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

Theory of Equation and Inequations

Total Questions: 50

21. Solve the following equation? [DSSSB PGT 2021]

Correct Answer: (a) 64
Solution:

22. If LCM and HCF of two quadratic are (๐“ยณ+2๐“ยฒ- ๐“-2) and (๐“+2) respectively then the euations are- [DSSSB PGT 2021]

Correct Answer: (b) ๐“ยฒ+3๐“+2 and ๐“ยฒ+๐“โ€“2
Solution:

23. Two quadratic equations f(๐“) and g(๐“) are having G.C.D. and L.C.M. (๐“ยฒ+๐“-2) and (๐“โด+3๐“ยณ-3๐“ยฒ-7๐“+6) respectively. [DSSSB PGT 2021]

If f(๐“) = ๐“ยณ+4๐“ยฒ+x-6, then what is the value of g(๐“) -

Correct Answer: (d) ๐“ยณ-3๐“+2
Solution:


24. If xโฟ-p๐“ยฒ+r = 0 is having equal roots, then relation between n, p and r is - [DSSSB PGT 2021]

Correct Answer: (a) nโฟrโฟโปยฒ = 4pโฟ (n-2)โฟโปยฒ
Solution:


25. Let P(๐“) be a quadratic polynomial such that P(0) = 1. If P(๐“) leaves remainder 4 when divided by ๐“ - 1, and it leaves remainder 6 when divided by ๐“+1, then [DSSSB PGT 2021]

Correct Answer: (b) P(-2) = 19
Solution:

26. The value of b, if ๐“ยฒ-5๐“ยฒ+4b๐“+3 be divisible by (๐“-3), is - [DSSSB PGT 2021]

Correct Answer: (d) 5/4
Solution:

27. The equation (๐“ -a)ยณ+(๐“ -b)ยณ+(๐“ -c)ยณ+(๐“ -d)ยณ = 0, where a, b, c, d are positive and not all equal, has - [DSSSB PGT 2021]

Correct Answer: (a) Only one real root
Solution:

28. The polynomial a๐“ยณ+ b๐“ + c is divisible by ๐“ ยฒ+ p๐“ +1 if: [DSSSB PGT 2021]

Correct Answer: (d) aยฒ-cยฒ = ab
Solution:

29. The remainder when 4๐“โด-10๐“ ยฒ+1 is divided by (๐“+2) is: [DSSSB PGT 2021]

Correct Answer: (d) 25
Solution:


Thus, Remainder = 25.

30. If 2 is the root of the equation ๐“ยณ-6๐“ยฒ+3๐“+10 = 0, then the other roots are [DSE TGT 2019]

Correct Answer: (b) -1,5
Solution: