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Soru 581Soru →

A city planner is inspecting a newly constructed botanical garden. She starts at the Main Gate and walks 80 m80\text{ m} straight North. She then turns 90∘90^{\circ} to her right and walks 30 m30\text{ m}. Following this, she turns 45∘45^{\circ} to her left and walks 202 m20\sqrt{2}\text{ m}. Finally, she turns 45∘45^{\circ} to her left again and walks 20 m20\text{ m} to reach the Central Greenhouse. What is the shortest distance between the Main Gate and the Central Greenhouse, and in which direction is the Greenhouse located with respect to the Main Gate?

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Cevap: 130 m130\text{ m}, North-East

Cevap

The shortest distance is 130 m130\text{ m} and the direction is North-East.
By plotting each movement sequentially on a Cartesian coordinate system, the final position resolves to 50 m50\text{ m} East and 120 m120\text{ m} North of the starting point. Using the Pythagorean theorem, the shortest straight-line distance is calculated as 502+1202=130 m\sqrt{50^2 + 120^2} = 130\text{ m}. Since the final coordinates are located in the upper-right quadrant relative to the starting point, the final direction is North-East.

Adım Adım Çözüm

1
Map the initial movement from the starting point.
The planner walks 80 m80\text{ m} North to the coordinate (0,80)(0, 80).
Establishing the Main Gate at the origin (0,0)(0,0) and translating the first movement along the y-axis.
2
Calculate the second movement after a 90∘90^{\circ} right turn.
The planner now faces East and walks 30 m30\text{ m}. The new position is (30,80)(30, 80).
A right turn from North corresponds to the East direction (+x axis).
3
Calculate the third movement after a 45∘45^{\circ} left turn.
The planner now faces North-East. Walking 202 m20\sqrt{2}\text{ m} adds 20 m20\text{ m} to the East and 20 m20\text{ m} to the North. The new position is (30+20,80+20)=(50,100)(30 + 20, 80 + 20) = (50, 100).
Resolving the diagonal distance into horizontal (Δx=202cos⁡45∘\Delta x = 20\sqrt{2} \cos 45^{\circ}) and vertical (Δy=202sin⁡45∘\Delta y = 20\sqrt{2} \sin 45^{\circ}) components.
4
Calculate the final movement after another 45∘45^{\circ} left turn.
The planner now faces straight North and walks 20 m20\text{ m}. The final position is (50,100+20)=(50,120)(50, 100 + 20) = (50, 120).
A 45∘45^{\circ} left turn from North-East points exactly North again.
5
Calculate the shortest distance and final direction from the origin.
Distance = 502+1202=2500+14400=16900=130 m\sqrt{50^2 + 120^2} = \sqrt{2500 + 14400} = \sqrt{16900} = 130\text{ m}. Since the final coordinate (50,120)(50, 120) is positive on both axes, the direction is North-East.
Applying the Pythagorean theorem to find the Euclidean distance from the starting point.

Anahtar Kavram

Vector displacement and directional rotation tracking on a 2D Cartesian plane.
Soru 582Soru →

A large solid cube of dimensions 5×5×55 \times 5 \times 5 is painted using three colors: Red, Blue, and Green. The painting is applied such that the Top and Bottom faces are Red, the Front and Right faces are Blue, and the Back and Left faces are Green. The large cube is then cut into 125 smaller, identical cubes of dimensions 1×1×11 \times 1 \times 1. Match the categories of the smaller cubes described in List I with their exact counts in List II.

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Öğeler

Cubes with exactly three faces painted, displaying three different colors
Cubes with exactly two faces painted, both displaying the same color
Cubes with exactly one face painted Blue
Cubes with no faces painted at all

Eşleşmeler

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Cevap

The correct matches are: Cubes with three different colors to 4; Cubes with two faces of the same color to 6; Cubes with one face Blue to 18; Cubes with no painted faces to 27.
The exact structural breakdown of the 5x5x5 cube under this specific adjacent-face coloring scheme yields exactly 4 three-color corners, 6 two-color edges (from 2 identical color intersections), 18 one-color blue face centers, and a 27-cube unpainted core.

Adım Adım Çözüm

1
Analyze the corner cubes (exactly 3 faces painted) to match the first category.
There are 8 corners. Top-Front-Left is Red-Blue-Green (3 colors). Top-Front-Right is Red-Blue-Blue (2 colors). Analyzing all 8 corners yields exactly 4 corners that touch three different colors.
Because Front/Right are both Blue and Back/Left are both Green, corners sharing these adjacent identical faces will not have three different colors.
2
Analyze the edge cubes (exactly 2 faces painted) to match the second category.
There are 12 edges, each containing (5-2) = 3 cubes with exactly two painted faces. The condition requires both faces to be the same color. This only happens on the Front-Right edge (Blue-Blue) and Back-Left edge (Green-Green). Thus, 2 edges × 3 cubes = 6 cubes.
Edges represent the intersection of two faces. Only adjacent faces painted with the same color produce these specific cubes.
3
Analyze the face center cubes (exactly 1 face painted) to match the third category.
Each of the 6 faces has a central grid of (5-2)² = 9 cubes that have exactly one face painted. Since exactly 2 faces are painted Blue (Front and Right), there are 2 × 9 = 18 such cubes.
This singles out the purely Blue surface area minus edges and corners.
4
Calculate the completely unpainted inner core cubes to match the fourth category.
The unpainted inner volume is a smaller cube of dimensions (5-2) × (5-2) × (5-2) = 3³ = 27 cubes.
Removing the outer layer (1 cube thick) from all 6 sides leaves the unpainted core.

Anahtar Kavram

Advanced visualization of 3D spatial properties, edge intersections, and non-standard coloring rules on a subdivided cube.
Soru 583Soru →

Biodiversity conservation strategies are broadly classified into on-site (in-situ) and off-site (ex-situ) approaches based on the location of conservation efforts. Which of the following is an example of an ex-situ conservation strategy?

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Cevap: Botanical Garden

Cevap

Botanical Garden is an ex-situ conservation strategy.
A Botanical Garden is an artificial, human-managed facility where living plant collections are cared for outside their natural geographic locations, which is the defining characteristic of ex-situ conservation.

Adım Adım Çözüm

1
Define and differentiate in-situ and ex-situ conservation.
In-situ conservation protects species in their natural ecosystems (on-site). Ex-situ conservation protects threatened organisms outside their natural surroundings in human-managed facilities (off-site).
Understanding the fundamental definition distinguishes off-site facilities from natural habitats.
2
Classify each option into in-situ or ex-situ categories.
Biosphere Reserves, National Parks, and Sacred Groves maintain species within natural wilderness ecosystems (in-situ). Botanical Gardens house species outside their wild habitats (ex-situ).
Evaluating each given method against the definitions yields the correct answer.

Anahtar Kavram

Distinction between In-situ and Ex-situ Biodiversity Conservation Methods
Tahmini Süre:45s
Soru 584Soru →

Eight executives—K, L, M, N, P, Q, R, and S—are seated in two parallel rows of four members each for a strategic meeting.

Members in Row 1 (P, Q, R, and S) are facing South.
Members in Row 2 (K, L, M, and N) are facing North.
Each executive in Row 1 sits exactly opposite to and faces one executive in Row 2.

The seating arrangement follows these conditions:
1. P sits second to the right of Q.
2. The executive facing Q sits to the immediate right of K.
3. M sits at one of the extreme ends of the row and does not face Q.
4. R sits to the immediate right of P.
5. N is an immediate neighbor of M.

Based on the above arrangement, which of the following statements is true?

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Cevap: S faces the executive who sits to the immediate left of L.

Cevap

The statement 'S faces the executive who sits to the immediate left of L' is true.
Based on the deductions, Row 1 (South) from left to right is R, P, S, Q. Row 2 (North) from left to right is M, N, K, L. The executive sitting to the immediate left of L (who faces North) is K. The executive facing K is S. Therefore, the statement accurately describes the arrangement.

Adım Adım Çözüm

1
Determine the layout of Row 1 (South-facing) using conditions 1 and 4.
Row 1 left-to-right (viewer's perspective) is R, P, S, Q.
Since Row 1 faces South, their 'right' is the viewer's left. P sits second to the right of Q means Q is at position 4 and P is at position 2. R sits to the immediate right of P places R at position 1. The remaining seat (position 3) belongs to S.
2
Locate K in Row 2 (North-facing) using condition 2.
K sits at position 3 (viewer's perspective).
Q is at position 4, so the executive facing Q is also at position 4. This person sits to the immediate right of K. Since Row 2 faces North, K must be at position 3 for position 4 to be its immediate right.
3
Place M and N in Row 2 using conditions 3 and 5.
M is at position 1 and N is at position 2.
M is at an extreme end (position 1 or 4) but does not face Q (who is at 4). Therefore, M is at position 1. N is M's immediate neighbor, placing N at position 2.
4
Complete Row 2 and evaluate the options.
Row 2 left-to-right is M, N, K, L. Evaluating the correct option: L is at 4, immediate left is K (at 3), and S (at 3) faces K.
L is the only remaining executive for position 4. Checking the valid spatial relationships against the options proves only one statement is factually accurate.

Anahtar Kavram

Linear Seating Arrangement in Dual Parallel Rows
Tahmini Süre:2m 0s
Soru 585Soru →

Which of the following represents the correct chronological sequence of seral stages during primary hydrarch ecological succession (hydrosere) in a newly formed freshwater lake, from the initial pioneer stage to the terrestrial community?

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Cevap

The correct chronological sequence of seral stages in primary hydrarch succession (hydrosere) is: Phytoplankton stage → Submerged plant stage → Floating plant stage → Reed-swamp stage → Scrub stage.
Primary hydrarch succession begins in a water body with microscopic phytoplankton as pioneers. Organic matter accumulation progressively shallow-up the basin, allowing rooted submerged plants to take root, followed by floating plants, amphibious reed-swamp plants, woody scrubs, and ultimately a terrestrial climax forest.

Adım Adım Çözüm

1
Identify the pioneer community in an aquatic basin
The Phytoplankton stage is the pioneer stage consisting of unattached microscopic algae that colonize open water.
Pioneer species must be able to survive in deep, open aquatic environments without rooted anchorage.
2
Trace the early rooted submerged and floating vegetation stages
Dead phytoplankton create organic mud, allowing the Submerged plant stage (e.g., Vallisneria) followed by the Floating plant stage (e.g., Nymphaea) to form.
As organic matter and silt reduce water depth, light penetration and substrate depth favor rooted species.
3
Trace the transition from aquatic to semi-terrestrial and land vegetation
Decreasing water levels lead to the amphibious Reed-swamp stage, followed by soil drying which enables the Woody Scrub stage.
Transpiration by amphibious plants rapidly dries out the wetland, allowing terrestrial shrubs and eventually climate-adapted trees to replace aquatic species.

Anahtar Kavram

Hydrarch Ecological Succession (Hydrosere)
Soru 586Soru →

Match the clean and renewable energy technologies in List-I with their corresponding fundamental operational principles or key structural features in List-II:

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Öğeler

Pyrolysis (Thermochemical Conversion)
Solar Power Tower (CSP)
Proton Exchange Membrane Fuel Cell (PEMFC)
Oscillating Water Column (OWC)

Eşleşmeler

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Cevap

Pyrolysis matches thermal decomposition of biomass without oxygen; Solar Power Tower matches heliostats focusing sunlight onto a central molten salt receiver; Proton Exchange Membrane Fuel Cell matches electrochemical reaction across a solid polymer membrane at low temperature; Oscillating Water Column matches trapped air driving a bidirectional Wells turbine.
Each clean energy technology is correctly paired with its defining operational principle: Pyrolysis corresponds to anaerobic thermal decomposition of organic biomass; Solar Power Tower corresponds to heliostat sun-tracking concentrating solar rays onto a central molten salt receiver; PEMFC corresponds to low-temperature electrochemical conversion across a solid polymer membrane; and Oscillating Water Column corresponds to ocean wave pneumatic pressure driving a Wells turbine.

Adım Adım Çözüm

1
Analyze Pyrolysis (Thermochemical Conversion)
Pyrolysis is defined by high-heat biomass breakdown under oxygen-deprived conditions to generate bio-char, bio-oil, and combustible gas mixtures.
Differentiates thermochemical pyrolysis from gasification (partial oxidation) or anaerobic digestion (biological breakdown).
2
Analyze Solar Power Tower (Concentrated Solar Power)
Solar towers utilize fields of dual-axis tracking mirrors called heliostats to concentrate sunlight onto an elevated central thermal receiver.
Distinguishes point-focus power towers from line-focus parabolic trough solar collector systems.
3
Analyze Proton Exchange Membrane Fuel Cell (PEMFC)
PEMFC technology utilizes a solid polymer membrane electrolyte operating under low-temperature conditions (60∘C−80∘C60^\circ\text{C}-80^\circ\text{C}) to convert hydrogen and oxygen into electricity.
Distinguishes polymer membrane cells from high-temperature Solid Oxide Fuel Cells (SOFC) or Molten Carbonate Fuel Cells (MCFC).
4
Analyze Oscillating Water Column (OWC)
OWC devices capture wave energy by compressing an enclosed air column to rotate a self-rectifying Wells turbine.
Distinguishes wave-action OWC devices from tidal barrages or ocean thermal energy conversion (OTEC) systems.

Anahtar Kavram

Working principles and technological classifications of renewable energy systems and clean technology devices
Soru 587Soru →

Arrange the following stages in the constitutional procedure for the creation of a State Legislative Council under Article 169 of the Constitution of India in the correct chronological sequence from first to last:

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Cevap

The correct chronological sequence for creating a State Legislative Council under Article 169 is: First, passing of a resolution by the State Legislative Assembly by a special majority; Second, introduction of a bill in Parliament; Third, passing of the bill by Parliament by a simple majority; and Fourth, assent to the bill by the President of India.
Under Article 169 of the Constitution of India, the creation of a State Legislative Council requires a sequential four-step process: the State Legislative Assembly must first pass a resolution by a special majority, followed by the introduction of an enacting bill in Parliament, its passage by Parliament via a simple majority, and finally receiving the assent of the President of India.

Adım Adım Çözüm

1
Identify the initiating constitutional step at the state level.
Under Article 169, the State Legislative Assembly must initiate the proposal by passing a resolution by a special majority (majority of total membership and at least two-thirds of members present and voting).
Parliament cannot enact legislation to create a State Legislative Council without a prior formal request from the concerned state assembly.
2
Determine the parliamentary legislation stage.
After receiving the state resolution, a bill is introduced in Parliament and passed by a simple majority.
Article 169 specifies that parliamentary law for this purpose is passed by simple majority and is not treated as a constitutional amendment under Article 368.
3
Identify the final enactment stage.
The bill receives the assent of the President of India to become an Act.
Presidential assent completes the legislative process required to officially establish the new legislative body.

Anahtar Kavram

Procedure for Creation of State Legislative Council under Article 169
Soru 588Soru →

Match the following State Constitutional Bodies and Authorities (List-I) with their corresponding Constitutional Articles (List-II).

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Öğeler

Advocate General for the State
State Finance Commission
State Public Service Commission
Duties of Chief Minister to furnish information to Governor

Eşleşmeler

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Cevap

The correct pairings are: Advocate General for the State matches with Article 165; State Finance Commission matches with Article 243-I; State Public Service Commission matches with Article 315; and Duties of Chief Minister to furnish information to Governor matches with Article 167.
Each item in List-I corresponds directly to its constitutional Article in List-II: the Advocate General for the State is appointed under Article 165, the State Finance Commission is constituted under Article 243-I, Public Service Commissions for the States are established under Article 315, and the constitutional duties of the Chief Minister relative to the Governor are detailed under Article 167.

Adım Adım Çözüm

1
Match Advocate General for the State with its constitutional provision.
Advocate General for the State pairs with Article 165.
Article 165 specifies the appointment, qualifications, and duties of the Advocate General for the State.
2
Match State Finance Commission with its constitutional provision.
State Finance Commission pairs with Article 243-I.
Article 243-I specifies the constitution and function of the State Finance Commission.
3
Match State Public Service Commission with its constitutional provision.
State Public Service Commission pairs with Article 315.
Article 315 establishes Public Service Commissions at the Union and State levels.
4
Match Duties of Chief Minister to furnish information to Governor with its constitutional provision.
Duties of Chief Minister pairs with Article 167.
Article 167 outlines the Chief Minister's administrative obligations toward the Governor.

Anahtar Kavram

Constitutional Provisions governing State Polity and Administrative Authorities
Soru 589Soru →

Phulkari, a traditional hand-embroidery craft known for its geometric floral patterns worked with untwisted silk thread on coarse cotton fabric, represents an iconic cultural heritage of which Indian state?

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Cevap: Punjab

Cevap

Punjab is the correct answer because Phulkari embroidery is a celebrated domestic folk craft deeply embedded in the cultural tradition and festivities of Punjab.
Punjab is correct because Phulkari is the ancestral folk embroidery art of Punjab where colorful silk threads are meticulously stitched onto khaddar fabric in geometric and floral motifs.

Adım Adım Çözüm

1
Analyze the art form's structural details and technique mentioned in the stem
The stem describes 'Phulkari', an embroidery craft utilizing silk thread to make geometric floral patterns on coarse cotton cloth (khaddar).
Identifying core cultural characteristics helps map the craft to its state of origin.
2
Match the heritage craft with its official geographic and state origin
Phulkari is an authentic folk tradition of Punjab, traditionally practiced by women during weddings and auspicious life ceremonies.
Phulkari holds a Geographical Indication (GI) status associated primarily with the state of Punjab.

Anahtar Kavram

Traditional Textile and Folk Craft Heritage of Indian States
Tahmini Süre:45s
Soru 590Soru →

Kalinga temple architecture represents a prominent regional school of temple art and heritage in eastern India. Arrange the following famous heritage temples of Odisha in the correct chronological order of their construction, starting from the earliest built to the latest.

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Cevap

The correct chronological sequence from earliest to latest is Parasurameswara Temple (7th century CE), Mukteswara Temple (10th century CE), Lingaraja Temple (11th century CE), and Sun Temple at Konark (13th century CE).
The correct sequence follows the historical progression of Kalinga architectural styles over six centuries: Parasurameswara Temple (7th century CE, early phase) → Mukteswara Temple (10th century CE, transitional phase) → Lingaraja Temple (11th century CE, mature phase) → Sun Temple at Konark (13th century CE, monumental culmination).

Adım Adım Çözüm

1
Determine the era of Parasurameswara Temple
7th century CE (Early Kalinga phase).
Built under the Shailodbhava dynasty, it is one of the oldest surviving stone temples in the region.
2
Determine the era of Mukteswara Temple
10th century CE (Transitional Kalinga phase).
Patronized by the Somavamshi dynasty, it introduced intricate arched gateways (toranas).
3
Determine the era of Lingaraja Temple
11th century CE (Mature Kalinga phase).
Represents the grandest structural peak of Somavamshi temple construction in Bhubaneswar.
4
Determine the era of Sun Temple at Konark
13th century CE (Late/Culmination Kalinga phase).
Commissioned by Eastern Ganga King Narasimhadeva I as a monumental chariot temple.

Anahtar Kavram

Chronological evolution of Kalinga temple architecture and state heritage
Soru 591Soru →

Photochemical smog is a major type of air pollution observed in urban areas with high motor vehicle traffic. Which of the following statements regarding the formation, precursors, and components of photochemical smog are correct?

Geçerli olan tümünü seçin

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Cevap: Nitrogen oxides (NOxNO_x) and volatile organic compounds (VOCsVOCs) act as primary precursor pollutants in its formation.; Bright sunlight and high atmospheric temperatures accelerate the chemical reactions that generate photochemical smog.; Ground-level ozone (O3O_3) and peroxyacetyl nitrate (PANPAN) are major secondary pollutants formed during the photochemical process.

Cevap

Photochemical smog formation requires nitrogen oxides (NOxNO_x) and volatile organic compounds (VOCsVOCs) as primary precursors, is accelerated by bright sunlight and warm temperatures, and produces secondary pollutants such as ground-level ozone (O3O_3) and peroxyacetyl nitrate (PANPAN).
Photochemical smog is an oxidizing smog formed by the action of ultraviolet light on atmospheres containing hydrocarbons and nitrogen oxides (NOxNO_x). The primary reaction components are NOxNO_x and volatile organic compounds (VOCsVOCs). Solar energy fuels the reaction pathways, leading to the formation of toxic secondary pollutants including tropospheric ozone (O3O_3), peroxyacetyl nitrate (PANPAN), and aldehydes.

Adım Adım Çözüm

1
Identify the primary precursor gases of photochemical smog.
Nitrogen oxides (NOxNO_x) and volatile organic compounds (VOCsVOCs) are identified as the necessary primary precursors.
Primary pollutants emitted from vehicles and industrial sources undergo chemical transformations under atmospheric conditions.
2
Analyze the environmental conditions required for the photochemical reactions.
Bright sunlight and high ambient temperatures increase reaction rates.
Ultraviolet radiation breaks down nitrogen dioxide (NO2NO_2) into nitric oxide (NONO) and atomic oxygen (OO), starting the chain reaction.
3
Distinguish between the secondary pollutants produced and other forms of atmospheric smog.
Ground-level ozone (O3O_3) and PANPAN are recognized as secondary products, while sulfur dioxide (SO2SO_2) driven smog in cold weather represents classical industrial smog.
Classical smog relies on sulfur pollutants and damp cold, whereas photochemical smog requires solar energy, NOxNO_x, and hydrocarbons.

Anahtar Kavram

Precursors, Environmental Factors, and Secondary Pollutants of Photochemical Smog
Soru 592Soru →

Match the following administrative actions taken by a District Election Officer (DEO) during election preparation with their corresponding elements in the communication process.

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Öğeler

Translating technical Election Commission guidelines into a simplified local dialect manual.
Using a secure official messaging network to distribute the instructional manual.
Presiding officers interpreting the simplified instructions to set up the Electronic Voting Machines.
Presiding officers submitting a digital confirmation receipt upon receiving the instructions.

Eşleşmeler

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Cevap

Translating guidelines corresponds to Encoding; Using the messaging network corresponds to Communication Channel; Interpreting instructions corresponds to Decoding; Submitting a confirmation receipt corresponds to Feedback Loop.
Effective communication follows a systematic sequence: a sender encodes a message, transmits it through a selected channel, and the receiver decodes it, followed by providing feedback. The given scenario perfectly maps these distinct, fundamental stages to practical administrative actions during an election deployment.

Adım Adım Çözüm

1
Analyze the action of translating technical guidelines into a manual.
Identified as Encoding.
The sender is converting thoughts and technical data into a format that can be easily understood by the target audience.
2
Analyze the action of using a secure messaging network.
Identified as Communication Channel.
This is the digital medium chosen to deliver the encoded message.
3
Analyze the action of interpreting the simplified instructions.
Identified as Decoding.
The receiver is processing and understanding the encoded message to extract its meaning.
4
Analyze the action of submitting a digital confirmation receipt.
Identified as Feedback Loop.
This completes the communication cycle by informing the sender that the message was received.

Anahtar Kavram

Process and Elements of Communication
Soru 593Soru →

In the mineral economy of Odisha, which district contains the Sukinda valley, which accounts for over 90% of India's total chromite ore reserves?

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Cevap: Jajpur district

Cevap

Jajpur district is the correct answer as it houses the Sukinda valley chromite belt.
Jajpur district contains the famous Sukinda valley ultramafic complex, which holds more than 90% of India's total reserves of chromite ore, making it the hub of India's ferro-chrome and chromite mining industry.

Adım Adım Çözüm

1
Identify the primary mineral in question and its main production center in India.
Chromite ore in India is predominantly mined in Odisha, specifically within the Sukinda valley.
Over 90% to 95% of India's chromite reserves are concentrated in this single geological formation.
2
Map the Sukinda valley to its parent administrative district in Odisha.
Sukinda valley is located in Jajpur district.
Administrative district mapping is essential for state-level general knowledge assessments.

Anahtar Kavram

State Natural Resources and Mineral Belts of Odisha
Soru 594Soru →

Arrange the following major mountain peaks of the Western Ghats in sequential order from North to South based on their latitudinal position:

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Cevap

The correct sequential order from North to South is Kalsubai, followed by Kudremukh, Anamudi, and Agasthyamalai.
Tracing the Western Ghats mountain chain from North to South, Kalsubai (Maharashtra, ~19.6° N) forms the northernmost point, followed by Kudremukh (Karnataka, ~13.2° N), Anamudi (Kerala, ~10.17° N), and Agasthyamalai (Kerala/Tamil Nadu, ~8.62° N) at the southern end.

Adım Adım Çözüm

1
Identify the geographical region and latitude of Kalsubai Peak.
Kalsubai lies in the Sahyadri Range of Maharashtra at approximately 19°36' N latitude.
This establishes the northernmost peak in the given set.
2
Determine the latitude of Kudremukh Peak.
Kudremukh is situated in the Chikkamagaluru district of Karnataka at approximately 13°13' N latitude.
This places Kudremukh south of the Sahyadris of Maharashtra but north of the Nilgiri and Anaimalai complexes.
3
Determine the latitude of Anamudi Peak.
Anamudi is located in the Anaimalai Hills of Kerala at approximately 10°10' N latitude.
Positioned south of the Palghat Gap, it lies south of Kudremukh.
4
Determine the latitude of Agasthyamalai Peak.
Agasthyamalai is located in the Ashambu Hills on the Kerala-Tamil Nadu border at approximately 8°37' N latitude.
This confirms Agasthyamalai as the southernmost peak among the given options.

Anahtar Kavram

Latitudinal spatial distribution of Western Ghats relief features across state boundaries.
Soru 595Soru →

Let N=5391−3182N = 53^{91} - 31^{82}. When the value of NN is divided by 1111, which of the following represents the correct remainder?

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Cevap: 5

Cevap

The correct remainder is 5.
By finding the remainders of the bases (53≡−2(mod11)53 \equiv -2 \pmod{11} and 31≡−2(mod11)31 \equiv -2 \pmod{11}) and reducing the exponents using Fermat's Little Theorem modulo 10 (91≡1(mod10)91 \equiv 1 \pmod{10} and 82≡2(mod10)82 \equiv 2 \pmod{10}), the expression simplifies to (−2)1−(−2)2=−6(-2)^1 - (-2)^2 = -6. Converting this negative remainder to a true positive remainder yields −6+11=5-6 + 11 = 5.

Adım Adım Çözüm

1
Determine the remainders of the bases 53 and 31 when divided by 11.
53≡9≡−2(mod11)53 \equiv 9 \equiv -2 \pmod{11} and 31≡9≡−2(mod11)31 \equiv 9 \equiv -2 \pmod{11}.
Converting to negative remainders significantly simplifies the calculations for large powers.
2
Apply Fermat's Little Theorem to reduce the exponents.
Since 11 is a prime number, the cyclicity is 11−1=1011 - 1 = 10. Reducing the exponents modulo 10 gives 91≡1(mod10)91 \equiv 1 \pmod{10} and 82≡2(mod10)82 \equiv 2 \pmod{10}.
Fermat's theorem states that ap−1≡1(modp)a^{p-1} \equiv 1 \pmod{p}, meaning exponents can be reduced by finding their remainder when divided by p−1p-1.
3
Evaluate the reduced expression under modulo 11.
(−2)1−(−2)2=−2−4=−6(-2)^1 - (-2)^2 = -2 - 4 = -6.
Substituting the simplified bases and exponents provides the intermediate remainder.
4
Convert the negative intermediate remainder into a valid positive remainder.
−6+11=5-6 + 11 = 5.
A final remainder must always be a non-negative integer strictly less than the divisor.

Anahtar Kavram

Applying Fermat's Little Theorem and correctly handling negative remainders in modular arithmetic.
Soru 596Soru →

In a basic encryption algorithm, a numerical value VV is generated using the formula V=4791−193V = 47^{91} - 19^{3}. The final security key is determined by the positive remainder when VV is divided by 1212. What is the value of the final security key?

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Cevap: 4

Cevap

4
The correct answer is found by applying modular arithmetic rules to reduce each part of the expression modulo 12. First, 47≡−1(mod12)47 \equiv -1 \pmod{12}, so 4791≡(−1)91=−147^{91} \equiv (-1)^{91} = -1. Second, 19≡7(mod12)19 \equiv 7 \pmod{12}, and since 72=49≡1(mod12)7^2 = 49 \equiv 1 \pmod{12}, we get 73≡7×1=77^3 \equiv 7 \times 1 = 7. Subtracting these yields −1−7=−8-1 - 7 = -8. To find the equivalent positive remainder, we add the divisor: −8+12=4-8 + 12 = 4.

Adım Adım Çözüm

1
Find the remainder of 479147^{91} modulo 12.
Since 47=12×4−147 = 12 \times 4 - 1, it is easier to use 47≡−1(mod12)47 \equiv -1 \pmod{12}. Therefore, 4791≡(−1)91=−1(mod12)47^{91} \equiv (-1)^{91} = -1 \pmod{12}.
Using negative remainders for numbers close to a multiple of the divisor simplifies large exponent calculations.
2
Find the remainder of 19319^{3} modulo 12.
Since 19=12×1+719 = 12 \times 1 + 7, we have 19≡7(mod12)19 \equiv 7 \pmod{12}. Thus, 193≡73(mod12)19^3 \equiv 7^3 \pmod{12}. We know 72=49≡1(mod12)7^2 = 49 \equiv 1 \pmod{12}. Multiplying by 7 gives 73≡1×7=7(mod12)7^3 \equiv 1 \times 7 = 7 \pmod{12}.
Reducing the base before exponentiation makes the calculation manageable without needing to calculate 19319^3 completely.
3
Subtract the individual remainders.
(−1)−7=−8(mod12)(-1) - 7 = -8 \pmod{12}.
Applying modular arithmetic properties to combine the terms in the original expression.
4
Convert the negative remainder to a positive remainder.
−8+12=4-8 + 12 = 4.
The standard remainder definition requires a non-negative integer strictly less than the divisor.

Anahtar Kavram

Modular arithmetic, negative remainders, and power reduction rules.
Soru 597Soru →

Consider the exponential equation:

4x−3⋅2x+2+32=04^x - 3 \cdot 2^{x+2} + 32 = 0

Determine the sum of all real values of xx that satisfy this equation.

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Cevap: 5

Cevap

5
By applying the laws of indices, the original expression transforms into a quadratic equation in terms of 2x2^x. Solving y2−12y+32=0y^2 - 12y + 32 = 0 yields y=4y=4 and y=8y=8, which correspond precisely to x=2x=2 and x=3x=3. Their sum is 5.

Adım Adım Çözüm

1
Express all terms with a common base of 2.
4x4^x becomes (2x)2(2^x)^2 and 2x+22^{x+2} becomes 4⋅2x4 \cdot 2^x.
Creating a common base allows the equation to be transformed into a standard polynomial form.
2
Rewrite the equation using the new terms.
(2x)2−12(2x)+32=0(2^x)^2 - 12(2^x) + 32 = 0
Simplifying the coefficients makes it easier to spot the quadratic structure.
3
Perform a substitution to solve the quadratic equation.
Letting y=2xy = 2^x gives y2−12y+32=0y^2 - 12y + 32 = 0. Factoring yields (y−4)(y−8)=0(y - 4)(y - 8) = 0, so y=4y = 4 or y=8y = 8.
Substitution converts a complex exponential equation into a simple quadratic one.
4
Solve for the original variable xx.
2x=4  ⟹  x=22^x = 4 \implies x = 2, and 2x=8  ⟹  x=32^x = 8 \implies x = 3.
The question asks for the values of xx, not the intermediate substitution variable yy.
5
Calculate the sum of all valid xx values.
2+3=52 + 3 = 5
This addresses the specific final requirement of the question stem.

Anahtar Kavram

Solving exponential equations reducible to quadratics using index laws.
Tahmini Süre:1m 30s
Soru 598Soru →

Consider the provided statements to be absolutely true, ignoring commonly known facts. Based solely on these statements, which of the deduced conclusions logically hold?

Statements:
• All Tier-9 security clearances are restricted mandates.
• No restricted mandate is a public disclosure.
• Some public disclosures are controversial leaks.

Conclusions:
[I] No Tier-9 security clearance is a public disclosure.
[II] Some Tier-9 security clearances are restricted mandates.
[III] Some controversial leaks are not restricted mandates.

Which of the following is correct?

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Cevap: Conclusion I and conclusion III logically hold

Cevap

Conclusion I and conclusion III logically hold
Conclusion I is valid because the set of Tier-9 clearances is a subset of restricted mandates, which is entirely disjoint from public disclosures. Conclusion III is valid because there is a proven overlap between controversial leaks and public disclosures; since public disclosures are strictly disjoint from restricted mandates, that specific overlapping segment cannot be restricted. Conclusion II is properly excluded because deriving 'some' directly from 'all' commits the existential fallacy.

Adım Adım Çözüm

1
Analyze the relationship between Tier-9 security clearances and public disclosures to evaluate Conclusion I.
Since all Tier-9 clearances are completely contained within restricted mandates, and restricted mandates share no overlap with public disclosures, Tier-9 clearances cannot overlap with public disclosures.
Validates Conclusion I: No Tier-9 security clearance is a public disclosure.
2
Evaluate Conclusion II against the rules of formal categorical propositions regarding existential import.
The premise states 'All Tier-9 security clearances are restricted mandates'. Under modern formal logic, universal premises (All/No) do not guarantee that the subject exists. Deducing a particular conclusion ('Some') from a universal premise without proof of existence commits the existential fallacy.
Invalidates Conclusion II as it assumes existential import.
3
Analyze the relationship between controversial leaks and restricted mandates to evaluate Conclusion III.
We know some controversial leaks intersect with public disclosures. Because no public disclosures are allowed to be restricted mandates, that specific intersecting portion of controversial leaks can never be restricted mandates.
Validates Conclusion III: Some controversial leaks are not restricted mandates.

Anahtar Kavram

Syllogistic validity, categorical intersections, and the existential fallacy.
Soru 599Soru →

A biomedical research facility tags its genetic samples using a specialized alphabetical encryption logic to maintain anonymity. In this system, the word PLASMA is coded as LPAIOA and the word SERUM is coded as IWJGO. Based on this specific coding logic, how will the word VIRUS be coded?

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Cevap: FSJGI

Cevap

The correct sequence is FSJGI.
The established coding rule dictates that each letter is first replaced by its reverse alphabetical counterpart (e.g., A becomes Z, B becomes Y), and then shifted forward by one letter (+1). Applying this to VIRUS: V becomes E (+1 = F), I becomes R (+1 = S), R becomes I (+1 = J), U becomes F (+1 = G), and S becomes H (+1 = I), yielding FSJGI.

Adım Adım Çözüm

1
Analyze the transformation applied to the word PLASMA to produce LPAIOA.
P(16) reverses to K(11), K+1 = L. L(12) reverses to O(15), O+1 = P. A(1) reverses to Z(26), Z+1 = A. S(19) reverses to H(8), H+1 = I. M(13) reverses to N(14), N+1 = O. A(1) reverses to Z(26), Z+1 = A.
To decode the underlying multi-step logic by testing position values and reverse alphabet mappings.
2
Verify the identified rule (Reverse Letter + 1) using the second example, SERUM.
S reverses to H, H+1 = I. E reverses to V, V+1 = W. R reverses to I, I+1 = J. U reverses to F, F+1 = G. M reverses to N, N+1 = O. The result IWJGO matches the given code.
To confirm the encryption rule is consistent and completely understood before applying it to the target word.
3
Apply the verified two-step rule to the target word VIRUS.
V reverses to E, E+1 = F. I reverses to R, R+1 = S. R reverses to I, I+1 = J. U reverses to F, F+1 = G. S reverses to H, H+1 = I.
To determine the final encrypted tag for the target sample.

Anahtar Kavram

Multi-step letter coding involving reverse alphabetical indexing and positional shifts.
Soru 600Soru →

A Principal Secretary is reviewing a severely delayed infrastructure project with an Executive Engineer. Wanting to maintain a constructive administrative atmosphere, the Secretary deliberately uses open palm gestures, maintains a relaxed seated posture, and smiles occasionally. However, the Secretary dictates the revised project deadlines using a rapid speaking rate, a clipped and sharp tone, and an elevated volume. The Engineer leaves the meeting feeling highly anxious, perceiving the interaction as a severe reprimand rather than a constructive review.

Which of the following best analyzes the communication dynamics in this scenario?

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Cevap: The paralinguistic elements of the Secretary's message dominated the interaction, overriding the accommodating non-verbal body language.

Cevap

The paralinguistic elements of the Secretary's message dominated the interaction, overriding the accommodating non-verbal body language.
In the communication process, when verbal or kinesic messages contradict paralinguistic cues, the receiver tends to rely heavily on how things are said (paralinguistics) rather than what is said or the accompanying posture. Despite the relaxed body language (kinesics), the sharp tone, high volume, and rapid pace conveyed a dominant message of severity that the Engineer accurately decoded as a strict reprimand.

Adım Adım Çözüm

1
Analyze the Secretary's physical behavior (open palms, relaxed posture, smiling).
These are identified as kinesic cues that intentionally project a relaxed, open, and constructive environment.
Categorizing the physical movements is necessary to understand one layer of the non-verbal communication.
2
Analyze the Secretary's vocal delivery (rapid rate, clipped tone, elevated volume).
These are identified as paralinguistic cues that project urgency, strictness, and potential severity.
Categorizing the vocal characteristics reveals a second, contradictory layer of non-verbal communication.
3
Evaluate the overall communication impact based on the receiver's decoding.
The Engineer's anxious reaction demonstrates that the vocal delivery (paralinguistics) overpowered the physical gestures (kinesics) when the mixed signals were processed.
Understanding how mixed messages are received is a core element of the communication process.

Anahtar Kavram

Paralinguistics vs Kinesics in the Communication Process
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