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

Q) Which term of the G.P.√3,3,3√3 ,…………………… is 729?
A) 10
B) 12
C) 14
D) 16

View Answer
B) 12
Explanation: √3,3,3√3……………..G.P.
Here a = √3, r = 3/√3 = √3, an = 729
an = a. rn-1
729 = √3 (√3)n-1
729 = (√3)n => 729 = 3n/2
=> 36 = 3n/2
=> 6 = n/2 => n = 12

Q) Roots of 5 x2– 8x = 4 are:
A) 2,-2/5
B) 1,8/5
C) 2,1/5
D) 2,7

View Answer
A) 2,-2/5
Explanation: 5 x2-8x = 4
=>5 x2-8x-4 = 0
=>5 x2-10x + 2x-4 = 0
=>5x(x-2) + 2(x-2) = 0
=> (x -2) (5x + 2) = 0
=> x – 2 = 0 (or) 5x + 2 = 0
=> x = 2 (or) x = -2/5

Q) 5=
A) 7log125
B) 7log57
C) 7log75
D) None

View Answer
C) 7log75
Explanation: 5 = 7log75
[∴a loga m = m]

Q) logx2 + logx22 + logx23+………..+ logx2n = \frac{n(n+1)}2, then x =
A) n
B) 1
C) 5
D) 2

View Answer
D) 2
Explanation: logx2 + logx22 + logx23+………..+ logx2n = n(n+1)/2
logx2 + 2 logx2 + 3 logx2 +…………………+n logx2 = n(n+1)/2
logx2 (1+2+3 +……………..+n) = n(n+1)/2
logx2 [n(n+1)/2] = n(n+1)/2
logx2 = 1 => x1 = 2
=> x = 2

Q) If A = {a}, B = {a, b}, C = {a, b, c}, then A∩B⋂C=
A) {a}
B) {b}
C) {c}
D) None

View Answer
A) {a}
Explanation: A = {a}, B = {a, b}, C = {a, b, c)
BnC = {a, b)n {a, b, c) = {a, b}
An B n C = [a) n (a, b) = {a}

Q) 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

Q) 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’

Q) 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

Q) 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

Q) 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
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