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

Theory of Equation and Inequations

Total Questions: 50

31. If α₁, α,...., αₙ are the roots of an equation f(𝓍) = 0, then -α₁,-α₂,...., -αₙ are the roots of [DSE TGT 2019 ]

Correct Answer: (b) f(-𝓍) = 0
Solution:

32. If p, q and r are the roots of the equation 𝓍³ 9𝓍² + 26𝓍 - 24 = 0, then the value of sum of squares of p, q and r is [DSE TGT 2019]

Correct Answer: (b) 29
Solution:

33. Let f(𝓍) be a polynomial of degree n > 0 and a ∈ C, then (𝓍 - a) is a factor of f(𝓍) if there exists a polynomial q(𝓍) such that f(𝓍) = [DSE TGT 2019]

Correct Answer: (a) (𝓍-a)q(𝓍)
Solution:

By division algorithm
Dividend = quotient × divisor + remainder
Since, (𝓍-a) is a factor of f(𝓍), then remainder will be zero.
Therefore, if q(𝓍) is quotient, then f(𝓍) divided by (𝓍-a) will be
f(𝓍) = (𝓍-a) q(𝓍) +0
⇒ f(𝓍) =(𝓍-a) q(𝓍)

34. General solution of linear equation 2y+0𝓍+3 =0 in two variables is: [OAVS TGT 2021]

Correct Answer: (c)
Solution:

Given,
2y+ 0𝓍 +3=0
⇒ 2y=-3
⇒ y = (-3/2)
Since, coefficient of 𝓍 is 'O'.
Therefore, 𝓍 may be any real number.
Hence, solution will be a, (-3/2) a is real.

35. If 4𝓍³+a𝓍²-b𝓍+1= p(𝓍), then find p(0)+p(-1). [OAVS TGT 2021]

Correct Answer: E. (*)
Solution:

36. If 𝓍²+y²+’ – 𝓍y - yz - z𝓍 = 0, then: [OAVS TGT 2021]

Correct Answer: (c) 𝓍 = y = z
Solution:

37. If m be the ratio of the roots of the equation a𝓍² + b𝓍 + c = 0, then which of the following relations is true? [OAVS TGT 2021]

Correct Answer: (d)
Solution:

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

Correct Answer: (b) 50
Solution:

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

Correct Answer: (b) 167/9
Solution:


40. 2𝓍 -3𝓍³ - a𝓍²+b𝓍-2 divided by (𝓍 - 2) leaves remainder 6, divided by (𝓍 + 3) leaves remainder 196. Find the remainder when it is divided by 𝓍 + 2. [OAVS TGT 2021]

Correct Answer: (c) 30
Solution: