Correct Answer: 1

Solution : $\frac{p^{2} - (q - r)^{2}}{(p + r)^{2} - (q)^{2}}$ + $\frac{q^{2} - (p - r)^{2}}{(p + q)^{2} - (r)^{2}}$ + $\frac{r^{2} - (p – q)^{2}}{(q + r)^{2} - (p)^{2}}$
= $\frac{(p + q - r)(p - q + r)}{(p + q + r)(p - q + r)} + \frac{(p + q - r)(-p + q + r)}{(p + q + r)(p + q - r)} + \frac{(p - q + r)(–p+ q + r)}{(p + q + r)(–p + q + r)}$
= $\frac{p + q - r - p + q + r + p -q + r}{p + q+ r}$
= $\frac{p + q + r}{p + q + r}$
= $1$
Hence, the correct answer is 1.

Correct Answer:

Solution : According to the given figure series, in every alternate box, the geometrical figures/ numbers/ letters shift their position following the below pattern –
1. From Box 1 to Box 2 – Top centre ⇔ Bottom centre; Bottom left ⇔ Bottom right; Top left→Centre of the box→Top right→Top left

2. From Box 2 to Box 3 – Top centre→Bottom centre→Centre of the box→Top centre; Top left→Top right→Bottom left→Bottom right

3. After every two boxes, the bottom right symbol changes to an uncommon symbol (not used previously in the given figure series) while shifting its position to the top left.
So, following the above pattern, the required figure will be –

Hence, the first option is correct.

Correct Answer: Diluted acetic acid

Solution : The correct answer is Diluted acetic acid.

Vinegar is a diluted acetic acid solution often comprising 4-8% acetic acid in water. Glacial acetic acid, on the other hand, is pure acetic acid in its concentrated state and often appears as a clear, colourless liquid. Although vinegar includes Acetic acid, it differs from glacial acetic acid due to its lower concentration and the presence of other components in the solution.

Correct Answer: $3 \frac{1}{4}$

Solution : Given: $[\frac{85}{34}×\frac{1}{18}–${${{(\frac{46}{69}÷\frac{27}{135})}}–(\frac{86}{129}×\frac{91}{14})$} of $\frac{112}{36}]$
$=[\frac{85}{34}×\frac{1}{18}–${${{(\frac{46}{69}×\frac{135}{27})}}–(\frac{86}{129}×\frac{91}{14})$} of $\frac{112}{36}]$
$=[\frac{5}{2}×\frac{1}{18}–${${{(\frac{2}{3}×\frac{5}{1})}}–(\frac{1}{3}×\frac{13}{1})$} of $\frac{28}{9}]$
$=[\frac{5}{36}–${${{\frac{10}{3}}}–\frac{13}{3}$} ×$\frac{28}{9}]$
$=[\frac{5}{36}+{\frac{3}{3}}×\frac{28}{9}]$
$=[\frac{5}{36}+\frac{28}{9}]$
$=[\frac{5+112}{36}]$
$=\frac{117}{36} = 3 \frac{1}{4}$
Hence, the correct answer is $3 \frac{1}{4}$.

Correct Answer: up the creek

Solution : The fourth option is the correct choice.

The idiom, up the creek means to be in serious trouble or a predicament.

The meanings of the other options are as follows:

• A Devil's advocate is a person who expresses an unpopular opinion in order to provoke debate or test the strength of other arguments.
• Off-base means mistaken.
• The lion's share means the largest part of something.

Correct Answer: true colours

Solution : The first option is the correct answer.

Explanation:

• True colours: A person's genuine character or intentions are often revealed when they face difficult situations.
• Bed of Roses: A situation that is easy and comfortable.
• Hot potato: It is a controversial or sensitive issue or topic that is difficult to handle or resolve.
• White elephant: It is an expensive possession that is more trouble than it's worth.

The correct answer is true colours, meaning the person's true intentions.

Correct Answer: She said to me, “I know you want to help me but I can manage on my own.”

Solution : The correct choice is the third option.

Narration Conversion:

• The reporting verb told is changed to said in the direct form.
• The third-person pronoun she in the reported speech becomes I in the direct speech when quoting the speaker directly.
• The simple past tense (knew) is changed to the simple present tense (know) in direct speech.
• The words of the speaker are enclosed in quotation marks.

Therefore, the correct sentence in the direct form is: She said to me, “I know you want to help me, but I can manage on my own.”

Correct Answer: 16 : 64 

Solution : Let's check the options –
First option: 81 – 243→81 × 3 = 243
Second option: 16 – 64→16 × 3 = 48 ≠ 64
Third option: 64 – 192→64 × 3 = 192
Fourth option: 25 – 75→25 × 3 = 75

Hence, the second option is correct.

Correct Answer: which

Solution : The correct choice is the fourth option.

Using which here connects the sentence logically, indicating that the developed nations were affected by these specific technological breakthroughs, making it the suitable choice to maintain coherence in the sentence.

Correct Answer: PRSQ

Solution : The second option is the correct answer.

It starts by presenting the decision not to include any kind of wealth or income tax (P). Following this, it introduces the alternative solution of implementing an income tax, which is suggested to be a fairer option for addressing the social care funding crisis (R). The sentence then specifies the purpose of this alternative, emphasising that it aims to solve the social care funding crisis (S). Finally, the sentence concludes by stating that this decision has proven controversial (Q).

Therefore, the correct answer is PRSQ.