The problem asks us to decode a word based on a given coding pattern. We need to identify the rule by which each letter of the original word is transformed into two letters in the coded word.
Correct Option: B) OQHJDF
The problem involves finding the sum of the next three numbers given the sum of the first three consecutive numbers. We can represent the consecutive numbers using a variable and then form an equation based on the given information. Once the numbers are identified, we can calculate the sum of the next three.
Let the six consecutive numbers be \(n, n+1, n+2, n+3, n+4, n+5\).
The sum of the first three numbers is given as 27. So, we can write the equation:
\[ n + (n+1) + (n+2) = 27 \]Simplify the equation:
\[ 3n + 3 = 27 \]Subtract 3 from both sides:
\[ 3n = 27 - 3 \]\[ 3n = 24 \]Divide by 3 to find the value of \(n\):
\[ n = \frac{24}{3} \]\[ n = 8 \]So, the first number is 8. The six consecutive numbers are 8, 9, 10, 11, 12, 13.
We need to find the sum of the next three numbers, which are \(n+3, n+4, n+5\). These are 11, 12, and 13.
Calculate their sum:
\[ 11 + 12 + 13 = 36 \]C) 36 is the sum of the next three numbers (11, 12, 13).
The value of \(\sqrt{16+\sqrt{80+\sqrt{5000-4999}}}\) is:
To find the value of the given expression, we need to simplify it by working from the innermost square root outwards. We will evaluate each square root step by step.
Start with the innermost part of the expression:
\[ \sqrt{5000-4999} \]Calculate the difference inside the square root:
\[ 5000-4999 = 1 \]Now, evaluate the square root:
\[ \sqrt{1} = 1 \]Substitute this value back into the original expression:
\[ \sqrt{16+\sqrt{80+1}} \]Simplify the term inside the next square root:
\[ 80+1 = 81 \]Evaluate the square root of 81:
\[ \sqrt{81} = 9 \]Substitute this value back into the expression:
\[ \sqrt{16+9} \]Simplify the term inside the outermost square root:
\[ 16+9 = 25 \]Finally, evaluate the outermost square root:
\[ \sqrt{25} = 5 \]Thus, the value of the entire expression is 5.
B) 5
Study the given pattern carefully and select the number that can replace the question mark (?) in it.
| 12 | 51 | 18 |
| 8 | 13 | ? |
| 26 | 12 | 12 |
| 30 | 50 | 23 |
If \( \frac{1}{8} \) of a pencil is black, half of the remaining pencil is yellow and the remaining 3\( \frac{1}{2} \)cm of the pencil is blue, then what is the total length of the pencil?
The problem can be solved by working backward from the known length of the blue part of the pencil, or by setting up an equation for the total length and solving for it. We will use the latter approach, representing the total length as a variable and expressing each colored part as a fraction of the total.
Let the total length of the pencil be \(L\) cm.
The black part of the pencil is \( \frac{1}{8} \) of the total length. So, length of black part \( = \frac{1}{8} L \).
The remaining part of the pencil after the black part is removed is \[L - \frac{1}{8} L = \frac{7}{8} L\].
Half of this remaining pencil is yellow. So, the length of the yellow part is \[\frac{1}{2} \times \frac{7}{8} L = \frac{7}{16} L\].
The remaining part after the black and yellow parts are accounted for is blue. This remaining part is given as \( 3\frac{1}{2} \) cm, which is \( \frac{7}{2} \) cm.
The fraction of the pencil that is blue can be found by subtracting the black and yellow fractions from the total length (which is 1, or \( \frac{16}{16} \)).
Fraction of blue part \[= 1 - \frac{1}{8} - \frac{7}{16}\]
To subtract these fractions, find a common denominator, which is 16.
Fraction of blue part \[= \frac{16}{16} - \frac{2}{16} - \frac{7}{16}\]
Fraction of blue part \[= \frac{16 - 2 - 7}{16} = \frac{16 - 9}{16} = \frac{7}{16}\].
We know that the length of the blue part is \( \frac{7}{2} \) cm. So, we can set up the equation:
\[ \frac{7}{16} L = \frac{7}{2} \]To solve for \(L\), multiply both sides by \( \frac{16}{7} \):
\[ L = \frac{7}{2} \times \frac{16}{7} \]\[ L = \frac{16}{2} \]\[ L = 8 \]Therefore, the total length of the pencil is 8 cm.
C) 8 cm is the correct answer. The calculations show that the total length of the pencil is 8 cm.
The electricity bill consists of a fixed charge and a variable charge per unit consumed. We can set up a system of two linear equations based on the given information and solve for the fixed charge and the variable charge per unit. Once these values are known, we can calculate the bill for any given number of units consumed.
Let \(F\) be the fixed charge (in ₹) and \(V\) be the variable charge per unit (in ₹/unit).
From the first scenario:
When 540 units were consumed, the bill was ₹1,800. This can be written as an equation:
\[ F + 540V = 1800 \quad \text{(Equation 1)} \]From the second scenario:
When 620 units were consumed, the bill was ₹2,040. This gives us the second equation:
\[ F + 620V = 2040 \quad \text{(Equation 2)} \]Now, we solve this system of linear equations. Subtract Equation 1 from Equation 2:
\[ (F + 620V) - (F + 540V) = 2040 - 1800 \] \[ 80V = 240 \]Calculate the variable charge \(V\):
\[ V = \frac{240}{80} \] \[ V = 3 \text{ ₹/unit} \]Substitute the value of \(V\) into Equation 1 to find the fixed charge \(F\):
\[ F + 540(3) = 1800 \] \[ F + 1620 = 1800 \] \[ F = 1800 - 1620 \] \[ F = 180 \text{ ₹} \]Now we have the fixed charge \(F = 180\) ₹ and the variable charge \(V = 3\) ₹/unit.
Calculate the bill for a month when 500 units are consumed:
Bill \( = F + 500V \)
Bill \( = 180 + 500(3) \)
Bill \( = 180 + 1500 \)
Bill \( = 1680 \text{ ₹} \)
Correct Option: C) ₹1,680
The question asks about the effect of extending an arm of an angle on the measure of the angle itself. We need to understand the definition of an angle and how its measure is determined.
D) remains the same
Extending an arm of an angle does not change the angular separation between the two rays that form the angle. The measure of an angle depends only on the relative orientation of its two arms, not on their physical length.
The problem states the passing percentage and the marks obtained by a candidate who failed by a certain margin. We need to find the total marks for the examination. We can determine the passing marks first and then use the passing percentage to calculate the total marks.
The candidate scored 210 marks and failed by 21 marks. This means if the candidate had scored 21 more marks, they would have passed.
\[ \text{Passing Marks} = \text{Marks Obtained} + \text{Marks Needed to Pass} \]\[ \text{Passing Marks} = 210 + 21 = 231 \]The problem states that 33% marks are required to pass the examination.
Let the total marks for the examination be \(T\). We know that 33% of the total marks is equal to the passing marks (231).
\[ 33\% \text{ of } T = 231 \]\[ \frac{33}{100} \times T = 231 \]To find \(T\), we can rearrange the equation:
\[ T = 231 \times \frac{100}{33} \]\[ T = 7 \times 100 \]\[ T = 700 \]Thus, the total marks for the examination are 700.
B) 700 is the correct answer. This is derived by first calculating the passing marks (210 + 21 = 231) and then using the given passing percentage (33%) to find the total marks (231 / 0.33 = 700).
The question asks about the symbolism of the olive branches in the United Nations Emblem. To answer this, one needs to recall the established meanings of symbols used by international organizations, particularly the UN.
C) Peace throughout the world. The olive branches are a universally recognized symbol of peace, and their placement in the UN emblem signifies the organization's dedication to achieving and maintaining global peace.
The question asks to identify the Sarangi player who was awarded the Padma Shri in 2014. This requires knowledge of prominent Indian classical musicians and their awards.
Correct Option: C) Ustad Moinuddin Khan
Ustad Moinuddin Khan is a celebrated Sarangi player belonging to the Jaipur Gharana. He was honored with the Padma Shri, India's fourth-highest civilian award, in 2014 for his significant contributions to the field of Indian classical music.