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

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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
$\frac\alpha\beta+\frac\beta\alpha$

= α²+β²/ 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 6^th 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 2^15-5
= 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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