#### Numbers and Sequences Two Marks Question

10th Standard EM

Reg.No. :
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Maths

Time : 00:45:00 Hrs
Total Marks : 20
10 x 2 = 20
1. We have 34 cakes. Each box can hold 5 cakes only. How many boxes we need to pack and how many cakes are unpacked?

2. Find the remainders when 70004 and 778 is divided by 7

3. Find the number of integer solutions of 3x $\equiv$ 1 (mod 15).

4. Write an A.P. whose first term is 20 and common difference is 8.

5. Find the number of terms in the A.P. 3, 6, 9, 12,…, 111.

6. A mother devides Rs.207 into three parts such that the amount are in A.P. and gives it to her three children. The product of the two least amounts that the children had Rs 4623. Find the amount received by each child.

7. Find the sum of
13+23+33+..+163

8. Find the least positive value of x such that
98 $\equiv$  (x + 4) (mod 5)

9. Show that any positive odd integer is of the form 4q + 1 or 4q + 3, where q is some integer.

10. Prove that $\sqrt { 3 }$ is irrational