Correct Answer: – and ×

Solution : Given:
75 ÷ 15 × 8 + 14 – 5 = 67

Replace the given symbols in the options one by one with the original symbols in the given equation.
First option: ÷ and ×
⇒ 75 × 15 ÷ 8 + 14 – 5 = 67
= 140.625 + 14 – 5
= 149.625 ≠ 67
Second option: – and ÷
⇒ 75 – 15 × 8 + 14 ÷ 5 = 67
= 75 – 120 + 2.8
= 42.2 ≠ 67
Third option: – and ×
⇒ 75 ÷ 15 – 8 + 14 × 5 = 67
= 5 – 8 + 70
= 67
Fourth option: + and –
⇒ 75 ÷ 15 × 8 – 14 + 5 = 67
= 40 – 9
= 31 ≠ 67

Here, only the third option satisfies the R.H.S. of the given equation. Hence, the third option is correct.

Correct Answer: Rs. 13,991

Solution : Let the donation amount for Saturday be Rs. $x$.
We know, Average = $\frac{\text{Sum of collection}}{\text{Number of days}}$
So, $8000= \frac{(7230+6435+6927+6855+6562+x)}{6}$
$\therefore x= 13991$
Hence, the correct answer is Rs. 13,991.

Correct Answer: Nek Chand

Solution : The correct answer is Nek Chand.

Nek Chand designed the Rock Garden in Chandigarh. He started constructing it in 1957, and it is a 40-acre sculpture garden. It is most famous for its recycled ceramic use. Chandigarh is the joint capital of Punjab, and Haryana and lies in the foothills of the Sivalik Range. Chandigarh is the first planned city in India.

Correct Answer: breach

Solution : The correct choice is the third option.

Commitment refers to a pledge or obligation to do something. It implies a promise or a dedication to fulfilling a particular task or agreement. Its antonym, "breach" means the violation or breaking of an agreement, duty, or obligation.

The meanings of the other options are as follows:

• Feeble means lacking strength or being weak.
• Drape refers to hanging or covering something with fabric.
• Hale means strong and healthy, especially in reference to a person's health.

Correct Answer: 2

Solution : We know that $\sin(90° - \theta) = \cos\theta$
$\sin7x = \cos11x$
$⇒\sin7x = \sin (90° - 11x)$
$⇒7x = 90° - 11x$
$⇒18x = 90°$
$⇒x = 5°$
Substituting $x = 5°$ in $\tan9x+\cot9x$,
$\therefore\tan45° + \cot45°=1 + 1= 2$
Hence, the correct answer is $2$.

Correct Answer: yours impromptu performance.

Solution : The correct choice is in the second option.

Explanation:

The error lies in the use of the possessive pronoun "yours". "Yours" is a possessive pronoun and does not require an additional subject. The correct form is "your impromptu performance", where your functions as a possessive pronoun indicating possession by the subject.

Therefore, the correct sentence is: I will never judge you for your impromptu performance.

Correct Answer: Below Basic

Solution : Average performance = $\frac{\text{Sum of performances in all subjects}}{\text{Number of subjects}}$ 
Average performance for Below Basic = $\frac{40+19+41+34+8}{5}$ = 28.4
Average performance for Basic = $\frac{35+45+29+21+5}{5}$ = 27
Average performance for Proficient = $\frac{20+25+25+33+34}{5}$ = 27.4
Average performance for Advance = $\frac{5+11+5+12+52}{5}$ = 17
Hence, the correct answer is Below Basic.

Correct Answer: Mother Teresa

Solution : The correct answer is Mother Teresa.

Mother Teresa, formally known as Saint Teresa of Calcutta, was a Roman Catholic missionary who spent most of her life working in Bengal, primarily in Kolkata (formerly Calcutta). She arrived in India in 1929 and spent the majority of her life there.

Correct Answer: 3, 5, 2, 4, 1

Solution : Given:
1. Mouth 2. Mount 3. Moult 4. Mouse 5. Mound

Step 1: The first three letters of each word are the same M, o, and u, so move on to the next letter.
Step 2: The fourth letter of each word is t, n, l, s, n. Based on the alphabetical order of these letters, we can arrange them – Moult, Mount, Mound, Mouse, Mouth
Step 3: Compare the fifth letter of (Mount, Mound). Mound will come before Mount in the sequence as d comes before t in the alphabetical system. 

So, the sequence is Moult, Mound, Mount, Mouse, Mouth, or 3, 5, 2, 4, 1. Hence, the first option is correct.

Correct Answer: Rs. 3,000

Solution : Let the opening shares of A, B, and C be $5x$, $4x$, and $3x$.
Ratio of profit = Ratio of investment × Ratio of time
The share of A,
$=5x\times12=60x$
The share of B,
$=4x\times12+1000\times8=48x+8000$
The share of C,
$=3x\times12+2000\times4=36x+8000$
According to the question,
$\frac{60x}{48x+8000}=\frac{15}{14}$
$⇒56x=48x+8000$
$⇒x=1000$
Therefore, the investment of C at the beginning = 3 × 1000 = Rs. 3,000
Hence, the correct answer is Rs. 3,000.