Euclid’s division lemma states that for positive integers a and b, there exist unique integers q and r such that a = bq + r , where r must satisfy

(a)

1 < r < b

(b)

0 < r < b

(c)

0 \(\le\) r < b

(d)

0 < r \(\le\) b

7^4k \(\equiv \) ________ (mod 100)

(a)

1

(b)

2

(c)

3

(d)

4

An A.P. consists of 31 terms. If its 16^th term is m, then the sum of all the terms of this A.P. is

(a)

16 m

(b)

62 m

(c)

31 m

(d)

\(\frac { 31 }{ 2 } \) m

The next term of the sequence \(\frac { 3 }{ 16 } ,\frac { 1 }{ 8 } ,\frac { 1 }{ 12 } ,\frac { 1 }{ 18 } \), ..... is

(a)

\(\frac { 1 }{ 24 } \)

(b)

\(\frac { 1 }{ 27 } \)

(c)

\(\frac { 2 }{ 3 } \)

(d)

\(\frac { 1 }{ 81 } \)

The value of (1³ + 2³ + 3³ +...+15³) - (1 + 2 + 3 +...+ 15)is 

(a)

14400

(b)

14200

(c)

14280

(d)

14520

We have 34 cakes. Each box can hold 5 cakes only. How many boxes we need to pack and how many cakes are unpacked?

Find the greatest number that will divide 445 and 572 leaving remainders 4 and 5 respectively.

Solve 8x \(\equiv \) 1 (mod 11)

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

In an A.P., sum of four consecutive terms is 28 and their sum of their squares is 276. Find the four numbers.

Find the sum of
1 + 3 + 5 +..+ to 40 terms

Find the sum of
9³ + 10³ +.......+ 21³

Is 7 x 5 x 3 x 2 + 3 a composite number? Justify your answer 

The sum of first n, 2n and 3n terms of an A.P are S₁, S₂ and S₃ respectively prove that S₃ = 3 (S₂ - S₁)

Find the general term for the following sequences.
\(\frac { 1 }{ 2 } ,\frac { 2 }{ 3 } ,\frac { 3 }{ 4 } \)

A man has 532 flower pots. He wants to arrange them in rows such that each row contains 21 flower pots. Find the number of completed rows and how many flower pots are left over.

Today is Tuesday. My uncle will come after 45 days. In which day my uncle will be coming?