Class 9 Maths Worksheet | Chapter: Number System (संख्या पद्धति)
Number System – Practice Worksheet
Section A: Multiple Choice Questions
Q1. The product of any two irrational numbers is:
(A) always an irrational number
(B) always a rational number
(C) always an integer
(D) sometimes rational, sometimes irrational
दो अपरिमेय संख्याओं का गुणनफल होता है:
Q2. The value of 1.999… in the form p/q, where p and q are integers and q ≠ 0, is:
(A) 19/10 (B) 1999/1000 (C) 2 (D) 1/9
1.999… का p/q रूप में मान ज्ञात कीजिए।
Q3. \(2\sqrt{3} \times \sqrt{3} + 1\) is equal to:
(A) \(2\sqrt{9}\) (B) 6 (C) 7 (D) \(4\sqrt{6}\)
दिए गए व्यंजक का मान ज्ञात कीजिए।
Q4. Between two rational numbers:
(A) there is no rational number
(B) there is exactly one rational number
(C) there are infinitely many rational numbers
(D) there are only rational numbers and no irrational numbers
दो परिमेय संख्याओं के बीच कितनी परिमेय संख्याएँ होती हैं?
Q5. Which of the following is equal to x?
(A) \(x^{12/7} - x^{5/7}\)
(B) \(\sqrt{(x^4)^{1/3}}\)
(C) \((\sqrt{x^3})^{2/3}\)
(D) \(x^{12/7} \times x^{7/12}\)
निम्नलिखित में से कौन x के बराबर है?
Section B: Short Answer Questions
Q6. Find three rational numbers between:
(i) −1 and −2 (ii) 0.1 and 0.11
(iii) 5/7 and 6/7 (iv) 1/4 and 1/5
तीन परिमेय संख्याएँ ज्ञात कीजिए।
Q7. Represent geometrically on the number line:
√4.5, √5.6, √8.1, √2.3
संख्या रेखा पर निरूपण कीजिए।
Q8. Simplify:
\(16^{-1/4} \times \sqrt{16^4}\)
सरलीकरण कीजिए।
Q9. Find the value of x:
\(3 + 2^x = 64^{1/2} + 27^{1/3}\)
x का मान ज्ञात कीजिए।
Q10. If a = −2 and b = −1, find:
\(a^{-b} − b^a\)
दिया गया मान ज्ञात कीजिए।
Section C: Long Answer Questions
Q11. Find the value of \(x^2 + y^2 + xy\).
Q12. Find the value of \(x^2 − y^2\).
Q13. Determine rational numbers p and q for the given condition.
Q14. Simplify the given expression.
Q15. Simplify the given expression.
Q16. Show that the given statement is true.
Q17. If the given condition holds, find the value of:
\(qx^2 − 2px + q\)
Q18. Show that the given statement is true.
Q19. If the given condition holds, find the required value.
Q20. Find the value of a and b:
(i) \((5 + 2\sqrt{3}) / (7 + 4\sqrt{3}) = a − b\sqrt{3}\)
(ii) \((\sqrt{2} + \sqrt{3}) / (3\sqrt{2} − 2\sqrt{3}) = a + b\sqrt{6}\)
Q21.
(i) Write the decimal form of 2/11
(ii) Write the p/q form of 0.38
(iii) If p/q form of 0.38 is m/n, find (m + n)
दशमलव एवं भिन्न रूप से संबंधित प्रश्न।
Answer Key / Solutions
Section A: Multiple Choice Questions
Q1. (D) sometimes rational, sometimes irrational
Q2. (C) 2
Q3. (C) 7
Q4. (C) there are infinitely many rational numbers
Q5. (C)
Section B: Short Answer Questions
Q6.
(i) −1.25, −1.5, −1.75
(ii) 0.101, 0.105, 0.109
(iii) 51/70, 52/70, 53/70
(iv) 9/36, 10/36, 11/36
Q7. Required irrational numbers are represented on the number line using the standard geometric construction method.
Q8.
16−1/4 × √(164) = (24)−1/4 × 162 = 2−1 × 256 = 128
Q9.
3 + 2x = 8 + 3 = 11 ⇒ 2x = 8 ⇒ x = 3
Q10.
a−b − ba = (−2)1 − (−1)−2 = −2 − 1 = −3
Section C: Long Answer Questions
Q11. x2 + y2 + xy = (x + y)2 − xy
Q12. x2 − y2 = (x − y)(x + y)
Q13. p and q are rational numbers satisfying the given condition.
Q14. Expression simplifies to the required rational form.
Q15. Expression simplifies using laws of exponents.
Q16. LHS = RHS, hence proved.
Q17. Required value is obtained by substituting p and q in
qx2 − 2px + q
Q18. Given identity is verified step by step.
Q19. Required value obtained by simplification.
Q20.
(i) a = 1, b = 0
(ii) a = 1, b = 1
Q21.
(i) 2/11 = 0.1818…
(ii) 0.38 = 19/50
(iii) m + n = 69