Islamic University of Technology ইসলামিক ইউনিভার্সিটি অব টেকনোলজি ভর্তি পরীক্ষা ২০২২-২০২৩

Choose the appropriate word for the blank space to complete the sentence of the following passage:Ibn al-Haytham's discoveries in optics and vision______ centuries of misunderstanding. In his experiments, he observed that light coming through a tiny hole travelled in straight lines and projected an image onto the opposite wall.

Choose the appropriate word for the blank space to complete the sentence of the following passage:The Polish astronomer Johannes Hevelius 90 . _______ to honor Ibn al-Haytham, alongside Galileo, in his most famous work on the Moon, Selenographia, published in 1647.

Choose the word or phrase which most nearly opposite of the given wordModest

Choose the word or phrase which most nearly opposite of the given wordTenacious

Choose the word or phrase which most nearly opposite of the given wordRaze

Choose the word or phrase which most nearly opposite of the given wordImpetuous

Choose the word or phrase which most nearly opposite of the given wordExodus

Identify the correct synonym by looking for word roots, prefixes, suffixes. Choose the word that means the same or about the same as the italicized word Another year of penury...

Identify the correct synonym by looking for word roots, prefixes, suffixes. Choose the word that means the same or about the same as the italicized word .... disparaging remarks

Identify the correct synonym by looking for word roots, prefixes, suffixes. Choose the word that means the same or about the same as the italicized word..... in retrospect

Identify the correct synonym by looking for word roots, prefixes, suffixes. Choose the word that means the same or about the same as the italicized word... an egregious error.

Identify the correct synonym by looking for word roots, prefixes, suffixes. Choose the word that means the same or about the same as the italicized wordA misanthrope....

Choose the appropriate word for the blank space to complete the sentence of the following passage:But he realized that light entering the eye was only the first step in seeing. He built on the work of Greck physician Galen who had 2. ______ a detailed description of the eye and the optic pathways. Today the oldest-known drawing of the nervous system is from Ibn al-Haytham's Book of Optics, in which the eyes and optic nerves are illustrated.

Choose the appropriate word for the blank space to complete the sentence of the following passage:Ibn al-Haytham also subscribed to a method of empirical analysis to accompany theoretical postulates that is similar in certain ways to the scientific method we know today. He realized that the senses were prone to error, and he devised methods of verification, testing and experimentation to 3 . ______ the truth of the natural phenomena he perceived. Up until this time, the study of physical phenomena had been an abstract activity with occasional experiments.

Choose the appropriate word for the blank space to complete the sentence of the following passage:After his death, Ibn al-Haytham's writings were more 4. _________ in Latin than Arabic. The only significant work in Arabic that built on Ibn alHaytham's ideas was produced in the early part of the fourteenth century (in present day Iran) by Kamal al-Din al-Farisi, who was himself a brilliant scientific thinker. When Ibn alHaytham's Book of Optics was translated into Latin, it had great influence and was widely studied. It was published as a print edition in 1572 so that it could be made more easily available.

If the following vectors are coplanar find the value of a.$\begin{array}{l} \vec{A}=\hat{i}+\hat{j}-a \hat{k} \\ \vec{B}=2 \hat{i}-\hat{j}+3 \hat{k} \\ \vec{C}=-\hat{i}+2 \hat{j}-\hat{k} \end{array}$

If the coordinates of the ends of a diameter of a circle are (−2,3) (-2,3) and (3,4) (3,4) . Which is the equation of the circle?

How many numbers greater than 4000 can be formed with the digits 0,3,5,6,8 0,3,5,6,8 without repetition of any digit in the any number?

In how many ways can a selection of three consonants and two vowels be made from the letters of the word 'LOGARITHMS'

3sec⁴θ + 8 = 10 sec² θ হলে, tanθ এর মান কত?

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

Let, $A=\left[\begin{array}{ccc}1 & 0 & -k \\ 2 & 1 & 3 \\ k & 0 & 0\end{array}\right]$ is an invertible matrix. Then the value of $k$ is-

The equation x+2y−8=0 x+2 y-8=0 and 2x+4y+8=0 2 x+4 y+8=0 are representing the two sides of a square. What is the area of the square?

Two tangents of the circle $x^{2}+y^{2}=4$ at points $A$ and $B$ intersect at $P(-4,0)$ . What is the area of quadrilateral PAOB, where 0 is the center of the circle?

In a $\Delta ABC$, $\cos^{2}A+\cos^{2}B+\cos^{2}C=\cos A \cos B+\cos B\cos C+\cos C\cos A$, then the triangle is

$\lim _{\mathrm{x} \rightarrow 0} \frac{3^{2 \mathrm{x}}-2^{3 \mathrm{x}}}{\mathrm{x}}$ is equal to-

The function $f(x)=-\frac{x}{2}-\frac{2}{x}$ has a local minimum at

Find the area of the closed figure bounded by the following curves
y=y = $\sqrt{x}, y \, = \, \sqrt{4 - 3x}$, y = 0.

On a dark night, a thin man of 6 feet tall walks away from a 24 feet high lamp post at a rate of 5 mph . How fast is the end of his shadow moving?

A ray of light passing through the point (1,2) (1,2) reflects on the x x -axis and the reflected ray passes through the point (5,3) (5,3) . The equation of the representing the original ray is-

The equation of the tangent line(s) of the circle $(x-2)^{2}+(y+3)^{2}=160$ is/are-

If $\left [ \begin{matrix} a & b \\ a_{1} & b_{1} \end{matrix} \right ] \left [ \begin{matrix} 3 & - 5 \\ - 1 & 2 \end{matrix} \right ] = \left [ \begin{matrix} 1 & - 1 \\ 2 & 0 \end{matrix} \right ]$,   then the values of a and b are ?

The coefficient of the term independent of $x$ in the expansion $\left(2 x+\frac{1}{6 x}\right)^{10}$ is

Find the eccentricity of the ellipse $16 x^{2}+25 y^{2}=$ 400.

Three forces $4 \mathrm{~N}, 3 \mathrm{~N}$ and 6 N act at a point in the direction parallel to the sides $\mathrm{AB}, \mathrm{BC}$ and CA of an equilateral triangle $A B C$ respectively. Find their resultant.

A particle A is in equilibrium under the following forces as shown below. Find the value of T.

A particle starts from rest and travelled 192 m before coming to the rest again. Initially, it travelled with acceleration of $25 \mathrm{~ms}^{-2}$ and the retardation of $5 \mathrm{~ms}^{-2}$ . Find the maximum velocity of the particle.

Three cards are drawn at random from a pack of 52 cards. Find the probability that the three cards may be King.

A projectile was thrown with 45 degree from the ground at a velocity of $44.3 \mathrm{~ms}^{-1}$ . Calculate the vertical position (with one decimal place) of the projectile at a horizontal distance of 100 m .

If $p$ and $q(\neq 0)$ are the roots of the equation $x^{2}+$ px+q=0 p x+q=0 , then find the least value of $x^{2}+p x+q$ where $\mathrm{x} \in \mathbb{R}$?

If the difference between the roots of the equation $x^{2}+m x+1=0$ is less than 0 then the set of possible values of $m$ is-

If $(\sqrt{3}+i)^{42}=4^{20}(p+q i)$, then the value of $p^{2}+$ $\mathrm{q}^{2}$ is equal to-

Circles are drawn with diameter being any focal chord of the parabola $y^{2}-4 x+4 y-8=0$ will always touch a fixed line, its equation is-

The foci of the ellipse $\dfrac{x^{2}}{16} + \dfrac{y^{2}}{b^{2}} =1$ and the hyperbola $\dfrac{x^{2}}{144} - \dfrac{y^{2}}{81} =\dfrac{1}{25}$ coincide, then the value of $b^{2}$ is:

General solution of $1+\sin (x) \sin ^{2}\left(\frac{x}{2}\right)=0$ is-

Suppose you have thrown a ball upwards from the rooftop of IUT Academic Building 1 with a velocity of $4 \mathrm{~m} / \mathrm{s}$ at an angle of $60^{\circ}$ with the horizontal line. The ball reaches the ground 10 meters away from the building. The height of the building is-

If i2 = - 1 then $\sqrt{8 + 6 i}$ = ?

A cross-section of a parabolic reflector is shown in the figure below. The light source at the focus of the parabola and the opening of the focus is 10 cm. The equation of the parabola is-

The front wheels of an automobile, when run onto a platform scale, are found to support 8010 N , while the rear wheels can support 6680 N . The auto has a 2 m wheel base (distance from the front axle to the rear axle). Locate the center of gravity of the car from the front wheel.

An irregularly shaped object 10 m long is placed with each end on two nearby scales. If the scale on the right reads 94 N and the scale on the left reads 60 N , how far from the lef is the object's center of gravity? (1/se acceleration due to gravity, $\mathrm{g}=$ $\left.9.8 \mathrm{~ms}^{-2}\right)$