TS Polycet (Polytechnic) 2021 Previous Question Paper with Answers And Model Papers With Complete Analysis

16) Solution of the equations 3x-4y=7 and 2x+3y=-1 is not equal to ……

A) $\frac{22}{22},\frac{33}{33}$
B) $\frac{33}{33},-\frac{44}{44}$
C) $\frac{44}{44},-\frac{77}{77}$
D) $\frac{77}{77},-\frac{11}{11}$

View Answer

A) $\frac{22}{22},\frac{33}{33}$

Explanation:Eliminate incorrect solution:
You are given equations:
⇒1. 3x – 4y = 7
⇒2. 2x + 3y = -1
Now test the options by substituting values.
⇒A. $x = \frac{22}{22} = 1, y = \frac{33}{33} = 1$
1st: $3(1) - 4(1) = 3 - 4 = -1 ≠ 7$
So, this is incorrect.
Correct Answer: $\frac{22}{22}, \frac{33}{33}$
(does notsatisfy the equations)

17) If Σn = 45, then n= ……

A) 9
B) 10
C) 11
D) 12

View Answer

A) 9

Explanation:If Σn = 45, then n = ?
We assume this means the sum of first n natural numbers:
$\sum n = \frac{n(n+1)}{2} = 45 ⇒ n(n+1) = 90$
Try n = 9:
9 × 10 = 90

18) The centre of a circle with (1, 2) and (7,-4) as end points of the diameter is

A) (-4,1)
B) (4,-1)
C) (-4,-1)
D) (4,1)

View Answer

B) (4,-1)

Explanation:Midpoint of diameter endpoints (1, 2) and (7, -4)
Use midpoint formula:
$\left( \frac{1 + 7}{2}, \frac{2 + (-4)}{2} \right) = \left( \frac{8}{2}, \frac{-2}{2} \right) = (4, -1)$
Correct Answer: (4, -1)

19) Area of a triangle formed by the line xcosα+ysinα=p with the coordinate axes

A) $\frac{P^2}{2\sin\left(\alpha\right)\cos\left(\alpha\right)}$
B) $\frac{P^2}{\sin\left(\alpha\right)\cos\left(\alpha\right)}$
C) $\frac P{2\sin\left(\alpha\right)\cos\left(\alpha\right)}$
D) $\frac P{\sin\left(\alpha\right)\cos\left(\alpha\right)}$

View Answer

A) $\frac{P^2}{2\sin\left(\alpha\right)\cos\left(\alpha\right)}$

Explanation:Area of triangle formed by line with axes
Equation: xcosα + ysinα = p
Find x- and y-intercepts:
Put y = 0:
$x = \frac{p}{\cosα}$
Put x = 0:
$y = \frac{p}{\sinα}$
Area of triangle =
$\frac{1}{2} \cdot \frac{p}{\cosα} \cdot \frac{p}{\sinα} = \frac{p^2}{2\sinα\cosα}$
Correct Answer: $\frac{P^2}{2\sinα\cosα}$

20) If x+7y=7 and 7x-3y=-3, then y =

A) 1
B) 7
C) -3
D) 0

View Answer

A) 1

Explanation:Solve:
1) } x + 7y = 7
2) } 7x – 3y = -3
From (1):x = 7 – 7y
Substitute into (2):
7(7 – 7y) – 3y = -3
49 – 49y – 3y = -3 ⇒ -52y = -52 ⇒ y = 1

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