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

Q). The following Venn-diagram design represented by C equals

A) {1,2,5, 6}
B) {6,5,4}
C) {4,5,6,7}
D) {2,5,6}

Q). The shaded area in the figure is

A) A∩(B⋃C)
B) A∩(B∩C)
C) A⋃(B∩C)
D) A∪(B∪C)

Q). The remainder of 3x³ -2x² + x + 2 when divided by 3x + 1 is
A) 4/3
B) 3/4
C) -4/3
D) None

View Answer

D) None
Explanation: p(x) = 3 x³ -2 x² + x + 2
3x + 1 = 0 ⇒ x = -1/3
P(-1/3) = 3(-1/3) ³ – 2(-1/3)²+(-1/3)+2
= -3 x 1/27 -2 x1/9-1/3+2/1
=1/9-2/9-1/3+2/1
=
=
= 14/9

Q). If α, β are the roots of 5×2 + 5x + 6 = 0, then (1 + α) (1 + β) =
A) 4/5
B) 3/5
C) 6/5
D) -6/5

Q). If the difference of two numbers is 5 and their product is 84, then the numbers are
A) 14,6
B) 12,7
C) 21,4
D) 14,9

Q). If the perimeter of a rectangular room is 34 and the length of the diagonal is 13, then the dimensions of the room are
A) 7,6
B) 11,6
C) 12,5
D) 12,6

View Answer

C) 12,5
Explanation: perimeter of a rectangle = 34
2(l + b) = 34 ⇒ l + b = 17

length of the diagonal = = 13
l² + b² = 169
(l + b)² = l² + b² + 2/b
(17)² = 169 + 2lb
⇒ 289- 169 = 2lb
2lb = 120 ⇒ lb = 60
(l – b)²= (l + b)²-4lb
= (17)²-4x 60 = 289-240 = 49
L – b=-749 = 7
l + b= 17
l – b =27
________
2l = 24 ⇒ l = 12, b = 17 – 12 = 5
∴ The dimensions of the room are 12 and 5

Q). If 9x + 11y = 51 and 11x + 9y = 49, then x =
A) -1
B) -2
C) 1
D) 2

Q). If the pair of equations a₁x + b₁y + c₁= 0 and a₂x + b₂y + c₂ = 0 has unique solution, then
A) a₁/ a₂ = b₁/ b₂
B) a₁/ a₂ ≠ b₁/ b₂
C) b₁/ b₂≠ c₁/ c₂
D) b₁/ b₂= c₁/ c₂

Q). The graph of y + x² = 0 lies in the quadrants
A) Q₁,Q₂
B) Q₂,Q₃
C) Q₃,Q₄
D) Q₄,Q₁

Q). The line x = 2017 is
A) Slope not defined
B) Parallel to y-axis
C) Slope not defined and Parallel to y-axis
D) None