Correct Answer: (C) 2 / 5

Explanation:

Step 1: Solve for x
Multiply both sides by x to eliminate the fraction:
x^2 + 1 = 2x

Rearrange the equation:
x^2 – 2x + 1 = 0

This can be factored as:
(x – 1)^2 = 0
So, x = 1

Step 2: Substitute x = 1 into the expression
We need to find the value of:
(2x^2 + 2) / (3x^2 + 4x + 3)
Substitute x = 1:
Numerator:
2(1)^2 + 2 = 2 + 2 = 4

Denominator:
3(1)^2 + 4(1) + 3 = 3 + 4 + 3 = 10

So, the expression becomes:
4 / 10 = 2 / 5

Answer: (C) 2 / 5

Correct Answer: (C) 22338

Explanation:

To solve this problem, we use the relationship between the Highest Common Factor (HCF) and the Least Common Multiple (LCM) of two numbers:

HCF × LCM = Product of the two numbers

Step 1: Write down the given values
– HCF(306, 657) = 9
– The two numbers are 306 and 657.

Step 2: Calculate the product of the two numbers
The product of the two numbers is:
306 × 657 = 201042

Step 3: Use the formula to find LCM
We know:
HCF × LCM = Product of the two numbers
Substitute the values:
9 × LCM = 201042

Solve for LCM:
LCM = 201042 ÷ 9 = 22338

Final Answer: (C) 22338

Answer: (A) is higher in power hierarchy

Explanation: In social interactions, body language often reflects one’s position in the power hierarchy. The person who appears more relaxed and at ease typically signals confidence and dominance, which are traits associated with being higher in the power hierarchy. While age or socio-economic status might influence behavior, the question specifically focuses on body language, which is most directly linked to power dynamics. Hence, the correct answer is “is higher in power hierarchy.”

Correct Answer: (C) Speech style

Explanation: Speech style is influenced by the inter-personal context because the way people communicate often changes depending on the social situation, relationship dynamics, and the individuals involved. For example, people may use formal speech in professional settings and informal speech with friends. While gestures, posture, education, and problem-solving can also be influenced by context, “speech style” is most directly shaped by interpersonal interactions. Hence, the correct answer is “Speech style.”

Correct Answer: (A) 233/990

Explanation:

To solve 0.235, we need to convert the repeating decimal into a fraction.

Step 1: Represent the repeating decimal
Let x = 0.235, where 35 is the repeating part.

Step 2: Eliminate the repeating part
Multiply x by 1000 to shift the decimal point three places to the right (since the repeating part has two digits):
1000x = 235.35

Now, multiply x by 10 to shift the decimal point one place to the right:
10x = 2.35

Step 3: Subtract the two equations
Subtract 10x from 1000x:
1000x – 10x = 235.35 – 2.35
990x = 233

Step 4: Solve for x
x = 233/990

Final Answer:
The fraction representation of 0.235 is 233/990.

Correct Option: (A) 233/990

Correct Answer: (C) 48

Explanation:

To determine the number of people who like neither tea nor coffee, let’s use the principle of inclusion-exclusion.

1. Total number of people (N): 200
2. Number of people who like tea (T): 90
3. Number of people who like coffee (C): 108
4. Number of people who like both tea and coffee (T ∩ C): 46

First, calculate the number of people who like either tea or coffee (or both):

|T ∪ C| = |T| + |C| – |T ∩ C|
|T ∪ C| = 90 + 108 – 46 = 152

This means 152 people like either tea or coffee or both. To find the number of people who like neither:

Number of people who like neither = N – |T ∪ C|
Number of people who like neither = 200 – 152 = 48

Answer: (C) 48

Correct Answer: (A) median

Explanation:

Ogive curves are graphical representations of cumulative frequency distributions. There are two types of ogive curves:

1. ‘Less than’ ogive: This is plotted using the cumulative frequencies for the “less than” values of the data.

2. ‘More than’ ogive: This is plotted using the cumulative frequencies for the “more than” values of the data.

When these two curves are plotted on the same graph, they intersect at a point that corresponds to the median of the data.

The median is the value that divides the dataset into two equal halves, where 50% of the data lies below it and 50% lies above it. At the intersection point of the ‘less than’ and ‘more than’ ogives, this condition is satisfied, making it the median.

Thus, the correct answer is (A) median.

Correct Answer: (B) 5

Explanation:

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Correct Answer: (D) 59

Explanation:

Step 1: Analyze the word “CONSTABLE”

The word “CONSTABLE” has 9 letters. Let’s assign numerical values to each letter based on their position in the English alphabet:

– C = 3, – O = 15, – N = 14, – S = 19, – T = 20
– A = 1, – B = 2, – L = 12, – E = 5

Now, sum up these values: 3 + 15 + 14 + 19 + 20 + 1 + 2 + 12 + 5 = 91
Thus, the code for “CONSTABLE” is the sum of the alphabetical positions of its letters.

Step 2: Apply the same logic to “STABLE”

The word “STABLE” has 6 letters. Assign numerical values to each letter:

– S = 19, – T = 20, – A = 1
– B = 2, – L = 12, – E = 5

Now, sum up these values: 19 + 20 + 1 + 2 + 12 + 5 = 59

Correct option: (D) 59

Correct Answer: (C) BTEAE

Explanation:

Breakdown of the Coding Pattern:

– BELONGINGS → TABLESTESF

– B → T
– E → A
– L → B
– O → L
– N → E
– G → S
– I → T
– N → E
– G → S
– S → F

Applying the Same Pattern to “LINEN”:

– L → B
– I → T
– N → E
– E → A
– N → E

So, LINEN is coded as BTEAE.

Final Answer: Option (C) BTEAE