TS Polycet (Polytechnic) 2022 Previous Question Paper with Answers And Model Papers With Complete Analysis

6) The pair of equations 3x+4y=k and 9x+12y=6 has infinitely many solutions if k=

A) 3
B) 2
C) 6
D) 5

View Answer
B) 2

Explanation:Pair of equations has infinitely many solutions if they are multiples of each other.
Equations: 3x + 4y = k and 9x + 12y = 6
Multiply first equation by 3: 9x + 12y = 3k
To match second equation: 3k = 6 → k = 2

7) The base of common logarithm is

A) 2
B) 5
C) 10
D) 1

View Answer
C) 10

Explanation:The base of the common logarithm is always 10

8) The pair of equations \frac32x+\frac53y=7, 9x-10y=12, represents the following

A) Parallel lines
B) No solution
C) Infinitely many solutions
D) One solution

View Answer
D) One solution

Explanation:(3/2)x + (5/3)y = 7 and 9x − 10y = 12

9) If the given lines 2x+ky-1 and 3x-5y=7 are parallel, then the value of k is

A) -7
B) \frac{10}3
C) -13
D) -\frac{10}3

View Answer
D) -\frac{10}3

Explanation:Two lines are parallel if their slopes are equal.
Convert both to slope-intercept form:
First line: 2x + ky = 1 → ky = −2x + 1 → slope = −2/k
Second line: 3x − 5y = 7 → −5y = −3x + 7 → slope = 3/5
Now equate: −2/k = 3/5 → cross-multiply: −10 = 3k → k = −10/3

10) The zero’s of a quadratic polynomial 4y2+8y are

A) 0,4
C) 0,8
B) 0,2
D) 0,-2

View Answer
D) 0,-2

Explanation:4y² + 8y = 4y(y + 2) → Zeroes: y = 0 and y = −2

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