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) ∅

Correct Answer: (D) 997

Explanation:

A prime number is a natural number greater than 1 that has no divisors other than 1 and itself. To determine the largest 3-digit prime number, we start with the largest 3-digit number, which is 999, and check downward until we find a prime number.

1. 999: Not a prime number because it is divisible by 3 (999 ÷ 3 = 333).

2. 998: Not a prime number because it is even (divisible by 2).

3. 997: Check divisibility by all prime numbers less than √997 (approximately 31.5). The prime numbers to check are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31.

– 997 is not divisible by any of these primes, so it is a prime number.

Thus, the largest 3-digit prime number is 997.

Correct Answer: (A) 1

Explanation:

Let’s solve each inequality step by step.

1. Solving -n + 2 ≥ 0:
-n + 2 ≥ 0
-n ≥ -2
n ≤ 2

2. Solving 2n ≥ 4:
2n ≥ 4
n ≥ 2

Combining Both Inequalities:
From the solutions above:
n ≤ 2 and n ≥ 2

The only integer that satisfies both conditions is:
n = 2; Answer: 1

Correct Answer: (B) 10%

Explanation:

Step 1: Define the variables
Let the selling price (SP) of one pen be Rs. x.
The total selling price of 45 pens = 45x.
The problem states that the loss is equal to the selling price of 5 pens.
Thus, the total loss = 5x.

Step 2: Understand the cost price (CP)
The cost price (CP) of 45 pens can be calculated as:
CP = SP + Loss
Substitute the values:
CP = 45x + 5x = 50x

Step 3: Calculate the loss percentage
The formula for loss percentage is:
Loss % = (Loss / CP) × 100
Substitute the values:
Loss % = (5x / 50x) × 100
Loss % = (1/10) × 100 = 10%

Correct option: (B) 10%

Correct Answer: (A) ₹1200

Explanation:

To determine the principal amount based on the difference between compound interest (CI) and simple interest (SI) over 2 years at an annual interest rate of 10%, follow these steps:

1. Calculate Simple Interest (SI):
SI = P × Rate × Time = P × 10% × 2 = 0.2P

2. Calculate Compound Interest (CI):
CI = P × (1 + Rate)^2 – P = P × (1.1)^2 – P = P × 1.21 – P = 0.21P

3. Find the Difference Between CI and SI:
Difference = CI – SI = 0.21P – 0.2P = 0.01P

Given that the difference is ₹12:
0.01P = 12 ⇒ P = 12 / 0.01 = 1200

Answer: ₹1200 Option (A)

The correct answer is (B) 8.

Explanation:

The number of subsets of a set is determined by the formula:
Number of subsets = 2^n, where n is the number of elements in the set.
Here, the set A = {0, 1, 2} has n = 3 elements. Substituting n = 3 into the formula:

Number of subsets = 2^3 = 8

The subsets of A are:
1. ∅ (the empty set)
2. {0}
3. {1}
4. {2}
5. {0, 1}
6. {0, 2}
7. {1, 2}
8. {0, 1, 2}

Final Answer: (B) 8