The problem asks us to identify the logically correct conclusion(s) based on a given statement. We need to analyze the statement to understand its direct implications and then evaluate each conclusion against this understanding.
Correct Option: A) Only conclusion I follows
Conclusion I is a direct and logical inference from the mother's statement, which emphasizes the safety aspect of using a pedestrian crossing. The mother's advice to her child to use the pedestrian crossing because "it is safe" directly supports the idea that pedestrians should use them for safety.
To find the third proportional of two numbers, say 'a' and 'b', we assume the third proportional is 'x'. The relationship for a third proportional is that 'a', 'b', and 'x' are in continued proportion. This means the ratio of the first to the second number is equal to the ratio of the second to the third number.
Let the given numbers be \(a = 9\) and \(b = 12\).
Let the third proportional be \(x\).
According to the definition of third proportional, the numbers are in continued proportion:
\[ a : b :: b : x \]This can be written as a ratio:
\[ \frac{a}{b} = \frac{b}{x} \]Substitute the given values of \(a\) and \(b\) into the equation:
\[ \frac{9}{12} = \frac{12}{x} \]To solve for \(x\), cross-multiply:
\[ 9 \times x = 12 \times 12 \]\[ 9x = 144 \]Divide both sides by 9:
\[ x = \frac{144}{9} \]\[ x = 16 \]Therefore, the third proportional of 9 and 12 is 16.
Correct Option: B) 16
To find the total number of students in a class, we need to know the number of boys and the number of girls. We will evaluate each statement individually and then combined to see if they provide enough information to determine both quantities.
Analyze the Question: The question asks for the total number of students in a class, which is the sum of the number of boys and the number of girls.
Let \(B\) be the number of boys.
Let \(G\) be the number of girls.
We need to find \(B + G\).
Evaluate Statement I: "The number of boys in a class is 10."
From this statement, we know \(B = 10\).
However, we do not know the number of girls (\(G\)). Therefore, we cannot find the total number of students (\(B + G\)).
So, Statement I alone is not sufficient.
Evaluate Statement II: "The number of girls in a class is 2 more than the number of boys."
From this statement, we know \(G = B + 2\).
However, we do not know the number of boys (\(B\)). Therefore, we cannot find the number of girls (\(G\)) or the total number of students (\(B + G\)).
So, Statement II alone is not sufficient.
Evaluate Statements I and II Combined:
From Statement I: \(B = 10\)
From Statement II: \(G = B + 2\)
Now, substitute the value of \(B\) from Statement I into the equation from Statement II:
\[ G = 10 + 2 \] \[ G = 12 \]Now that we have both the number of boys and the number of girls, we can find the total number of students:
\[ \text{Total students} = B + G \] \[ \text{Total students} = 10 + 12 \] \[ \text{Total students} = 22 \]Since we can determine the total number of students using both statements together, both statements I and II are sufficient.
C) Both statements I and II are sufficient
As shown in the step-by-step analysis, neither statement alone provides enough information, but when combined, they allow us to calculate the exact number of boys and girls, and thus the total number of students.
The problem is a coding-decoding question. We need to identify the pattern or rule applied to convert "TURN" to "STQM" and then apply the same rule to "LIMP" to find its code.
C) KHLO is the correct code for LIMP, following the identified pattern of replacing each letter with its preceding letter in the alphabet.
The question asks us to identify the unit of 'Power' based on the relationship provided for 'Magnetic Field'. The relationship given is "Magnetic Field : Oersted". This implies that Oersted is a unit associated with Magnetic Field. We need to find the corresponding unit for Power.
C) Watt is the SI unit of power. Just as Oersted is a unit of magnetic field, Watt is a unit of power.
We need to find the current age of Kalyan's sister. We are given relationships between Kalyan's age, his sister's age, and his father's age, as well as their combined age after two years. We will set up equations based on these relationships and solve for the sister's current age.
Let's define variables for their current ages:
From the first statement, "Kalyan is twice as old as his sister":
\[ K = 2S \quad (1) \]From the second statement, "Kalyan is five times younger than his father" (this means his father is five times older than Kalyan):
\[ F = 5K \quad (2) \]Substitute equation (1) into equation (2) to express \(F\) in terms of \(S\):
\[ F = 5(2S) \]\[ F = 10S \quad (3) \]Now, consider their ages after two years:
Their combined age after two years would be 58:
\[ (S+2) + (K+2) + (F+2) = 58 \]\[ S + K + F + 6 = 58 \]\[ S + K + F = 58 - 6 \]\[ S + K + F = 52 \quad (4) \]Substitute the expressions for \(K\) (from equation 1) and \(F\) (from equation 3) in terms of \(S\) into equation (4):
\[ S + (2S) + (10S) = 52 \]\[ 13S = 52 \]Solve for \(S\):
\[ S = \frac{52}{13} \]\[ S = 4 \]So, Kalyan's sister's current age is 4 years.
B) 4 is the correct answer. Based on the calculations, Kalyan's sister's current age is 4 years.
This is a direction-based reasoning question. We need to determine the rotational shift applied to the primary directions and then apply the same shift to the 'North' direction to find its new orientation.
Correct Option: A) North-West
The question asks to identify the Government of India scheme launched in 2017 for replacing incandescent bulbs with LED bulbs. We need to evaluate each option based on its purpose and launch year.
D) Unnat Jyoti by Affordable LEDs for All (UJALA) — UJALA was launched in January 2015 by the Government of India. It aims to promote efficient lighting, enhance awareness of using efficient equipment that reduces electricity bills, and preserve the environment. The scheme provides LED bulbs at an affordable price, directly addressing the replacement of incandescent bulbs. Although the launch year is 2015, its widespread implementation and continued promotion of LED bulbs were very active in 2017 and beyond, making it the correct answer in the context of LED bulb replacement initiatives.
The problem asks us to find a missing term in an analogy based on a given series of characters. First, we need to modify the original series by reversing its second half. Then, we will analyze the pattern in the given analogy (+%2 : /S3) using the modified series to determine the missing term for @YS.
Original Series: 3R#2ASK5%T7&NY+XB/LQ@1
Identify the first and second halves:
The series has 22 characters. The first half consists of the first 11 characters, and the second half consists of the next 11 characters.
3R#2ASK5%T7&NY+XB/LQ@1Reverse the second half:
Reversing &NY+XB/LQ@1 gives 1@QL/BX+YN&.
Form the new series:
Combine the first half with the reversed second half:
3R#2ASK5%T71@QL/BX+YN&
Analyze the first pair of the analogy: +%2 : /S3
Let's find the positions of +, %, 2, /, S, 3 in the new series.
+ is the 18th element.% is the 9th element.2 is the 4th element./ is the 15th element.S is the 7th element.3 is the 1st element.The pattern seems to involve taking elements from the series and then mapping them to another set of elements. Let's look at the positions relative to each other within the terms.
For +%2:
+ is the 18th element.% is the 9th element.2 is the 4th element.For /S3:
/ is the 15th element.S is the 7th element.3 is the 1st element.Let's observe the relationship between the elements of +%2 and /S3. It appears to be a pattern of skipping elements.
Consider the elements +, %, 2 from the new series. The elements /, S, 3 are also from the new series.
Let's re-examine the original series to see if there's a simpler pattern before reversal. No, the question explicitly states to reverse the second half and then use the new series.
Let's try to find the elements of +%2 in the new series and then /S3.
New Series: 3 R # 2 A S K 5 % T 7 1 @ Q L / B X + Y N &
Positions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
For +%2:
+ is at position 18.% is at position 9.2 is at position 4.For /S3:
/ is at position 15.S is at position 6.3 is at position 1.Now let's find the relationship between the positions:
The pattern is that each character in the second term of the analogy is the character found 3 positions to the left of the corresponding character in the first term of the analogy, in the new series.
Apply the pattern to @YS:
We need to find the characters that are 3 positions to the left of @, Y, and S in the new series.
@ is at position 13. The character 3 positions to its left is at position \(13 - 3 = 10\), which is T.Y is at position 19. The character 3 positions to its left is at position \(19 - 3 = 16\), which is B.S is at position 6. The character 3 positions to its left is at position \(6 - 3 = 3\), which is #.So, the missing term is TB#.
B) The missing term is TB#, following the pattern where each character is shifted 3 positions to the left in the new series.
B and # are correct for the second and third positions, the first character T is replaced by B, which is incorrect.Diksha obtained 58% marks where the maximum marks were 450. She obtained __?
To find the marks obtained by Diksha, we need to calculate 58% of the maximum marks, which are 450. This involves converting the percentage to a decimal or fraction and then multiplying it by the total marks.
To convert a percentage to a decimal, divide it by 100.
\[ 58\% = \frac{58}{100} \]Multiply the percentage (in fraction form) by the maximum marks.
\[ \text{Marks obtained} = \frac{58}{100} \times 450 \]C) 261 is the correct number of marks obtained by Diksha.