Logarithms & Binary Numbers · NDA previous year questions

What is the sum of the binary numbers $(10110110{)}_2$ and $(100011{)}_2$

1. A.$(11011001{)}_2$
2. B.$(110001000{)}_2$
3. C.$(110000100{)}_2$
4. D.$(100100000{)}_2$

What is the binary number equivalent to decimal number 1011 ?

1. A.1011
2. B.111011
3. C.111111001
4. D.1111110011

If ${\log }_{10}2{\log }_{2}10+{\log }_{10}(10^x)=2$, then what is the value of x?

1. A.0
2. B.1
3. C.${\log }_{2}10$
4. D.${\log }_{5}2$

The number $(1101101+1011011{)}_2$ can be written in decimal system as

1. A.$(198{)}_{10}$
2. B.$(199{)}_{10}$
3. C.$(200{)}_{10}$
4. D.$(201{)}_{10}$

What is the value of $\frac{1}{10}{\log }_{5}1024-{\log }_{5}10+\frac{1}{5}{\log }_{5}3125$ ?

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

If $x={\log }_c(ab)$, $y={\log }_a(bc)$, $z={\log }_b(ca)$, then which of the following is correct?

1. A.$xyz=1$
2. B.$x+y+z=1$
3. C.$(1+x{)}^{-1}+(1+y{)}^{-1}+(1+z{)}^{-1}=1$
4. D.$(1+x{)}^{-2}+(1+y{)}^{-2}+(1+z{)}^{-2}=1$

A binary number is represented by $(cdccddcccddd{)}_2$, where $c>d$. What is its decimal equivalent?

1. A.1848
2. B.2048
3. C.2842
4. D.2872

The sum of the binary numbers $(11011{)}_2$, $(10110110{)}_2$ and $(10011x0y{)}_2$ is the binary number $(101101101{)}_2$. What are the values of x and y?

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

What is the sum of all three-digit numbers that can be formed using all the digits 3, 4 and 5, when repetition of digits is not allowed ?

1. A.2664
2. B.3882
3. C.4044
4. D.4444

The binary number expression of the decimal number 31 is

1. A.1111
2. B.10111
3. C.11011
4. D.11111

What is $$\frac{1}{{\log }_{2}N}+\frac{1}{{\log }_{3}N}+\frac{1}{{\log }_{4}N}+\dots +\frac{1}{{\log }_{100}N}$$ equal to $(N\ne 1)$?

1. A.$\frac{1}{{\log }_{100!}N}$
2. B.$\frac{1}{{\log }_{99!}N}$
3. C.$\frac{99}{{\log }_{100!}N}$
4. D.$\frac{99}{{\log }_{99!}N}$

What is the greatest integer among the following by which the number $5^5+7^5$ is divisible?

1. A.6
2. B.8
3. C.11
4. D.12

The remainder and the quotient of the binary division $(101110{)}_2÷(110{)}_2$ are respectively

1. A.$(111{)}_2$ and $(100{)}_2$
2. B.$(100{)}_2$ and $(111{)}_2$
3. C.$(101{)}_2$ and $(101{)}_2$
4. D.$(100{)}_2$ and $(100{)}_2$

In the binary equation $(1p101{)}_2+(10q1{)}_2=(100r00{)}_2$ where $p,q$ and $r$ are binary digits, what are the possible values of $p,q$ and $r$ respectively?

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

If the number 235 in decimal system is converted into binary system, then what is the resulting number ?

1. A.$(11110011{)}_2$
2. B.$(11101011{)}_2$
3. C.$(11110101{)}_2$
4. D.$(11011011{)}_2$

What is the number of four-digit decimal numbers ($<1$) in which no digit is repeated?

1. A.3024
2. B.4536
3. C.5040
4. D.None of the above

What is the number of different messages that can be represented by three 0's and two 1's?

1. A.10
2. B.9
3. C.8
4. D.7

What is the binary equivalent of the decimal number 0.3125?

1. A.0.0111
2. B.0.1010
3. C.0.0101
4. D.0.1101

If ${\log }_a(ab)=x$, then what is ${\log }_b(ab)$ equal to?

1. A.$\frac{1}{x}$
2. B.$\frac{x}{x+1}$
3. C.$\frac{x}{1-x}$
4. D.$\frac{x}{x-1}$

The decimal number $(127.25{)}_{10}$, when converted to binary number, takes the form

1. A.$(1111111.11{)}_2$
2. B.$(1111110.01{)}_2$
3. C.$(1110111.11{)}_2$
4. D.$(1111111.01{)}_2$

If $(11101011{)}_2$ is converted to decimal system, then the resulting number is

1. A.235
2. B.175
3. C.160
4. D.126

If $2p+3q=18$ and $4p^2+4pq-3q^2-36=0$ then what is $(2p+q)$ equal to?

1. A.6
2. B.7
3. C.10
4. D.20

The number 251 in decimal system is expressed in binary system by:

1. A.11110111
2. B.11111011
3. C.11111101
4. D.11111110

The number 83 is written in the binary system as

1. A.100110
2. B.101101
3. C.1010011
4. D.110110

A number in binary system is 110001. It is equal to which one of the following numbers in decimal system?

1. A.45
2. B.46
3. C.48
4. D.49