TS Polycet (Polytechnic) 2020 Previous Question Paper with Answers And Model Papers With Complete Analysis

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11)Product of the polynomials (x3+8), (x-8) is denoted by p(x) = a x4 + b x3 + c x2 + dx + e, then p(8) =

A) 0

B) 1

C) 2

D) 3

View Answer

A) 0
Explanation:p(x) = (x3 + 8) (x – 8) p(8) = (83 + 8)(8-8) = (83 + 8) (0) = 0

12)If 7 divides a2, then

A) 7 divides ‘a’

B) 7 divides √a

C) a divides 7

D) None

View Answer

A) 7 divides ‘a’
Explanation:7 divides a2, then 7 divides ‘a’

13)In the formula logaxy = logax + logay, which of the following is true?

A) x > 0, y > 0, a = 1

B) x < 0, y < 0, a = 1

C) a>0,y >0, x = 1

D) x> 0, y > o, a≠1

View Answer

D) x> 0, y > o, a≠1
Explanation:logaxy = logax + logay, then x>0,y>0, a≠1

14)X/2019+Y/2020 = 2, 2x/2019 – Y/2020 = 1 ∴ (x,y)

A) (2019, 2020)

B) (2020, 2019)

C) (2019, 2019)

D) (2020, 2020)

View Answer

A) (2019, 2020)
Explanation:X/2019 + Y/2020 = 2 2X/2019 – Y/2020 = 1 Verify option (1) (2019, 2020) (1) => 2019/2019 + 2020/2020 = 1+1 = 2 (2) => 2×2019/2019 – 2020/2020 = 2-1 = 1

15)x + y = √3 , x -y = 0, then x =

A) √3

B) -√3

C) √3/2

D) -√3/2

View Answer

C) √3/2
Explanation:x+ y= √3 x-y= 0 ———– 2x = √3 => x = √3/2

16)logxb – logxa = logxc – logxb ∴ ac =

A) a2

B) b2

C) c2

D) None

View Answer

B) b2
Explanation:logxb – logxa = logxc – logxb => logx(b/a) = logx(c/b) =>b/a = c/b=> b2 = ac

17)A = {P, O, L, Y, T, E, C, H, N, 1, Q}, B = {P, O, L, Y, C, E, T, 2020}, B – A =

A) {20}

B) {2020}

C) {40}

D) None

View Answer

B) {2020}
Explanation:A = {P, O, L, Y, T, E; C, H, N, I, Q} B = {P, O, L, Y, C, E, t 2020} B -A = {P, O,- L, Y, C, E, T, 2020} -{P, 6, L, Y, T, E, C, H, N, I, Q) = {2020}

18)If (5, 2) is the solution of 2x + 5y = 20, ax -by = 0, then (a, b) =

A) (2, 5)

B) (5, 2)

C) (-2, 5)

D) (-5, 2)

View Answer

A) (2, 5)
Explanation:(5, 2) is the solution of 2x + 5y = 20, ax – by = 0, then 5a-2b = 0 Verify option (1) (2, 5) =>5(2)-2(5) = 10-10 = 0

19)If the system of equations x – y = 1, ax + y = 2 has unique solution, then

A) a = 1

B) a = -1

C) a ≠ 1

D) a ≠ -1

View Answer

D) a ≠ -1
Explanation:a1/a2≠b1/b2 => 1/a ≠ -1/1 =>1/a ≠ -1 =>A ≠ 1

20)If α, β are the roots of x2– 1 = 0, then α+ β =

A) 0

B) 1

C) -1

D) 2

View Answer

A) 0
Explanation:b2 — 1 = 0 a = 1, b = 0, c = —1 α + β = -b/a = – 0/1 = 0
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