**UNIVERSITY OF LAGOS
2006 POST-UTME
MATHEMATICS**

1. If

n P 3 = 6

n C 2

find the value of n

A. 6

B. 3

C. 5

D. 1

2. Express

3x – 1

(x + 1)(x – 3)

as partial fractions

A. 1/(x + 1) + 2/(x – 3)

B. 2/(x + 1) – 1(x – 3)

C. 2/(x + 3) + 1(x – 1)

D. 1(x – 1) + 2(x – 3)

3. T he letters of the word “MATRICULATION” are cut and put in a box. One letter is drawn at random from the box. Find the probability if a vowel is drawn

A. 7/13

B. 3/13

C. 6/13

D. 4/13

4. T he sum to infinity of a Geometric progression is 100. Find its first term if the common ratio is 1/4

A. 75

B. 70

C. 65

D. 60

5. D ivide x 3 + 64x 2 by x + 4

A. x 2 + 4x – 16

B. x 2 – 4x + 16

C. x(4 -x 3 )

D. x 2 + 4x + 16

6. F ind x if (x base2 ) 2 = 100100 base2

A. 6

B. 100

C. 12

D. 110

7. T wo distinct sectors in the same circle subtend 100 0 and 30 0 respectively at the centre of the circle. Their corresponding arcs are in the ratio

A. 1 : 100

B. 3 : 1

C. 5 : 2

D. 10 : 3

8. A steel ball of radius 1cm is dropped into a cylinder of radius 2cm and height 4cm. If the cylinder is now filled with water, whatis the volume of the water in the cylinder?

N:B ’22/7′ represents ‘pi’

A. 44(22/7) / 3cm 3

B. 12(22/7)cm 3

C. 40(22/7)cm 3 / 3

D. 32(22/7)cm 3

9. PQRS is a cyclic quadrilateral with PQ as diameter of the circle. If

Thanks.

VNTI ̈́ ͂ ̷̐ ̈́ ̈́ ͂

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