Algebra (Mathematics Chapterwise Solved Papers for Teaching) (Part-5)

Theory of Equation and Inequations

Total Questions: 50

1. The sum of all real values of 𝓍 satisfying the equation (𝓍 - 5𝓍 + 5) ˣ²⁺⁴ˣ⁻⁶⁰ = 1 is: [KVS PGT 23-12-2018]

Correct Answer: (d) 3
Solution:

2. If a and b are natural numbers such that a² b² is prime number, then a²-b² equals: [KVS PGT 23-12-2018]

Correct Answer: (d) a+b
Solution:

Consider,
a²-b²= (a+b)(a–b) is prime (given)
∴ a²-b² either divisible by 1 or the number itself
∴ a-b= 1 and a²-b² =a + b {a+b≠1 as a, b ∈ ℕ}
Therefore, a²-b² = a+b

3. Let α, β be the roots of the equation 𝓍²+a𝓍+a³=0, a≠0. If (α,β) lies on the parabola y²=𝓍, then the roots of the equation are [UP PGT-2016 (02-02-2019)]

Correct Answer: (b) 4,-2
Solution:


4. If the roots of the equation 𝓍²+𝓍+a=0, a>0 are real and distinct, then the roots of the equation 𝓍²-4√a𝓍+1=0 are [UP PGT-2016 (02-02-2019)]

Correct Answer: (c) imaginary
Solution:

5. If a, b, c are rational numbers and a𝓍²+b𝓍+c=0 and 2𝓍²+𝓍-2=0 have a common root, then 4a-2b+3c is equal to [UP PGT-2016 (02-02-2019)]

Correct Answer: (c) 0
Solution:

6. Which of the following is a binomial in one variable of degree 5? [DSSSB 23 SEP 2018 (9 AM-11 AM)]

Correct Answer: (c)
Solution:

7. If 𝓍+5 is a factor of the polynomial 𝓍³+ a𝓍²+ a𝓍 - 15. Then what will be the value of a? [DSSSB 23 SEP 2018 (9 AM-11 AM)]

Correct Answer: (b) 7
Solution:

8. Which of the following is not a polynomial in one variable? [DSSSB 23 SEP 2018 (9 AM-11 AM)]

Correct Answer: (d)
Solution:

9. At how many points does the polynomial 𝓍³-𝓍²+𝓍-1 intersect the x-axis? [DSSSB 23 SEP 2018 (9 AM-11 AM)]

Correct Answer: (b) 1
Solution:

10. What should be the value of k so that the linear equation 31𝓍+124y = k in two variables 𝓍 and y has an integer value [DSSSB 23 SEP 2018 (9 AM-11 AM)]

Correct Answer: (d) 155
Solution: