Advertisements
Advertisements
प्रश्न
If Δ is an operation such that for integers a and b we have a Δ b = a × b – 2 × a × b + b × b (–a) × b + b × b then find 4 Δ (–3) Also show that 4 ∆ (–3) ≠ (–3) ∆ 4.
Advertisements
उत्तर
We have, a Δ b = a × b – 2 × a × b + b × (b) (–a) × b + b × b
Now, put a = 4 and b = (–3)
4 Δ (–3) = 4 × (–3) – 2 × 4(–3) + (–3) × (–3) × (– 4) × (–3) + (–3) × (–3)
= –12 – 2 × (–12) + (9)(12) + 9
= –12 + 24 + 108 + 9
= –12 + 141
= 129
Now, put a = –3 and b = 4
⇒ (–3) Δ 4 = (–3) × 4 – 2 × (–3) × (4) + 4 × 4{–(–3)} × 4 + 4 × 4
= (–12) + 24 + 16(3) × 4 + 16
= (–12) + 24 + 192 + 16
= 220
Clearly, 4 Δ (–3) ≠ (–3) Δ 4
APPEARS IN
संबंधित प्रश्न
Find the product, using suitable properties:
26 × (− 48) + (− 48) × (− 36)
Find the product, using suitable properties:
8 × 53 × (−125)
Find the product, using suitable properties:
625 × (− 35) + (− 625) × 65
Find the product, using suitable properties:
(− 57) × (− 19) + 57
Find the following product: (– 25) × 37 × 4
Find (– 35) × (– 98).
If * is an operation such that for integers a and b we have a * b = a × b + (a × a + b × b) then find (–3) * (–5)
If * is an operation such that for integers a and b we have a * b = a × b + (a × a + b × b) then find (–6) * 2
The given table shows the freezing points in °F of different gases at sea level. Convert each of these into °C to the nearest integral value using the relation and complete the table,
`C = 5/9 (F - 32)`
| Gas | Freezing Point at Sea Level (°F) |
Freezing Point at Sea Level (°C) |
| Hydrogen | –435 | |
| Krypton | –251 | |
| Oxygen | –369 | |
| Helium | –458 | |
| Argon | –309 |
In a test, +3 marks are given for every correct answer and –1 mark are given for every incorrect answer. Sona attempted all the questions and scored +20 marks though she got 10 correct answers.
- How many incorrect answers has she attempted?
- How many questions were given in the test?
