Problem 1 :

The scientific notation of the number 0.00005896 is

(A)  5.896 × 10-5   (B)  5896 × 105   (C)  58.96 × 10-4

Solution  :

To convert the given decimal into scientific notation, we have to move the decimal 5 digits to the right.

Since we move the decimal to the right, the exponent of 10 will have negative sign.

So, the scientific notation is 5.896 x 10-5

Problem 2 :

The decimal form of the number 5.243 × 10-6 is

(A)  5.243   (B)  0.000005243   (C)  0.05243

Solution :

Since the power of 6 has a negative sign, we are supposed to move the decimal 6 digits to the left. Since we have only one digit before the decimal, we have to use five more zeroes.

So, the decimal form is 0.000005243

Problem 3 :

Which of the following is the decimal expansion of 10/3 ?

(A)  333.33...   (B)  33.333...   (C)  3.3333...

Solution :

The value of 10/3 is 3.333...

So, the given fraction will have non-terminating and repeating decimal expansion.

Problem 4 :

Find the value of log55

(A)  2   (B)  0   (C)  1

Solution :

We know that, logaa  =  1

So, the value of log55  =  1.

Problem 5 :

Which of the following is an irrational number between 1/7 and 2/7 ?

(A)  0.3500...   (B)  0.4501...   (C)  0.1501...

Solution :

The value of 1/7  =  0.142857142857.....

The value of 2/7  =  0.285714285714.....

Here, the two decimal expansions are non-terminating and repeating.

So, 1/7 and 2/7 are rational numbers.

We know that, between any two rational numbers, there are infinitely many irrational numbers.

So, the irrational number between 1/7 and 2/7 is 0.1501

Problem 6 :

If U  =  {x/x < 10, x Є N}, A  =  {x/x < 9, x is even N}, and B  = {x/x ≤ 8, x is prime N}. Find A - B

(A)  {4}   (B)  {4, 6, 8}   (C)  {6, 8}

Solutio  :

U  =  {1, 2, 3, 4, 5, 6, 7, 8, 9}

A  =  {2, 4, 6, 8}

B  =  {2, 3, 5, 7}

To find A - B, elements only in A not in B.

A - B  =  {4, 6, 8}

Problem 7 :

2√2 + 5√3 and √2 - 3√3

(A)  √3 - 2√2   (B)  √2 + 2√3   (C)  3√2 + 2√3

Solution :

(2√2 + 5√3) + (√2 - 3√3)

By combining like terms,

=  2√2 + √2 + 5√3 - 3√3

=  √2(2 + 1) + √3(5 - 3)

=  3√2 + 2√3

Problem 8 :

Simplify (5 + √5) and (5 - √5)

(A)  10   (B)  5   (C)  20

Solution :

=  (5 + √5) (5 - √5)

=  (5 × 5) - (5 × √5) + (√5 × 5) - (√5)2

=  25 - 5√5 + 5√5 - 5

=  25 - 5

=  20

Problem 9 :

What is the degree of the polynomial 2 - y- y3 + 2y8

(A)  8   (B)  2   (C)  3

Solution :

Given polynomial,

Highest power  =  8

So, the degree of the polynomial is 8.

Problem 10 :

What is the value of the polynomial

p(x)  =  5x- 3x + 7 at x  =  1

(A)  8   (B)  9   (C)  6

Solution :

Given,

p(x)  =  5x- 3x + 7

If x  =  1

p(1)  =  5(1)- 3(1) + 7

=  5 - 3 + 7

=  9

So, the value of the polynomial is 9.

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