This question tests knowledge about current affairs, specifically the themes chosen for India's Republic Day celebrations. Aspirants need to be aware of the official themes announced for significant national events.
Correct Option: A) Swarnim Bharat: Virasat Aur Vikas
The question asks for India's poverty rate in 2021, specifically at the $2.15 a day (2017 PPP) threshold, according to World Bank data. This requires recalling specific data points related to international poverty lines and India's economic indicators as reported by international organizations.
Correct Option: A) 12.92% is the correct poverty rate for India at $2.15 a day (2017 PPP) in 2021, as per World Bank data. This figure reflects the percentage of the population living below the international poverty line.
The question asks to identify the personality known as the 'Mother of Indian Revolution' who also unfurled the first version of the Indian national flag abroad. This requires knowledge of key figures in the Indian independence movement and their specific contributions.
Correct Option: C) Madam Bhikaji Cama is famously known as the 'Mother of Indian Revolution' and was the first person to unfurl the Indian national flag (a version designed by her and others) on foreign soil at the International Socialist Conference in Stuttgart, Germany, in 1907. This act was a powerful symbol of India's aspiration for independence.
The question asks to identify the specific name for crescent-shaped sand dunes found in the Thar Desert. This requires knowledge of common geomorphological features, particularly types of sand dunes.
Crescent-shaped sand dunes are a very distinct type of dune formed by winds blowing predominantly from one direction. These dunes are known as Barchans.
Correct Option: C) Barchans are crescent-shaped sand dunes, typically found in deserts like the Thar Desert, where there is a limited supply of sand and a constant wind direction. They have two 'horns' pointing downwind and a gently sloping windward side and a steep leeward side.
The problem involves two squares with sides \(p\) and \(q\). We are given two pieces of information: the sum of their areas and the sum of their perimeters. We need to find the product of \(p\) and \(q\). This can be solved by setting up a system of two equations based on the given information and then manipulating them to find the required product.
Correct Option: A) 154 cm²
This is a logical reasoning problem involving arrangement based on given conditions. We need to determine the exam schedule for P, Q, R, S, T, U, and V over a week (Monday to Sunday) and then count the number of people having exams after Q.
P has an exam on Wednesday.
| Day | Person |
|---|---|
| Monday | |
| Tuesday | |
| Wednesday | P |
| Thursday | |
| Friday | |
| Saturday | |
| Sunday |
Exactly 3 people have an exam between P and S. Since P is on Wednesday, S can be placed either 3 days before P or 3 days after P.
| Day | Person |
|---|---|
| Monday | |
| Tuesday | |
| Wednesday | P |
| Thursday | |
| Friday | |
| Saturday | |
| Sunday | S |
V has an exam immediately after T, and Q has an exam immediately before T. This means Q, T, V must be in consecutive days in that order (Q-T-V).
Only 3 people have an exam between U and T.
Let's consider the possible positions for the Q-T-V block:
So, Q is on Thursday, T is on Friday, and V is on Saturday.
| Day | Person |
|---|---|
| Monday | |
| Tuesday | |
| Wednesday | P |
| Thursday | Q |
| Friday | T |
| Saturday | V |
| Sunday | S |
Only 3 people have an exam between U and T. T is on Friday. The days between T and U must be 3. The only remaining empty slots are Monday and Tuesday. If U is on Monday, then Tuesday, Wednesday, Thursday are between U and T (3 people). This fits the condition.
| Day | Person |
|---|---|
| Monday | U |
| Tuesday | |
| Wednesday | P |
| Thursday | Q |
| Friday | T |
| Saturday | V |
| Sunday | S |
The only person left is R, and the only day left is Tuesday.
| Day | Person |
|---|---|
| Monday | U |
| Tuesday | R |
| Wednesday | P |
| Thursday | Q |
| Friday | T |
| Saturday | V |
| Sunday | S |
How many people have an exam after Q?
Q has an exam on Thursday. The people having exams after Q are T (Friday), V (Saturday), and S (Sunday).
There are 3 people.
A) 3. As determined in the step-by-step arrangement, T, V, and S have exams after Q.
To calculate the simple interest, we need to determine the principal amount, the annual rate of interest, and the time period in years. The principal and rate are given. We must calculate the exact number of days between the given dates and convert this into a fraction of a year. Since 2024 is a leap year, February will have 29 days.
Since 2024 is a leap year, there are 366 days in the year.
\[ T_{\text{years}} = \frac{\text{Number of days}}{\text{Days in a leap year}} = \frac{61}{366} \text{ years} \]The formula for simple interest is:
\[ SI = \frac{P \times R \times T}{100} \]Substitute the values:
\[ SI = \frac{3000 \times 8 \times \frac{61}{366}}{100} \] \[ SI = \frac{3000 \times 8 \times 61}{100 \times 366} \] \[ SI = \frac{30 \times 8 \times 61}{366} \]Notice that \(366 = 6 \times 61\). So, we can simplify:
\[ SI = \frac{30 \times 8 \times 61}{6 \times 61} \] \[ SI = \frac{30 \times 8}{6} \] \[ SI = 5 \times 8 \] \[ SI = 40 \text{ ₹} \]Correct Option: B) 40
We are given the ratio of the length and breadth of a rectangular park and its perimeter. We need to find the area of the park. We will use the given ratio to express length and breadth in terms of a common variable, then use the perimeter formula to find the value of that variable. Once the actual length and breadth are known, we can calculate the area.
Define variables based on the ratio:
Let the length of the rectangular park be \(L\) and the breadth be \(B\).
Given the ratio of length to breadth is 3 : 8. This means:
We can write \(L = 3x\) and \(B = 8x\) for some common multiplier \(x\).
Use the perimeter formula:
The perimeter of a rectangle is given by the formula \(P = 2(L + B)\).
We are given that the perimeter \(P = 264\) m.
Substitute the expressions for \(L\) and \(B\) into the perimeter formula:
\[ 2(3x + 8x) = 264 \]Solve for \(x\):
\[ 2(11x) = 264 \]\[ 22x = 264 \]\[ x = \frac{264}{22} \]\[ x = 12 \]Calculate the actual length and breadth:
Length \(L = 3x = 3 \times 12 = 36\) m
Breadth \(B = 8x = 8 \times 12 = 96\) m
Calculate the area:
The area of a rectangle is given by the formula \(A = L \times B\).
D) 3456 — The calculated area of the park is 3456 m\(^2\).
The problem requires us to identify the highest and lowest numbers from a given set of three-digit numbers, then extract specific digits from them, and finally perform a subtraction operation.
The resultant is 1.
D) 1 is the correct answer because the second digit of the lowest number (190) is 9, and the second digit of the highest number (781) is 8. Subtracting 8 from 9 gives 1.
To find the sum of the roots of a quadratic equation, we can use Vieta's formulas. For a general quadratic equation of the form \( ax^2 + bx + c = 0 \), the sum of the roots is given by \( -b/a \).
Alternatively, one could first simplify the equation by dividing by 7:
A) The sum of the roots is 4, as calculated using Vieta's formulas.