Algebra (Mathematics Chapterwise Solved Papers for Teaching)

Theory of Equation and Inequations

Total Questions: 50

1. The value of 'a' for which one root of the quadratic equation [EMRS PGT-2023 ]

(aĀ² - 5a + 3)š“Ā² + (3a ā€“ 1) š“ + 2 = 0 is twice as large as the other, is :

Correct Answer: (a) 2/3
Solution:

2. Let p and q be the roots of the equation š“Ā² - 2š“ + A = 0 and let r and s be the roots of the equation š“Ā² - 10š“ + B = 0. If p < q < r < s are in A.P., then the values of A and B are: [EMRS PGT-2023]

Correct Answer: (d) A = -3, B = 77
Solution:



3. Solve the following equation. [EMRS PGT-2023]

Ī± and Ī² be the roots of the equation pš“Ā² + qš“ + r = 0 (pā‰ 0). If p,q r are in A.P and (1/Ī±) + (1/Ī²) = 4 then the value of |Ī±-Ī²| is:

Correct Answer: (c)
Solution:

4. The pair of equations 3š“ - 5y = 7 and -6š“ +10y = 7 has [Bihar (TRE 2.0)-2023]

Correct Answer: (c) no solution
Solution:

5. Which of the following statements is correct? [Bihar (TRE 2.0)-2023]

Correct Answer: (d) More than one of the above
Solution:

We know that
(a) A polynomial equation has at least one root
(b) A polynomial equation of degree n has n roots

6. nĀ²< 2āæ is true for all natural numbers, if [Bihar (TRE 2.0)-2023]

Correct Answer: (a) nā‰„5
Solution:

7. The maximum number of positive real roots of the equation 2š“ā· - š“ā“ +4š“Ā³- 5 = 0 is [Bihar (TRE 1.0) -2023]

Correct Answer: (b) 3
Solution:

8. If š“ and a are real numbers and a >0, |x| > a, then: [EMRS TGT-2023]

Correct Answer: (c) x āˆˆ (-āˆž, -a) āˆŖ (a, āˆž)
Solution:

9. The solution set of |3-4š“| ā‰„9 is: [EMRS TGT-2023]

Correct Answer: (d)
Solution:

10. Solve the following equation: [EMRS TGT-2023]

Correct Answer: (c) x āˆˆ (-12,-5)
Solution: