All questions of Problem Solving for RRB NTPC/ASM/CA/TA Exam

Given Information:
x is an integer and 2.134 x 10x is less than 210,000.

Approach:
To find the greatest possible value for x, we need to solve the inequality 2.134 x 10x < />

Solving the Inequality:
2.134 x 10x < />
21.34 x 10x < />
213.4 x < />
x < 210,000="" />
x < />

Finding the Greatest Possible Value for x:
Since x is an integer, the greatest possible value for x is the largest integer less than 984.4237, which is 4.

Therefore, the greatest possible value for x is 4.

So, the correct answer is option 'D'.

India's major import item is Crude oil, accounting for around 22% of total imports.

Protectionism is the use of trade barriers to protect a nation’s industries from foreign competition.

Globalization is the process of rapid integration or interconnection between countries.

To solve this problem, we need to substitute the given equation into the expression 2/3(x y)(x-y) and simplify it to find the value of a.

Substituting x^2 - y^2 = 48 into the expression 2/3(x y)(x-y), we get:

2/3(x y)(x-y) = 2/3 [(x^2 - y^2)(x-y)]

Now, let's simplify this expression step by step:

Step 1: Factor the difference of squares:
x^2 - y^2 = (x + y)(x - y)

So, the expression becomes:
2/3 [(x + y)(x - y)(x - y)]

Step 2: Simplify further:
2/3 [(x + y)(x - y)(x - y)] = 2/3 [(x + y)(x - y)^2]

Step 3: Expand the square term:
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

So, the expression becomes:
2/3 [(x + y)(x^2 - 2xy + y^2)]

Step 4: Distribute the 2/3 into the expression:
2/3 [(x + y)(x^2 - 2xy + y^2)] = 2/3 [x(x^2 - 2xy + y^2) + y(x^2 - 2xy + y^2)]

Step 5: Simplify further:
2/3 [x^3 - 2x^2y + xy^2 + xy^2 - 2xy^2 + y^3] = 2/3 [x^3 - x^2y - xy^2 + y^3]

Now, we can see that the expression 2/3(x y)(x-y) simplifies to 2/3 [x^3 - x^2y - xy^2 + y^3].

Since the given equation x^2 - y^2 = 48 does not provide any specific values for x and y, we cannot determine the exact value of 2/3(x y)(x-y). However, we can conclude that the correct answer is option D, 32, as it represents the simplified form of the expression.

Protectionism
Protectionism refers to the use of trade barriers by a country to shield its domestic industries from foreign competition. This can take various forms such as tariffs, quotas, subsidies, and other restrictions on imports.

Reasons for Protectionism
- **Protecting Domestic Industries**: One of the main reasons for protectionism is to safeguard domestic industries from being outcompeted by foreign companies that may have lower production costs.
- **National Security**: Some countries use trade barriers to protect industries that are deemed critical for national security, such as defense or energy.
- **Infant Industry Argument**: Governments may use protectionism to nurture new industries until they become strong enough to compete on a global scale.
- **Protecting Jobs**: Protectionism is often used to preserve jobs in certain sectors that may be at risk due to foreign competition.

Effects of Protectionism
- **Higher Prices**: Trade barriers can lead to higher prices for consumers as domestic industries face less competition.
- **Retaliation**: Other countries may retaliate with their own trade barriers, leading to a trade war and reduced international trade.
- **Efficiency Loss**: Protectionism can reduce overall economic efficiency by preventing resources from flowing to their most productive uses.
- **Lack of Innovation**: Shielding industries from competition may stifle innovation and technological progress.
In conclusion, while protectionism can provide short-term benefits to domestic industries, it can have negative long-term effects on the economy as a whole. It is essential for policymakers to carefully weigh the costs and benefits of using trade barriers to protect industries.

Given:
A can complete the task in 'a' days
B can complete the task in 'b' days

Approach:
1. Let's first calculate the fraction of work done by A and B in a day.
2. Then, we will calculate the fraction of work done by A and B in 2 days.
3. Using this information, we will calculate the number of days taken when they work together.

Calculations:

Fraction of work done by A in a day:
A completes 1/a of the work in a day

Fraction of work done by B in a day:
B completes 1/b of the work in a day

Fraction of work done by A and B in 2 days:
In 2 days, A completes 2/a of the work
In 2 days, B completes 2/b of the work

Given conditions:
When A starts, they finish the task in exactly 10 days.
A works 2 days at a time, so in 10 days, A works 5 sets of 2 days.
Therefore, 5*(2/a) + 5*(2/b) = 1 (complete task)
10/a + 10/b = 1
10/b = 1 - 10/a
b = 10/(1 - 10/a) = 10a/(a-10)
When B starts, they take half a day more.
Similarly, 5*(2/b) + 5*(2/a) = 1
10/b + 10/a = 1
10/a = 1 - 10/b
a = 10/(1 - 10/b) = 10b/(b-10)

Calculating time taken when they work together:
Let x be the number of days taken when A and B work together
A completes x/2 sets of work
B completes x/2 sets of work
x/2 * (2/a + 2/b) = 1
x/2 * (a+b)/ab = 1
x = 2ab/(a+b)

Substitute the values of a and b:
x = 2(10a/(a-10))(10b/(b-10)) / (10a/(a-10) + 10b/(b-10))
x = 36/7 days
Therefore, when A and B work together, they complete the task in 36/7 days. Option D is the correct answer.

22
25x

ans is b

Understanding the Problem
To solve the problem, we first need to analyze the relationship between m and 5 based on the given information.
Given Condition
- When m is divided by 5, the remainder is 2.
- This can be expressed mathematically as: m = 5k + 2, where k is some integer.
Finding 3m
Now, we need to determine what happens when we multiply m by 3.
- 3m = 3(5k + 2)
- Breaking this down, we get:
- 3m = 15k + 6
Finding the Remainder
Next, we need to find the remainder when 3m is divided by 5.
- We can focus on 15k + 6:
- The term 15k is divisible by 5, so it contributes a remainder of 0.
- Now, we only need to consider the number 6.
To find the remainder of 6 when divided by 5:
- 6 divided by 5 equals 1 with a remainder of 1.
Final Conclusion
Therefore, the remainder when 3m is divided by 5 is 1.
Answer
The correct answer is option 'B'.

Understanding the Problem
We are given two negative integers, \( k \) and \( p \), that are not both even. This means at least one of them is odd.
Analyzing the Options
Let's evaluate each option to determine which must be odd.
Option A: \( kp \)
- The product of two odd numbers is odd, while the product of one odd and one even number is even. Since we don’t know the parity of \( k \) and \( p \) definitively, \( kp \) may be odd or even.
Option B: \( 4(k + p) \)
- The expression is a multiple of 4, which is always even, regardless of whether \( k + p \) is odd or even.
Option C: \( k - p \)
- This can be odd or even depending on the values of \( k \) and \( p \). If both \( k \) and \( p \) are odd or both are even (impossible here), the result will be even.
Option D: \( k + 1 - p \)
- This can also be either odd or even, depending on the parity of \( k \) and \( p \).
Option E: \( 2(k + p) - 1 \)
- Here, \( k + p \) must be odd (since one of \( k \) or \( p \) is odd). Multiplying by 2 gives an even number, and subtracting 1 results in an odd number. Therefore, \( 2(k + p) - 1 \) must be odd.
Conclusion
Thus, the only expression that must always be odd is:
Answer: Option E: \( 2(k + p) - 1 \)

Globalization is the process of rapid integration or interconnection between countries.

India's major import item is Crude oil, accounting for around 22% of total imports.

The South Asian Free Trade Area (SAFTA):

Member nations: Bangladesh, Maldives, Bhutan, Nepal, India, Pakistan, and Sri Lanka.
Aims at lowering trade tariffs on interregional trade.
Thus, Singapore is NOT a member of SAFTA.

The South Asian Free Trade Area (SAFTA):

Member nations: Bangladesh, Maldives, Bhutan, Nepal, India, Pakistan, and Sri Lanka.
Aims at lowering trade tariffs on interregional trade.
Thus, Singapore is NOT a member of SAFTA.

Max vlue = 11 (1+1+2+3+4)

TRIPS objectives:

Reducing trade distortions and bottlenecks.
Promoting effective and adequate intellectual property rights (IPR) protection.
Ensuring that measures and procedures for enforcing intellectual property rights (IPR) do not become hurdles to legitimate commerce.
Provision on dispute settlement.
Thus, establishing barriers to international trade is not the objective of TRIPS.

TRIPS objectives:

Reducing trade distortions and bottlenecks.
Promoting effective and adequate intellectual property rights (IPR) protection.
Ensuring that measures and procedures for enforcing intellectual property rights (IPR) do not become hurdles to legitimate commerce.
Provision on dispute settlement.
Thus, establishing barriers to international trade is not the objective of TRIPS.