The question asks for the total strength of elected members in the Lok Sabha. This requires knowledge of the current constitutional provisions regarding the composition of the Lok Sabha.
Correct Option: B) 543
The Lok Sabha currently consists of 543 elected members. These members are elected directly from territorial constituencies in the states and Union Territories.
The question asks to identify the counsel who represented India at the International Court of Justice (ICJ) in the case concerning Kulbhushan Jadhav. This is a factual question related to a prominent international legal case involving India and Pakistan.
B) Harish Salve — Harish Salve, a distinguished Indian lawyer and former Solicitor General of India, represented India at the International Court of Justice in the Kulbhushan Jadhav case. He successfully argued India's position, leading to the ICJ ordering a stay on Jadhav's execution and directing Pakistan to review and reconsider his conviction and sentence.
This problem involves a series of profit calculations. We need to work backward from the final price paid by Amar to find the original cost price to Abir. We will use the concept of percentage profit to determine the cost price at each stage of the transaction.
Define variables:
Calculate Kunal's selling price:
Amar pays ₹5,060 for the article. This is Kunal's selling price to Amar, and Kunal made a 10% profit.
So, \(S_K = 5060\).
The formula for selling price with profit is: \[\text{Selling Price} = \text{Cost Price} \times \left(1 + \frac{\text{Profit Percentage}}{100}\right)\]
For Kunal:
\[S_K = C_K \times \left(1 + \frac{10}{100}\right)\] \[5060 = C_K \times \left(1 + 0.10\right)\] \[5060 = C_K \times 1.10\] \[C_K = \frac{5060}{1.10}\] \[C_K = 4600\]So, Kunal's cost price (which is Abir's selling price) is ₹4,600.
Calculate Abir's cost price:
Abir sold the article to Kunal for ₹4,600, making a 15% profit. So, \(S_A = 4600\).
Using the same formula for Abir:
\[S_A = C_A \times \left(1 + \frac{15}{100}\right)\] \[4600 = C_A \times \left(1 + 0.15\right)\] \[4600 = C_A \times 1.15\] \[C_A = \frac{4600}{1.15}\] \[C_A = 4000\]Thus, the original cost price of the article was ₹4,000.
D) ₹4,000 is the original cost price of the article.
The question asks to identify the author of Indian origin who has NOT won the Man Booker Prize for literature as of October 2020. This requires knowledge of past Man Booker Prize winners and their origins.
Correct Option: D) Jhumpa Lahiri
The question describes a tree that breaks at a height of 8 m, with its broken upper part touching the ground at a distance of 6 m from its foot. This forms a right-angled triangle. We need to apply the Pythagorean theorem to find the length of the broken upper part and then add it to the remaining upright portion to determine the original height of the tree.
Identify the given information:
Understand the right-angled triangle:
Let A be the foot of the tree, B be the point where the tree broke, and C be the point where the broken upper part touches the ground.
The remaining upright portion AB is perpendicular to the ground AC.
Therefore, triangle ABC is right-angled at A.
We have:
\[ AB=8\text{ m} \] \[ AC=6\text{ m} \]The broken upper part BC forms the hypotenuse of the triangle.
Apply the Pythagorean theorem:
In right-angled triangle ABC:
\[ BC^2=AB^2+AC^2 \]Substituting the given values:
\[ BC^2=8^2+6^2 \] \[ BC^2=64+36 \] \[ BC^2=100 \]Taking the square root:
\[ BC=\sqrt{100} \] \[ BC=10\text{ m} \]Therefore, the length of the broken upper part is 10 m.
Calculate the original height of the tree:
The original height is the sum of the remaining upright portion and the broken upper part.
\[ \text{Original Height}=AB+BC \] \[ =8+10 \] \[ =18\text{ m} \]Therefore, the original height of the tree was 18 m.
Correct Option: C) 18 m — The tree broke at a height of 8 m, and its upper part touched the ground 6 m from the foot. Using the Pythagorean theorem, the length of the broken part is:
\[ \sqrt{8^2+6^2}=\sqrt{100}=10\text{ m} \]
Adding this to the remaining upright portion:
\[ 8+10=18\text{ m} \]
Hence, Option C is the correct answer.
A) 15 m: This is incorrect because the original height is the sum of the 8 m upright portion and the 10 m broken portion, giving 18 m, not 15 m.
B) 16 m: This is incorrect because the broken portion measures 10 m, not 8 m. Therefore, the original height is 18 m, not 16 m.
D) 24 m: This is incorrect because the correct calculation gives an original height of 18 m, not 24 m.
This question tests knowledge of current affairs and the leadership of prominent scientific organizations in India. Specifically, it asks for the Director General of the Council of Scientific and Industrial Research (CSIR) as of October 2020. To answer this, one needs to recall or identify the person holding that position during the specified period.
A) Dr. Shekhar Mande was indeed the Director General of the Council of Scientific and Industrial Research (CSIR) in October 2020. He served in this capacity from October 2018 to April 2022.
The question asks to identify the common name of the plant whose botanical name is Butea monosperma, specifically mentioning its native status to the Indian subcontinent. This requires knowledge of common botanical names and their corresponding common plant names prevalent in India.
Butea monosperma is famously known as Palash or Flame of the Forest due to its vibrant orange-red flowers. It is indeed native to the Indian subcontinent.
B) Palash — Butea monosperma is the botanical name for the Palash tree, also known as the 'Flame of the Forest' due to its striking orange-red flowers. It is widely distributed across the Indian subcontinent and is culturally significant.
A man travels 360 km in 4 h, partly by air and partly by train. If he had travelled all the way by air, he would have saved \( \frac{4}{5} \) of the time he travelled by train, and he would have arrived at his destination 2 h early. Find the distance he travelled by air.
This problem involves calculating distances and times for a journey taken by two different modes of transport (air and train). We need to set up equations based on the given information about total distance, total time, and hypothetical scenarios. We will use variables for the time spent by air and train, and then use the given conditions to form a system of equations to solve for these variables.
Let \(t_a\) be the time travelled by air and \(t_t\) be the time travelled by train.
The total time taken is 4 hours. So, we have the first equation:
\[ t_a + t_t = 4 \quad \text{(Equation 1)} \]The problem states that if he had travelled all the way by air, he would have saved \(\frac{4}{5}\) of the time he travelled by train, and he would have arrived 2 hours early.
If he travelled all the way by air, the total time would be \(t_a'\). He would arrive 2 hours early, meaning the total time would be \(4 - 2 = 2\) hours.
The time saved would be \(\frac{4}{5}\) of the time he travelled by train (\(t_t\)). So, the time saved is \(\frac{4}{5} t_t\).
The original total time was \(t_a + t_t\). The new total time (all by air) would be \(t_a + t_t - \frac{4}{5} t_t\).
So, the time if travelled all by air is \(t_a + \frac{1}{5} t_t\). This time is equal to 2 hours.
\[ t_a + \frac{1}{5} t_t = 2 \quad \text{(Equation 2)} \]Now we have a system of two linear equations:
Equation 1: \(t_a + t_t = 4\)
Equation 2: \(t_a + \frac{1}{5} t_t = 2\)
Subtract Equation 2 from Equation 1:
\[ (t_a + t_t) - (t_a + \frac{1}{5} t_t) = 4 - 2 \]\[ t_t - \frac{1}{5} t_t = 2 \]\[ \frac{4}{5} t_t = 2 \]\[ t_t = \frac{2 \times 5}{4} = \frac{10}{4} = 2.5 \text{ hours} \]Substitute the value of \(t_t\) back into Equation 1 to find \(t_a\):
\[ t_a + 2.5 = 4 \]\[ t_a = 4 - 2.5 = 1.5 \text{ hours} \]Now we know the time spent by air (\(t_a = 1.5\) hours) and by train (\(t_t = 2.5\) hours).
Let \(S_a\) be the speed of the air travel and \(S_t\) be the speed of the train travel.
The total distance is 360 km. So, \(S_a t_a + S_t t_t = 360\).
\[ S_a (1.5) + S_t (2.5) = 360 \quad \text{(Equation 3)} \]If he had travelled all the way by air, the total distance (360 km) would have been covered in 2 hours. So, the speed of air travel \(S_a\) can be calculated:
\[ S_a = \frac{\text{Total Distance}}{\text{Time if all by air}} = \frac{360}{2} = 180 \text{ km/h} \]The distance travelled by air is \(D_a = S_a \times t_a\).
\[ D_a = 180 \text{ km/h} \times 1.5 \text{ h} \]\[ D_a = 270 \text{ km} \]We can also find the distance by train to verify. Substitute \(S_a = 180\) into Equation 3:
\[ 180 (1.5) + S_t (2.5) = 360 \]\[ 270 + S_t (2.5) = 360 \]\[ S_t (2.5) = 360 - 270 \]\[ S_t (2.5) = 90 \]\[ S_t = \frac{90}{2.5} = \frac{900}{25} = 36 \text{ km/h} \]Distance travelled by train \(D_t = S_t \times t_t = 36 \text{ km/h} \times 2.5 \text{ h} = 90 \text{ km}\).
Total distance \(D_a + D_t = 270 + 90 = 360 \text{ km}\), which matches the given total distance.
A) The distance he travelled by air is 270 km.
To find the smallest number which when diminished by 3 is divisible by 21, 24, 30, and 40, we first need to find the Least Common Multiple (LCM) of these numbers. The number we are looking for will be 3 more than this LCM.
First, find the prime factorization of each number:
To find the LCM, take the highest power of all prime factors present:
\[ \text{LCM}(21, 24, 30, 40) = 2^3 \times 3 \times 5 \times 7 \]\[ \text{LCM} = 8 \times 3 \times 5 \times 7 \]\[ \text{LCM} = 24 \times 35 \]\[ \text{LCM} = 840 \]The problem states that when the smallest number is diminished by 3, it is divisible by 21, 24, 30, and 40. This means that the number minus 3 is equal to the LCM.
Let the required number be \(N\).
\[ N - 3 = \text{LCM}(21, 24, 30, 40) \]\[ N - 3 = 840 \]\[ N = 840 + 3 \]\[ N = 843 \]Thus, the smallest number is 843.
C) 843 – When 843 is diminished by 3, it becomes 840, which is the LCM of 21, 24, 30, and 40, and therefore divisible by all of them.
This problem involves analyzing statements and deriving logical conclusions, a common type of question in competitive exams. We will use Venn diagrams to represent the given statements visually and then check which of the conclusions logically follow from these diagrams.
B) Both conclusions 2 and 3 follow. Based on our analysis, conclusion 2 ("Some lamps are beds") and conclusion 3 ("Some lamps are side-tables") are logically derived from the given statements.