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Maths Assertion (A) & Reason (B) MCQ

Linear Equations in Two Variables · CBSE STD 10 (CBSE - English Medium). 8 questions.

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Assertion (A) & Reason (B) MCQ

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8 questions · timed · auto-graded

MCQ 11 Mark
Statement-1 (A) : The area of the trapezium formed by the lines $3 x+4 y-12=0$ and $3 x+4 y=6$ is $\frac{9}{2}$ square units.
Statement-2 (R): The system of equations $a_1 x+b_1 y+c_1=0$ and $a_2 x+b_2 y+c_2=0$ is inconsistent, if $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$.
  • A
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is True, Statement-2 is False.
  • D
    Statement-1 is False, Statement-2 is True.
Answer
(C)Statement-1 is True, Statement-2 is False.
Image
Graphs of the given lines are shown in Fig.
Area of trapezium $A C D B=$ Area of $\triangle O A B-$ Area of $\triangle O C D$
$\begin{array}{l}
=\frac{1}{2}(O A \times O B)-\frac{1}{2}(O C \times O D) \\
=\frac{1}{2}(4 \times 3)-\frac{1}{2}\left(2 \times \frac{3}{2}\right)=4.5 \text { sq. units }
\end{array}$
So, Statement- 1 is true.
Clearly, statement-2 is false. Hence, option (c) is correct.


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MCQ 21 Mark
Statement-1 (A): The system of equations $2 x+y+9=0$ and $x+3 y+7=0$ is consistent having unique solution.
Statement-2 (R): The system of equations $a x+b y+c=0$ and $p x+q y+r=0$ is always consistent with unique solution, if $a q \neq b p$.
  • ✓
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is True, Statement-2 is False.
  • D
    Statement-1 is False, Statement-2 is True.
Answer
Correct option: A.
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
(A)Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
The system of equations $a x+b y+c=0$ and $p x+q y+r=0$ is consistent, if $\frac{a}{p} \neq \frac{b}{q}$ i.e. $a q \neq b p$. So, statement- 2 is true.
For the system of equations $2 x+y+9=0$ and $x+3 y+7=0$, we find that $\frac{2}{1} \neq \frac{1}{3}$. So, it is a consistent system with unique solution. So, statement- 1 is also true and statement- 2 is a correct explanation for statement-1. Hence, option (a) is correct.
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MCQ 31 Mark
Statement-1 (A): The system of linear equations $2 x+3 y=7$ and $k x+\frac{9}{2} y=12$ have no solution, if $k=3$.
Statement -2(R) : The system of linear equations $a_1 x+b_1 y+c_1=0$ and $a_2 x+b_2 y+c_2=0$ have no solution, if $\frac{a_1}{a_2}=\frac{b_1}{b_2}$.
  • A
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
  • ✓
    Statement-1 is True, Statement-2 is False.
  • D
    Statement-1 is False, Statement-2 is True.
Answer
Correct option: C.
Statement-1 is True, Statement-2 is False.
(C)Statement-1 is True, Statement-2 is False.
The system of linear equations in statement-2 have no solution, if $\frac{a_1}{a_2}=\frac{b_1}{b_2} \neq \frac{c_1}{c_2}$. So, statement- 2 is false. The system of linear equations in statement- 1 will have no solution, if $\frac{k}{2}=\frac{9 / 2}{3} \neq \frac{12}{7}$ or, $\frac{k}{2}=\frac{3}{2} \neq \frac{12}{7}$ or, $k=3$.
So, the statement-1 is true. Hence, option (c) is correct.
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MCQ 41 Mark
Statement-1 $(A)$ : The system of linear equations $9 x+3 y+12=0$ and $18 x+6 y+24=0$ have infinitely many solutions.
Statement-2 $(R)$ : The system of linear equations $a_1 x+b_1 y+c_1=0$ and $a_2 x+b_2 y+c_2=0$ have infinitely many solutions, if $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$.
  • ✓
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is True, Statement-2 is False.
  • D
    Statement-1 is False, Statement-2 is True.
Answer
Correct option: A.
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
(A) Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
The statement-2 is true (see Theory). For the system of equations given in statement-1, we find that $\frac{9}{18}=\frac{3}{6}=\frac{12}{24}$ i.e. $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$. So, the system of equations in statement- 1 has infinitely many solutions. Thus statement- $1^2$ is also true. Also, statement-2 is a correct explanation for statement-1. Hence, option (a) is correct.
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MCQ 51 Mark
Statement-1 (A): If the system of equations $3 x+6 y=10$ and $2 x-k y+5=0$ is inconsistent, then $k=-4$.
Statement-2 $(R)$ : The system of equations $a_1 x+b_1 y+c_1=0$ and $a_2 x+b_2 y+c_2=0$ is inconsistent iff $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$.
  • A
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement- 2 is not a correct explanation for Statement-1.
  • ✓
    Statement-1 is true, Statement-2 is false.
  • D
    Statement-1 is false, Statement-2 is true.
Answer
Correct option: C.
Statement-1 is true, Statement-2 is false.
C
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MCQ 61 Mark
Statement-1 (A) If a pair of linear equations represent coincident lines, then the equations are consistent and have a unique solution.
Statement-2 (R) A pair of linear equations $a_1 x+b_1 y+c_1=0$ and $a_2 x+b_2 y+c_2=0$ represents coincident lines iff $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$.
  • A
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement- 2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • ✓
    Statement-1 is false, Statement-2 is true.
Answer
Correct option: D.
Statement-1 is false, Statement-2 is true.
D
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MCQ 71 Mark
Statement-1 (A): The area of the rectangle formed by the lines representing $x=8, y=6$ with the coordinate axes is 24 sq. units.
Statement-2 (R): The system of equations $x=8, y=6$ is consistent with a unique solution.
  • A
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement- 2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • ✓
    Statement-1 is false, Statement-2 is true.
Answer
Correct option: D.
Statement-1 is false, Statement-2 is true.
D
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MCQ 81 Mark
Statement-1 (A): The system of linear equations $3 x+5 y-4=0$ and $15 x+25 y-25=0$ is inconsistent.
Statement-2 (R): The pair of linear equations $a_1 x+b_1 y+c_1=0$ and $a_2 x+b_2 y+c_2=0$ represents parallel lines, if $\frac{a_1}{a_2}=\frac{b_1}{b_2} \neq \frac{c_1}{c_2}$.
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement- 2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • D
    Statement-1 is false, Statement-2 is true.
Answer
Correct option: A.
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
A
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Assertion (A) & Reason (B) MCQ - Maths STD 10 Questions - Vidyadip