Algebra (Mathematics Chapterwise Solved Papers for Teaching) (Part-4)

Theory of Equation and Inequations

Total Questions: 50

1. Given that 𝓍, y and a are real numbers and 𝓍 < y, a < 0 then

Correct Answer: (c)
Solution:If 𝓍, y and a are real numbers such that 𝓍 < y & a <0 then we have

2. Solve the following equation? [UP TGT 2021]

Correct Answer: (c) 1/3
Solution:

3. Solve the following equation? [UP TGT 2021]

Correct Answer: (d) 36
Solution:

4. If 2ⁿ – 15= 𝓍² then [UP Higher Asst. Prof. 2021]

Correct Answer: (b) n = 4 or n = 6
Solution:

5. If f(𝓍) = a𝓍² + 2b𝓍 + 1, a and b are positive real numbers and b²<a, then which of the following is correct? [UP PGT 2021]

Correct Answer: (b) f(𝓍) > 0 ∀ 𝓍 ∈ R
Solution:

6. If the difference of the roots of the equation 𝓍²+p𝓍+12 = 0 is one then the values of p are- [UP PGT 2021]

Correct Answer: (a) ±7
Solution:

7. If the two roots of the equation 𝓍³ - 5𝓍²- 16𝓍 + 80 = 0 are 4 and -4 then the third root of this equation is [UP PGT 2021]

Correct Answer: (d) 5
Solution:

Given, Equation: 𝓍³ - 5𝓍²- 16𝓍 + 80 = 0
Let the third root be r.
4 + (-4) + r = 5 (sum of roots)
⇒ r = 5

8. If α and β are roots of 𝓍²+ 𝓍 + 1 = 0, then the equation whose roots are α and β is - [UP PGT 2021]

Correct Answer: (d) 𝓍²+𝓍+1= 0
Solution:

9. The harmonic mean of the roots of the equation a𝓍² + b𝓍 + c = 0 is [UPPSC GIC 2021]

Correct Answer: (a) -(2c/b)
Solution:

10. Find the condition that the roots of the cubic equation 𝓍³ - p𝓍² + q𝓍 - r = 0 be in a geometric progression- [UPPSC GIC 2021, UPPSC Ashram Paddhati 2021]

Correct Answer: (c) p³r-q³ = 0
Solution: