Using Euclid’s division lemma, if the cube of any positive integer is divided by 9 then the possible remainders are

(a)

0, 1, 8

(b)

1, 4, 8

(c)

0, 1, 3

(d)

0, 1, 3

The sum of the exponents of the prime factors in the prime factorization of 1729 is

(a)

1

(b)

2

(c)

3

(d)

4

Given F₁ = 1, F₂ = 3 and F_n = F_n-1 + F_n-2 then F₅ is

(a)

3

(b)

5

(c)

8

(d)

11

In an A.P., the first term is 1 and the common difference is 4. How many terms of the A.P. must be taken for their sum to be equal to 120?

(a)

6

(b)

7

(c)

8

(d)

9

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)

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

If a and b are the two positive integers when a > b and b is a factor of a then HCF (a, b) is ____________

(a)

b

(b)

a

(c)

ab

(d)

\(\frac { a }{ b } \)

If m and n are the two positive integers then m² and n² are ____________

(a)

Co-prime

(b)

Not co-prime

(c)

Even

(d)

odd

The difference between the remainders when 6002 and 601 are divided by 6 is ____________

(a)

2

(b)

1

(c)

0

(d)

3

Given a₁ = -1, \(a=\frac { { a }_{ n } }{ n+2 } \), then a₄ is ____________

(a)

\(-\frac { 1 }{ 20 } \)

(b)

\(-\frac { 1 }{ 4 } \)

(c)

\(-\frac { 1 }{ 840 } \)

(d)

\(-\frac { 1 }{ 120 } \)

How many terms are there in the G.P : 5, 20, 80, 320,..., 20480

(a)

5

(b)

6

(c)

7

(d)

9

Sum of infinite terms of G.P is 12 and the first term is 8. What is the fourth term of the G.P?

(a)

\(\frac { 8 }{ 27 } \)

(b)

\(\frac { 4 }{ 27 } \)

(c)

\(\frac { 8 }{ 20 } \)

(d)

\(\frac { 1 }{ 3 } \)

A square is drawn by joining the mid points of the sides of a given square in the same way and this process continues indefinitely. If the side of the first square is 4 cm, then the sum of the area of all the squares is ____________

(a)

8 cm²

(b)

16 cm²

(c)

32 cm² 

(d)

64 cm²

The sum of first n terms of the series a, 3a, 5a...is ____________

(a)

na

(b)

(2n - 1)a

(c)

n² - a

(d)

n²a²

In an A.P if the p^th term is q and the q^th term is p, then its n^th term is ____________

(a)

p+q-n

(b)

p+q+n

(c)

p-q+n

(d)

p-q-n

Sum of first n terms of the series \(\sqrt { 2 } +\sqrt { 8 } +\sqrt { 18 } +...\) is ____________

(a)

\(\frac { n(n+1) }{ 2 } \)

(b)

\(\sqrt { n } \)

(c)

\(\frac { n\left( n+1 \right) }{ \sqrt { 2 } } \)

(d)

1