The question asks to identify the Buddhist monument built by Emperor Ashoka in Madhya Pradesh to honor Lord Buddha. This requires knowledge of major Buddhist stupas and their historical patrons and locations.
Correct Option: C) Sanchi Stupa
The Sanchi Stupa, located in Sanchi, Madhya Pradesh, is one of the oldest and most significant Buddhist monuments in India. It was originally commissioned by Emperor Ashoka in the 3rd century BCE. While it underwent several additions and renovations in later periods, its foundation and initial construction are attributed to Ashoka, making it a direct answer to the question.
The question asks to identify the organization founded by Kailash Satyarthi. This requires knowledge of prominent social activists and the organizations they are associated with, particularly in the context of child rights in India.
Correct Option: C) Bachpan Bachao Andolan. Kailash Satyarthi founded the Bachpan Bachao Andolan (Save the Childhood Movement) in 1980. This organization has been instrumental in rescuing over 100,000 children from child labor, slavery, and trafficking, and rehabilitating them. His efforts through this organization led to him being awarded the Nobel Peace Prize in 2014, jointly with Malala Yousafzai.
The problem involves ratios of salaries over two different years for two individuals. We need to find the present salary of Laxman given the total present salaries. We will use variables to represent the salaries and set up equations based on the given ratios to find the individual present salaries.
Let Laxman's salary last year be \(L_1\) and Gopal's salary last year be \(G_1\).
Given that the ratio of Laxman's salary to Gopal's salary one year ago was 3 : 5, we can write:
\[ \frac{L_1}{G_1} = \frac{3}{5} \]Let Laxman's present salary be \(L_2\) and Gopal's present salary be \(G_2\).
The ratio of Laxman's individual salary of last year to that of the present year is 2 : 3. So,
\[ \frac{L_1}{L_2} = \frac{2}{3} \]The ratio of Gopal's individual salary of last year to that of the present year is 4 : 5. So,
\[ \frac{G_1}{G_2} = \frac{4}{5} \]From step 2, we can express \(L_1\) in terms of \(L_2\):
\[ L_1 = \frac{2}{3} L_2 \]From step 3, we can express \(G_1\) in terms of \(G_2\):
\[ G_1 = \frac{4}{5} G_2 \]Substitute the expressions for \(L_1\) and \(G_1\) from steps 4 and 5 into the ratio from step 1:
\[ \frac{\frac{2}{3} L_2}{\frac{4}{5} G_2} = \frac{3}{5} \]\[ \frac{2}{3} L_2 \times \frac{5}{4 G_2} = \frac{3}{5} \]\[ \frac{10 L_2}{12 G_2} = \frac{3}{5} \]\[ \frac{5 L_2}{6 G_2} = \frac{3}{5} \]Now, we can find the ratio of \(L_2\) to \(G_2\):
\[ 5 L_2 \times 5 = 3 \times 6 G_2 \]\[ 25 L_2 = 18 G_2 \]\[ \frac{L_2}{G_2} = \frac{18}{25} \]Let \(L_2 = 18x\) and \(G_2 = 25x\) for some constant \(x\).
Given that their total salaries for the present year are ₹4,300:
\[ L_2 + G_2 = 4300 \]\[ 18x + 25x = 4300 \]\[ 43x = 4300 \]\[ x = \frac{4300}{43} \]\[ x = 100 \]Now, calculate Laxman's present salary \(L_2\):
\[ L_2 = 18x = 18 \times 100 = 1800 \]D) ₹1,800
The question asks to identify the first female jawan in the Indian Army who joined the 969 Railway Engineer Regiment of the Territorial Army (TA) in 2011. This requires knowledge of significant milestones and personalities in the Indian armed forces.
A) Sapper Shanti Tigga was indeed the first female jawan in the Indian Army. She joined the 969 Railway Engineer Regiment of the Territorial Army (TA) in 2011, making history by breaking gender barriers in combat roles. She was awarded the title of best recruit.
This problem involves simple interest. We are given a scenario where an increase in the rate of interest leads to a specific increase in the simple interest earned over a fixed period. We can use the formula for simple interest to set up an equation and solve for the principal amount (initial sum invested).
Let the initial sum invested be \(P\).
Let the original rate of interest per annum be \(R\%\).
The time period is \(T = 2\) years.
The formula for simple interest (SI) is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
According to the problem, if the rate of interest were 3% higher, the simple interest would be ₹240 more. This means the new rate of interest would be \((R+3)\%\).
The new simple interest (\(\text{SI}_\text{new}\)) would be:
\[ \text{SI}_\text{new} = \frac{P \times (R+3) \times 2}{100} \]
The original simple interest (\(\text{SI}_\text{old}\)) was:
\[ \text{SI}_\text{old} = \frac{P \times R \times 2}{100} \]
We are given that \(\text{SI}_\text{new} - \text{SI}_\text{old} = 240\).
Substitute the expressions for \(\text{SI}_\text{new}\) and \(\text{SI}_\text{old}\):
\[ \frac{P \times (R+3) \times 2}{100} - \frac{P \times R \times 2}{100} = 240 \]
Factor out common terms:
\[ \frac{P \times 2}{100} \left[ (R+3) - R \right] = 240 \]
\[ \frac{2P}{100} \left[ 3 \right] = 240 \]
\[ \frac{6P}{100} = 240 \]
Now, solve for \(P\):
\[ 6P = 240 \times 100 \]
\[ 6P = 24000 \]
\[ P = \frac{24000}{6} \]
\[ P = 4000 \]
Thus, the initial sum invested is ₹4,000.
B) ₹4,000
The problem asks for the least number that satisfies two conditions: first, it leaves a remainder of 3 when divided by 8, 12, and 16; and second, it leaves no remainder (i.e., is perfectly divisible) when divided by 7. We can solve this by finding the Least Common Multiple (LCM) of the divisors, adding the common remainder, and then checking the divisibility by 7.
Find the LCM of 8, 12, and 16:
The LCM is the product of the highest powers of all prime factors involved:
\[ \text{LCM}(8, 12, 16) = 2^4 \times 3^1 = 16 \times 3 = 48 \]Formulate the general expression for the number:
Since the number leaves a remainder of 3 when divided by 8, 12, and 16, it can be expressed in the form:
\[ N = \text{LCM}(8, 12, 16) \times k + 3 \]where \(k\) is a positive integer.
\[ N = 48k + 3 \]Apply the second condition (divisibility by 7):
The number \(N\) must be perfectly divisible by 7. So, \(N \equiv 0 \pmod{7}\).
\[ 48k + 3 \equiv 0 \pmod{7} \]We can simplify 48 modulo 7:
\[ 48 = 6 \times 7 + 6 \]So, \(48 \equiv 6 \pmod{7}\) or \(48 \equiv -1 \pmod{7}\).
Substituting this into the congruence:
\[ 6k + 3 \equiv 0 \pmod{7} \]or
\[ -k + 3 \equiv 0 \pmod{7} \] \[ 3 \equiv k \pmod{7} \]The smallest positive integer value for \(k\) that satisfies this condition is \(k=3\).
Calculate the least number:
Substitute \(k=3\) back into the expression for \(N\):
\[ N = 48 \times 3 + 3 \] \[ N = 144 + 3 \] \[ N = 147 \]Verify the conditions:
All conditions are satisfied.
D) 147 is the least number that satisfies all the given conditions.
To find the greatest number that divides two given numbers and leaves specific remainders, we first subtract the respective remainders from the numbers. The problem then reduces to finding the HCF (Highest Common Factor) of the resulting numbers. The HCF will be the greatest number that divides the original numbers with the given remainders.
C) 42 — The greatest number that divides 2400 and 1810 leaving remainders 6 and 4 respectively is 42, as calculated by finding the HCF of \((2400-6)\) and \((1810-4)\).
The question asks about the specific Article in the Constitution of India that outlines the procedure for the impeachment of the President. To answer this, one needs to recall the relevant constitutional provisions related to the President's office and impeachment.
Correct Option: D) Article 61
Article 61 of the Constitution of India describes the procedure for the impeachment of the President. It states that the President can be impeached for violation of the Constitution. The process involves charges being preferred by either House of Parliament, investigation of these charges, and a resolution passed by a two-thirds majority of the total membership of both Houses.
This question tests understanding of wave phenomena, specifically how sound waves behave when encountering obstacles or openings. The ability to hear sounds from an adjacent room implies that the sound waves are bending around corners or spreading through openings, which is characteristic of a specific wave property.
Correct Option: B) diffraction. Diffraction is the bending of waves around the corners of an obstacle or opening into the region of geometrical shadow of the obstacle. This is precisely why we can hear people speaking in adjacent rooms, as the sound waves bend around the doorframes or walls.
The question asks to identify the two freedom fighters who threw smoke bombs in the Delhi Central Legislative Assembly in 1929. This is a direct factual recall question from Indian history, specifically related to the Indian independence movement.
C) Bhagat Singh and Batukeshwar Dutt are the correct pair. On April 8, 1929, they threw smoke bombs and leaflets in the Central Legislative Assembly in Delhi to protest against oppressive British laws, famously stating their intention was "to make the deaf hear."