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Class 10 Maths Test Paper | Chapter: Polynomials (बहुपद)
Polynomials – Practice Worksheet
Section A: Multiple Choice Questions (1 Mark Each)
Q1. A graph of a polynomial intersects the x-axis at 3 points. How many zeroes does it have?
एक बहुपद का ग्राफ x-अक्ष को 3 बिंदुओं पर काटता है। इसके कितने शून्यक होंगे?
(a) 1 (b) 2 (c) 3 (d) 0
Q2. Find the zeroes of the quadratic polynomial \(x^2 - 2x - 8\).
द्विघात बहुपद \(x^2 - 2x - 8\) के शून्यक ज्ञात कीजिए।
(a) 4, −2 (b) −4, 2 (c) 4, 2 (d) −4, −2
Q3. If \(\alpha\) and \(\beta\) are zeroes of the polynomial \(x^2 - 5x + 6\), then find the value of \(\alpha + \beta\).
यदि \(\alpha\) और \(\beta\) बहुपद \(x^2 - 5x + 6\) के शून्यक हैं, तो \(\alpha + \beta\) का मान क्या होगा?
(a) 5 (b) 6 (c) −5 (d) 1
Q4. Find the product of zeroes of the polynomial \(4x^2 + 1\).
बहुपद \(4x^2 + 1\) के शून्यकों का गुणनफल ज्ञात कीजिए।
(a) −1 (b) 1 (c) 1/4 (d) 4
Q5. What is the shape of the graph of a quadratic polynomial?
द्विघात बहुपद के ग्राफ का आकार कैसा होता है?
(a) Straight Line (सीधी रेखा) (b) Circle (वृत्त) (c) Parabola (परवलय) (d) Square (वर्ग)
Section B: Short Answer Questions (3 Marks Each)
Q6. Form a quadratic polynomial whose sum of zeroes is 0 and product of zeroes is −4.
एक द्विघात बहुपद बनाइए जिसके शून्यकों का योग 0 तथा गुणनफल −4 हो।
Q7. If the sum of zeroes of the polynomial \(x^2 - kx + 6\) is 5, find the value of \(k\).
यदि बहुपद \(x^2 - kx + 6\) के शून्यकों का योग 5 है, तो \(k\) का मान ज्ञात कीजिए।
Q8. Check whether −2 and 5 are the zeroes of the polynomial \(x^2 - 3x - 10\).
जाँच कीजिए कि क्या −2 और 5 बहुपद \(x^2 - 3x - 10\) के शून्यक हैं।
Q9. Find the zeroes of the polynomial \(x^2 - 7x + 10\) and verify the relationship between zeroes and coefficients.
बहुपद \(x^2 - 7x + 10\) के शून्यक ज्ञात कीजिए तथा शून्यकों और गुणांकों के बीच संबंध की जाँच कीजिए।
Q10. If \(\alpha\) and \(\beta\) are the zeroes of the polynomial \(2x^2 - 7x + 3\), find the value of \[ \frac{1}{\alpha} + \frac{1}{\beta} \]
यदि \(\alpha\) और \(\beta\) बहुपद \(2x^2 - 7x + 3\) के शून्यक हैं, तो \[ \frac{1}{\alpha} + \frac{1}{\beta} \] का मान ज्ञात कीजिए।
💡 Important Exam & Study Tips
- Master NCERT Fundamentals: Ensure thorough familiarity with standard textbook definitions, formulas, and in-text examples before solving advanced problems.
- Step-by-Step Presentation: In board examinations, neat presentation, correct formula application, and labeled steps earn maximum step-marking.
- Practice Under Timed Conditions: Regular practice with previous years' question papers (PYQs) builds exam speed and accuracy.
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❓ Frequently Asked Questions (FAQs)
Q1: Are these solutions aligned with the latest rationalized syllabus?
Yes, all study notes and practice questions on StudyMats strictly follow the updated NCERT textbook pattern and CBSE assessment guidelines.
Q2: How can I prepare this chapter for highest marks?
Review the theory thoroughly, solve all textbook exercise questions, and repeatedly practice the high-frequency questions provided in this guide.