On squaring both sides, we get

x² + 1/x² + 2 = 100

⇒ x² + 1/x² = 98

Again on squaring on both sides, we get

x⁴ + 1/x⁴ + 2 = 9604

⇒ x⁴ + 1/x⁴ = 9602

Hence, option B is the correct answer.

Given Expression (3x + 5)² + (3x – 5)²

9x² + 25 +15x + 9x² +25 - 15x

2(9x²+25)

Hence, option D is the correct answer.

10R + 4M = 210000

5R + 2M = 105000     ……. (i)

6R + 2M = 122000     ……. (ii)

By subtracting equation (i) from (ii), we get

R = 17000

By putting the value of R in equation (i), we get

5(17000) + 2M = 105000

⇒ 2M = 20000

⇒ M = 10000

∴ Cost of one refrigerator and two mobile phones

= 17000 + 2(10000) = 37000

Hence, option A is the correct answer.

5x + y = 17

xy = 6

we know that,

125x³ + y³ = (5x)³ + y³

=

= 4913 – 1530

= 3383

a² + b² + c² – 2ab – 2bc + 2ca

we know that,

(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

So,

(a – b + c)² = a² + b² + c² – 2ab – 2bc + 2ca

a³ = b³ + 988

a³ - b³ = 988

or, (a – b)(a² + ab + b²)=988

or, 4(a² + ab + b²) = 988

or, 2(a² + ab + b²) = 988/2 = 494

(2a² + 2ab + 2b²) = 494

Now, a + 1/a = 8

∴ a² + 1/a² = (8)² – 2 = 64 – 2 = 62

∴ a⁴ + 1/a⁴ = (62)² – 2 = 3844 – 2 = 3842

Hence, option C is the correct answer.

=

=

=

=

=

Hence, option B is the correct answer.

(a² + b² + 4c² – ab – 2bc – 2ca) (a + b + 2c)

= (a + b + 2c) {(a)² + (b)² + (2c)² – a × b – b × 2c – 2c × a}

We know that,

Here x = a, y = b and z = 2c

= (a + b + 2c) {(a)² + (b)² + (2c)² – a × b – b × 2c – 2c × a}

= (a)³ + (b)³ + (2c)³ – 3 × a × b × 2c

= a³ + b³ + 8c³ – 6abc

Hence, option D is the correct answer.

x⁷ + x^–7 + x² + x^–2

= (-1)⁷ + (-1)^–7 + (-1)² + (-1)^–2

= - 1 – 1 + 1 + 1 = 0

Hence, option D is the correct answer.