Algebra (Mathematics Chapterwise Solved Papers for Teaching) (Part-2)

Theory of Equation and Inequations

Total Questions: 50

41. Solve the following equation? [OAVS TGT 2021]

Correct Answer: (a) 11/30
Solution:

42. Solve the following question? [OAVS TGT 2021]

Correct Answer: (c)
Solution:

43. The quadratic polynomial whose sum of zeroes is 6 and product of zeroes is –16 is: [OAVS TGT 2021]

Correct Answer: (c) 𝓍²-6𝓍-16
Solution:

If sum of zeros = 6
i.e. Ξ±+Ξ² = 6 & product of zeros =-16
i.e. Ξ± Ξ² = -16
Where, Ξ±, Ξ² are the zeros of polynomial.
Then, quadratic polynomial = 𝓍² - (Ξ±+Ξ²)𝓍 + Ξ±Ξ²
= 𝓍² - 6𝓍 -16

44. If the difference between the roots of the equation 𝓍² + 2k𝓍+1 = 0 is less than 2√3, then _______ is the set of possible values of k. [OAVS TGT 2021]

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

45. What is the value of 10mΒ³ + 3mΒ² - 5m - 279 if (2m, -m) is a solution of 15𝓍 + 13y =51? [OAVS TGT 2021]

Correct Answer: (a) 3
Solution:

46. If P(k) be the statement that 'A' set with elements has 2ᡏ subsets', then for P(0), the number of subsets are: [OAVS TGT 2021]

Correct Answer: (b) 1
Solution:

If P(k) is statement such that 'A' set with elements has 2ᡏ subjects.
Then for P(0), the number of subsets will be 2⁰, = 1

47. The degree of the polynomial 𝓍 (𝓍+ 2) (𝓍³-𝓍+𝓍⁴+3) is [OAVS TGT 2021]

Correct Answer: (b) 6
Solution:

Given f(𝓍) = 𝓍 (𝓍+ 2) (𝓍³-𝓍+𝓍⁴+3)
i.e. f(𝓍) = 𝓍(𝓍+2) (𝓍⁴+𝓍³-𝓍+3)
Degree of polynomial = highest power of 𝓍 in above polynomial.
i.e. degree = 6

48. If 2𝓍⁴ - a𝓍³ - b𝓍² + c𝓍 - 3, divided by 𝓍 -2 leaves a remainder of 5, divided by 𝓍 + 2 leaves remainder 29, what is the value of b? [OAVS TGT 2021]

Correct Answer: (a) 3
Solution:

49. Solution of the absolute value of inequality 3|3𝓍+9| <54 is: [OAVS TGT 2021]

Correct Answer: (a) -9<𝓍< 3
Solution:

50. 𝓍²-3𝓍+|m|= 0 has real roots. How many integer values can m take? [OAVS TGT 2021 ]

Correct Answer: (b) 5
Solution: