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JAMB Mathematics Past Questions & Answers - Page 10

46.

Solve the following quadratic inequality: x2x - 4 ≤ 2

A.

3<x<2

B.

2x3

C.

x2,x3

D.

2<x<3

Correct answer is B

x2x42
Subtract two from both sides to rewrite it in the quadratic standard form:
= x2x4222
= x2x60
Now set it = 0 and factor and solve like normal.
= x2x - 6=0
= (x3)(x+2)=0
x + 2 = 0 or x - 3 = 0
x = -2 or x = 3
So the two zeros are -2 and 3, and will mark the boundaries of our answer interval. To find out if the interval is between -2 and 3, or on either side, we simply take a test point between -2 and 3 (for instance, x = 0) and evaluate the original inequality.
= x2x42
= (0)2(0)42
= 0042
42
Since the above is a true statement, we know that the solution interval is between -2 and 3, the same region where we picked our test point. Since the original inequality was less than or equal, we include the endpoints.
2x3.

47.

Let a binary operation '*' be defined on a set A. The operation will be commutative if

A.

a*b = b*a

B.

(a*b)*c = a*(b*c)

C.

(b ο c)*a = (b*a) ο (c*a)

D.

None of the above

Correct answer is A

A binary operation '*' defined on a set A is said to be commutative only if a*b=b*a, ∀a, b∈A. If (a*b)*c=a*(b*c), then the operation is said to associative ∀ a, b∈ A. If (b ο c)*a=(b*a) ο (c*a), then the operation is said to be distributive ∀ a, b, c ∈ A.

48.

If 2x3+6x2+17x - 21 is divided by (x+1), then the remainder is

A.

32

B.

30

C.

-30

D.

-32

Correct answer is C

Let p(x)=2x3+6x2+17x21

Using the remainder theorem

Let x+1=0

x=1

Since, (x+1) divides p(x), then, remainder will be p(-1)

⇒ p(-1) = -2(-1)3+6(1)2 + 17(-1) - 21

∴ p(-1) = -30

49.

How many students scored at least 25%

A.

16

B.

19

C.

3

D.

8

Correct answer is A

Number of students who scored atleast 25% = 5 + 3 + 8 = 16

50.

Find the matrix A

A [0121][2110]

 

A.

[211/21/2]

B.

[011/21/2]

C.

[2101]

D.

[211/22]

Correct answer is B

Let A = [abcd]

i.e [abcd] [0121][2110]

[a(0)+b(2)a(1)+b(1)c(0)+d(2)c(1)+d(1)][2110]

[2bab2dcd][2110]

By comparing

2b = 2

a - b = -1

2d = 1 and

c - d = 0

∴ b = 2/2 = 1

a - b = -1

⇒ a - 1 = -1

∴ a = 0

∴ d = 1/2

⇒ c = d

∴ c = 1/2

∴The matrice A = [011/21/2]