CBSE Class 10 Pair of Linear Equations in Two Variables Sure Shot Questions Set 11

Question. The line \( x = h \) and \( y = k \), where \( h \neq 0 \) and \( k \neq 0 \), are
(a) parallel
(b) intersecting
(c) overlapping
(d) None of the options
Answer: (b) intersecting

Question. The pair of equations \( x = 0 \) and \( x = 4 \) has
(a) no solution
(b) one solution
(c) two solutions
(d) infinitely many solutions
Answer: (a) no solution

Question. If the system of equations \( 2x + ky = 8 \) and \( x + y = 6 \) has no solution, then the value of \( k \) is
(a) 2
(b) \( -\frac{3}{2} \)
(c) -2
(d) \( \frac{3}{2} \)
Answer: (a) 2

Question. One equation of a pair of dependent linear equation is \( 3x + 5y = 4 \). Then, second equation can be
(a) \( 15x + 25y = 15 \)
(b) \( 15x + 25y = 20 \)
(c) \( -15x - 25y = 20 \)
(d) \( 15x - 25y = 20 \)
Answer: (b) \( 15x + 25y = 20 \)

Question. If the lines given by \( 2x + ky = 1 \) and \( 3x - 5y = 7 \) has unique solution, then the value of \( k \) is
(a) all real values of \( k \)
(b) all real values of \( k \) except \( k = -\frac{10}{3} \)
(c) all real value of \( k \) except \( k = \frac{10}{3} \)
(d) None of the options
Answer: (b) all real values of \( k \) except \( k = -\frac{10}{3} \)

Question. If the system of equations \( (k + 2)x + 21y - 3k = 0 \) and \( 4x + 7y - 10 = 0 \) has infinitely many solutions, then value of \( k \) is
(a) 11
(b) 10
(c) 12
(d) -12
Answer: (b) 10

Question. The pair of linear equations \( 2x + 3y = 5 \) and \( 4x + 6y = 10 \) is
(a) consistent
(b) inconsistent
(c) dependent consistent
(d) None of the options
Answer: (c) dependent consistent

Question. The nature of the lines representing the linear equations \( 2x - y = 3 \) and \( 4x - y = 5 \) is
(a) intersecting
(b) parallel
(c) coincident
(d) None of the options
Answer: (a) intersecting

Question. The solution of the pair of equations \( 2x - y + 3 = 0 \) and \( 3x - 5y + 1 = 0 \) is
(a) \( x = 1 \) and \( y = 2 \)
(b) \( x = -2 \) and \( y = 1 \)
(c) \( x = -2 \) and \( y = -1 \)
(d) \( x = 2 \) and \( y = -1 \)
Answer: (c) \( x = -2 \) and \( y = -1 \)

Question. The solution of the system of equations \( \frac{x}{a} + \frac{y}{b} = 2 \) and \( ax - by = a^2 - b^2 \) is
(a) \( a \) and \( b \)
(b) \( b \) and \( a \)
(c) \( -a \) and \( -b \)
(d) \( -b \) and \( -a \)
Answer: (a) \( a \) and \( b \)

Question. The area of figure formed by the lines \( x = -3 \) and \( y = 2 \) and along with coordinate axes is
(a) 5 sq units
(b) 6 sq units
(c) 3 sq units
(d) None of the options
Answer: (b) 6 sq units

Question. The cost of 6 chairs and 4 tables be ₹ 8050 and the cost of 4 chairs and 2 tables be ₹ 4800. The cost of each chair and table will be
(a) ₹ 700 and ₹ 890
(b) ₹ 775 and ₹ 850
(c) ₹ 720 and ₹ 870
(d) None of the options
Answer: (b) ₹ 775 and ₹ 850

Question. Suppose the sum of age of mother and twice daughter is 61 yr and their difference of ages is 40 yr. The ages of mother and daughter are
(a) 35 yr and 8 yr
(b) 40 yr and 5 yr
(c) 47 yr and 7 yr
(d) None of the options
Answer: (c) 47 yr and 7 yr