Algebra – Free Practice Questions

Algebra is part of Maths (Quantitative Aptitude) in government exams such as SSC MTS, SSC CHSL, SSC CGL, RRB Group D / Level-1, RRB NTPC and others. This page has 236 free practice questions in English and Hindi, with correct answers and explanations and short revision notes.

बीजगणित – हिंदी और अंग्रेज़ी में 236 निःशुल्क अभ्यास प्रश्न, उत्तर और व्याख्या के साथ।

Read short notes Practise with explanations Quick quiz (10 questions)Timed topic test

Questions: 236 · Sets of 50: 5 · Difficulty mix: 95 easy, 7 hard, 134 medium · Languages: English and Hindi

Sample Algebra questions with answers

Q1. If x + 1/x = 7, find the value of x² + 1/x².

यदि x + 1/x = 7, तो x² + 1/x² का मान ज्ञात करें।

Answer: 47. (x + 1/x)² = x² + 1/x² + 2. So x² + 1/x² = 7² − 2 = 47.
(x + 1/x)² = x² + 1/x² + 2। अतः x² + 1/x² = 7² − 2 = 47

Q2. Solve for x: 6x + 13 = 79

x का मान ज्ञात करें: 6x + 13 = 79

Answer: 11. 6x = 79 − 13 = 66, so x = 66 ÷ 6 = 11.
6x = 79 − 13 = 66, अतः x = 66 ÷ 6 = 11

Q3. Solve: 3x + 6 = 9x − 36

हल करें: 3x + 6 = 9x − 36

7
9
8
−7

Answer: 7. 3x − 9x = −36 − 6, so −6x = −42, x = 7.
3x − 9x = −36 − 6, अतः −6x = −42, x = 7

Q4. Solve for x: 5x + 11 = 51

x का मान ज्ञात करें: 5x + 11 = 51

Answer: 8. 5x = 51 − 11 = 40, so x = 40 ÷ 5 = 8.
5x = 51 − 11 = 40, अतः x = 40 ÷ 5 = 8

Q5. If a + b = 21 and a − b = -5, find ab.

यदि a + b = 21 और a − b = -5, तो ab ज्ञात करें।

Answer: 104. ab = [(a + b)² − (a − b)²]/4 = (441 − 25)/4 = 104.
ab = [(a + b)² − (a − b)²]/4 = (441 − 25)/4 = 104

Q6. If a + b = 25 and a − b = 7, find ab.

यदि a + b = 25 और a − b = 7, तो ab ज्ञात करें।

Answer: 144. ab = [(a + b)² − (a − b)²]/4 = (625 − 49)/4 = 144.
ab = [(a + b)² − (a − b)²]/4 = (625 − 49)/4 = 144

Q7. Solve: 5x + 9 = 4x + 13

हल करें: 5x + 9 = 4x + 13

−4
4
6
5

Answer: 4. 5x − 4x = 13 − 9, so 1x = 4, x = 4.
5x − 4x = 13 − 9, अतः 1x = 4, x = 4

Q8. If x + 1/x = 8, then x³ + 1/x³ = ?

यदि x + 1/x = 8, तो x³ + 1/x³ = ?

Answer: 488. x³ + 1/x³ = (x + 1/x)³ − 3(x + 1/x) = 512 − 24 = 488.
x³ + 1/x³ = (x + 1/x)³ − 3(x + 1/x) = 512 − 24 = 488।

Q9. If a − b = 4 and ab = 19, then a³ − b³ = ?

यदि a − b = 4 और ab = 19, तो a³ − b³ = ?

Answer: 292. a³ − b³ = (a − b)³ + 3ab(a − b) = 64 + 3 × 19 × 4 = 292.
a³ − b³ = (a − b)³ + 3ab(a − b) = 64 + 3 × 19 × 4 = 292।

Q10. Find the value of 12² − 7² using a² − b² = (a + b)(a − b).

a² − b² = (a + b)(a − b) का प्रयोग करके 12² − 7² का मान ज्ञात करें।

Answer: 95. (12 + 7)(12 − 7) = 19 × 5 = 95.
(12 + 7)(12 − 7) = 19 × 5 = 95।

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