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

TS Polycet Mock Test

Q). (0, 0), (1, 0), (0, -4) are the vertices of a _____________ triangle.
A) equilateral
B) isosceles
C) right-angled isosceles
D) scalene

View Answer

D) scalene
Explanation: A(0,0)B(1,0)and C(0,-4)
AB = $\sqrt{1^2+0^2}$

= 1
BC = $\sqrt{1^2+4^2} = \sqrt{17}$

CA = $\sqrt{4^2}$

= 4
The points forms a scalene triangle.

Q). If (8,1), (k, -4), (2, -5) are collinear, then k =
A) 1
B) 2
C) 3
D) 4

View Answer

C) 3
Explanation: $(\begin{pmatrix}X_1&Y_1\\8&1\end{pmatrix}) (\begin{pmatrix}X_2&Y_2\\k&-4\end{pmatrix}) (\begin{pmatrix}X_3&Y_3\\2&-5\end{pmatrix})$

,given points are collinear, △ = 0
△ = $\frac12\begin{vmatrix}x_1-X_2&Y_1-Y_2\\X_1-X_3&Y_1-Y_3\end{vmatrix}$

=0
= $\frac12\begin{vmatrix}8-k&1-(-4)\\8-2&1-(-5)\end{vmatrix}$

= 0
= $\frac12\begin{vmatrix}8-k&5\\6&6\end{vmatrix}$

= 0
= $\frac12\begin{vmatrix}8-k&1+4\\6&1+5\end{vmatrix}$

=0
6(8 – k) – 6 x 5 = 0
48-6k-30 = 0
⇒18-6k = 0
⇒6(3-k) = 0
⇒k=3

Q). If the slope of the line through (2, -7) and (x, 5) is 3 then x =
A) 4
B) 5
C) 6
D) 7

View Answer

C) 6
Explanation: $\begin{pmatrix}X_1&Y_1\\2&-7\end{pmatrix} and \begin{pmatrix}X_2&Y_2\\k&5\end{pmatrix}$

Slope of the line = m= $\frac{Y_2-Y_1}{X_2-X_1}$

= $\frac{5-(-7)}{X-2}$

= 3
12 = 3x-6
3x = 18
X = 18/3
X = 6

Q). The distance between the points (cosθ, sinθ) and (-sinθ, cosθ) is
A) 1
B) √2
C) 2
D) √3

View Answer

B) √2
Explanation: (cosθ, sinθ) and (-sinθ, cosθ)
= $\sqrt{\left(X_{2\;}-X_1\right)^2\;+}(Y_2-Y_1)^2$

= $\sqrt{\left(-\sin\theta-\cos\theta\right)^2\;+}(Cos\theta-Sin\theta)^2$

= $\sqrt{\sin^2\theta-\cos^2\theta\;+2\sin\theta cos\theta+\sin^2\theta-\cos^2\theta-2Sin\theta\cos\theta}$

= $\sqrt{1+1}$

=√2

Q). The number of elements in a triangle is
A) 3
B) 4
C) 6
D) 5

View Answer

C) 6

Q). In the figure

If MN || BC, AN = 3, NC = 18, MB = 24, then AM =
A) 2
B) 4
C) 6
D) 8

View Answer

C) 6
Explanation: AN/NC = AM/MB ⇒ 3/18 = AM/24
AM = 3×24/18
=4

Q). If two triangles have the same base and area then they lies between
A) parallel lines
B) two straight lines
C) perpendicular lines
D) intersecting lines

View Answer

A) parallel lines

Q). A 1.5 m tall boy casts 2 m shadow. At the same instance, a lamppost casts a shadow of 10 m. Then the height of the lamppost is
A) 6.5 m
B) 7.5 m
C) 8.5 m
D) None

View Answer

B) 7.5 m

Q). In the figure, x =

A) 45°
B) 135°
C) 90°
D) 15°

View Answer

B) 135°
Explanation: x° = 55° + 80° = 135°

Q). In the figure, x =

A) 100°
B) 90°
C) 110°
D) 80°

View Answer

A) 100°
Explanation: ∠AOB = 2∠ACB = 2 x 50° = 100°

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