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

C)
Explanation:We are given that α and β are roots of the quadratic equation:\frac{1}{α} + \frac{1}{β}\frac{1}{α} + \frac{1}{β} = \frac{α + β}{α β}α + β = -\frac{b}{a}α β = \frac{c}{a}\frac{1}{α} + \frac{1}{β} = \frac{-\frac{b}{a}}{\frac{c}{a}} = -\frac{b}{c}-\frac{b}{c}α^2 + β^2\lceil \frac{10}{7} \rceil = 2 ⇒ 2 × 7 = 14\lfloor \frac{99}{7} \rfloor = 14 ⇒ 14 × 7 = 98\text{Count} = \frac{(98 – 14)}{7} + 1 = \frac{84}{7} + 1 = 12 + 1 = 13a = 3S_n = \frac{n}{2} [2a + (n – 1)d]S_{15} = \frac{15}{2} [2(3) + (15 – 1)(3)] = \frac{15}{2} [6 + 42] = \frac{15}{2} × 48 = 15 × 24 = 360\frac{9}{4} \frac{22}{22},\frac{33}{33}\frac{33}{33},-\frac{44}{44}\frac{44}{44},-\frac{77}{77}\frac{77}{77},-\frac{11}{11}\frac{22}{22},\frac{33}{33}x = \frac{22}{22} = 1, y = \frac{33}{33} = 13(1) – 4(1) = 3 – 4 = -1 ≠ 7\frac{22}{22}, \frac{33}{33}\sum n = \frac{n(n+1)}{2} = 45
⇒ n(n+1) = 90\left( \frac{1 + 7}{2}, \frac{2 + (-4)}{2} \right) = \left( \frac{8}{2}, \frac{-2}{2} \right) = (4, -1)\frac{P^2}{2\sin\left(\alpha\right)\cos\left(\alpha\right)}\frac{P^2}{\sin\left(\alpha\right)\cos\left(\alpha\right)}\frac P{2\sin\left(\alpha\right)\cos\left(\alpha\right)}\frac P{\sin\left(\alpha\right)\cos\left(\alpha\right)}\frac{P^2}{2\sin\left(\alpha\right)\cos\left(\alpha\right)}x = \frac{p}{\cosα}y = \frac{p}{\sinα}\frac{1}{2} \cdot \frac{p}{\cosα} \cdot \frac{p}{\sinα} = \frac{p^2}{2\sinα\cosα}\frac{P^2}{2\sinα\cosα}$

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