Correct Answer: $\frac{\left (a+b-c \right)}{2}$

Solution :
Let the circle touch the sides BC, CA, and AB of the right triangle ABC at D, E, and F, respectively, where BC = a, CA = b and AB = c
Since lengths of tangents drawn from an external point are equal.

Correct Answer: 5

Solution : 15 = 5 × 3
30 = 5 × 3 × 2
40 = 5 × 2 × 2 × 2
$\therefore$ HCF of 15, 30, and 40 = 5
Hence, the correct answer is 5.

Correct Answer: 35

Solution : Given:
7² A 7 B 9 = 16; 5² A 5 B 7 = 12

7² A 7 B 9 = 16
= ((7)² ÷ 7) + 9 = (49 ÷ 7) + 9 = 7 + 9 = 16
5

Correct Answer: 20%

Solution : Let the cost price of 1 kg of goods be Rs. 100.
If the dealer sells his goods at a 10% loss, he sells 1 kg of goods for Rs. 90. 
However, he uses 25% less weight, which means he actually gives only 0.75 kg

Correct Answer: The solution, salt water and Brass

Solution : The correct answer is Solution, salt water and brass.

Solution, saltwater and brass are examples of homogeneous mixtures. A solution is formed when one substance (the solute) is uniformly dissolved in another substance (the solvent) at the molecular

Correct Answer: Civilised

Solution : The fourth option is correct.

Explanation: We have to find a word that contrasts with the primitive or uncivilised nature of barbaric. Civilised is the suitable antonym, as it denotes a state of advanced social and cultural development, opposite to the barbaric or

Correct Answer: 36

Solution : $\frac{1 \frac{1}{2} \div 3 \frac{1}{4}+\frac{1}{2} \div \frac{13}{14}+\frac{1}{5}}{\frac{1}{5} \times 3 \frac{1}{2}-\frac{1}{3} \div 1 \frac{3}{4} \times 3 \frac{1}{2}}$
= $\frac{\frac{1 \frac{1}{2}}{3 \frac{1}{4}} + \frac{\frac{1}{2}}{\frac{13}{14}}+\frac{1}{5}}{\frac{1}{5} ×\ 3 \frac{1}{2} - \frac{\frac{1}{3}} {1\frac{3}{4}} \times 3 \frac{1}{2}}$
= $\frac{\frac{\frac{3}{2}}{\frac{13}{4}} +\frac{7}{13} + \frac{1}{5}}{\frac{1}{5} \times  \frac{7}{2} - \frac{\frac{1}{3}} {\frac{7}{4}} \times  \frac{7}{2}}$
= $\frac{\frac{6}{13}

Correct Answer: celebrate

Solution : The fourth option is the correct answer.

Lament means to express sorrow, grief, or regret, often in a vocal and demonstrative manner. 

On the other hand, celebrating means observing an occasion or event with joy, festivity, and acknowledgement.

The meanings of the other options are

Correct Answer: Monera

Solution : The correct answer is Monera.

The nuclear membrane is absent in organisms classified under the kingdom Monera. Monera comprises unicellular organisms like bacteria and blue-green algae. Unlike eukaryotic cells, which have a distinct nucleus enclosed by a nuclear membrane, Monera's prokaryotic cells lack this

Correct Answer: 20

Solution : Add the cube root of 8, 27, and 64 and the square root of 121 to get the answer.
= ∛(8) + ∛(27) + ∛(64) + √(121)
= 2 + 3 + 4 + 11
= 20

So, 20 is the missing number in the