Chapter 3 Pair of Linear Equations in Two Variables Bits for 10th Class AP Board
Multiple Choice Questions (MCQs) :
Question 1.
The value of m for which the linear equations mx – y = 2 and 6x – 2y = 3 has a unique solution, is ……………. .
A) ≠3
B) 12
C) 3
D) ≠12
Answer:
A) ≠3
Question 2.
The value of k for which the linear equations 3x + 5y = 0 and kx + 10y = 0 has a non-zero solution is ……………… .
A) 8
B) 6
C) 4
D) 2
Answer:
B) 6
Question 3.
The value of ‘a’ for which the system equations 2x + 3y = 5 and 4x + ay = 10 has infinite number of solutions is ……………… .
A) 4
B) 5
C) 6
D) 7
Answer:
C) 6
Question 4.
If 3x + y = 1 and (2m – 1)x + (m – 1)y = 2m + 1 are inconsistent then m = ……………… .
A) 1
B) 2
C) 3
D) 0
Answer:
B) 2
Question 5.
3x + y = 1 and (2p – 1)x + (p – l)y = 2p + 1 are inconsistent then p = ……………….. .
A) 1
B) 2
C) 3
D) 0
Answer:
B) 2
Question 6.
If the 2x + 3y = 5, 4x + ay = 10 has infinitely many solutions then a = ……………….. .
A) 2
B) 6
C) 4
D) 8
Answer:
B) 6
Question 7.
If a1b2 ≠ b1a2 then the linear equations
a1x + b1y = c1 and a2x + b2y = c2 has ………………. .
A) No solution
B) Infinitely many solutions
C) A unique solution
D) None of these
Answer:
C) A unique solution
Question 8.
If a pair of linear equations in two variables is consistent then the lines represented by two equations are ………………….. .
A) parallel
B) coincident and intersecting
C) intersecting
D) coincident
Answer:
B) coincident and intersecting
Question 9.
Angle between the lines x = 1 and y – 2 is ………………. .
A) 45°
B) 30°
C) 70 °
D) 90°
Answer:
D) 90°
Question 10.
If two lines are intersecting at one point, then the number of solutions is ………………. .
A) 1
B) 2
C) 3
D) 6
Answer:
A) 1
Question 11.
The condition that two lines are coincident is ……………… .
A) \(\frac{a_1}{a_2}=\frac{b_1}{b_2} \neq \frac{c_1}{c_2}\)
B) \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\)
C) \(\frac{a_1}{a_2} \neq \frac{b_1}{b_2} \neq \frac{c_1}{c_2}\)
D) None
Answer:
B) \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\)
Question 12.
If two lines will intersect at 60°, then the two lines are ……………… lines.
A) Intersecting
B) Coincident
C) Parallel
D) None
Answer:
A) Intersecting
Question 13.
If the equations kx – 5y = 2, 6x + 2y = 7 has no solution, then k = ………………. .
A) -15
B) 10
C) -10
D) 3
Answer:
A) -15
Question 14.
If the pair of equations 3x + 5y – 3 and 6x + ky = 8 has no solution in common then k = ……………… .
A) 16
B) 8
C) 10
D) 9
Answer:
C) 10
Question 15.
Solution to x + y = 0 and y – x = 0 is …………. .
A) (1,1)
B) (1,-1)
C) (0, 0)
D) (8, 4)
Answer:
C) (0, 0)
Question 16.
The pair of equations x = 3 and y = 4 graphically represents lines which are ……………. .
A) Intersecting at (3, 4)
B) Parallel
C) Coincident
D) None
Answer:
A) Intersecting at (3, 4)
Question 17.
Solve x + 2y – 3 = 0; 3x – 2y + 7 = 0.
A) (-1,2)
B) (2, -1)
C) (1, 5)
D) (3, 2)
Answer:
A) (-1,2)
Question 18.
Frame the two linear equations “5 pencils and 7 pens together cost ₹ 50, whereas 7 pencils and 5 pens together cost ₹ 43.
A) 7x + 5y = 50
5x + 3y = 43
B) 5x + 7y = 50
7x + 5y = 43
C) 7x + 9y = 50
3x + 5y = 43
D) 8x – 5y = 50
7x – 15y = 43
Answer:
B) 5x + 7y = 50
7x + 5y = 43
Question 19.
The angle between the lines x + 2y + 7 = 0 and 3x + 6y + 1 = 0 is ……………… .
A) 0°
B) 30°
C) 40°
D) 30°
Answer:
A) 0°
Question 20.
The value of k if the system of equations kx + 3y + (3-k) = 0 and 12x + ky – k = 0 has infinitely many solutions.
A) 7
B) 6
C) 8
D) 9
Answer:
B) 6
Question 21.
The pair of equations x = 0 and x = 5 has
A) no solution
B) two solutions
C) infinitely many solutions
D) one solutior
Answer:
B) two solutions
Question 22.
For what value of m, do the equations 2x – 3y + 10 = 0 and 3x + my = -15 represent coincident lines ?
Answer:
A) -11
B) -7
C) \(\frac{9}{2}\)
D) \(\frac{-9}{2}\)
Answer:
D) \(\frac{-9}{2}\)
Question 23.
If two railway tracks are defined by the parallel lines 2x + ky = 1 and 3x + 5y = 7 are parallel, then k = …………….. …….. .
A) \(\frac{-1}{2}\)
B) \(\frac{1}{3}\)
C) \(\frac{3}{10}\)
D) \(\frac{10}{3}\)
Answer:
D) \(\frac{10}{3}\)