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 , 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)
C) -13
D)
View Answer
D)
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