This problem can be solved using the property of parallel lines and transversals, specifically the Basic Proportionality Theorem (Thales's Theorem) or its corollary. When three parallel lines are intersected by two transversals, the ratio of the intercepts made on one transversal is equal to the ratio of the corresponding intercepts made on the other transversal.
Correct Option: C) 3 : 4
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 | 9 | 5 | 3 | # | 6 | & | 7 | @ | % | 8 | 2 |
| Code | L | K | J | H | G | F | D | S | A | P | B |
Conditions:
(i) If the first two elements are numbers and the last is a symbol, then interchange the codes for the second number and the last symbol.
(ii) If the second element is a symbol and the last is a symbol, then all the symbols are to be coded as C.
(iii) If the question has any number which is immediately preceded by a prime number, then interchange the codes of the first and last number appearing in the question.
What will be the code for 7 9 & 8 % # 3?
The problem requires us to code a given sequence of numbers and symbols based on a provided table and a set of conditions. We need to first find the direct codes for each element in the sequence and then apply the conditions sequentially to modify the codes if applicable.
The final code after applying all applicable conditions is JLFPAHD.
D) JLFPAHD is the correct code after applying Condition (iii).
The question asks to determine the number of C-C bonds, C-H bonds, and the total number of covalent bonds in a cyclohexane molecule. Cyclohexane is a cyclic alkane with the chemical formula \(\text{C}_6\text{H}_{12}\).
Therefore, cyclohexane contains 6 C-C bonds, 12 C-H bonds, and a total of 18 covalent bonds.
C) 6, 12, 18 — This option correctly identifies 6 C-C bonds, 12 C-H bonds, and a total of 18 covalent bonds in cyclohexane.
The question asks about the components that constitute the armature of an electric motor. Understanding the basic structure and function of an electric motor is key to identifying these parts.
Correct Option: D) Both (i) and (ii)
Study the given letter, symbol series and answer the question that follows.
#91@4*7^53#91<54@3$#2*6!42&9<36#2%2@7
If all even numbers in the given series are replaced with a number which is prime and even, how many numbers are there in the resultant series which are immediately preceded by a prime number and immediately followed by a symbol?
The problem requires us to modify a given series of letters, symbols, and numbers, and then count specific patterns in the modified series. First, we need to identify all even numbers in the original series and replace them with the only prime and even number, which is 2. After creating the new series, we will look for numbers that are immediately preceded by a prime number and immediately followed by a symbol.
#91@4*7^53#91<54@3\(#2*6!42&9<36#2%2@74, 4, 2, 6, 4, 2, 6, 2, 2#91@4*7^53#91<54@3\)#2*6!42&9<36#2%2@7#91@2*7^53#91<52@3\(#2*2!22&9<32#2%2@72, 7, 5, 3, 2, 3, 2, 2, 7 (Note: 1 is not a prime number).#, @, *, ^, #, <, @, \), #, *, !, &, <, #, %, @#91@2*7^53#91<52@3\(#2*2!22&9<32#2%2@7@2*: Here, 2 is a number. It is preceded by @ (symbol), not a prime number. So, this doesn't fit.*7^: Here, 7 is a number (and prime). It is preceded by * (symbol), not a prime number. So, this doesn't fit.^53: Here, 5 is a number (and prime). It is preceded by ^ (symbol), not a prime number. So, this doesn't fit.3#9: Here, 3 is a number (and prime). It is followed by # (symbol). It is preceded by 5 (prime). This is a match! (5 3 #)<52: Here, 5 is a number (and prime). It is preceded by < (symbol), not a prime number. So, this doesn't fit.2@3: Here, 2 is a number (and prime). It is followed by @ (symbol). It is preceded by 5 (prime). This is a match! (5 2 @)3\)#: Here, 3 is a number (and prime). It is followed by $ (symbol). It is preceded by @ (symbol), not a prime number. So, this doesn't fit.#2*: Here, 2 is a number (and prime). It is followed by * (symbol). It is preceded by # (symbol), not a prime number. So, this doesn't fit.*2!: Here, 2 is a number (and prime). It is followed by ! (symbol). It is preceded by * (symbol), not a prime number. So, this doesn't fit.!22: Here, the first 2 is a number (and prime). It is followed by 2 (number), not a symbol. So, this doesn't fit.2&9: Here, 2 is a number (and prime). It is followed by & (symbol). It is preceded by 2 (prime). This is a match! (2 2 &)&9<: Here, 9 is a number. It is followed by < (symbol). It is preceded by & (symbol), not a prime number. So, this doesn't fit.<32: Here, 3 is a number (and prime). It is followed by 2 (number), not a symbol. So, this doesn't fit.2#2: Here, the first 2 is a number (and prime). It is followed by # (symbol). It is preceded by 3 (prime). This is a match! (3 2 #)#2%: Here, 2 is a number (and prime). It is followed by % (symbol). It is preceded by # (symbol), not a prime number. So, this doesn't fit.%2@: Here, 2 is a number (and prime). It is followed by @ (symbol). It is preceded by % (symbol), not a prime number. So, this doesn't fit.@7: Here, 7 is a number (and prime). It is preceded by @ (symbol), not a prime number. So, this doesn't fit.5 3 #5 2 @2 2 &3 2 #The question asks to identify the river that originates from the Amarkantak Hills. This requires knowledge of the geographical origins of major Indian rivers.
Correct Option: C) Narmada originates from the Amarkantak Hills. It flows westwards into the Arabian Sea, forming an estuary.
The problem involves decoding a pattern based on the given examples. We need to find the numerical value assigned to each letter and then apply the same logic to the target word 'FARE'. The common approach for such problems is to use the alphabetical position of letters.
Correct Option: A) 36
What fraction of the positions in all panchayat institutions is reserved for women?
\( \frac{1}{4} \)
\( \frac{1}{3} \)
\( \frac{1}{2} \)
\( \frac{2}{3} \)
This question tests knowledge of the constitutional provisions regarding reservations for women in Panchayat Raj Institutions in India. The 73rd Constitutional Amendment Act is key to understanding this.
Correct Option: B) \( \frac{1}{3} \)
This problem requires us to substitute the given new meanings for mathematical operators into the provided equation and then solve the resulting expression following the order of operations (BODMAS/PEMDAS).
The original equation is: \(16 - 2 + 9 - 3 \times 3 = ?\)
Applying the changes:
So the new equation becomes: \(16 \times 2 - 9 \times 3 \div 3 = ?\)
First, perform multiplication and division from left to right.
Substitute these values back into the equation:
\[ 32 - 27 \times 1 \]Wait, let's re-check the order of operations for the expression \(16 \times 2 - 9 \times 3 \div 3\). The operations are multiplication, subtraction, multiplication, and division.
According to BODMAS/PEMDAS, multiplication and division have the same precedence and are performed from left to right. Subtraction is performed last.
Therefore, the value of the expression is 23.
D) 23 — After correctly substituting the operators and applying the order of operations (BODMAS/PEMDAS), the final result is 23.
A redox reaction (reduction-oxidation reaction) involves the transfer of electrons between species, resulting in a change in their oxidation states. To identify a redox reaction, we need to determine the oxidation state of each element in the reactants and products. If there is a change in the oxidation state of any element, it is a redox reaction. If no oxidation states change, it is not a redox reaction.
Here, Zinc's oxidation state changes from \(+2\) to \(0\) (reduction), and Carbon's oxidation state changes from \(0\) to \(+2\) (oxidation). Thus, this is a redox reaction.
Here, Manganese's oxidation state changes from \(+4\) to \(+2\) (reduction), and Chlorine's oxidation state changes from \(-1\) (in HCl) to \(0\) (in Cl\(_2\)) (oxidation). Thus, this is a redox reaction.
Here, Sodium's oxidation state changes from \(0\) to \(+1\) (oxidation), and Oxygen's oxidation state changes from \(0\) to \(-2\) (reduction). Thus, this is a redox reaction.
In this reaction, the oxidation states of all elements remain unchanged:
Since there is no change in oxidation states, this is not a redox reaction. It is a double displacement (precipitation) reaction.
D) iv — Reaction (iv) is \( \text{AgNO}_3 + \text{NaCl} \to \text{AgCl} + \text{NaNO}_3 \). In this reaction, the oxidation states of all elements remain constant. Silver remains \(+1\), Nitrogen \(+5\), Oxygen \(-2\), Sodium \(+1\), and Chlorine \(-1\). Therefore, no oxidation or reduction occurs, and it is not a redox reaction.