TS Polycet (Polytechnic) 2017 Previous Question Paper with Answers And Model Papers With Complete Analysis

Q). \sqrt{6+\sqrt{6+\sqrt{6+.....................\infty}}} =
A) 1
B) 2
C) 3
D) 4

View Answer
C) 3
Explanation: x = \sqrt{6+\sqrt{6+\sqrt{6+.....................\infty}}}
⇒ x= \sqrt{6+x}
x2 = 6 + x ⇒ x2-x-6 = 0
x2 – 3x + 2x – 6 = 0
x(x-3) + 2(x-3) = 0
⇒ (x-3) (x + 2) = 0
X = 3 (or) x
= -2

Q). If x+\frac1x = 2, then x^2+\frac1{x^2} =
A) 0
B) 2
C) 4
D) 8

View Answer
B) 2
Explanation: x+\frac1x = 2
⇒(x+1/x)2 = (2)2
x^2+\frac1{x^2} +2. x+\frac1x = 4
x^2+\frac1{x^2} +2=4
x^2+\frac1{x^2}
= 4-2
=2

Q). The discriminant of the quadratic equation x2 + bx + c = 0 is
A) b2 – 4ac
B) a2 – 4bc
C) c2 – 4ab
D) None

View Answer
A) b2 – 4ac

Q). If α, β are the roots of x2+ 2x + 5 = 0 then \frac\alpha\beta+\frac\beta\alpha =
A) 6/5
B) 4/5
C) -6/5
D) -4/5

View Answer
C) -6/5
Explanation: a=1,b = 2,c = 5
α+β = -b/a =-2
αβ = c/a = 5
\frac\alpha\beta+\frac\beta\alpha
= α22/ αβ
= \frac{(\alpha+\beta)^2-2\alpha\beta}{\alpha\beta}
= \frac{(-2)^2-2x5}5
= \frac{4-10}5
=-6/5

Q). Which is the three digit number divisible by 7?
A) 100
B) 133
C) 137
D) 143

View Answer
B) 133

Q). The 6th term in the GP 2, 8, 32,…………. is
A) 512
B) 128
C) 2048
D) 256

View Answer
C) 2048
Explanation: a = 2, r = 8/2 = 4
ar5 = 2 (8/2)5
= 2x 85/25
= 2×215/25
=2 x 215-5
= 2 X 210
= 2 X 1024
= 2048

Q). 1 + 1 + 1 +…………… n terms =
A) n/2
B) \frac{n-1}2
C) n
D) \frac{n+1}2

View Answer
C) n
Explanation: Sum of first ‘n’ ones is ‘n’

Q). 1 + 3 + 6 + 10 +…………….. n terms =
A) \frac{n(n+1)(n+2)}4
B) \frac{n(n+1)(n+2)}8
C) \frac{n(n+1)(n+2)}6
D) None

View Answer
C) \frac{n(n+1)(n+2)}6

Q). If (k, 2) lies in II quadrant then (-k, -2) lies in the quadrant
A) I
B) II
C) III
D) IV

View Answer
D) IV
Explanation: (k, 2) ∈ Q2
point in Q2 is (-x, y) where k = -x
(-k, -2) = (-(-x), -2) = (x, -2) ∈ Q4

Q). The point of intersection of the lines 2x + 3y – 5 = 0 and 3x – 4y + 1 = 0 lies in which quadrant?
A) I
B) II
C) III
D) IV

View Answer
A) I
Explanation: 2x + 3y-5 = 0 ⇒ 4(2x + 3y-5 = 0)
3x – 4y + 1 = 0 ⇒ 3(3x -4y + 1 = 0)
8x+ 12y-20 = 0
9x-12y + 3 = 0
___________
17x- 17 = 0 ⇒ x = 1
____________
3y = 5-2x ⇒ 3y = 5- 2 x 1=3
⇒ y=1
(x,y) = (1,1)

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