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

11) If α,β are the roots of a quadratic equation ax²+bx+c=0, a≠0 then $\frac1\alpha+\frac1\beta$ = ……..

A) $-\frac ba$
B) $\frac ca$
C) $-\frac bc$
D) $\frac bc$

View Answer

C) $-\frac bc$

Explanation:We are given that α and β are roots of the quadratic equation:
ax² + bx + c = 0, a ≠ 0
We need to find the value of:
$\frac{1}{α} + \frac{1}{β}$
Shortcut Trick:
$\frac{1}{α} + \frac{1}{β} = \frac{α + β}{α β}$
From the standard formulas for a quadratic:
$α + β = -\frac{b}{a}$
$α β = \frac{c}{a}$
So,
$\frac{1}{α} + \frac{1}{β} = \frac{-\frac{b}{a}}{\frac{c}{a}} = -\frac{b}{c}$
Final Answer: $-\frac{b}{c}$

12) 10th term of an arithmetic progression 2,-1,-4,…… is

A) -21
B) -23
C) -25
D) -27

View Answer

C) -25

Explanation:We are given the arithmetic progression:
2,-1,-4,…
Step 1: Identify first term and common difference
First term a = 2
Common difference d = -1 – 2 = -3
Step 2: Use formula for nth term of AP:
T_n = a + (n-1)d
For the 10th term:
TT₁₀ = 2 + (10-1)(-3) = 2 + 9(-3) = 2 – 27 = -25

13) How many two digit numbers are divisible by 7?

A) 10
B) 11
C) 12
D) 13

View Answer

D) 13

Explanation:To find how many two-digit numbers are divisible by 7, follow this shortcut method:
Step 1: Two-digit numbers range from 10 to 99.
Step 2: Find the first two-digit number divisible by 7:
$\lceil \frac{10}{7} \rceil = 2 ⇒ 2 × 7 = 14$
Step 3: Find the last two-digit number divisible by 7:
$\lfloor \frac{99}{7} \rfloor = 14 ⇒ 14 × 7 = 98$
Step 4: Use AP count formula:
$\text{Count} = \frac{(98 - 14)}{7} + 1 = \frac{84}{7} + 1 = 12 + 1 = 13$

14) The sum of 15 terms of A.P. 3, 6, 9……

A) 315
B) 360
C) 415
D) 460

View Answer

B) 360

Explanation:We are given an A.P.:3, 6, 9, …
This is a common A.P. where:
First term $a = 3$ Common difference d = 6 – 3 = 3
Number of terms n = 15
Use shortcut formula for sum of n terms of A.P.:
$S_n = \frac{n}{2} [2a + (n - 1)d]$
Plug in values:
$S_{15} = \frac{15}{2} [2(3) + (15 - 1)(3)] = \frac{15}{2} [6 + 42] = \frac{15}{2} × 48 = 15 × 24 = 360$

15) The value of x which satisfies the equation 2x-(4-x)=5-x is

A) 4.5
B) 3
C) 2.25
D) 0.5

View Answer

C) 2.25

Explanation:Solve:
2x – (4 – x) = 5 – x
Simplify LHS:
2x – 4 + x = 5 – x ⇒ 3x – 4 = 5 – x
Bring all terms to one side:
3x + x = 5 + 4 ⇒ 4x = 9 ⇒ x = $\frac{9}{4}$ = 2.25

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