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

41) The degree of the equation x²(x²+x+1)=x⁴+x³-x²+3x-1 is

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

View Answer

B) 2

Explanation:To determine the degree of the given equation:
$x^2(x^2 + x + 1) = x^4 + x^3 - x^2 + 3x - 1$
Step 1: Expand the Left Side
$x^2 \cdot x^2 + x^2 \cdot x + x^2 \cdot 1 = x^4 + x^3 + x^2$
So, the equation becomes:
$x^4 + x^3 + x^2 = x^4 + x^3 - x^2 + 3x - 1$
Step 2: Simplify the Equation
Subtract $x^4 + x^3$ from both sides:
$x^2 = -x^2 + 3x - 1$
Bring all terms to one side:
$x^2 + x^2 - 3x + 1 = 0$
Combine like terms:
$2x^2 - 3x + 1 = 0$
Step 3: Determine the Degree
The simplified equation is:
$2x^2 - 3x + 1 = 0$
The degree of an equation is the highest power of $x$ present. Here, the highest power is $x^2$ , so the degree is 2.
Final Answer:
$\boxed{2}$
Correct Option: 2

42) If 18, x, 36 are in arithmetic progression, then x=

A) 9
B) 18
C) 27
D) 26

View Answer

C) 27

Explanation:We are given that 18, x, 36 are in an arithmetic progression (A.P.)
Shortcut method:
In an A.P., the middle term is the average of the first and third terms:
$x = \frac{18 + 36}{2} = \frac{54}{2} = 27$
Final Answer: 27

43) If a, b, c are in arithmetic progression, then a+c=

A) b
B) 2b
C) b-a
D) b+a

View Answer

B) 2b

Explanation:If a, b, c are in arithmetic progression (A.P.), then:
$b = \frac{a + c}{2}$
Multiply both sides by 2:
$2b = a + c$
Final Answer: 2b

44) The common difference of the arithmetic progression 781, 806, 831, … is

A) 26
B) 24
C) 25
D) 23

View Answer

C) 25

Explanation:To find the common difference (d) in an Arithmetic Progression (A.P.), subtract any term from the next term:
d = 806 – 781 = 25
Final Answer: 25

45) The product of two numbers is 91 and their arithmetic mean is 10, then the two numbers are

A) 10, 10
B) 12, 8
C) 13, 7
D) 14, 6

View Answer

C) 13, 7

Explanation:We are given:
Product = 91
Arithmetic Mean = 10 → So,
$\frac{x + y}{2} = 10 \Rightarrow x + y = 20$
We now solve using sum and product shortcut:
We need two numbers whose:
Sum = 20
Product = 91
Try options:
Option C: 13 and 7
13 + 7 = 20 and 13 × 7 = 91
Both conditions are satisfied.
Final Answer: 13, 7

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