This problem involves setting up and solving a system of two linear equations with two variables. We will represent the present ages of Renu and Manav with variables, translate the given statements into mathematical equations, and then solve these equations simultaneously to find their individual ages. Finally, we will calculate the sum of their ages.
B) The sum of the present ages of Renu and Manav is 32 years, which matches our calculation.
The question asks about the nature of magnetic field lines at the north pole of a magnet. To answer this, we need to recall the fundamental properties and conventions of magnetic field lines.
C) Lines emerging from the pole. This accurately describes the behavior of magnetic field lines at the North pole, as they are conventionally defined to originate from the North pole.
Refer to the following letter, number, symbol series and answer the question.
(Left) H ^ 2 K L 4 D & 3 $ D @ 5 7 % J B # S (Right)
How many such symbols are there which are immediately preceded by a letter and also immediately followed by a number?
The problem asks us to identify symbols in a given series that are immediately preceded by a letter and immediately followed by a number. We need to scan the series from left to right and check each symbol against this condition.
A) 3 — There are three symbols (^, &, @) in the series that are immediately preceded by a letter and immediately followed by a number.
The question asks to identify the recipient of the Major Dhyan Chand Khel Ratna award in 2021 from the given options. This requires knowledge of major sports awards and their recipients in specific years.
D) Ravi Kumar — Ravi Kumar Dahiya is an Indian freestyle wrestler who won a silver medal at the 2020 Tokyo Olympics in the 57 kg category. He was awarded the Major Dhyan Chand Khel Ratna award in 2021 for his outstanding achievements in sports.
We need to find the measure of each interior angle of a regular polygon, given a relationship between the sum of its interior angles and the sum of its exterior angles. We will use the standard formulas for the sum of interior and exterior angles of a polygon, set up an equation based on the given condition, solve for the number of sides, and then calculate the measure of each interior angle.
Let \(n\) be the number of sides of the regular polygon.
The sum of the interior angles of a polygon with \(n\) sides is given by:
\[ \text{Sum of Interior Angles} = (n-2) \times 180^\circ \]The sum of the exterior angles of any convex polygon (including regular polygons) is always:
\[ \text{Sum of Exterior Angles} = 360^\circ \]The problem states that the sum of the interior angles is 200% more than the sum of its exterior angles. This means the sum of interior angles is \(100\% + 200\% = 300\%\) of the sum of exterior angles, or 3 times the sum of exterior angles.
\[ \text{Sum of Interior Angles} = 3 \times (\text{Sum of Exterior Angles}) \]Substitute the formulas from Step 1:
\[ (n-2) \times 180^\circ = 3 \times 360^\circ \]Divide both sides by \(180^\circ\):
\[ n-2 = 3 \times \frac{360^\circ}{180^\circ} \]\[ n-2 = 3 \times 2 \]\[ n-2 = 6 \]\[ n = 6 + 2 \]\[ n = 8 \]So, the polygon is a regular octagon.
For a regular polygon, each interior angle is equal to the sum of interior angles divided by the number of sides, or it can be found using the formula:
\[ \text{Each Interior Angle} = \frac{(n-2) \times 180^\circ}{n} \]Alternatively, each exterior angle is \(\frac{360^\circ}{n}\), and each interior angle is \(180^\circ - \text{Each Exterior Angle}\).
Using the second method:
Each exterior angle \(= \frac{360^\circ}{8} = 45^\circ\)
Each interior angle \(x^\circ = 180^\circ - 45^\circ = 135^\circ\)
Using the first method:
\[ x^\circ = \frac{(8-2) \times 180^\circ}{8} \]\[ x^\circ = \frac{6 \times 180^\circ}{8} \]\[ x^\circ = \frac{1080^\circ}{8} \]\[ x^\circ = 135^\circ \]Thus, the value of \(x^\circ\) is \(135^\circ\).
Correct Option: A) 135°
The Himalayas are traditionally divided into regional sections based on river valleys. This question asks to identify the rivers that demarcate the Kumaun Himalayas.
B) Sutlej and Kali — The Kumaun Himalayas are indeed located between the Sutlej River in the west and the Kali River in the east.
The problem asks us to identify a triad of letter-clusters that follows the same logic as the given triads. We need to analyze the pattern within the given triads first, which involves understanding the positional values of letters in the English alphabet and the differences between them.
C) FGH : IKM : NQT follows the same logic. The first transition (FGH to IKM) is +3, +4, +5 for the respective letters. The second transition (IKM to NQT) is +5, +6, +7 for the respective letters.
The problem involves decoding a pattern in a given code language. We need to identify the rule applied to transform the letters of the original words into their coded forms. Once the rule is established, it can be applied to the new word 'BROKE' to find its coded form.
The pattern for 'ANGLE' seems to be adding 2, 3, 4, 5, 6 to the alphabetical position of each letter.
The pattern holds true: +2, +3, +4, +5, +6 for consecutive letters.
So, 'BROKE' will be coded as 'DUSPK'.
A) DUSPK is the correct code for 'BROKE' based on the identified pattern of adding +2, +3, +4, +5, +6 to the alphabetical position of each letter.
Five friends P, Q, R, S, and T live in a five-storeyed building numbered from 1 (lowest floor) to 5 (topmost floor). Each of them lives on a different floor of the building. R lives on the floor below Q’s floor. T does not live on the top floor. There are an equal number of people living above and below the floor on which S lives. Two people live between the floors where T and R live. Q does not live above or below the floor where S lives. Who lives on the second floor?
This is a logical reasoning problem involving arrangement. We need to deduce the floor on which each person lives based on the given clues. We will use a systematic approach, starting with the most definitive clues and building upon them.
Identify the floors: The building has 5 floors, numbered 1 (lowest) to 5 (topmost).
Clue 1: There are an equal number of people living above and below the floor on which S lives.
This means S lives on the middle floor. In a 5-storey building, the middle floor is the 3rd floor (2 floors above, 2 floors below).
So, S lives on Floor 3.
Clue 2: Q does not live above or below the floor where S lives.
Since S lives on Floor 3, Q cannot live on Floor 1, 2, 4, or 5. This contradicts the statement that Q lives on a different floor from S. Let's re-read the clue carefully: "Q does not live above or below the floor where S lives." This implies Q does not live on any floor other than S's floor. However, the problem states "Each of them lives on a different floor." This means Q cannot live on the same floor as S. Therefore, this clue must mean that Q does not live directly above or directly below S. This is a common phrasing in such puzzles. Let's assume it means Q is not on Floor 2 or Floor 4. So, Q can be on Floor 1 or Floor 5.
Clue 3: R lives on the floor below Q's floor.
This implies Q cannot be on Floor 1 (as there is no floor below Floor 1). So, Q must live on Floor 5.
Consequently, R lives on Floor 4 (the floor below Q's floor).
Clue 4: T does not live on the top floor.
The top floor is Floor 5. We already placed Q on Floor 5, so T cannot be on Floor 5. This is consistent.
Clue 5: Two people live between the floors where T and R live.
We know R lives on Floor 4. If two people live between T and R, then T must be on Floor 1. (Floors 3 and 2 are between Floor 4 and Floor 1).
So, T lives on Floor 1.
Summarize current placements:
Floor 5: Q
Floor 4: R
Floor 3: S
Floor 2: ?
Floor 1: T
Identify the remaining person and floor:
The remaining person is P, and the remaining floor is Floor 2.
Therefore, P lives on Floor 2.
Final check:
Floor 5: Q
Floor 4: R
Floor 3: S
Floor 2: P
Floor 1: T
All conditions are met.
C) P lives on the second floor.