Consider the postfix expression 4 5 6 a b 7 8 a c, where a, b, c are operators. Operator a has higher precedence over operators b and c. Operators b and c are right associative. Then, equivalent infix expression is

Assume that the operators +,-, X are left associative and ^ is right associative. The order of precedence (from highest to lowest) is ^, X, +, -. The postfix expression for the infix expression a + b X c – d ^ e ^ f is?

A

abc X+ def ^^ –

B

abc X+ de^f^ –

C

ab+c Xd – e ^f^

D

-+aXbc^ ^def

Consider the grammar given below E? E+E | EE | E-E | E/E | E^E | (E) | id Assume that + and ^ have the same but least precedence, and / have the next higher precedence but the same precedence and finally ^ has the highest precedence. Assume + and ^ associate to the left like * and / and that ^ associates to the right. Choose the correct for the ordered pairs (^,^), (-,-), (+,+), (,) in the operator precedence table constructed for the grammar.

A

All <

B

All >

C

< >, =

D

< > > >

To convert the postfix expression into the infix expression we use stack and scan the postfix expression from left to right.

A

True

B

False

Here is an infix expression: 4 + 3(63-12). Suppose that we are using the usual stack algorithm to convert the expression from infix to postfix notation. The maximum number of symbols that will appear on the stack AT ONE TIME during the conversion of this expression?

A

1

B

2

C

3

D

4

Convert the following Infix expression to Postfix form using a stack. x + y * z + (p * q + r) * s, Follow usual precedence rule and assume that the expression is legal.

A

xyz*+pq*r+s*+

B

xyz*+pq*r+s+*

C

xyz+*pq*r+s*+

D

xyzp+**qr+s*+

If a + b + c + d = 4, then find the value of $$\frac{1}{{\left( {1 - a} \right)\left( {1 - b} \right)\left( {1 - c} \right)}}$$ + $$\frac{1}{{\left( {1 - b} \right)\left( {1 - c} \right)\left( {1 - d} \right)}}$$ + $$\frac{1}{{\left( {1 - c} \right)\left( {1 - d} \right)\left( {1 - a} \right)}}$$ + $$\frac{1}{{\left( {1 - d} \right)\left( {1 - a} \right)\left( {1 - b} \right)}}$$ is?

A

0

B

5

C

1

D

4

If a + b + c + d = 4, then the value of $$\frac{1}{{\left( {1 - a} \right)\left( {1 - b} \right)\left( {1 - c} \right)}}$$ + $$\frac{1}{{\left( {1 - b} \right)\left( {1 - c} \right)\left( {1 - d} \right)}}$$ + $$\frac{1}{{\left( {1 - c} \right)\left( {1 - d} \right)\left( {1 - a} \right)}}$$ + $$\frac{1}{{\left( {1 - d} \right)\left( {1 - a} \right)\left( {1 - b} \right)}}$$ is?

A

0

B

1

C

4

D

1 + abcd

Given two processes (conversion of postfix equation to infix notation and conversion of prefix notation to infix notation), which of the following is easier to implement?

A

Both are easy to implement

B

Conversion of postfix equation to infix equation is harder than converting a prefix notation to infix notation

C

Conversion of postfix equation to infix equation is easier than converting a prefix notation to infix notation

D

Insufficient data

The postfix expression abc+de/*- is equivalent to which of the following infix expression?

A

abc+-de*/

B

(a+[-d/e*c

C

a-(b+[*(d/e)

D

abc+*-(d/e)

The transfer function of a discrete time LTI system is given by
$$H\left( z \right) = {{2 - {3 \over 4}{z^{ - 1}}} \over {1 - {3 \over 4}{z^{ - 1}} + {1 \over 8}{z^{ - 2}}}}$$
Consider the following statements:
S₁ : The system is stable and causal for
$$ROC:\left| z \right| > {1 \over 2}$$
S₂ : The system is stable but not causal for
$$ROC:\left| z \right| S₃ : The system is neither stable nor causal for
$$ROC:{1 \over 4} Which one of the following statements is valid?

A

Both S1 and S2 are true

B

Both S2 and S3 true

C

Both S1 and S3 are true

D

S1, S2 and S3 are all true