Correct Answer: –1

Solution : Given: $2+4x<5-\frac{x}{2}$ and $3x+3>-5-3x$
Or, $2+4x<\frac{10-x}{2}$ and $3x+3x>-5-3$
Or, $2(2+4x)<10-x$ and $6x>-8$
Or, $4+8x<10-x$ and $x>\frac{-8}{6}$
Or, $x+8x<10-4$ and $x>\frac{-4}{3}$
Or, $9x<6$ and $x>-1.33$
Or, $x<\frac{6}{9}$ and $x>-1.33$
Or, $x<0.67$ and $x>-1.33$
Or, $-1.33<x<0.67$
Amongst all the given values –1 satisfies the above condition.
Hence,

Correct Answer: $1$

Solution : $abc = 5$
⇒ $b = \frac{5}{ac}$
⇒ $b^{-1} = \frac{ac}{5}$
⇒ $\frac{c}{5} = \frac{1}{ab}$
Now, $(\frac{1}{1+a+b^{-1}}+\frac{1}{1+b+5 c^{-1}}+\frac{1}{1+\frac{c}{5}+a^{-1}})$
= $(\frac{1}{1+a+\frac{ac}{5}}+\frac{1}{1+ \frac{5}{ac}+5 c^{-1}}+\frac{1}{1+ \frac{1}{ab}+a^{-1}})$
= $(\frac{5}{5+5a+ac} +\frac{ac}{5+ 5a +ac}+\frac{5a}{5+5a+ac})$
= $\frac{5+5a+ac}{5+5a+ac}$
= $1$
Hence, the correct answer is $1$.

Correct Answer: 14

Solution : Given: $\sqrt{3^{n}} = 2187$
$⇒\sqrt{3^{n}} = 3^{7}$
By squaring both sides,
$⇒(\sqrt{3^{n}})^{2} = (3^{7})^{2}$
$⇒3^{n} = 3^{14}$
$\therefore n=14$
Hence, the correct answer is 14.

Correct Answer:

Solution : As per the mirror image properties, closer things appear close to the mirror in the reflection.
Here, according to the information provided, the mirror is placed on the right side of the figure (on line AB). So, the left side of the reflected image will appear

Correct Answer: (4)

Solution : The correct choice is the fourth option.

There is no error in the given sentence and the sentence is grammatically correct and follows the standard structure.

The phrase "much too heavy" is used to indicate that the homework is excessively or extremely difficult, so it

Correct Answer: To do something without special preparation.

Solution : The first option is the correct answer.

Play it by ear is an idiomatic expression that means to handle a situation in an impromptu or flexible manner without having a predetermined plan. It implies adapting to circumstances as they unfold

Correct Answer: (10 × 7) – 2 < (10 – 2) × 7

Solution : Let's check the options –
First option: (10 + 2) ÷ 7 < (10 ÷ 7) + 2
On replacing with symbols as directed, we get –
(10 ÷ 2) – 7 < (10 –

Correct Answer: Sandwitch

Solution : The correct choice is the third option.

The incorrectly spelt word is "sandwitch". The correct spelling is sandwich, which is a food item consisting of one or more fillings between slices of bread.

The other words are correctly spelt, and their meanings are as

Correct Answer: After knowing truth

Solution : The correct answer is the third option.

This part should be "After knowing the truth", by adding the article the before "truth". The definite article the is used when referring to a specific or known truth.

The correct sentence is: "After knowing

Correct Answer: $1$

Solution : Given: $a+b=2c$
⇒ $a-c=c-b$
Now, $\frac{a}{a-c}+\frac{c}{b-c}$ can be written as,
$=\frac{a}{a-c}-\frac{c}{c-b}$
$=\frac{a}{a-c}-\frac{c}{a-c}$
$=\frac{a-c}{a-c}= 1$
Hence, the correct answer is $1$.