Class 10th Maths NCERT Solutions

Class 10th Maths NCERT Solutions

Class 10th Maths Exercise 4.1 Solutions Quadratic Equations

Class 10 Maths Exercise 4.1 Solutions

Question 1:

Check whether the following are quadratic equations:

(i) (x + 1)² = 2(x – 3)

(ii) x² – 2x = (-2)(3 – x)

(iii) (x – 2)(x + 1) = (x – 1)(x + 3)

(iv) (x – 3)(2x + 1) = x(x + 5)

(v) (2x – 1)(x – 3) = (x + 5)(x – 1)

(vi) x² + 3x + 1 = (x – 2)²

(vii) (x + 2)³ = 2x(x² – 1)

(viii) x³ – 4x² – x + 1 = (x – 2)³

Question 1: Check whether the following are quadratic equations: (i) (x + 1)² = 2(x – 3) (ii) x² – 2x = (-2)(3 – x) (iii) (x – 2)(x + 1) = (x – 1)(x + 3)
Class 10 Maths Exercise 4.1 Solutions Question 1: Check whether the following are quadratic equations: (i) (x + 1)² = 2(x – 3) (ii) x² – 2x = (-2)(3 – x) (iii) (x – 2)(x + 1) = (x – 1)(x + 3) (iv) (x – 3)(2x + 1) = x(x + 5) (v) (2x – 1)(x – 3) = (x + 5)(x – 1) (vi) x² + 3x + 1 = (x – 2)²
Class 10 Maths Exercise 4.1 Solutions Question 1: Check whether the following are quadratic equations: (i) (x + 1)² = 2(x – 3) (ii) x² – 2x = (-2)(3 – x) (iii) (x – 2)(x + 1) = (x – 1)(x + 3) (iv) (x – 3)(2x + 1) = x(x + 5) (v) (2x – 1)(x – 3) = (x + 5)(x – 1) (vi) x² + 3x + 1 = (x – 2)²

Question 2:

Represent the following situations in the form of quadratic equations:
(i) The area of a rectangular plot is 528 m². The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.

(ii) The product of two consecutive positive integers is 306. We need to find the integers.

(iii) Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.

(iv) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.

Question 2: Represent the following situations in the form of quadratic equations: (i) The area of a rectangular plot is 528 m². The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot. (ii) The product of two consecutive positive integers is 306. We need to find the integers. (iii) Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age. (iv) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.
Question 2: Represent the following situations in the form of quadratic equations: (i) The area of a rectangular plot is 528 m². The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot. (ii) The product of two consecutive positive integers is 306. We need to find the integers. (iii) Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age. (iv) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.
Question 2: Represent the following situations in the form of quadratic equations: (i) The area of a rectangular plot is 528 m². The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot. (ii) The product of two consecutive positive integers is 306. We need to find the integers. (iii) Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age. (iv) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.

Class 10th Maths Exercise 4.2 Solutions Quadratic Equations

Question 1:

Find the roots of the following quadratic equations by factorisation:
(i). x² – 3x – 10 = 0

(ii). 2x² + x – 6 = 0

(iii). √2x² + 7x + 5√2 = 0

(iv). 2x² – x + 1/8 = 0

(v). 100x² – 20x + 1 = 0

Question 2:

Solve the problems given in Example 1.

x² – 45x + 324 = 0 and x² – 55x + 750 = 0.

Question 3:

Find two numbers whose sum is 27 and product is 182.

Question 4:

Find two consecutive positive integers, sum of whose squares is 365.

Why Choose NCERT Solutions from ShikshaClasses.com?

ShikshaClasses.com stands out among educational websites by offering a learner-friendly experience tailored for Class 10 students. Here’s why thousands of students trust it:

✅ Comprehensive Chapter-wise Solutions

Each solution is aligned with the latest CBSE curriculum and presented in a step-by-step manner. From Real Numbers to Probability, every chapter is covered with clear explanations.

✅ Easy to Understand Language

Mathematical jargon can often be confusing. ShikshaClasses uses simple language that makes even complex problems easier to understand for every student, regardless of their learning level.

✅ Concept Clarity

The solutions are designed not just to give the answer, but to explain the why and how. This builds a strong conceptual foundation and prepares students for competitive exams like NTSE, Olympiads, and even JEE Foundation.

✅ Time-Saving and Exam-Ready

No more flipping through multiple books! These solutions are concise, focused, and help you revise faster, especially during exam season.

✅ Accessible Anytime, Anywhere

The website is optimized for mobile and desktop, allowing students to study on the go. Whether you’re at home, on the bus, or waiting for tuition, your solutions are just a click away.

Key Benefits of Using ShikshaClasses for Class 10 Maths

  • 📚 Free Access to Quality Content
    No hidden fees. Students can access detailed solutions without any cost.

  • 🧠 Improved Problem-Solving Skills
    Each solution includes alternate methods and tips, enhancing analytical thinking.

  • 📈 Better Marks in Exams
    With focused revision and accurate solutions, students can expect better performance in board exams.

  • 🔁 Revision Made Easy
    Well-structured summaries and solutions make last-minute preparation hassle-free.

Frequently Asked Questions (FAQs)

❓ Are these solutions based on the latest CBSE syllabus?

Yes. All NCERT Class 10 Maths solutions on ShikshaClasses are updated regularly to match the latest CBSE guidelines.

❓ Can I use these solutions to prepare for board exams?

Absolutely. These solutions are board-exam oriented and help you understand how to present answers effectively.

❓ Are the solutions suitable for self-study?

Yes. They are designed to help students study independently without needing external help.

❓ Is there a download option available?

Yes. Students can easily download PDFs of NCERT Maths solutions for offline use.

❓ What if I have doubts while studying?

ShikshaClasses also provides guidance through additional learning resources and may offer interactive doubt-clearing features or expert support.

Conclusion

Class 10 Maths is a milestone in every student’s academic journey. With the right guidance and reliable study material, it becomes a lot easier to master. NCERT Solutions from ShikshaClasses.com empower students with clarity, confidence, and convenience. If you’re serious about scoring well and truly understanding mathematics, this is the perfect place to start

Class 10th Maths Exercise 1.1 Solutions

Scroll to Top
×