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

6) $\frac1{\sqrt2}$ is ……….

A) Natural number
B) Rational number
C) Irrational number
D) An integer

View Answer

C) Irrational number

Explanation:We are given the number:
$\frac{1}{\sqrt{2}}$
Step-by-step shortcut:
$\sqrt{2}$ is irrationalThe reciprocal of an irrational number is also irrational
(unless it simplifies to a rational, which $\frac{1}{\sqrt{2}}$ does not)
Final Answer: Irrational number

7) If 2^x = 8² then x=

A) 2
B) 4
C) 6
D) 8

View Answer

C) 6

Explanation:We are given:
2^x = 8²
Shortcut method:
Rewrite 8 as a power of 2:
8 = 2³ ⇒ 8² = (2³)² = 2⁶
So,
2^x = 2⁶ ⇒ x = 6

8) A={C,O,V,I,D,19,2020}, B={C,O,V,I,D,19,2021} then B-A=

A) (2020)
B) (2021)
C) (2020, 2021)
D) (C,O,V,I,D,19,2020, 2021)

View Answer

B) (2021)

Explanation:We are given two sets:
A = {C, O, V, I, D, 19, 2020}
B = {C, O, V, I, D, 19, 2021}
We are asked to find B − A, which means the elements that are in Bbut not in A.
Shortcut:
Compare both sets:
Common elements: C, O, V, I, D, 19Bhas 2021which Adoes not.
So:
$B - A = \{2021\}$
Final Answer: (2021)

9) Find the value of log_o.1 0.01

A) 1
B) 2
C) 3
D) 4

View Answer

B) 2

Explanation:We are asked to find:
$\log_{0.1}(0.01)$
Shortcut Method:
Write both numbers as powers of 10:
$0.1 = 10^{-1}$ $0.01 = 10^{-2}$
So the expression becomes:
$\log_{10^{-1}}(10^{-2})$
Use change of base formula:
$\log_{a}(b) = \frac{\log_{10}(b)}{\log_{10}(a)}$
$= \frac{\log_{10}(10^{-2})}{\log_{10}(10^{-1})} = \frac{-2}{-1} = 2$

10) The roots of x²+x-6=0 are

A) 2,-3
B) -2,3
C) 2,3
D) -2,-3

View Answer

A) 2,-3

Explanation:We are given the quadratic equation:
$x^2 + x - 6 = 0$
Shortcut Method: Splitting the middle term
We need two numbers that multiply to -6and add to +1(coefficient of x):
Numbers: 3 and -2
So we factor:
x² + 3x – 2x – 6 = 0
x(x + 3) -2(x + 3) = 0
(x – 2)(x + 3) = 0
Roots are: x = 2, -3

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