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

Correct Answer: (A) Table

Explanation: The other three options (Window, Door, and Gate) are all parts of a structure or building that serve as openings or entry/exit points. A table, on the other hand, is a piece of furniture and does not serve this purpose. Hence, “Table” is the odd one out.

Correct Answer: (B) Frame

Explanation: A ‘poster’ is typically placed or displayed on a ‘wall’. Similarly, a ‘photograph’ is often placed or displayed in a ‘frame’. The relationship is based on where the object is commonly displayed or associated with. Hence, the correct answer is “Frame”.

Correct Answer: (A) -136/27

Explanation:

To find the remainder when dividing the polynomial f(x) = x^3 – 6x^2 + 2x – 4

by the linear divisor -3/2 x + 1, we can use the Remainder Theorem.

Steps:

1. Identify the value of x that makes the divisor zero:
-3/2 x + 1 = 0 implies x = 2/3

2. Evaluate f(2/3) to find the remainder:
f(2/3) = (2/3)^3 – 6(2/3)^2 + 2(2/3) – 4
= 8/27 – 6(4/9) + 4/3 – 4
= 8/27 – 24/9 + 4/3 – 4
= 8/27 – 72/27 + 36/27 – 108/27
= (8 – 72 + 36 – 108)/27 = -136/27

Answer: (A) -136/27

Correct Answer: (A) Archimedes

Explanation: Archimedes, the ancient Greek mathematician, is credited with being the first to calculate an accurate approximation of the value of π (pi). He used a geometric method involving inscribed and circumscribed polygons to estimate the value of π as being between 3.1408 and 3.1429. This was a significant achievement in mathematics and laid the foundation for future studies of π. While other mathematicians like Aryabhatta and Pythagoras contributed to mathematics, Archimedes’ work on π is particularly notable.

Correct Answer: (B) ∅

Explanation:

1. Given Sets:
– A = {a, b, c, e, f, g}
– B = {b, c, d, f, g, h}
– C = {c, d, e, g, h, i}

2. Calculate A – B:
– Elements in A but not in B: {a, e}

3. Calculate A – C:
– Elements in A but not in C: {a, b, f}

4. Calculate (A – B) – (A – C):
– Subtract A – C from A – B: {a, e} – {a, b, f} = {e}

5. Calculate C – B:
– Elements in C but not in B: {e, i}

6. Final Calculation {e} – {e, i}:
– Subtract C – B from the previous result: {e} – {e, i} = ∅
Therefore, the value of ((A – B) – (A – C) – (C – B)) is ∅.

Answer: (B) ∅