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TS Polycet (Polytechnic) 2019 Previous Question Paper with Answers And Model Papers With Complete Analysis

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21)Which term of the A.P.: 21,18, 15,……………is -30?

A) 16

B) 18

C) 17

D) 19

View Answer

B) 18
Explanation:a = 21, d =-3, a _n = a + (n – 1)d =-30
=> 21 + (n – 1)(-3)=-30
=> n-1 = $\frac{\cancel{-51}}{\cancel{-3}}$

= 17
∴ n = 18

22)In A.P., sum of n terms, S_n =

A) $\frac n2\left[2a+\left(n-1\right)d\right]$

B) $\frac n2\left[a+\left(n-1\right)d\right]$

C) $\frac{n2}2\left[2a+\left(n-1\right)d\right]$

D) None

View Answer

A) $\frac n2\left[2a+\left(n-1\right)d\right]$

Explanation:S_n = $\frac n2$

[2a + (n-1)d]

23)If a, b, c are in G.P., then a/b =

A) b/c

B) c/b

C) 1/ab

D) b/a

View Answer

A) b/c
Explanation:a, b, c are In GP.
b/a = c/b => a/b = b/c

24)Distance between the points (-2,3), (2, -3)

A) √52

B) 0

C) 52

D) 20

View Answer

A) √52
Explanation: $\sqrt{42+62} = \sqrt{16+36}$

= √52

25)If (P, 2), (-3, 4) and (7, -1) are collinear, then P =

A) -1

B) 0

C) -2

D) 1

View Answer

D) 1
Explanation:A (P, 2), B (-3, 4), C (7, -1)
Slope of AB = Slope of BC
$\frac{4-2}{-3-P} = \frac{-1-4}{7+3}$

= $\frac2{-3-P} = \frac{-5}{10}$

= $\frac2{-3-P} = \frac{-1}2$

4 = 3 + P => P = 1

26)Centroid of a triangle divides each median in the ratio:

A) 2 : 1

B) 1 : 2

C) 1 : 3

D) 3 : 1

View Answer

A) 2 : 1
Explanation:2:1

27)Slope of the line joining the points (4, -8), (5,-2)

A) 1/6

B) -6

C) 6

D) -1/6

View Answer

C) 6
Explanation: $\frac{Y2\;-Y1}{x2\;-x1}=\frac{-2\;+\;8}{5-4}\;=\frac61$

= 6

28)If two triangles are similar such that ratio of their areas is 25 : 361, then find the, ratio of their corresponding medians.

A) 10 : 20

B) 5 : 19

C) 20 : 19

D) 18 : 5

View Answer

B) 5 : 19
Explanation:√25 : 361 = 5 : 19

29)The angles of a triangle are in the ratio 1:2: 3, then the least angle is

A) 15°

B) 20°

C) 25°

D) 30°

View Answer

D) 30°
Explanation:Ratio = 1:2:3
A:B:C= 1 :2:3
A/1 = B/2 = C/3 = K
A = K, B = 2K, C = 3K
A+B+C= 180°
K + 2K + 3K = 180°
6K = 180° => K i 30°
Angles = 30°, 60°, 90°
∴Least angle = 30°

30)The angles of a triangle are 3x + 12°, 5x – 6° and x + 3°, then measure of largest angle is

A) 69°

B) 59°

C) 79°

D) 89°

View Answer

D) 89°
Explanation:A = 3x + 12°, B = 5x- 6°, C = x + 3°
A + B + C = 180°
3x + 12° + 5x-6° + x + 3° = 180°
9x + 9 = 180°
9x= 171 =>x= 19°
∴A = 3x + 12° = 3(19) + 12 = 69°
B = 5x-6 = 5 (19) – 6 = 89°
C = x + 3 = 19 + 3 = 22°
∴ Largest angle = 89°

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