Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Binary Numbers

NDA 2017 · Mathematics · Binary Numbers

In the binary equation (1 p 101)_2+(10 ql)_2=(100 r 00)_2 where p,...

In the binary equation (1p101)2+(10ql)2=(100r00)2(1 \mathrm{p} 101)_2+(10 \mathrm{ql})_2=(100 \mathrm{r} 00)_2 where p,q\mathrm{p}, \mathrm{q} and r are binary digits, what are the possible values of p,qp, q and rr respectively?

Options

  1. A0,1,0
  2. B1,1,0
  3. C0,0,1
  4. D1,0,1

Correct answer

A. 0,1,0

Step-by-step solution

(1p101)2+(10q1)2=(100r00)2⇒(1×24+p×23+1×22+0×21+1×20)+(1×23+0×22+q×21+1×20)=1×25+0+0+r×22+0+0\begin{aligned} & (1 \mathrm{p} 101)_2+(10 \mathrm{q} 1)_2=(100 \mathrm{r} 00)_2 \\ & \Rightarrow\left(1 \times 2^4+\mathrm{p} \times 2^3+1 \times 2^2+0 \times 2^1+1 \times 2^0\right) \\ & +\left(1 \times 2^3+0 \times 2^2+\mathrm{q} \times 2^1+1 \times 2^0\right) \\ & =1 \times 2^5+0+0+\mathrm{r} \times 2^2+0+0\end{aligned}⇒16+8p+4+1+8+2q+1=32+4r⇒30+8p+2q=32+4r⇒8p+2q=2+4r\begin{aligned} & \Rightarrow 16+8 p+4+1+8+2 q+1=32+4 r \\ & \Rightarrow 30+8 p+2 q=32+4 r \\ & \Rightarrow 8 p+2 q=2+4 r \end{aligned}fromoptions,substitutefrom options, substitute\mathrm{p}=0, \mathrm{q}=1, \mathrm{r}=0wegetwe get0+2(1)=2+0 \Rightarrow 2=2 \text{. }$
Practice Binary Numbers on Quantrex Academy →

More from Binary Numbers

What is the binary number equivalent to decimal number 1011? NDA 2023If x^3+y^3=(100010111)_2 and x+y=(11111)_2 , then what is (x-y)^2+x y equal to? NDA 2022What is (1110011)_2 ÷(10111)_2 equal to? NDA 2022The number (1101101+1011011)_2 can be written in decimal system as NDA 2020A binary number is represented by (c d c c d d c c c d d d)_2 , where c > d . What is its… NDA 2019The binary number expression of the decimal number 31 is NDA 2018The sum of the binary numbers (11011)_ 2, (10110110)_2 and (10011 x 0 y)_2 is the binary… NDA 2018The remainder and the quotient of the binary division (101110)_2 ÷(110)_2 are respectively NDA 2017What is the binary equivalent of the decimal number 0.3125? NDA 2016If the number 235 in decimal system is converted into binary system, then what is the… NDA 2016What is (1000000001)_2-(0.0101)_2 equal to ? NDA 2015The decimal number (127.25)_ 10 , when converted to binary nunber, takes the form NDA 2015If (11101011)_2 is converted decimal system, then the resulting number is NDA 2015What is the sum of the two numbers (11110)_2 and (1010)_2 ? NDA 2014What is (1001)_2 equal to? NDA 2014The number 251 in decimal system is expressed in binary system by: NDA 2014 Full Binary Numbers list Binary Numbers JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs