Correct Answer: $\frac{97}{36}$

Solution : Given:
$2x+\frac{9}{x}=9$
Multiplying both sides by $x$, we get,
$⇒2x^2-9x+9=0$
$⇒(2x-3)(x-3)=0$
So, $x= \frac{3}{2},3$
Putting the values of $x$ in the equation, we get
When $x=\frac{3}{2}$, 
$x^2+\frac{1}{x^2}=(\frac{3}{2})^2+\frac{1}{(\frac{3}{2})^2}=\frac{97}{36}=2.69$
When $x=3$,
$x^2+\frac{1}{x^2}=3^2+\frac{1}{3^2}=\frac{82}{9}=9.11$
So, the minimum value is $\frac{97}{36}$.
Hence, the correct answer is $\frac{97}{36}$.

Correct Answer: $140\sqrt{2}$

Solution : $\left(x+\frac{1}{x}\right)=2 \sqrt{2}$
Squaring both sides.
⇒ $ (x+\frac{1}{x})^2= 8$
⇒ $(x-\frac{1}{x})^2 = (x+\frac{1}{x})^2-4$
⇒ $(x-\frac{1}{x})^2=8-4=4$
⇒ $(x-\frac{1}{x})= 2$
So, $(x^2-\frac{1}{x^2})=(x+\frac{1}{x})(x-\frac{1}{x})= 2\sqrt{2}×2=4\sqrt{2}$
Cubing both sides, we get
⇒ $x^6-\frac{1}{x^6}-3(x^2-\frac{1}{x^2})=64×(2\sqrt{2})$
⇒ $x^6-\frac{1}{x^6}-3(4\sqrt{2})=128\sqrt{2}$
⇒ $x^6-\frac{1}{x^6}=140\sqrt{2}$
Hence, the correct answer is $140\sqrt{2}$.

Correct Answer: 11

Solution : The given figure can be labeled as shown below –

There are a total of 11 rectangles in the above figure. They are ABCD, EFGH, IJKL, MFNQ, EMQR, EFNR, QNOD, NJPO, QJPD, RNGH, MFOD.

Hence, the third option is correct.

Correct Answer: loss of Rs. 1000

Solution : Let the cost price of the television be $x$ and the cost price of the refrigerator be $y$.
Given that the television was sold at a loss of 20% of the cost.
$⇒12000 = x - 0.20x = 0.80x$
$⇒x = \frac{12000}{0.80}

Correct Answer: Gymnosperms are seedless flowering plants.

Solution : The correct answer is Gymnosperms are seedless flowering plants.

• They consist of woody shrubs, trees, or lianas, with very few epiphytes and no true aquatics. The tallest, largest, and longest-living individual plants on Earth are within the gymnosperm family, which

Correct Answer: Himachal Pradesh

Solution : The correct answer is Himachal Pradesh.

A city must use only renewable energy and eliminate all other non-renewable energy sources to achieve zero carbon emissions; thus, a zero-carbon city is one with a renewable energy economy. Himachal Pradesh wants to be the second carbon-free

Correct Answer: The declarations which came out from that office were not dependable.

Solution : The correct choice is the fourth option.

The correct sentence is: The declarations which came out from that office were not dependable.

Correct Answer: 60

Solution : Speed of train = $36 × \frac{5}{18}$
= 10 m/s
Time taken = 25 seconds
Length of train = 25 × 10
= 250 m
Length of bridge = 350 m
Total length = length of tran + length of bridge
Total length = 250

Correct Answer: super conductors

Solution : The correct option is superconductors.

Superconductors are substances that fully loose their electrical resistance at very low temperatures. When Heike Kamerlingh Onnes saw that the electrical resistance of mercury dropped to zero at temperatures close to absolute zero (around 273.15 degrees Celsius), he made

Correct Answer: 125

Solution : Let's check the options —

First option: 222; 222 ÷ 2 = 111. 222 is an even number.

Second option: 10; 10 ÷ 2 = 5. 10 is an even number.

Third option: 68; 68 ÷ 2 = 34. 68 is an even number.

Fourth