.5) cm, and time period T = (2.00 ± 0.01) s. Determine the percentage of error in acceleration due to gravity 'g'.

The recoil velocity of a gun of mass of 8 kg is 10 m/s when a bullet of mass of 10 g leaves from the gun. After penetrating 0.3 m inside the target the bullet stops. Calculate the applied resistance of the bullet?

A tennis ball coming with velocity, v₁ = 16ms-1 is sent back by a racket in the opposite direction with velocity, v₂ = 20ms-1. If the change of kinetic energy of the ball is ∆E = 9.25j, then calculate the change of momentum of the ball.

A space craft from the earth is moving towards the moon, find a location from the earth where at the gravitational force is zero. [Mass of the earth = 6 x 10²⁴ kg, Mass of the moon = 7.4 x 10²² kg, distance between the earth and the moon = 3.8 x 10⁸ m]

What is the height above the earth where the value of acceleration due to gravity is 40% of that on the earth's surface? (Radius of the earth, R= 6.38 x 10⁶ m)

A drop of water is falling through air. The terminal velocity of the drop is 1.2×10-2 m/s and co- efficient of viscosity of air, η= 1.8×10-5 Nsm-2 What is the diameter of the drop?