UNIBEN Engineering and Physical Sciences Post UTME General Paper Past Questions

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A radioactive sample initially contains N-atoms. After three half-lives the number of atoms that disintegrated is

For the correction of myopic defects in human eye we require

The operation of optical fibre is based on the principle of

A concave mirror has a focal length of 12 cm. At what distance from the mirror should an object be placed to give an image exactly as the object?

A piano wire 0.5 m long has a total mass of 0.01 kg and is stretched with a tension of 800 N. Calculate the frequency of the wire when it sounds its fundamental note

A wave of frequency 10 Hz forms a stationary wave pattern in a medium where the velocity is 20 cm/s. The distance between adjacent nodes is

Radio waves have a velocity of \(3\times10^8\ \mathrm{m/s}\). A radio station broadcasts at a frequency of 800 kHz. Find the wavelength of the broadcast.

Find the equation of a straight line of gradient 2 through the point (1,4)

What is the midpoint of the line joining the points \((2x,y)\) and \((x,2y)\)?

A binary operation on the set of real numbers excluding -1 is such that all \(m, n \in \mathbb{R}\), \(m \Delta n = m + n + mn\). Find the identity element of the operation.

Make \(r\) the subject of the formula \(\frac{x}{r+a} = \frac{a}{r}\)

Calculate and correct to 2 significant figures, the length of arc of a circle of radius 3.5 cm which subtends an angle of 75\(^{\circ}\) at the centre of the circle. (Take \(\pi = \frac{22}{7}\))

The angle of elevation of a point T on a tower from a point U on the horizontal ground is 30°. If TU = 54 m, how high is T above the horizontal ground?

X and Y are two events. The probability of X or Y is 0.7 and the probability of X is 0.4. If X and Y are independent, find the probability of Y.

The probability of an event P is \(\frac{3}{4}\) while that of another event Q is \(\frac{1}{6}\). The probability that both P and Q occur is \(\frac{1}{12}\). What is the probability that at least one of P and Q occurs?

Factorize \(14!-10(13!)\)

4.5 and 5 are respectively the averages of two sets of numbers 3, 4, x, y and 2x, y, 4, 3. Calculate the values of (x, y)

Find the area bounded by the curve \(y = x(2-x)\), the x-axis, \(x=0\) and \(x=2\)

The turning point on the curve \(y = 3x^2 - 9x + 12\) is

If \(\sin \theta = \frac{15}{17}\), where \(\theta\) is acute, find \(\tan \theta\)

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