Chapter Test Class IX: Real Numbers and Compound Interest

COMPLETE MCQ MATHEMATICS ASSESSMENT - Prime Maths

Full Marks: 32

Time: 55 minutes

Format: All Multiple Choice Questions

Group A [4 × 1 = 4]

Select the correct option in each case.

1. At present the population of a village is P and if the rate of increase of population per year be 2r%, the population after n years will be

(a)

\( P \left( 1 + \frac{r}{100} \right)^n \)

(b)

\( P \left( 1 + \frac{r}{50} \right)^n \)

(c)

\( P \left( 1 + \frac{r}{100} \right)^{2n} \)

(d)

\( P \left( 1 - \frac{r}{100} \right)^n \)

2. A person deposited Rs. 100 in a bank and received Rs. 121 after two years, the rate of compound interest is

(a)

10%

(b)

20%

(c)

5%

(d)

10.5%

3. \(\sqrt{5} - 3 = 2\) is

(a)

A rational number

(b)

A natural number

(c)

Equal to zero

(d)

An irrational number

4. Which of the following rational numbers have a terminating decimal expression?

(a)

\( \frac{125}{441} \)

(b)

\( \frac{77}{210} \)

(c)

\( \frac{15}{1600} \)

(d)

\( \frac{129}{2^2 \times 5^2 \times 7^2} \)

Group B [4 × 2 = 8]

All questions converted to multiple choice format.

1. To prove that \( 3\sqrt{7} \) is not a rational number, which approach is correct?

(a)

Assume \(3\sqrt{7}\) is rational, then \(\sqrt{7} = \frac{a}{3b}\) where a, b are integers, which implies \(\sqrt{7}\) is rational - a contradiction

(b)

Assume \(3\sqrt{7}\) is rational, then \(\sqrt{7} = \frac{a}{b}\) where a, b are integers with no common factors - leads to contradiction as 7 divides a²

(c)

Since \(\sqrt{7}\) is irrational and 3 is rational, their product must be rational

(d)

\(3\sqrt{7}\) can be written as \(\sqrt{63}\), and since 63 is not a perfect square, it's rational

2. If a sum of money doubles itself at certain rate compounded annually in n years, in how many years will the sum become four times of itself?

(a)

n years

(b)

2n years

(c)

3n years

(d)

n² years

3. Using the formula of simple interest, the amount at the end of 2nd year for a sum P at the compound interest rate of r% per annum is:

(a)

\( P \left(1 + \frac{r}{100}\right)^2 \)

(b)

\( P \left(1 + \frac{2r}{100}\right) \)

(c)

\( P \left(1 + \frac{r}{50}\right) \)

(d)

\( P + \frac{2Pr}{100} \)

4. Which of the following is an irrational number between 2 and 3?

(a)

2.5

(b)

\( \sqrt{4} \)

(c)

\( \sqrt{5} \)

(d)

\( \sqrt{9} \)

Group C [5 × 4 = 20]

All questions converted to multiple choice format. For questions with "OR", both parts are included as separate options.

1. The expression \( \left( 3 + 2\sqrt{5} \right)^2 \) is:

(a)

Irrational because it simplifies to \( 29 + 12\sqrt{5} \), which is a sum of rational and irrational

(b)

Rational because it equals \( 49 \)

(c)

Irrational because \( \sqrt{5} \) is irrational

(d)

Rational because it simplifies to \( 29 + 12\sqrt{5} \) and \( 12\sqrt{5} \) is rational

2. If p is a prime number, \( \sqrt{p} \) is:

(a)

Always rational

(b)

Always irrational

(c)

Rational if p is even, irrational if p is odd

(d)

Irrational except when p = 4

3. After rationalizing the denominator, \( \frac{1}{3-2\sqrt{2}+\sqrt{5}} \) simplifies to:

(a)

\( \frac{3+2\sqrt{2}-\sqrt{5}}{2} \)

(b)

\( \frac{3-2\sqrt{2}+\sqrt{5}}{12} \)

(c)

\( \frac{3+2\sqrt{2}-\sqrt{5}}{12} \)

(d)

\( \frac{3-2\sqrt{2}-\sqrt{5}}{4} \)

OR

The simplest value of \( \frac{\sqrt{7}-\sqrt{3}}{\sqrt{7}+\sqrt{3}} + \frac{\sqrt{7}+\sqrt{3}}{\sqrt{7}-\sqrt{3}} \) is:

(e)

2

(f)

5

(g)

10

(h)

\( \frac{10}{\sqrt{21}} \)

4. If simple interest and compound interest on a certain sum for two years are Rs. 8400 and Rs. 8652 respectively, then:

(a)

Rate = 5%, Sum = Rs. 80,000

(b)

Rate = 6%, Sum = Rs. 70,000

(c)

Rate = 8%, Sum = Rs. 60,000

(d)

Rate = 10%, Sum = Rs. 50,000

5. In how many years will Rs. 50000 amount to Rs. 60500 at 10% compound interest per annum?

(a)

1 year

(b)

2 years

(c)

3 years

(d)

4 years

OR

The height of a tree increases at 20% yearly. If present height is 28.8m, its height 2 years before was:

(e)

20 m

(f)

22 m

(g)

24 m

(h)

26 m

Assessment Results

Your Score: 0/32

Group A

0/4

4 × 1 mark questions

Group B

0/8

4 × 2 mark questions

Group C

0/20

5 × 4 mark questions

Question-wise Results:

Note: For questions with "OR" options, only one part needs to be answered. If you answer both, only the first selected option is considered.

Complete MCQ Mathematics Assessment - Irrationals & Compound Interest | For Class IX | © Prime Maths - 9038126497