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What is the remainder when \( 4^{1012}\) is divided by 7?

A) 1
B) 2
C) 3
D) 4

Correct Answer:

A) 1

Part of solved CDS Maths(1) questions and answers : Exams >> CDSE >> CDS Maths(1)

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Similar Questions

1). What is the highest common facter of \( 2x^{3}\)+\( x^{2}\)-\( x\)-\( 2\) and \( 3x^{3}\)-\( 2x^{2}\)+\( x\)-\( 2\)?

A). \( x-1\)

B). \( x+1\)

C). \( 2x+1\)

D). \( 2x-1\)

2). What is the remainder when \( \left( 1235 \times 4523 \times 2451\right)\) is divided by 12?

A). 1

B). 3

C). 5

D). 7

3). What is the remainder when \( \left(17^{23} + 23^{23} + 29^{23}\right)\) is divided by 23?

A). 0

B). 1

C). 2

D). 3

4). \( p\),\( q\) and r are prime numbers. Such that p< q

A). 1

B). 2

C). 3

D). None of these

5). The LCM of two numbers is 90 times their HCF. The sum of DCM and HCF is 1456. If one of the numbers is 160; then what is the other number?

A). 120

B). 136

C). 144

D). 184

6). The LCM of two integers is 1237. What is their HCF?

A). 37

B). 19

C). 1

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7). What is \( \Large \frac{1}{a-b} \)-\( \Large \frac{1}{a+b} \)-\( \Large \frac{2b}{a^{2}+b^{2}} \)-\( \Large \frac{4b^{3}}{a^{4}+b^{4}} \)-\( \Large \frac{8b^{7}}{a^{8}-b^{8}} \)

A). \( a+b\)

B). \( a-b\)

C). \( 1\)

D). \( 0\)

8). A man rides one third of the distances from A to B at the rate of \( x\)km/hr and the remainder at the rate of \( 2y\) km/hr. If he had travelled at a uniform rate of \( 6z\) km/hr, he could have ridden from A to B and back again in he same time Which one of the following is correct?

A). \( z\) = \( x\) + \( y\)

B). \(3 z\) = \( x\) + \( y\)

C). \( \Large \frac{1}{z} \) = \( \Large \frac{1}{x} \)+\( \Large \frac{1}{y} \)

D). \( \Large \frac{1}{2z} \) = \( \Large \frac{1}{x} \)+\( \Large \frac{1}{y} \)

9). If \( ax\) + \( by\) - \( 2\) = 0 and \( axby\) = \( 1\), where \( a\) \( \ne\)\( 0\),\( b\) \( \ne\)\( 0\) then what is \( \left( a^{2} x + b^{2 y}\right)\) equal to?

A). \( a\) +\( b\)

B). \( 2ab\)

C). \( a^{3}\) +\( b^{3}\)

D). \( a^{4}\) +\( b^{4}\)

10). Consider the following statements :
1. \( \left( a - b - c \right)\) is one of the factors of \( 3abc\) + \( b^{3}\) + \( c^{3}\) - \( a^{3}\)
2. \( \left( b + c - 1 \right)\) is one of the factors of \( 3abc\) + \( b^{3}\) + \( c^{3}\) - \( 1\)
Which of the above statements is/are correct?

A). 1 only

B). 2 only

C). Both 1 and 2

D). Neither 1 nor 2