Questions and Answers
What is the time taken by the larger pipe to fill the tank?
25 hours
What is the time taken by the smaller pipe to fill the tank?
15 hours
What is the volume of water in the pond?
462 m³
What is the diameter of the pipe used to fill the pond?
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What is the time required to fill the pond?
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What is the cost of the canvas to be purchased?
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The radius of the pipe is ___ m.
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What is the area of canvas to be purchased?
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What is the median number of students that obtained marks in the given range?
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What is the mode of the marks obtained by students?
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Find the coordinates of the central midfielder.
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What is the distance the bird flew after hitting the tree?
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What is the speed of the bird in m/sec?
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What is the expression for 'xy squared'?
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How many zeros are there and what is the first zero?
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What is the condition for a, b, and c?
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How many distinct real roots does the equation have?
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What is the solution for the equation given the value?
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What is the ratio of a:b?
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How many solutions does the given equations have?
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What expression represents the relationship between a, b, and c?
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What is the angle measure in degrees?
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What is the length of the given measure?
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What is the expression to evaluate in the roots?
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What is the trigonometric function at angle A?
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What is the value of the angle?
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What is the distance between two specified points?
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What is the measure in meters?
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What is the area expression given?
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What is the sum of the numbers given?
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What is the next number in the sequence?
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What is the calculated angle measure?
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Are both the assertion (A) and reason (R) true?
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What is the status of assertion (A) and reason (R)?
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What is the conclusion regarding √2?
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What is the ratio in parallelogram ABCD?
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What is the perimeter of triangle PCD?
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What is the angle sum results in?
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What are the numbers when digits differ by 2?
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What does x equal when the equation is formed by tangential points?
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What is the mean of the lengths of leaves?
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What is the speed of the stream calculated?
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Study Notes
Class X Mathematics Standard Marking Scheme (Session 2023-24)
- Total duration: 3 hours
- Maximum marks: 80
Section A: 20 Questions (1 mark each)
- Consists of straightforward questions covering core mathematical concepts.
- Key topics include algebra, geometry, trigonometry, and number theory.
- Examples of questions:
- Given a polynomial at a specific point.
- Equations leading to distinct real roots.
- Ratio and proportion applications.
- Basic trigonometric identities and angle measures.
Section B: 5 Questions (2 marks each)
- Focuses on more detailed problems requiring short explanations or proofs.
- Key concepts include:
- Proving irrationality (example: √2).
- Parallelogram properties and geometric similarity.
- Circle tangents and perimeter proofs.
- Solving equations involving trigonometric identities.
Section C: 6 Questions (3 marks each)
- Elaborate problems that may require step-by-step calculations or derivations.
- Topics include:
- Finding the highest common factor (HCF) and applying it in real-life scenarios.
- Quadratic equations and their roots, including sums and products of roots.
- Word problems translating conditions into mathematical expressions.
- Area calculations involving geometric figures such as triangles and circles.
Section D: 4 Questions (5 marks each)
- Involves comprehensive problems demanding thorough reasoning and multiple steps.
- Examples include:
- Speed of streams and boats using relative motion concepts.
- Techniques for solving equations in practical contexts, such as filling tanks and flow rates.
- Must demonstrate understanding of problem-solving methods and formulating correct equations.
General Preparation Tips
- Focus on understanding concepts rather than rote memorization.
- Practice solving problems using various strategies.
- Review previous years’ question papers for better familiarity with patterns.
- Work on time management to ensure completion of each section within the allowed time.### Geometry and Proof
- A statement is provided with proof involved in establishing relationships between segments in triangles.
- Method employs properties such as the Basic Proportionality Theorem (BPT) and the Midpoint Theorem.
- Key relationships between segments (CF, FD, GE) deduced from triangle properties and angle relationships.
Volume and Pipe Calculations
- Pond dimensions: Length = 50 m, Width = 44 m.
- Water level increase: h = 21 cm → Volume = 50 m x 44 m x (21/100) m = 462 m³.
- Diameter of water pipe: 14 cm, radius = 7 cm → Cross-sectional area = π(7/100)² m² = 154/10000 m².
- Water flow rate: 15 km/h → Volume flowing in 1 hour = 154 m² x 15000 m = 2310000 m³.
- Time to fill pond = 462 m³ / (154 m² x 15000) = 2 hours.
- Speed required for 1-hour rise = 30 km/h.
Geometry of Tent
- Cylindrical tent parameters: Radius = 14 m, Height = 13.5 m (3 m cylinder, 10.5 m cone).
- Slant height of cone: l = √(10.5² + 14²) = 17.5 m.
- Curved surface area of cylinder = 2πrh = 264 m².
- Curved surface area of cone = πrl = 770 m², Total = 1034 m².
- Canvas area including wastage = 1060 m²; Total cost for canvas = ₹5,30,000.
Statistics and Frequency Distribution
- Cumulative frequency established with classes for marks ranging from 20 to 90.
- Median derived using formula with length of interval and frequencies.
- P and Q variables calculated to maintain total samples.
- Mode calculated from the frequency distribution.
Progressive Sequences
- Arithmetic sequence calculations for both throws during camp and weekly progression.
- Total throws can be determined using sum formula Sn = n/2[2a + (n-1)d] with respective a (first term) and d (common difference).
Coordinate Geometry
- Midpoint theorem applied to locate coordinates based on given points and ensure B is the midpoint.
- Distance measures between points computed using the distance formula to establish collinearity or equidistance of points.
Trigonometry Applications
- Angles calculated using tangent values for various scenarios involving distances.
- Distance traveled by the bird computed from the derived relationships using trigonometric functions.
Speed Computation
- Speed of the bird calculated based on distance traveled and time taken, with conversions between units for clarity, highlighting effective speed in multiple formats (m/sec and m/min).
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Description
Test your knowledge on calculating the time taken by pipes to fill a tank and determining the volume of water in a pond. This quiz covers various concepts related to flow rates, pipe diameters, and associated costs for materials like canvas. Perfect for students studying basic fluid mechanics and geometry.