Number System-Test 3

Answer: Option B

Explanation

A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole number that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.

Answer: Option C

Explanation

let the number be 'x', Then its reciprocal is $\frac{1}{x}$

∴ We have $x+\frac{1}{x}=\frac{17}{4}$

Multiplying every term by 4x, we get 

$= 4x\times x+4x\times \frac{1}{x}= 4x\times \frac{17}{4}$

= 4x²+4=17x

= 4x²-17x+4=0

= 4x²-16x-x+4=0

= 4x(x-4)-1(x-4)=0

= (4x-1)(x-4)=0

$\therefore x=4 or \frac{1}{4}$

Hence, Option C is correct.

Answer: Option C

Explanation

Let the number be 'x', Then its reciprocal is $\frac{1}{x}$

Given that,

$$\begin{gathered} = x\frac{1}{x}=\frac{26}{5} \\ = \frac{x^2+1}{x}=\frac{26}{5} \end{gathered}$$

= 5(x²+1)=26x

= 5x²+5-26=0   [By factorising]

= 5x²-25x-x+5=0

= 5x(x-5)-1(x-5)=0

= (5x-1)(x-5)=0

= x=5 or $\frac{1}{5}$ 

Hence, Option C is correct.

Answer: Option D

Explanation

Let the ten's digit be 'x'

Then, number (10x+3)+ sum of digits = (x+3)

So,

⇒ (x+3)=$\frac{2}{11}$(10x+3)

⇒ (11x+33)=(20x+6)

= (11x-20x)=6-33

= -9x=-27

= x=3

∴ the number 33.

Hence, Option D is correct.

Answer: Option A

Explanation

The difference between the two numbers is 50

let the numbers be x+y

∴ y-x=50

y=x+50

$$\begin{gathered} =\frac{x}{y}=\frac{3}{8} \\ =x=\frac{3y}{8} \\ =y-\frac{3y}{8}=50 \\ =8y-\frac{3y}{8}=50 \\ =5y=400 \\ \therefore x=y-50=30 \end{gathered}$$

The largest number is 80 and smallest number is 30.

Hence, Option A is correct.