Understanding the Custom Operation $\nabla$
The question defines a custom binary operation $\nabla$. For any two numbers, say $a$ and $b$, the operation $a \nabla b$ means adding the first number ($a$) to thrice the second number ($3b$). We can express this mathematically as:
$a \nabla b = a + 3b$
Evaluating $(4 \nabla 5) \nabla 6$ Step-by-Step
We need to calculate the value of the expression $(4 \nabla 5) \nabla 6$. This involves two steps:
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First Calculation: Evaluate $(4 \nabla 5)$
Using the definition $a \nabla b = a + 3b$, where $a=4$ and $b=5$:
$4 \nabla 5 = 4 + (3 \times 5)$
$4 \nabla 5 = 4 + 15$
$4 \nabla 5 = 19$
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Second Calculation: Evaluate $(19) \nabla 6$
Now, we use the result from the first step (19) as the new first number ($a$) and 6 as the second number ($b$). Applying the definition $a \nabla b = a + 3b$:
$19 \nabla 6 = 19 + (3 \times 6)$
$19 \nabla 6 = 19 + 18$
$19 \nabla 6 = 37$
Final Result
The value of the expression $(4 \nabla 5) \nabla 6$ is 37.
Similar Questions
- What will come in the place of the question mark (?) in the following equation, if '+' and '−' are interchanged and '×' and '÷' are interchanged?
65 × 5 − 19 ÷ 3 + 25 = ? - What will come in place of the question mark (?) in the following equation if '×' and '+' are interchanged and '−' and '÷' are interchanged?
32 ÷ 2 × 72 − 9 + 5 = ? - If '+' means '$\div$', '$-$' means '$\times$', '$\div$' means '+' and '$\times$' means '$-$', then find the value of $2 - 1 \times 4 \div 4 + 2$?
Study the given pattern carefully and select the numbers from among the options that can replace the question marks (?).
Study the given pattern carefully and select the number from among the given option that can replace the question mark (?).
- If '+' means 'division', '-' means 'addition', '$\times$' means 'subtraction' and '$\div$' means 'multiplication', then what will be the value of the following expression?
$\frac{[ \{ (20 \times 18) - (9 \div 3) \} + (5 - 2) ]}{1}$ - What will come in the place of the question mark (?) in the following equation, if ‘+’ and ‘−’ are interchanged and ‘×’ and ‘÷’ are interchanged?
25 − 9 × 3 + 4 ÷ 2 = ? - What will come in place of the question mark (?) in the following equation, if ‘+’ and ‘−’ are interchanged and ‘×’ and ‘÷’ are interchanged?
12 ÷ 6 + 28 × 4 − 11 = ? - If '+' means 'subtraction', '$\div$' means 'addition', '$-$' means 'multiplication' and '$\times$' means 'division', then what is the value of $15 \div (5 + 8)$?
If '$+$' means 'subtraction', '$\div$' means 'addition', '$-$' means 'multiplication' and '$\times$' means 'division', then what is the value of $(8 + 2 - 19) - (4 + 27 \times 3)$?
Important Questions from Mathematical Operations
Select the set, from the given options, in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(6, 13, 78)
(5, 22, 110)
If + means -, - means ×, × means ÷, ÷ means +, then what will come in place of the question mark (?) in the following equation?
28 - 6 ÷ 4 + 14 × 14 = ?
In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Which numbers should replace X and Y so that the pattern followed by the two numbers on the left side of :: is the same as that on the right side of :: ?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 Operations on 13 such as adding/subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
X : 649 :: 956 : Y
Which two numbers should be interchanged to make the given equation correct?
75 ÷ 5 + 15 × 4 - 17 × 3 + (60 ÷ 6) × 10 = 100
(Note: Interchange should be done of the entire number and not individual digits of a given number.)
If '+' means minus, '-' means multiplication, '÷' means plus, and 'x' means division, then solve the equation:
15 - 3 + 10 x 5 ÷ 5
