1.

\(\sqrt{x + 6\sqrt{2}} - \sqrt{x - 6\sqrt{2}} = 2\sqrt{2}.\)
Find \( x \).

2.

The terms \(x_5 = -4\), \(x_1, x_2, \dots, x_{100}\) are in an arithmetic progression (AP). It is also given that \(2x_6 + 2x_9 = x_{11} + x_{13}\). Find \(x_{100}\).

• -194
• 206
• 204
• -196

3.

If \( x \) and \( y \) satisfy the equations
\(|x| + x + y = 15 \quad \text{(1)},\)
\(x + |y| - y = 20 \quad \text{(2)}.\)
Find the value of \( x - y \).

4.

If Rajesh’s age were to be the present age of Shivani, their age ratio would be \(3:2\). Then what would be their present age ratio?

• 2:3
• 3:2
• 4:2
• 1:2

5.

Read the Passage carefully and answer the following questions.
An air conditioner (AC) unit has three operating modes: Eco, Normal, and Turbo. The power consumption in each mode is as follows: Eco mode consumes 1000 watts, Normal mode consumes 1200 watts, and Turbo mode consumes 1500 watts. Yesterday, the AC was in operation from 2 PM to 10 PM. From 2 PM to 6 PM it ran in Eco mode. From 6 PM to 8 PM, it ran in Normal mode. From 8 PM to 10 PM it ran in Turbo mode.

6.

\(3^{3333}\) divided by 11, then the remainder would be?