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1
combinatorics problem
In how many ways can 12 different( not same) coloured balls be distributed among 3 boys so that each gets atleast 1 ball? ans:- 519156
In how many ways can 12 different( not same) coloured balls be distributed among 3 boys so that each gets atleast 1 ball? ans:- 519156
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2
No. of ways in which 2n white and 2n black balls can be arranged such that no consecutive n white balls are together
The number of ways in which $2n$ white and $2n$ black balls can be arranged such that no consecutive $n$ white balls are together, is${}^{2n+1}C_2 + {}^{4n}C_{2n}$${}^{2n...
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3
Find the coefficient of x7 in expansion of (1+3x-2x3)10.
Find the coefficient of x7 in expansion of (1+3x-2x3)10. How to apply multinomial theorem to solve this types of problems?
Find the coefficient of x7 in expansion of (1+3x-2x3)10. How to apply multinomial theorem to solve this types of problems?
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4
Regular Expression and strings
Let L1 = 0*1*, L2 = 1*0*, L3 = (0+1)* and L4 = 0*1*0*. Then the number of strings in the following language L are ________. L = (L1 ∩ L2 ) – (L3 ∩ L4 )
Let L1 = 0*1*, L2 = 1*0*, L3 = (0+1)* and L4 = 0*1*0*. Then the number of strings in the following language L are ________. L = (L1 ∩ L2 ) &nd...
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5
Find the no. of gates
In a multiplication of two 3 digit numbers (a2 a1 a0 ) and (b2 b1 b0) how many AND,XOR and OR gates required?
In a multiplication of two 3 digit numbers (a2 a1 a0 ) and (b2 b1 b0) how many AND,XOR and OR gates required?
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Made Easy FLT
Assume Am × n, Bn × p and Cp × q are matrices where m > n > p > q. How many minimum number of multiplications are required to perform the following operation? Am × n × Bn × p × Cp × q [= (A B C)m × q] a) mnp+npq b) mnp+mpq c)mnq+npq d) mnq+mpq
Assume Am × n, Bn × p and Cp × q are matrices where m n p q. How many minimum number of multiplications are required to perform the following operation? ...
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Solve the subnetting problem
An organization is granted the block 190.76.0.0/16. The administrator wants to create 1024 subnets using 10 bits. The first and last addresses in subnet 1024 respectively are?
An organization is granted the block 190.76.0.0/16. The administrator wants to create 1024 subnets using 10 bits. The first and last addresses in subnet 1024 respectively...
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9
Find out the equivalent expression
(P∨Q)∧(P→R)∧(Q→S) is equivalent to- a) S∧R b)S→R c)S∨R d)None.
(P∨Q)∧(P→R)∧(Q→S) is equivalent to-a) S∧Rb)S→Rc)S∨Rd)None.
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11
what is the determinant of this matrix?
Find the Determinant of $\begin{pmatrix} -4& -1 &-1 &-1 \\ -1& 2& -1& 0\\ -1& -1 & 3 & -1\\ -1 & 0&-1 & 3 \end{pmatrix}$.
Find the Determinant of $\begin{pmatrix} -4& -1 &-1 &-1 \\ -1& 2& -1& 0\\ -1& -1 & 3 & -1\\ -1 & 0&-1 & 3 \end{pmatrix}$.
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12
construct the dfa
Give minimal DFA that performs as a MOD-3 1's counter,i.e outputs a '1' each time the number of 1's in the input sequence is a multiple of 3.
Give minimal DFA that performs as a MOD-3 1's counter,i.e outputs a '1' each time the number of 1's in the input sequence is a multiple of 3.
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13
What are the possible values of x and y after completion of the program
int x=0,y=0; par begin begin x=1; y=y+x; end begin y=2; x=x+3; end par end what are the possible values of x and y after completion of the program? a. x=1 ,y=2 b.x=1,y=3 c.x=4,y=6
int x=0,y=0;par beginbeginx=1;y=y+x;endbeginy=2;x=x+3;endpar endwhat are the possible values of x and y after completion of the program?a. x=1 ,y=2 b.x=1,y=3c.x=4,y=6
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14
Find out the probability
'X' is playing a dice game in which a dice is rolled 5 times.If a number turns up exactly 3 times then the game is won.'X' has thrown the dice 2 times and got number 4 both times.What is the probability that 'X' will win the game? a) 1/216 b) 75/216 c) 80/216 d) 90/216
'X' is playing a dice game in which a dice is rolled 5 times.If a number turns up exactly 3 times then the game is won.'X' has thrown the dice 2 times and got number 4 bo...
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15
How to solve this recurrence relation?
Solve the equation: $a_n = 5a_{n/3} + 7, \;\; a_1 = 5$ Note: $a_0$ is not given.
Solve the equation: $$a_n = 5a_{n/3} + 7, \;\; a_1 = 5$$Note: $a_0$ is not given.
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18
Find out the recurrence relation for the given problem
If $a_n$ is number of ternary sequences of length $n$ with even number of $0$'s, then the recurrence relation for $a_n$ is? Also find the value of $a_8$.
If $a_n$ is number of ternary sequences of length $n$ with even number of $0$'s, then the recurrence relation for $a_n$ is?Also find the value of $a_8$.
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19
Use generating function to solve question
Use generating function to determine the number of different ways 10 identical balloons can be given to 4 children if each children receives at least 2 balloons.
Use generating function to determine the number of different ways 10 identical balloons can be given to 4 children if each children receives at least 2 balloons.
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20
m-way merge sort
Assume 5 buffer pages are available to sort a file of 105 pages.The cost of sorting using m-way merge sort is-   a)206 b)618 c)840 d)926
Assume 5 buffer pages are available to sort a file of 105 pages.The cost of sorting using m-way merge sort is- a)206b)618c)840d)926
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22
Solve the problem
Find the sum of all the 4 digit numbers that can be formed with the digits 3,2,3,4. Ans- 39996
Find the sum of all the 4 digit numbers that can be formed with the digits 3,2,3,4.Ans- 39996
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23
Solve the problem
A boy sells apples for 12 cents each and pears for 7 cents each.Suppose the boy collected $3.21.How many apples and pears did he sell?
A boy sells apples for 12 cents each and pears for 7 cents each.Suppose the boy collected $3.21.How many apples and pears did he sell?
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24
How many zero address instructions are there?
X=(M+N*O)/(P*Q)  How many zero-address instructions are there? I did it.Just want to check whether it is right? PUSH P PUSH Q MUL PUSH N PUSH O MUL PUSH M ADD DIV POP X So total 10 instructions required.Correct?
X=(M+N*O)/(P*Q)  How many zero-address instructions are there?I did it.Just want to check whether it is right?PUSH PPUSH QMULPUSH NPUSH OMULPUSH MADDDIVPOP XSo total 10 ...
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27
Count the no. of clocks in a 4 stage pipeline
A 4-stage pipelined processor executed the following loop: for(i=1;i<=100;i++) { I1; I2; I3; I4; } What is the no. of clocks to execute the above loop? a.13 b.15 c.16 d.18 S1 S2 S3 S4 I1 1 2 1 2 I2 2 1 2 1 I3 1 1 2 1 I4 2 1 2 1
A 4-stage pipelined processor executed the following loop:for(i=1;i<=100;i++){I1; I2; I3; I4;}What is the no. of clocks to execute the above loop?a.13 b.15 c.16 ...
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28
Find out the min and max no. of page faults.
A process having access to f frames(initially all empty) makes m memory accesses to p distinct pages.What are the max and min. no. of page faults that will occur?
A process having access to f frames(initially all empty) makes m memory accesses to p distinct pages.What are the max and min. no. of page faults that will occur?
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29
Find the minterms of the product of two functions
Given f=f1.f2,  where f1=∑m(0,1,5)+d(2,3,7) and f2=∑m(1,2,4,5)+d(0,7) f=??
Given f=f1.f2,  where f1=∑m(0,1,5)+d(2,3,7)and f2=∑m(1,2,4,5)+d(0,7)f=??