From the first statement “Listening to music during exercise improves exercise performance and reduces discomfort. “ It is clear that listening to music has a positive effect on physical exercise.

From the statement “Scientists researched whether listening to music while studying can help students learn better and the results were inconclusive. “   it is clear that only on some students music has a positive effect.

Fold the sheet along the dotted line and join the shapes, we get option 2.

‘worse’, ‘better’ are comparative words which need the word ‘than’ for comparison. Out of the remaining two options ‘as well as’ is the correct answer.

A pen is used to write. Similarly, a knife is used to cut.

Given Initial ratio : 3:13:6

Total number of students initially = 3x+13x+6x = 22x

From the given question, we can write 3x+18 = 15y -----I

                                   13x+18 = 35y-----II

                                   6x+18 = 21y------III

 

                      I - II => -10X = -20Y

                                    X=2Y------IV

 

                      Put IV in III => 6(2y) + 18 = 21y

                                       12y + 18 = 21y

                                       9y = 18

                                        y = 2 -----V

                      Substitute V in I => 3x + 18 = 30

                                           3x = 12

                                           x = 4

   Number of initial students = 22x = 22(4) = 88

 According to the given data:

                        Year     Cost/unit   Number of units     Cost Price

                            1           ₹ 3                    100                     300

                            2           ₹ 2                     200                    400

                            3           ₹ 1                     300                    300

 Cost Price = Cost/unit x Number of units

Net Profit = Selling Price - (Cost Price + (Tax%  x selling price )

Year 2:

   296 = SP - (400 + (13/100) x SP)

   =>296 = 0.87SP - 400

   => 0.87SP = 696

    => SP = ₹ 800

Year 3: 

      210 = SP - (300 + (15/100) x SP)

     => 210 = 0.85SP - 300

    =>  0.85SP = 510

    => SP = ₹ 600

The ratio of selling price in Year 2 to the selling price in year 3 = 800:600 

                                                                                           = 4:3

Rotate 90 degrees to the left and flip the piece in Option 2.

Expand the given equation:

x²+1/4 - x -x² -9/4 +3x = x+2

   => -2 + 2x = x + 2

                    X = 4

The order will be PTSRUQ
Number of students taller than R = Number of students shorter than S = 3

 

Q will send the SYN bit = 1 to the connection establishment.

Q Seq number will be Y different from X

ACK bit = 1 because sending the ACK

ACK number = X+1 (Next seq number id)

FIN bit = 0 (Because establishing the connection) 

Transition table

 

	0	1
->*q0	q0	q1
q1	q2	q0
q2	q1	q2

 

DFA of divisible by 3

The regular expression will be

Three paths to reach to final state from initial state

Path 1: self loop of 0 on q0

Path 2: q0->q1->q0  hence 11

Path 3: q0->q1->q2->q1->q0 hence 10(1+00)*01

So finally the regular expression will be

(0+11+10(1+00)*01)*

Other regular expression is (if we consider two paths)

Path 1: Path 1: self loop of 0 on q0

Path 2: q0->q1->q2*->q1->q0 

Hence regular expression

(0+1 (01*0)*1)*

 

Another regular expression is (if we consider only one path and remaining part is present inside this path as cycles)

q0->q1->q2->q1->q0

Another regular expression is

(0*(1(01*0)*1)*)*

 

So A,B, C are correct.

Option D generates string 11100 which is not accepted by FA hence wrong.

Option A: L={w x w^R  x^R  | w, x ∈ {0,1}* }

This is not CFL as if we push “w” then “x” then we cannot match wR with “w” as top of stack contains x.

 

Option B: L={w w^R x x^R  | w, x ∈ {0,1}* }

This is CFL. We non deterministically guess the middle of the string. So we push “w” then match with wR  and again push x and match with xR  

 

Option C: L={w x  x^R w^R   | w, x ∈ {0,1}* } 

This is also CFL. We non deterministically guess the middle of the string. So we push “w” then push x and then  match with xR  and again match with wR 

 

Option D: L={w x  w^R   | w, x ∈ {0,1}* }

This is a regular language (hence CFL). In this language every string start and end with same symbol (as x can expand).

As we know the formula for In and OUT are

Total no. of records = 150000

Block size = 4096 bytes

Key size = 12 bytes

Record pointer size = 7 bytes

int foo(intx, int y, int q)

{

         if ((x <= 0) && (y <= 0))  //if 1

              return q;

         if (x <= 0)                      //if 2

              return foo(x, y-q, q);

         if (y <= 0)                     //if 3

              return foo(x-q, y, q);

         return foo(x, y-q, q) + foo(x-q, y, q);

}

int main()

{

         int r = foo(15, 15, 10);

         printf(“%d”, r);

         return 0;

}