Putting It Together

Q.

Prove that $\sqrt{5}$ is irrational number

Q.

Prove that $\sqrt{6}$ is an irrational number.

Q. $\sqrt{3}$ is proved irrational by _____.

1. factorisation
2. expansion
3. rationalisation
4. contradiction

Q.

Find the sum of all natural numbers between 250 and 1000 which are exactly divisible by 3.

1. 156375

2. 156324

3. 147687

4. 156342

Q. The fifth term of the H.P :
$2,2\frac{1}{2},3\frac{1}{3},......,$ will be

1. 
   $5\frac{1}{5}$
2. 
   $3\frac{1}{5}$
3. 
   $\frac{1}{10}$
4. 
   $10$

Q.

A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: ₹ 200 for the first day, ₹ 250 for the second day, ₹ 300 for the third day, etc., the penalty for each succeeding day being ₹ 50 more than for the preceding day. How much money the contractor has to pay as penalty, if he has delayed the work by 30 days?

1. ₹ 28550

2. ₹27500

3. ₹27750

4. ₹ 28050

Q. Write down the series whose $r^{th}term$ s ${3.2}^{r+1}?$

1. 
   $0,2,4,...$
2. 
   $10,20,30,...$
3. 
   $5,10,15,...$
4. 
   $12,24,48,...$

Q.

Find the sum of all odd numbers between 0 and 50.

1. 625

2. 675

3. 700

4. 650

Q.

Find the sum of the first 15 multiples of 8.

1. 1000

2. 960

3. 500

4. 820