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

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

If the HCF of 65 and 117 is expressible in the form of 65m - 117 , then the value of m is

(a)

4

(b)

2

(c)

1

(d)

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

The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is

(a)

2025

(b)

5220

(c)

5025

(d)

2520

7^4k \(\equiv \) ________ (mod 100)

(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

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

If 6 times of 6^th term of an A.P. is equal to 7 times the 7^th term, then the 13^th term of the A.P. is

(a)

0

(b)

6

(c)

7

(d)

13

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

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

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

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 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

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

(a)

14400

(b)

14200

(c)

14280

(d)

14520