In this question, a group of numbers/symbols is coded using letters as per the table given below and the conditions which follow. The correct combination of codes following the conditions is your answer.
| Number/Symbol | $ | 3 | @ | 8 | % | 2 | # | & | 6 | φ | π | 7 | 5 | Ñ„ |
| Code | A | V | L | K | R | M | B | F | N | T | E | C | S | W |
Conditions:
(i) If the first element is a symbol and the last element is a number, the codes for these two (the first and the last elements) are to be interchanged.
(ii) If the first element is an odd number and the last element is an even number, the first and last elements are to be coded as ©.
(iii) If both second and fourth elements are multiples of 3, both second and fourth elements are to be coded as the code for the second element.
#376φ%
The problem requires us to code a given sequence of numbers/symbols based on a provided table and three specific conditions. We need to apply the conditions sequentially and determine the final coded sequence.
Let's re-check the coding based on the provided solution 'C) BVCVTR'. There seems to be a discrepancy in my step-by-step derivation and the given correct answer. Let me re-evaluate the problem with the given options in mind.
Let's re-examine the table and the question carefully.
Number/Symbol: $ 3 @ 8 % 2 # & 6 φ π 7 5 Ñ„
Code: A V L K R M B F N T E C S W
The sequence to be coded is: #376φ%
Let's list the original codes for each element:
So, the initial coded sequence (without conditions) would be M A E F S K.
Now let's apply the conditions:
Condition (i): "If the first element is a symbol and the last element is a number, the codes for these two (the first and the last elements) are to be interchanged."
First element: # (Symbol)
Last element: % (Symbol)
Condition (i) does not apply because the last element is not a number.
Condition (ii): "If the first element is an odd number and the last element is an even number, the first and last elements are to be coded as ©."
First element: # (Symbol)
Condition (ii) does not apply because the first element is not an odd number.
Condition (iii): "If both second and fourth elements are multiples of 3, both second and fourth elements are to be coded as the code for the second element."
Second element: 3 (Multiple of 3)
Fourth element: 6 (Multiple of 3)
Condition (iii) applies. Both the second and fourth elements will be coded as the code for the second element (3).
The code for 3 is 'A'. So, the second and fourth elements will both be coded as 'A'.
Applying Condition (iii) to the original sequence #376φ%:
The resulting code is M A E A S K.
This result (M A E A S K) does not match any of the options directly.
Let's re-examine the table provided in the question. There might be a typo in the question's table or the options, or I might be misinterpreting the table's mapping. Let's assume the question's provided correct answer 'C) BVCVTR' is indeed correct and try to reverse-engineer the mapping or conditions.
Let's re-read the table carefully for potential misinterpretations:
Number/Symbol: $ 3 @ 8 % 2 # & 6 φ π 7 5 Ñ„
Code: A V L K R M B F N T E C S W
This is a direct mapping. Let's list it clearly:
Now, let's re-code the sequence #376φ% using this revised mapping:
So, the initial coded sequence (without conditions) would be B V C N T R.
Now let's apply the conditions with this new mapping:
Condition (i): "If the first element is a symbol and the last element is a number, the codes for these two (the first and the last elements) are to be interchanged."
First element: # (Symbol)
Last element: % (Symbol)
Condition (i) does not apply.
Condition (ii): "If the first element is an odd number and the last element is an even number, the first and last elements are to be coded as ©."
First element: # (Symbol)
Condition (ii) does not apply.
Condition (iii): "If both second and fourth elements are multiples of 3, both second and fourth elements are to be coded as the code for the second element.\
In the given reaction which substance undergoes oxidation?
2Cu + O2 → 2CuO
Copper oxide
Only copper
Copper and oxygen
Only oxygen
To determine which substance undergoes oxidation, we need to understand the definitions of oxidation in terms of electron transfer or change in oxidation states. Oxidation is the loss of electrons or an increase in oxidation state. Reduction is the gain of electrons or a decrease in oxidation state.
B) Only copper — Copper's oxidation state changes from \(0\) to \(+2\), indicating a loss of electrons (oxidation).
The question asks about Fleming's Right-Hand Rule and the context in which it determines the direction of induced current. This rule is fundamental in electromagnetism, specifically for generators.
B) magnetic field. Fleming's Right-Hand Rule is used to determine the direction of induced current when a conductor moves through a magnetic field. This is the core principle of electromagnetic induction in generators.
The question asks about the number of members nominated by the President to the Council of States (Rajya Sabha) based on their special knowledge or practical experience in specific fields. This is a direct factual question related to the composition of the Indian Parliament.
Correct Option: C) 12
Article 80(3) of the Indian Constitution states that "The members to be nominated by the President under sub-clause (a) of clause (1) shall consist of persons having special knowledge or practical experience in respect of such matters as literature, science, art and social service." Clause (1)(a) of Article 80 specifies that "12 members shall be nominated by the President in accordance with the provisions of clause (3)". Therefore, the President nominates 12 members to the Rajya Sabha.
We will solve this problem by setting up equations based on the given conditions. We'll assume the initial cost price (CP) to be a variable, calculate the selling price (SP) under the first condition, and then formulate a second equation based on the hypothetical scenario of a different CP and SP to find the original CP.
Define the initial Cost Price (CP):
Let the original Cost Price of the article be \( \text{CP} = \text{₹}x \).
Calculate the initial Selling Price (SP) based on a 15% loss:
Loss = 15% of CP
\[ \text{Loss} = \frac{15}{100} \times x = 0.15x \]\[ \text{SP}_1 = \text{CP} - \text{Loss} = x - 0.15x = 0.85x \]So, the first selling price is \( \text{₹}0.85x \).
Calculate the new Cost Price (CP') based on a 5% less purchase:
If he had bought the item at 5% less, the new CP would be:
\[ \text{CP'} = x - \left(\frac{5}{100} \times x\right) = x - 0.05x = 0.95x \]So, the new cost price is \( \text{₹}0.95x \).
Calculate the new Selling Price (SP') based on a 10% gain on CP':
If he had gained 10% on the new CP, the new SP would be:
\[ \text{SP'} = \text{CP'} + \left(\frac{10}{100} \times \text{CP'}\right) = 0.95x + (0.10 \times 0.95x) \]\[ \text{SP'} = 0.95x + 0.095x = 1.045x \]So, the new selling price is \( \text{₹}1.045x \).
Formulate the equation based on the difference in selling prices:
The problem states that if he had sold it for ₹195 more, he would have gained 10%. This means the new selling price (\(\text{SP'}\)) is ₹195 more than the original selling price (\(\text{SP}_1\)).
\[ \text{SP'} - \text{SP}_1 = 195 \]\[ 1.045x - 0.85x = 195 \]
Solve for x:
\[ 0.195x = 195 \]\[ x = \frac{195}{0.195} \]\[ x = \frac{195}{\frac{195}{1000}} \]\[ x = 195 \times \frac{1000}{195} \]\[ x = 1000 \]
Conclusion:
The original cost price of the article is ₹1000.
A) 1,000 is the correct answer. The calculations show that the original cost price is ₹1000.
The problem presents a statement involving inequalities and equalities between several variables. We need to analyze this statement and determine which of the given conclusions logically follows from it. This is a common type of question in reasoning sections of competitive exams, testing the ability to deduce relationships from given conditions.
B) W > B
Given the options and the provided correct answer, it is highly probable that 'W' in options A and B is a typo for 'X' or 'V'. If 'W' is 'X', then \(X=V\) is true (Option A becomes true). If 'W' is 'X', then \(X>B\) is true (Option B becomes true). If 'W' is 'V', then \(V=V\) is trivially true (Option A becomes true). If 'W' is 'V', then \(V>B\) is true (Option B becomes true). Since the provided correct answer is B, let's assume 'W' is a typo for 'X' or 'V' and the intended conclusion is \(X > B\) or \(V > B\). Both \(X > B\) and \(V > B\) are directly derivable from the statement \(X = V > B\).
Find the median of the frequency distribution given below.
| Marks | Frequency |
| 30 | 4 |
| 40 | 7 |
| 50 | 2 |
| 85 | 6 |
To find the median of a frequency distribution, we first need to calculate the cumulative frequencies. Then, we determine the total number of observations (\(N\)). The median position is given by \( (N+1)/2 \) for an odd number of observations or the average of the \( N/2 \) and \( (N/2)+1 \) observations for an even number of observations. For a discrete frequency distribution, we find the value corresponding to the median position in the cumulative frequency column.
First, let's list the given data and add a column for cumulative frequency.
| Marks (x) | Frequency (f) | Cumulative Frequency (cf) |
|---|---|---|
| 30 | 4 | 4 |
| 40 | 7 | 4 + 7 = 11 |
| 50 | 2 | 11 + 2 = 13 |
| 85 | 6 | 13 + 6 = 19 |
The total number of observations is the sum of all frequencies, which is the last value in the cumulative frequency column.
\[ N = \sum f = 19 \]Since \(N = 19\) (an odd number), the median is the value of the \( \left( \frac{N+1}{2} \right)^{\text{th}} \) observation.
\[ \text{Median position} = \frac{19+1}{2} = \frac{20}{2} = 10^{\text{th}} \text{ observation} \]Now, we look at the cumulative frequency column to find the value that corresponds to the 10th observation.
The 10th observation falls in the group where the cumulative frequency is 11. The marks corresponding to this cumulative frequency are 40.
Therefore, the median is 40.
D) 40 is the correct median as calculated by finding the \( (N+1)/2 \)th observation in the cumulative frequency distribution.
This question asks about the mechanism of action of tubectomy as a contraceptive method. Tubectomy is a surgical sterilization procedure for females. Understanding the anatomy of the female reproductive system and the path of the ovum is key to answering this question.
Correct Option: A) It blocks access to the fallopian tubes.
Tubectomy involves cutting or tying the fallopian tubes. This physical barrier prevents the ovum from passing through the fallopian tube to meet sperm, and also prevents sperm from reaching the ovum, thereby preventing fertilization. So, it effectively blocks access through the fallopian tubes.
In â–³ABC, m(\(\overline{AB}\)) = m(\(\overline{AC}\)), and m∠BAC = 30°. If the side BC of â–³ABC is extended to D, then find m∠ACD.
We are given an isosceles triangle \(\triangle ABC\) with \(AB = AC\) and \(\angle BAC = 30^\circ\). We need to find the measure of the exterior angle \(\angle ACD\) formed by extending side \(BC\) to \(D\). We will use the properties of isosceles triangles and the exterior angle theorem.
Identify the type of triangle: Given that \(m(\overline{AB}) = m(\overline{AC})\), \(\triangle ABC\) is an isosceles triangle.
Apply property of isosceles triangles: In an isosceles triangle, the angles opposite the equal sides are equal. Therefore, \(\angle ABC = \angle ACB\).
Use the angle sum property of a triangle: The sum of angles in any triangle is \(180^\circ\). So, in \(\triangle ABC\):
\[ \angle BAC + \angle ABC + \angle ACB = 180^\circ \]
Substitute the given value \(\angle BAC = 30^\circ\) and \(\angle ABC = \angle ACB\):
\[ 30^\circ + \angle ACB + \angle ACB = 180^\circ \] \[ 30^\circ + 2 \angle ACB = 180^\circ \] \[ 2 \angle ACB = 180^\circ - 30^\circ \] \[ 2 \angle ACB = 150^\circ \] \[ \angle ACB = \frac{150^\circ}{2} \] \[ \angle ACB = 75^\circ \]
Find the exterior angle \(\angle ACD\): Since \(BCD\) is a straight line, \(\angle ACB\) and \(\angle ACD\) form a linear pair. The sum of angles in a linear pair is \(180^\circ\).
\[ \angle ACB + \angle ACD = 180^\circ \] \[ 75^\circ + \angle ACD = 180^\circ \] \[ \angle ACD = 180^\circ - 75^\circ \] \[ \angle ACD = 105^\circ \]
Alternatively, by the exterior angle theorem, the exterior angle of a triangle is equal to the sum of the two opposite interior angles. So:
\[ \angle ACD = \angle BAC + \angle ABC \] Since \(\angle ABC = \angle ACB = 75^\circ\):
\[ \angle ACD = 30^\circ + 75^\circ \] \[ \angle ACD = 105^\circ \]
Correct Option: B) 105°
The problem presents a series of terms, each consisting of three letters and a number. To find the missing term, we need to identify the pattern in both the letters and the numbers separately.
A) PJL 15 is the correct option because it follows both the letter pattern (each letter decreases by 2 in alphabetical order) and the number pattern (each number increases by 4).