Islamic University of Technology ইসলামিক ইউনিভার্সিটি অব টেকনোলজি ভর্তি পরীক্ষা ২০১৩-২০১৪

The baseball players malice toward the referee was revealed in his (spiteful) remarks to the media.which almost ruined the referee career.

CARTOGRAPHER: MAP:

Although Zahid is much too inexperienced for the managerial position,he is willful young man  and (obdurately) refuse to withdraw his application.

Excited about winning award, Marium walked up to the podium and delivered an animated acceptance speech.
Choose the option that is similar in meaning to the underlined word:

The doctors were pleased that their theory had been fortified by the new research.
The underlined word ‘fortified’ can be best replaced by-

Because the excellent preservation of the fossil, anatomical details of early horseshoe crabs were...... For the first time, enabling experts to .....the evolution of the horseshoe crab.

The skeleton of ........bird that was recently discovered indicated that this ancient creature......... today's birds in that ,unlike earlier birds and unlike reptilian ancestors,it had not a tooth in it's head.

Program: concert:

ENTHUSIASM: MANIA:

TOUT

Synonym of SCOTCH is

PLUMB

_______have concluded that the volcanic eruption caused a tidal wave.

If the sides of a triangle are 5,12,13 cm respectively.  Then the Triangle is--

∣$\begin{vmatrix} a + x& a - x& a - x\\ a - x & a + x & a - x\\ a - x & a - x & a + x\end{vmatrix} = 0$ then $x$ =?

If y = $\tan^{- 1}{\left ( \frac{x}{\sqrt{1 - x^{2}}} \right )}$    then find the value of $\frac{dy}{dx}$.

If $x = a \cos^3 \theta$ and $y = b \sin^3 \theta$ then $\frac{dy}{dx}$ = ?

Which of the following point is the reflection (image) of the point (3, -3) in the line 2y = x + 1 ?

What is the distance between the lines 4x + 3y + 16 = 0 and 4x + 3y + 26 = 0 ?

If the circles x2 + y2 - 16x - 12y + 75 =0 and 5x2 + 5y2 - 32x - 24y + 75 =0  touch each other, then the equation of the common tangent of their point of contact is --

If point (a, 5) has equal distances from both the y-axis and a point (7, 2), then the of value of a is?

$x = \tan \sqrt{y}$ হল, x=1x=1 এর জন্য dy/dxdy/dx এর মান কত?

$\frac{d}{dx}\ln\left(\frac{\sin x}{1-\cos x}\right)$ = ?

The function x3 - 12x + 5 has a stationary value when --

Let g be a function whose derivative g' and is shown in the graph below.  For what value of x,  the value of g is minimum ?

A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 3 ft s-1. How rapidly is the area enclosed by the ripple increasing at the end of 10 s ?

$\int \tan^{3} 5x \sec^{2} 5x dx$ = ?

$\int_{0}^{\frac{3 \pi}{4}}|\cos x| d x$ = ?

Find the area of the region enclosed between the curves y = x2 and y = x + 6

sinx sin ( x+30°) + cosx cos( x + 30°) =?

The fundamental period of $\frac{1}{2} \cot \left(\frac{2}{3}\right) \theta$ is-

How many ways can you arrange the letters ABCDEFGH so that the word will contain the string ABC ?

Let n be a positive integer.  Then the value of $\sum_{k = 0}^{n} \left ( - 1 \right )^{k} \left ( \frac{n}{k} \right )$    is --

$\frac{1}{3} i$  এর বর্গমূল কোনটি?

The orbit of the earth around the sun is an ellipse with the sun at one focal point.  If the ellipse has a major axis of length 186 million miles and an eccentricity of approximately 0.016. Then, the shortest and greatest distances between the earth and the sun are --

Two listening posts, A and B are 500m apart. An explosion is heard at these posts. From the difference in times it is determined that the site of explosion is 800m closer to A then to B.  If the site of explosion lies on a hyperbolic curve,  then the equation of the hyperbola is --

A uniform beam AB of weight 100 N and 6m long had two bodies of weights 60 N and 80 N  suspended  from its two ends A and B,  respectively. At what distance from B, the beam should be supported so that it may rest horizontally?

In a study, it was discovered that 25% of the paintings of a certain art gallery are not original. A collector, in 15% cases, makes a mistake in judging if a painting is original or a copy. If she buys a painting thinking that it is original, what is the probability that it is not original ?

As a traffic light turns green, a waiting car starts with a constant acceleration of 6.0m/s² . At the instant the car begins to accelerate, a truck with a constant velocity of 21m/s passes the car through the next lane. How fast will the car be traveling when it overtakes the truck?

A race car has a mass of 710 kg. It starts from rest and travels 40.0m in 3.0 s. The car is uniformly accelerated during the entire time. What net force is exerted on it?

A partially inflated balloon contains 500m³ of Helium at 27°C at 1-atm pressure. What is the volume of the Helium at an altitude of 3000m, where the pressure is 0.5 atm and temperature is -3°C?

On July 19, 1969, Apollo 11's orbit around the moon was adjusted to an average orbit of 111 km. The radius of the moon is 1785 km, and the mass of the moon is 7.3 x 10²²kg. How many minutes did Apollo I take to orbit the moon once? G=6.67×10−11N−m2Kg−2 G = 6.67 × 10^{- 11} N - m ² K g^{- 2}

A platform is suspended by four wires at its corners. The wires are 3m long and have a diameter of 2.00mm. Young's modulus of the material of the wire is 1.8 x 10¹¹ N/m². How far will the platform drop due to the elongation of the wires if a 50kg load is placed at the centre of the platform?

When the velocity of a moving object is increased by 4m/s, its kinetic energy is doubled.What is the initial velocity of the object?

A marbel with speed 20cm/s rolls off the edge of a table 80cm high. How far, horizontally,from the tabel edge does the marble strike the floor?

When an electric fan rotating at an angular velocity of 30 rad/s is switched off, its velocity reduces to 10 rad/s after 20 revolution. What is the angular retardation of the fan?

It is required to install an electric pump to lift water from an underground tank to a 1000 liter overhead reservoir which has 25 m height. What must be the power of the electric motor to fill the tank in 10 mins.

A period has 3 velocities 10 m/s,  20 m/s and 30 m/s inclined at angle of 120° to one another.  The magnitude of the resultant velocity is --

An object is thrown vertically upward from the ground with an initial velocity of $80\ fts^{-1}$. Its heights above the ground is parabola and is given by the equation: $s=80t-16t^2$. How high does the object rise above the around?

An airplane is flying on a straight level  course at 200 Km/ hour at a height of 1000 m above the ground. An anti-aircraft gun located on the ground fires a shell with an initial velocity of 300 m/s,  at the instant when the plane  is vertically above it. At what inclination, to the horizontal, should the gun be fired to hit the plane ?