Pipes and Volume Calculations Quiz

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?

14 cm Signup and view all the answers

What is the time required to fill the pond?

2 hours Signup and view all the answers

What is the cost of the canvas to be purchased?

₹ 5,30,000 Signup and view all the answers

The radius of the pipe is ___ m.

0.07 Signup and view all the answers

What is the area of canvas to be purchased?

1060 m² Signup and view all the answers

What is the median number of students that obtained marks in the given range?

50 Signup and view all the answers

What is the mode of the marks obtained by students?

46.67 Signup and view all the answers

Find the coordinates of the central midfielder.

(3, 5) Signup and view all the answers

What is the distance the bird flew after hitting the tree?

80(√3 - 1) m Signup and view all the answers

What is the speed of the bird in m/sec?

20(√3 + 1) Signup and view all the answers

What is the expression for 'xy squared'?

xy^2 Signup and view all the answers

How many zeros are there and what is the first zero?

1 zero and the zero is 3 Signup and view all the answers

What is the condition for a, b, and c?

a = b ≠ c Signup and view all the answers

How many distinct real roots does the equation have?

2 distinct real roots Signup and view all the answers

What is the solution for the equation given the value?

7 Signup and view all the answers

What is the ratio of a:b?

1:2 Signup and view all the answers

How many solutions does the given equations have?

infinitely many Signup and view all the answers

What expression represents the relationship between a, b, and c?

ac = b + c Signup and view all the answers

What is the angle measure in degrees?

100° Signup and view all the answers

What is the length of the given measure?

11 cm Signup and view all the answers

What is the expression to evaluate in the roots?

√(b^2 - a^2) Signup and view all the answers

What is the trigonometric function at angle A?

cos A Signup and view all the answers

What is the value of the angle?

60° Signup and view all the answers

What is the distance between two specified points?

2 units Signup and view all the answers

What is the measure in meters?

10 m Signup and view all the answers

What is the area expression given?

4 - π Signup and view all the answers

What is the sum of the numbers given?

22 Signup and view all the answers

What is the next number in the sequence?

46 Signup and view all the answers

What is the calculated angle measure?

150 Signup and view all the answers

Are both the assertion (A) and reason (R) true?

Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) Signup and view all the answers

What is the status of assertion (A) and reason (R)?

Assertion (A) is true but reason (R) is false. Signup and view all the answers

What is the conclusion regarding √2?

√2 is irrational Signup and view all the answers

What is the ratio in parallelogram ABCD?

AP:BP = 2:3 Signup and view all the answers

What is the perimeter of triangle PCD?

20 cm Signup and view all the answers

What is the angle sum results in?

900 or 450 Signup and view all the answers

What are the numbers when digits differ by 2?

42 and 24 Signup and view all the answers

What does x equal when the equation is formed by tangential points?

x = 3 Signup and view all the answers

What is the mean of the lengths of leaves?

146.975 Signup and view all the answers

What is the speed of the stream calculated?

6 km/h Signup and view all the answers

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.