The question asks for the best description of 'Financial Inclusion'. We need to evaluate each option against the core concept of financial inclusion, which aims to provide financial services to all segments of society, especially the vulnerable and low-income groups, at an affordable cost.
Correct Option: C) Delivery of financial services at affordable cost to the poor
This option accurately captures the essence of financial inclusion, which is about extending financial services (like banking, credit, insurance, and payments) to underserved populations, particularly the poor, at prices they can afford.
To solve this problem, we need to determine the cost price (CP) of one item, then calculate the selling price (SP) of one item to achieve a 20% gain. Finally, we can find out how many items should be sold for a rupee at that selling price.
Calculate the Cost Price (CP) of one item:
The vendor bought 12 items for 1 rupee.
Calculate the Selling Price (SP) of one item for a 20% gain:
To gain 20%, the selling price must be 120% of the cost price.
Determine how many items should be sold for a rupee:
If the selling price of 1 item is \( \frac{1}{10} \) Rupee, it means that for 1 Rupee, the vendor should sell 10 items.
B) 10 is the correct answer. To gain 20%, the vendor should sell 10 items for a rupee.
The problem presents a series of alphanumeric terms. To find the missing term, we need to identify the patterns in the numbers and letters separately. We will analyze the first number, the letter, and the second number in each term to find their respective rules.
The series of first numbers is 16, 33, 50, 67.
The pattern for the first number is an addition of 17 to the previous number. So, the next first number will be \(67 + 17 = 84\).
The series of letters is S, M, G, A.
Let's look at the difference in their positions:
The pattern for the letter is a subtraction of 6 from the alphabetical position of the previous letter. Since A is the 1st letter, subtracting 6 from 1 would mean going backwards in the alphabet. If we consider the alphabet as cyclic (A=1, B=2, ..., Z=26, then A=27, B=28, etc. or A=1, Z=0, Y=-1 etc.), subtracting 6 from A (1) would lead to \(1 - 6 = -5\). Counting backwards from Z, -5 corresponds to U (Z=0, Y=-1, X=-2, W=-3, V=-4, U=-5). Alternatively, \(26 + 1 - 6 = 21\), which is the position of U. So the next letter is U.
The series of second numbers is 8, 12, 18, 26.
The pattern for the second number is an addition of an increasing even number (4, 6, 8, ...). The next number to be added will be 10. So, the next second number will be \(26 + 10 = 36\).
The next term in the series will be 84U36.
A) 84U36 is the correct option as it matches all three identified patterns.
A train covers a distance of 12 km in 25 minutes. If its speed is decreased by 5 km/hr, then the time (in minutes) taken by it to cover the same distance will be:
30 \( \frac{3}{119} \)
30 \( \frac{13}{119} \)
30 \( \frac{32}{119} \)
30 \( \frac{30}{119} \)
To solve this problem, we first need to calculate the initial speed of the train. Then, we will decrease this speed by 5 km/hr to find the new speed. Finally, we will use the new speed and the given distance to calculate the new time taken to cover the same distance.
Convert time to hours:
The given time is 25 minutes. To convert it to hours, we divide by 60:
\[ \text{Time} = 25 \text{ minutes} = \frac{25}{60} \text{ hours} = \frac{5}{12} \text{ hours} \]Calculate the initial speed:
The distance covered is 12 km and the time taken is \( \frac{5}{12} \) hours. The formula for speed is:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]\[ \text{Initial Speed} = \frac{12 \text{ km}}{\frac{5}{12} \text{ hours}} = 12 \times \frac{12}{5} \text{ km/hr} = \frac{144}{5} \text{ km/hr} = 28.8 \text{ km/hr} \]Calculate the new speed:
The speed is decreased by 5 km/hr:
\[ \text{New Speed} = \text{Initial Speed} - 5 \text{ km/hr} \]\[ \text{New Speed} = \frac{144}{5} - 5 = \frac{144 - 25}{5} = \frac{119}{5} \text{ km/hr} \]Calculate the new time taken:
The distance is still 12 km, and the new speed is \( \frac{119}{5} \) km/hr. The formula for time is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]\[ \text{New Time} = \frac{12 \text{ km}}{\frac{119}{5} \text{ km/hr}} = 12 \times \frac{5}{119} \text{ hours} = \frac{60}{119} \text{ hours} \]Convert the new time to minutes:
To convert hours to minutes, we multiply by 60:
\[ \text{New Time (in minutes)} = \frac{60}{119} \times 60 \text{ minutes} = \frac{3600}{119} \text{ minutes} \]Express the new time as a mixed fraction:
Divide 3600 by 119:
\[ 3600 \div 119 \]\[ 3600 = 119 \times 30 + 30 \]\[ \text{New Time} = 30 \frac{30}{119} \text{ minutes} \]Correct Option: D) 30 \( \frac{30}{119} \)
The question asks to identify India's first indigenous satellite launch vehicle. This requires knowledge of the history and development of India's space program, specifically the sequence of launch vehicles developed by ISRO.
SLV-3 (Satellite Launch Vehicle-3) was India's first experimental satellite launch vehicle. It was an all-solid, four-stage vehicle weighing 17 tonnes with a height of 22 m and was capable of placing 40 kg class payloads into Low Earth Orbit (LEO). Its first successful launch was on July 18, 1980, when it placed the Rohini satellite (RS-1) into orbit, marking India's entry into the exclusive club of space-faring nations.
The question asks about the primary deity whose life scenes are depicted in the Manipuri classical dance form. To answer this, one needs to recall the central themes and mythological references associated with Manipuri dance.
C) Krishna — Manipuri classical dance is predominantly characterized by its devotion to Lord Krishna. The most famous form, Ras Leela, specifically portrays the divine love story of Radha and Krishna and the playful activities (leelas) of Krishna with the gopis of Vrindavan. The entire dance tradition is deeply influenced by the Vaishnavite cult of Manipur, which reveres Krishna as the supreme being.
This question asks us to analyze the relationship between two events: Event A (Yamuna dam project came to a halt) and Event B (Yamuna dam project was crucial for the city's development). We need to determine if one is the cause or effect of the other, or if they are independent.
C) Event A is the effect but Event B is not its immediate and principal cause. This is correct because the project coming to a halt (Event A) is an outcome or effect. The fact that the project was crucial for the city's development (Event B) is a description of its importance, not a direct cause for its halt. The halt would be due to other reasons, making Event B not the immediate and principal cause of Event A.
This is a syllogism problem that can be solved using Venn diagrams or by analyzing the logical relationships between the statements. We need to assume the given statements are true, regardless of common knowledge, and then determine which conclusions logically follow.
D) Only conclusion B follows.
The value of sin 15° sin 30° sin 75° is:
\(\frac{1}{2\sqrt{2}}\)
\(\frac{1}{8}\)
\(\frac{3}{2}\)
\(\frac{1}{4}\)
To find the value of the given trigonometric expression, we will use standard trigonometric values for common angles and trigonometric identities. Specifically, we will use the known values of \(\sin 30^\circ\), \(\sin 15^\circ\), and \(\sin 75^\circ\).
We know that \(\sin 30^\circ = \frac{1}{2}\).
We can use the difference formula for sine: \(\sin(A - B) = \sin A \cos B - \cos A \sin B\).
Let \(A = 45^\circ\) and \(B = 30^\circ\).
\[ \sin 15^\circ = \sin (45^\circ - 30^\circ) = \sin 45^\circ \cos 30^\circ - \cos 45^\circ \sin 30^\circ \] \[ = \left(\frac{1}{\sqrt{2}}\right) \left(\frac{\sqrt{3}}{2}\right) - \left(\frac{1}{\sqrt{2}}\right) \left(\frac{1}{2}\right) \] \[ = \frac{\sqrt{3}}{2\sqrt{2}} - \frac{1}{2\sqrt{2}} = \frac{\sqrt{3} - 1}{2\sqrt{2}} \]We can use the sum formula for sine: \(\sin(A + B) = \sin A \cos B + \cos A \sin B\).
Let \(A = 45^\circ\) and \(B = 30^\circ\).
\[ \sin 75^\circ = \sin (45^\circ + 30^\circ) = \sin 45^\circ \cos 30^\circ + \cos 45^\circ \sin 30^\circ \] \[ = \left(\frac{1}{\sqrt{2}}\right) \left(\frac{\sqrt{3}}{2}\right) + \left(\frac{1}{\sqrt{2}}\right) \left(\frac{1}{2}\right) \] \[ = \frac{\sqrt{3}}{2\sqrt{2}} + \frac{1}{2\sqrt{2}} = \frac{\sqrt{3} + 1}{2\sqrt{2}} \]Alternatively, we know that \(\sin(90^\circ - \theta) = \cos \theta\). So, \(\sin 75^\circ = \sin (90^\circ - 15^\circ) = \cos 15^\circ\).
Using \(\cos 15^\circ = \cos(45^\circ - 30^\circ) = \cos 45^\circ \cos 30^\circ + \sin 45^\circ \sin 30^\circ\):
\[ = \left(\frac{1}{\sqrt{2}}\right) \left(\frac{\sqrt{3}}{2}\right) + \left(\frac{1}{\sqrt{2}}\right) \left(\frac{1}{2}\right) = \frac{\sqrt{3} + 1}{2\sqrt{2}} \]Now, substitute the calculated values into the expression:
\[ \sin 15^\circ \sin 30^\circ \sin 75^\circ = \left(\frac{\sqrt{3} - 1}{2\sqrt{2}}\right) \left(\frac{1}{2}\right) \left(\frac{\sqrt{3} + 1}{2\sqrt{2}}\right) \] \[ = \frac{(\sqrt{3} - 1)(\sqrt{3} + 1)}{2\sqrt{2} \cdot 2 \cdot 2\sqrt{2}} \]Using the identity \((a-b)(a+b) = a^2 - b^2\) for the numerator:
\[ = \frac{(\sqrt{3})^2 - (1)^2}{8 \cdot 2} \] \[ = \frac{3 - 1}{16} \] \[ = \frac{2}{16} \] \[ = \frac{1}{8} \]Correct Option: B) \(\frac{1}{8}\)
If a = 2b = 3c and a + b + c = 121 then \(\sqrt{a^2+b^2+c^2}\) is:
The problem provides a relationship between three variables \(a\), \(b\), and \(c\) as \(a = 2b = 3c\), and their sum \(a + b + c = 121\). We need to find the value of \(\sqrt{a^2+b^2+c^2}\). The strategy is to express \(b\) and \(c\) in terms of \(a\) (or any one variable), substitute these into the sum equation to find the value of \(a\), and then calculate \(b\) and \(c\). Finally, substitute these values into the expression \(\sqrt{a^2+b^2+c^2}\).
Express \(b\) and \(c\) in terms of \(a\):
From the given relation \(a = 2b\), we can write:
\[ b = \frac{a}{2} \]From the given relation \(a = 3c\), we can write:
\[ c = \frac{a}{3} \]Substitute these into the sum equation:
The given sum is \(a + b + c = 121\). Substitute the expressions for \(b\) and \(c\):
\[ a + \frac{a}{2} + \frac{a}{3} = 121 \]Solve for \(a\):
To sum the terms on the left side, find a common denominator, which is 6:
\[ \frac{6a}{6} + \frac{3a}{6} + \frac{2a}{6} = 121 \]\[ \frac{6a + 3a + 2a}{6} = 121 \]\[ \frac{11a}{6} = 121 \]Multiply both sides by 6 and divide by 11:
\[ 11a = 121 \times 6 \]\[ a = \frac{121 \times 6}{11} \]\[ a = 11 \times 6 \]\[ a = 66 \]Calculate \(b\) and \(c\):
Using \(a = 66\):
\[ b = \frac{a}{2} = \frac{66}{2} = 33 \]\[ c = \frac{a}{3} = \frac{66}{3} = 22 \]Calculate \(\sqrt{a^2+b^2+c^2}\):
Now substitute the values of \(a\), \(b\), and \(c\) into the expression:
\[ \sqrt{a^2+b^2+c^2} = \sqrt{(66)^2 + (33)^2 + (22)^2} \]\[ = \sqrt{4356 + 1089 + 484} \]\[ = \sqrt{5929} \]To find the square root of 5929, we can estimate or use prime factorization. Since the last digit is 9, the square root must end in 3 or 7. \(70^2 = 4900\) and \(80^2 = 6400\), so the number is between 70 and 80. Let's try \(77^2\):
\[ 77^2 = (70+7)^2 = 70^2 + 2 \times 70 \times 7 + 7^2 \]\[ = 4900 + 980 + 49 \]\[ = 5929 \]So,
\[ \sqrt{5929} = 77 \]B) 77 is the correct value for \(\sqrt{a^2+b^2+c^2}\).