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

7^4k \(\equiv \) ________ (mod 100)

(a)

1

(b)

2

(c)

3

(d)

4

The first term of an arithmetic progression is unity and the common difference is 4. Which of the following will be a term of this A.P.

(a)

4551

(b)

10091

(c)

7881

(d)

13531

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

If A = 2⁶⁵ and B = 2⁶⁴ + 2⁶³ + 2⁶² +...+ 2⁰ Which of the following is true?

(a)

B is 2⁶⁴ more than A

(b)

A and B are equal

(c)

B is larger than A by 1

(d)

A is larger than B by 1

If the sequence t₁, t₂, t₃... are in A.P. then the sequence t₆, t₁₂, t₁₈,.... is 

(a)

a Geometric Progression

(b)

an Arithmetic Progression

(c)

neither an Arithmetic Progression nor a Geometric Progression

(d)

a constant sequence

If a and b are the two positive intergs 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 3 is the least prime factor of number and 7 is least prime factor of b, then the least prime factor a + b is ____________

(a)

a + b

(b)

2

(c)

5

(d)

10

44 ≡ 8 (mod12), 113 ≡ 85 (mod 12), thus 44 x 113 ≡______(mod 12):

(a)

4

(b)

3

(c)

2

(d)

1

The first term of an A.P. whose 8^th and 12^th terms are 39 and 59 respectively is ____________

(a)

5

(b)

6

(c)

4

(d)

3

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 boy saves Rs. 1 on the first day Rs. 2 on the second day, Rs. 4 on the third day and so on. How much did the boy will save upto 20 days?

(a)

2¹⁹ + 1

(b)

2¹⁹- 1

(c)

2²⁰- 1

(d)

2²¹- 1

If p, q, r, x, y, z are in A.P, then 5p + 3, 5r + 3, 5x + 3, 5y + 3, 5z + 3 form ____________

(a)

a G.P

(b)

an A.P

(c)

a constant sequence

(d)

neither an A.P nor a G.P