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More solutions to some UTME past questions

Question 1

The energy of a photon having a wavelength of 10^-10m is{utme 2013}
A. 1.7 x 10-12J     B. 2.0 x 10-15J            C. 1.7 x 10-13J                 D. 2.0 x 10-12J

Solution

E = hf = hc/λ

h is the planck’s constant = 6.63 × 10–34 J s

c is the speed of light = 3 x10^8

λ is the wavelength

E = (6.63 × 10–34 * 3 x 10^8)/10^-10

E = 19.89 x 10^-16 = 1.989 x 10^-15 = 2 x 10^-15 J

B is the correct answer

Question 2

The bond between silicon and germanium is{utme 2013}
A. ionic          B. dative                   C. covalent                         D. trivalent

Solution

The bond is covalent. C is the correct option

Question 3

If a current of 2.5A flows through an electrolyte for 3 hours and 1.8g of a substance is deposited, what is the mass of the substance that will be deposited if a current of 4A flows through it for 4.8 hours?{UTME 2013}
A. 4.8g        B. 2.4g      C. 3.2g     D. 4.2g     E. 4.6g

Solution

M = ZIt

Z = M / It = 1.8 /2.5*3 = 0.24 g/Ah

Z is electrochemical equivalence and it is a constant

If the current and the time changes

M = 0.24*4*4.8 = 4.6g

E is the correct option

Question 4

An electric device is rated 2000W, 250V. Calculate the maximum current it can take.{utme 2013}
A. 6A         B. 9A          C. 8A       D. 7A

Solution

P = Iv

2000 = 250*I

I = 2000/250

I = 8A

C is the correct option

Question 5

A house has ten 40W and five 100W bulbs. How much will it cost the owner of the house to keep them lit for 10 hours if the cost of a unit is N5?{utme2013}

A. N20         B. N90          C. N50             D. N45

Solution

Total power = 10*40 + 5*100 = 900W =0.9kw

Energy =power x time(hour)= 0.9*10 =9kwh

1kwh = N5

9kwh = N5 *9 = N45

D is the correct answer

Question 6

Calculate the force acting on an electron of charge 1.5 x 10-19C placed in an electric field of intensity 105Vm-1.{utme 2013}
A. 1.5 x 10-14N            B. 1.5 x 10-11N              C. 1.5 x 10-12N                       D. 1.5 x 10-13N

Solution

Electric field intensity = force / charge

10^5 = force/1.5 x 10^-19

force = 1.5 x 10^-19 * 10^5 = 1.5 x 10^-14 N

A is the correct option

Solution 7

A man 1.5m tall is standing 3m in front of a pinhole camera whose distance between the hole and the screen is 0.1m.
What is the height of the image of the man on the screen?{utme 2013}
A. 1.00m        B. 0.05m         C. 0.15m                 D. 0.30m

Solution

Image distance/object distance = image height/object height

0.1/3 = image height / 1.5

image height = 1.5*0.1 /3 = 0.05 m

B is the correct option

Question 8

Two liquids X and Y having the same mass are supplied with the same quantity of heat. If the temperature rise in X is twice that of Y, the ratio of specific heat capacity of X to that of Y is{utme 2013}
A. 1 : 4                  B. 2 : 1                 C. 1 : 2                     D. 4 : 1

Solution

mxcxQx = mycyQy

mx = my

Qx = 2Qy

cx*2Qy = cyQy

cx/cy = 2/1 = 2:1

B is the correct option

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