$\oplus \text { and } \odot \text { are two operators on numbers p and q such that}$ $p \odot q = p - q, \text{ and } p \oplus q = p \times q$ $\text{Then, } (9 \odot (6 \oplus 7)) \odot (7 \oplus (6 \odot 5))=$
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
- An organization allows its employees to work independently on consultancy projects but charges an overhead on the consulting fee. The overhead is 20% of the consulting fee, if the fee is up to . 5,00,000. For higher fees, the overhead is . 1,00,000 plus 10% of the amount by which the fee exceeds . 5,00,000. The government charges a Goods and Services Tax of 18% on the total amount (the consulting fee plus the overhead). An employee of the organization charges this entire amount, i.e., the consulting fee, overhead, and tax, to the client. If the client cannot pay more than . 10,00,000, what is the maximum consulting fee that the employee can charge?
Three frictionless pulleys with rope attachment are in a static equilibrium as shown in the figure. The mass $m_1$ and $m_2$, in kg, respectively are
If the in-situ density of coal is 1320 kg/m$^3$ and the density of blasted coal is 952 kg/m$^3$, the swell factor is _____________ (rounded off to 3 decimal places)
A five-member truss system is shown in the figure. The maximum vertical force P in kN that can be applied so that loads on the member CD and BC do NOT exceed 50 kN and 30 kN, respectively is _____________(rounded off to 2 decimal places)
The Fourier transform and its inverse transform are respectively defined as $\tilde{f}(\omega) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{+\infty} f(x)e^{i\omega x}dx$ and $f(x) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{+\infty} \tilde{f}(\omega)e^{-i\omega x}d\omega$. Consider two functions $f$ and $g$. Another function $f * g$ is defined as
$(f * g)(x) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{+\infty} f(y)g(x - y)dy$
Which of the following relation is/are true?
Note: Tilde ($\sim$) denotes the Fourier transform.
