$\oplus \text { and } \odot \text { are two operators on numbers p and q such that}$ $p \odot q = p - q, \text{ and } p \oplus q = p \times q$ $\text{Then, } (9 \odot (6 \oplus 7)) \odot (7 \oplus (6 \odot 5))=$
Understanding the Operators
The problem defines two operators:
- $p \odot q = p - q$ (Subtraction)
- $p \oplus q = p \times q$ (Multiplication)
We need to evaluate the expression: $(9 ⊙ (6 ⊕> 7)) ⊙ (7 ⊕> (6 ⊙ 5))$
Evaluating the Left Side of the Main Operator
First, calculate the value inside the first main parenthesis: $(9 ⊙ (6 ⊕> 7))$
- Evaluate the inner operation: $6 \oplus 7 = 6 \times 7 = 42$
- Substitute the result back: $9 \odot 42 = 9 - 42 = -33$
So, the left side evaluates to -33.
Evaluating the Right Side of the Main Operator
Next, calculate the value inside the second main parenthesis: $(7 ⊕> (6 ⊙ 5))$
- Evaluate the inner operation: $6 \odot 5 = 6 - 5 = 1$
- Substitute the result back: $7 \oplus 1 = 7 \times 1 = 7$
So, the right side evaluates to 7.
Final Calculation
Now, combine the results of the left and right sides using the main $⊙$ operator:
- Left side result: -33
- Right side result: 7
- Combine: $(-33) \odot 7 = -33 - 7 = -40$
The final result of the expression is -40.
Important Questions from Numerical Computation
$A$ is an ($n \times n$) matrix. Consider the following two statements
Statement 1: Columns of matrix $A$ are linearly independent
Statement 2: Inverse of matrix $A$ exists
Which one of the following statements is TRUE?
- Consider the function $G(x, y, z) = 0$. This function allows us to implicitly define each of three variables as a function of the other two variables. Assume that all partial derivatives of the function $G(x, y, z)$ exist everywhere. Then, the value of $\left(\frac{\partial z}{\partial x} \times \frac{\partial x}{\partial y} \times \frac{\partial y}{\partial z}\right)$ is _________ (in integer)
- Levenshtein distance is used to measure the minimum edit distance between two strings by counting the minimum number of editing operations (such as, insertions, deletions, substitutions) required to transform one string to another. Consider an alternative version of the Levenshtein distance in which each insertion and each deletion has a cost of 1 and substitutions are not allowed.
Based on this alternative version, the Levenshtein distance between the strings, word and work is ______ (Answer in integer). - In a given collection of documents, let $N$ be the total number of documents and let $d$ be the number of documents in which the term $t$ occurs.
Which ONE of the following fractions is used to define the inverse document frequency (idf) of the term $t$? - The total number of unique character bigrams in the string thoughtsoftheghosts (which contains 19 characters) is ______.
