Logarithms & Binary Numbers · NDA previous year questions

The binary representation of the decimal number 45 is

1. A.110011
2. B.101010
3. C.1101101
4. D.101101

The decimal representation of the number $(1011{)}_2$ in binary system is:

1. A.5
2. B.7
3. C.9
4. D.11

The decimal number $(57.375{)}_{10}$ when converted to binary number takes the form:

1. A.$(111001.011{)}_2$
2. B.$(100111.110{)}_2$
3. C.$(110011.101{)}_2$
4. D.$(111011.011{)}_2$

If $({\log }_{3}x)({\log }_{x}2x)({\log }_{2x}y)={\log }_x{x}^2$, then what is y equal to?

1. A.4.5
2. B.9
3. C.18
4. D.27

The number 292 in decimal system is expressed in binary system by

1. A.100001010
2. B.100010001
3. C.100100100
4. D.101010000

What is the decimal number representation of the binary number $(11101.001{)}_2$?

1. A.30.125
2. B.29.025
3. C.29.125
4. D.28.025

In binary system the decimal number 0.3 can be expressed as

1. A.$(0.01001\dots {)}_2$
2. B.$(0.10110\dots {)}_2$
3. C.$(0.11001\dots {)}_2$
4. D.$(0.10101\dots {)}_2$

The number 10101111 in binary system is represented in decimal system by which one of the following numbers?

1. A.157
2. B.175
3. C.571
4. D.751

In the binary system of numbers let $a=00111$ and $b=01110$, then in decimal system what is $b/a$ equal to?

1. A.1
2. B.2
3. C.4
4. D.5

What is the binary number equivalent of the decimal number 32.25?

1. A.100010.10
2. B.100000.10
3. C.100010.01
4. D.100000.01

What is the equivalent binary number of the decimal number 13.625?

1. A.1101.111
2. B.1111.101
3. C.1101.101
4. D.1111.111

What is the value of ${\left(\frac{i+\sqrt{3}}{-i+\sqrt{3}}\right)}^{200}+{\left(\frac{i-\sqrt{3}}{i+\sqrt{3}}\right)}^{200}+1$?

1. A.$-1$
2. B.0
3. C.$i$
4. D.2

If $(10x010{)}_2-(11y1{)}_2=(10z11{)}_2$, then what are the possible values of the binary digits $x,y,z$ respectively ?

1. A.$0,0,1$
2. B.$0,1,0$
3. C.$1,1,0$
4. D.$0,0,0$

The number $0\cdot 0011$ in binary system represents

1. A.rational number $3/8$ in decimal system
2. B.rational number $1/8$ in decimal system
3. C.rational number $3/16$ in decimal system
4. D.rational number $5/16$ in decimal system

If $A=\{a,b,c\}$ and $R=\{(a,a),(a,b),(b,c),(b,b),(c,c),(c,a)\}$ is a binary relation on $A$, then which one of the following is correct?

1. A.$R$ is reflexive and symmetric, but not transitive
2. B.$R$ is reflexive and transitive, but not symmetric
3. C.$R$ is reflexive, but neither symmetric nor transitive
4. D.$R$ is reflexive, symmetric and transitive

If ${\log }_{10}(x+1)+{\log }_{10}5=3$, then what is the value of $x$?

1. A.$199$
2. B.$200$
3. C.$299$
4. D.$300$

What is the value of $2{\log }_{8}2-\frac{{\log }_{3}9}{3}$?

1. A.$0$
2. B.$1$
3. C.$8/3$
4. D.$16/3$

What is the decimal equivalent of $(101.101{)}_2$?

1. A.$(5.225{)}_{10}$
2. B.$(5.525{)}_{10}$
3. C.$(5.625{)}_{10}$
4. D.$(5.65{)}_{10}$

What is the binary equivalent of decimal number $(0.8125{)}_{10}$?

1. A.$(0.1101{)}_2$
2. B.$(0.1001{)}_2$
3. C.$(0.1111{)}_2$
4. D.$(0.1011{)}_2$

1. A.Either $x+y=z$ or $x=y$
2. B.Either $x+y=-z$ or $x=z$
3. C.Either $x+z=y$ or $z=y$
4. D.Either $z+y=x$ or $x=y$

1. A.$1$
2. B.$-1$
3. C.$2$
4. D.$0$