Question
Find the Value of the following using binomial expansion: $(2+\sqrt{5})^{5}+(2-\sqrt{5})^{5}$
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| Advertisement expenses (thousand ₹) | $20-39.9$ | $40-59.9$ | $60-79.9$ | $80-99.9$ | $100-119.9$ |
| No. of companies | $18$ | $20$ | $23$ | $22$ | $17$ |

| No. of pilgrims (less than) | $29$ | $49$ | $69$ | $99$ | $129$ | $149$ |
| No. of days | $8$ | $21$ | $48$ | $75$ | $90$ | $100$ |

| Shoulder length of $T$ –shirts (inches) | $12.0$ | $12.5$ | $13.0$ | $13.5$ | $14.0$ | $14.5$ | $15.0$ | $15.5$ | $16.0$ |
| No. of customers | $5$ | $20$ | $30$ | $47$ | $56$ | $56$ | $37$ | $16$ | $3$ |
| Units of power consumed | $10 – 15$ | $15 – 20$ | $20 – 25$ | $25 – 30$ | $30 – 35$ | $35 – 40$ |
| No. of machines | $5$ | $10$ | $15$ | $20$ | $25$ | $30$ |
| Age (years) | $25$ | $17$ | $20$ | $18$ | $26$ | $22$ | $28$ | $23$ |
| No. of youngsters | $22$ | $4$ | $19$ | $11$ | $7$ | $9$ | $3$ | $8$ |
| Age (years) | $15 – 20$ | $20– 25$ | $25-30$ | $30- 40$ | $40 – 50$ | $50 -60$ | $60 -80$ |
| No. of spectators | $6$ | $13$ | $19$ | $52$ | $34$ | $18$ | $8$ |