Which of the following statement is correct?

I. The value of 100² - 99² + 98² - 97² + 96² - 95² + 94² - 93² + ...... + 2² - 1² is 5050.

II. If 8x + \(\frac{8}{x}\)= -16 and x < 0, then the value of x¹⁹⁷ + x^-197 is 2.

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 02 Dec 2022 Shift 4)

Answer 1

Statement I:

1002 - 992 + 982 - 972 + 962 - 952 + 942 - 932 + ...... + 22 - 12

⇒ (1002 - 992) + (982 - 972) + (962 - 952) + (942 - 932) + ...... + (22 - 12)

⇒ (100 - 99)(100 + 99) + (98 - 97)(98 + 97) + (96 - 95)(96 + 95) + (94 - 93)(94 + 93) + ...... + (2 - 1)(2 + 1)

⇒ 1(100 + 99) + 1(98 + 97) + 1(96 + 95) + 1(94 + 93) + ...... + 1(2 + 1)

⇒ 100 + 99 + 98 + 97 + 96 + 95 + 94 + 93 + ...... + 2 + 1

Now,

We know some n number of consecutive term = n(n + 1)/2

So, [100(100 + 1)]/2

⇒ 50 × 101

⇒ 5050

So, the statement I is correct

Statement II:

If 8x + \(\frac{8}{x}\)= -16

⇒ x + \(\frac{1}{x}\) = - 2 [By dividing 8 from both sides]

Now, For x = - 1

x + \(\frac{1}{x}\) = - 2 is satisfying

Now,

x197 + x-197 = x¹⁹⁷ + \(\frac{1}{x^{197}}\)

⇒ (- 1)¹⁹⁷ + \(\frac{1}{(-1)^{197}}\)

⇒ - 1 - 1

⇒ - 2

So, statement II is not correct

∴ The correct answer is Option 1.

Download Solution PDF