MCQ 11 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : The slope of the line which lies in the second and fourth quadrant is negative.
Reason : The slope of the line $y= -x + 6$ is $-1$
- ✓
both assertion and reason are correct and reason is correct explanation for assertion
- B
both assertion and reason are correct but reason is correct explanation for assertion
- C
assertion is correct but reason is false
- D
both assertion and reason are false
AnswerCorrect option: A. both assertion and reason are correct and reason is correct explanation for assertion
View full question & answer→MCQ 21 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $(A)$ The value of $k$ for which the system of equations $k x-y=2,6 x-2 y=3$ has a unique solution is $3$ .
Reason: $(R)$ The system of linear equations $a_1 x+b_1 y+c_1=0$ and $a_2 x+b_2 y+c_2=0$ has a unique solutions, if $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$.
- A
$A$ is true, $R$ is true; $R$ is acorrect explanation for $A$.
- B
$A$ is true, $R$ is true; $R$ is not a correct explanation for $A$.
- C
$A$ is true; $R$ is False.
- ✓
$A$ is false; $R$ is true.
AnswerCorrect option: D. $A$ is false; $R$ is true.
$A$ is false; $R$ is true.
View full question & answer→MCQ 31 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : If a pair of linear equations is consistent, then the lines are intersecting or coincident
Reason : Because the two lines definitely have a solution.
- ✓
both assertion and reason are correct and reason is correct explanation for assertion
- B
both assertion and reason are correct but reason is correct explanation for assertion
- C
assertion is correct but reason is false
- D
both assertion and reason are false
AnswerCorrect option: A. both assertion and reason are correct and reason is correct explanation for assertion
View full question & answer→MCQ 41 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s) \ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : $3x - 4y = 7$ and $6x - 8y = k$ have infinite number of solution if $k = 14.$
Reason : $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ have a unique solution if $\frac{\text{a}_1}{\text{}a_2}\neq \frac{\text{b}_1}{\text{b}_2}$
- A
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
- ✓
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: B. Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
View full question & answer→MCQ 51 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s) \ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : $x$ and $y$ are $2$ different digits. If the sum of the two digit numbers formed by using both the digits is a perfect square, then value of $x + y$ is $11$
Reason : numbers that can be formed are $xy$ and $yx$ . Hence, $(10x + y) + (10y + x) = 11(x + y)$ if this is a perfect square that $x + y = 11$
- ✓
both assertion and reason are correct and reason is correct explanation for assertion
- B
both assertion and reason are correct but reason is correct explanation for assertion
- C
assertion is correct but reason is false
- D
both assertion and reason are false
AnswerCorrect option: A. both assertion and reason are correct and reason is correct explanation for assertion
View full question & answer→MCQ 61 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : A straight line is just a line with no curves.
Reason : a line that extends to both sides till infinity and has no curves is called a straight line.
- ✓
both assertion and reason are correct and reason is correct explanation for assertion
- B
both assertion and reason are correct but reason is correct explanation for assertion
- C
assertion is correct but reason is false
- D
both assertion and reason are false
AnswerCorrect option: A. both assertion and reason are correct and reason is correct explanation for assertion
View full question & answer→MCQ 71 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s) \ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : The graph of the linear equations $3 x+2 y=12$ and $5 x-2 y=4$ givesa pair of intersecting lines.
Reason : The graph of linear equations $a_1 x+b_1 y+c_1=0$ and $a_2 x+b_2 y+c_2=0$ givesa $b$ pair of intersecting lines if $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$
- ✓
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true
AnswerCorrect option: A. Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
We know that the system of near equations $a_1 x+b_1 y+c_1=0$ and $a_2 x+b_2 y+c_2=0$ has a unique solution if $\frac{ a _1}{b_2} \neq \frac{ b _1}{b_2}$ and gives a pair of intersecting lines.
So, Reason is correct
For Assertion, we shave, $a _1=3, b_1=2, a _2=5$ and $b _2=-2$
Now, $\frac{a_1}{b_2}=\frac{3}{5}$ and $\frac{b_1}{b_2}=\frac{2}{-2}=-1$
$ \Rightarrow \frac{a_1}{b_2} \neq \frac{b_1}{b_2}$
So, the 'pair of linear equations has unique solution and gives a pair of intersecting lines.
Hence Assertion is also correct based of Reason given.
View full question & answer→MCQ 81 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : The two lines intersect each other in a single point
Reason : The two lines are not intersecting that means these lines are parallel to each other
- ✓
both assertion and reason are correct and reason is correct explanation for assertion
- B
both assertion and reason are correct but reason is correct explanation for assertion
- C
assertion is correct but reason is false
- D
both assertion and reason are false
AnswerCorrect option: A. both assertion and reason are correct and reason is correct explanation for assertion
View full question & answer→MCQ 91 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following :
Assertion : The graph of the linear equation $x – 5y = 1$ passes through the point $(6, 1).$
Reason : Every point lying on graph is not a solution of $x – 5y = 1.$
- A
both assertion and reason are correct and reason is correct explanation for assertion
- B
both assertion and reason are correct but reason is correct explanation for assertion
- ✓
assertion is correct but reason is false
- D
both assertion and reason are false
AnswerCorrect option: C. assertion is correct but reason is false
View full question & answer→MCQ 101 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : If $kx - y -2=0$ and $6 x -2 y -3=0$ are inconsistent, then $k =3$
Reason : $a_1 x+b_1 y+c_1+0$ and $a_2 x+b_2 y+c_2=0$ are inconsistent of $\frac{a_1}{a_2}=\frac{b_1}{b_2} \neq \frac{c_1}{c_2}$
- ✓
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: A. Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
View full question & answer→MCQ 111 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R) $ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : If the lines $3x + 2ky - 2 = 0$ and $2x + 5y + 1 = 0$ are parallel, then the value of $k$ is $\frac{15}{4}$
Reason : The condition for parallel lines is $\frac{\text{a}_1}{\text{a}_2}=\frac{\text{b}_2}{\text{c}_2}\neq\frac{\text{c}_1}{\text{c}_2}$
- ✓
both assertion and reason are correct and reason is correct explanation for assertion
- B
both assertion and reason are correct but reason is correct explanation for assertion
- C
assertion is correct but reason is false
- D
both assertion and reason are false
AnswerCorrect option: A. both assertion and reason are correct and reason is correct explanation for assertion
View full question & answer→MCQ 121 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following :
Assertion : The angles of cyclic quadrilaterals $\text{ABCD}$ are : $A = (6x + 10), B = (5x)^\circ , C = (x + y)^\circ $and $D = (3y - 10)^\circ $. The value of $x$ and $y$ is $20^\circ $ and $30^\circ $
Reason : in cyclic quadrilaterals, the sum of the opposite angles are $180^\circ .$
- ✓
both assertion and reason are correct and reason is correct explanation for assertion
- B
both assertion and reason are correct but reason is correct explanation for assertion
- C
assertion is correct but reason is false
- D
both assertion and reason are false
AnswerCorrect option: A. both assertion and reason are correct and reason is correct explanation for assertion
View full question & answer→MCQ 131 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : The value of $\text{q}=\pm2$, if $x = 3, y = 1$ is the solution of the line $2x + y - q^2- 3 = 0.$
Reason : $(R)$ The solution of the line will satisfy the equation of the line.
- ✓
$A$ is true, $R$ is true; $R$ is acorrect explanation for $A$.
- B
$A$ is true, $R$ is true; $R$ is not a correct explanation for $A$.
- C
$A$ is true; $R$ is False.
- D
$A$ is false; $R$ is true.
AnswerCorrect option: A. $A$ is true, $R$ is true; $R$ is acorrect explanation for $A$.
$A$ is true, $R$ is true; $R$ is acorrect explanation for $A$.
View full question & answer→MCQ 141 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The lines $2 x-5 y=7$ and $6 x-15 y=8$ are parallel lines.
Reason: 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 $\frac{a_1}{b_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
- A
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
- ✓
Both assertion $(A)$ and reason $(R)$ are true but reason $(R$) is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: B. Both assertion $(A)$ and reason $(R)$ are true but reason $(R$) is not the correct explanation of assertion $(A)$.
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
View full question & answer→MCQ 151 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s) \ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : The pair of equations $x + 2y + 5 = 0$ and $–3x – 6y + 1 = 0$ have unique solution
Reason : an equations $\frac{\text{a}_1}{\text{a}_2}=\frac{\text{b}_1}{\text{b}_2}=\frac{\text{c}_1}{\text{c}_2}$ Hence, the given pair of equations have no solution
- A
both assertion and reason are correct and reason is correct explanation for assertion
- B
both assertion and reason are correct but reason is correct explanation for assertion
- C
assertion is correct but reason is false
- ✓
both assertion and reason are false
AnswerCorrect option: D. both assertion and reason are false
View full question & answer→MCQ 161 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s) \ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following :
Assertion : $(A)$ A two $-$ digit number is obtained by either multiplying sum of the digits by $8$ and adding $1$ or by multiplying the difference of digits by $13$ and adding $2.$ The number is $41.$
Reason : $(R)$ The linear equations used are $7x - 2y +1 = 0$ and $12x - 23y + 2 = 0$.
- A
$A$ is true, $R$ is true; $R$ is acorrect explanation for $A$.
- B
$A $ is true, $R$ is true; $R$ is not a correct explanation for $A$.
- ✓
$A$ is true; $R$ is False.
- D
$A$ is false; $R$ is true.
AnswerCorrect option: C. $A$ is true; $R$ is False.
View full question & answer→MCQ 171 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : $(A)$ Pair of linear equations: $9 x+3 y+12=0,18 x+6 y+24=0$ have infinitely many solutions.
Reason : $(R)$ Pair 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 $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
- ✓
$A$ is true, $R$ is true; $R$ is acorrect explanation for $A$.
- B
$A$ is true, $R$ is true; $R$ is not a correct explanation for $A$.
- C
$A$ is true; $R$ is False.
- D
$A$ is false; $R$ is true.
AnswerCorrect option: A. $A$ is true, $R$ is true; $R$ is acorrect explanation for $A$.
$A$ is true, $R$ is true; $R$ is acorrect explanation for $A$.
View full question & answer→MCQ 181 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : $3 x+4 y+5=0$ and $6 x+k y+9=0$ represent parallel lines if $k=8$.
Reason : $a_1 x+b_1 y+c_1=0$ and $a_2 x+b_2 y+c_2=0$ represent parallel lines ines if $\frac{a_1}{a_2}=\frac{b_1}{b_2} \neq \frac{c_1}{c_2}$
- ✓
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true
AnswerCorrect option: A. Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
In Assertion, given lines represent parallel lines if
$=\frac{3}{6}=\frac{4}{\text{k}}\neq\frac{5}{9}$
$=\text{k}=\frac{6\times4}{3}=8$
eason is also true Also, reason is the correct explanation for assertion.
View full question & answer→MCQ 191 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : If the lines intersect at a point, then that point gives the unique solution of the two equations. In this case, the pair of equations is consistent
Reason: pair of linear equation is given by $a_1 x+b_1 y+c_1=0$ and $a_2 x+b_2 y+c_2=0 \frac{a_1}{a_2}=\frac{b_1}{b_2} \neq \frac{c_1}{c_2}$ In this case,the pair of linear equations is consistent
- A
both assertion and reason are correct and reason is correct explanation for assertion
- B
both assertion and reason are correct but reason is correct explanation for assertion
- ✓
assertion is correct but reason is false
- D
both assertion and reason are false
AnswerCorrect option: C. assertion is correct but reason is false
assertion is correct but reason is false
View full question & answer→MCQ 201 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : lines are $x + 2y - 4 = 0$ and $2x + 4y - 12 = 0$ the graphical representation of line is parallel line.
Reason : if pair of given lines are parallel then $\frac{\text{a}_1}{\text{a}_2}=\frac{\text{b}_1}{\text{b}_2}\neq\frac{\text{c}_1}{\text{c}_2}$
- ✓
both assertion and reason are correct and reason is correct explanation for assertion
- B
both assertion and reason are correct but reason is correct explanation for assertion
- C
assertion is correct but reason is false
- D
both assertion and reason are false
AnswerCorrect option: A. both assertion and reason are correct and reason is correct explanation for assertion
View full question & answer→MCQ 211 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The value of $k$ for which the system of equations $3 x + ky =0,2 x - y =0$ has a unique solution is $k \neq-\frac{3}{2}$.
Reason: The system of linear equations $a_1 x+b_1 y+c_1=0$ and $a_2 x+b_2 y+c_2=0$ has a unique solution if $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$
- A
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- ✓
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true
AnswerCorrect option: C. Assertion $(A)$ is true but reason $(R)$ is false.
Assertion $(A)$ is true but reason $(R)$ is false.
We know that the system of linear equations $a_1 x+b_1 y+c_1=0$ and $a_2 x+b_2 y+c_2=0$ hasinfinitely many solutions if $\frac{ a _1}{ a _2}=\frac{ b _1}{b_2}=\frac{ c _1}{ c _2} \cdot$
So, Reason is not correct
For Assertion, we have, $a_1=3, b_1=-4, c_1=-7, a_2=6, b_2=-8$ and $c_2=-k$
Now, $\frac{ a _1}{ a _2}=\frac{3}{6}=\frac{1}{2}, \frac{b_1}{b_2}=\frac{-4}{-8}=\frac{1}{2}$, and $\frac{ c _1}{ c _2}=\frac{-7}{- k }$
$\Rightarrow \frac{-7}{-k}=\frac{1}{2} $
$\Rightarrow k=14$
So, Assertion is correct.
View full question & answer→MCQ 221 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s) \ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : The linear equations $x - 2y - 3 = 0$ and $3x+ 4y - 20 = 0$ have exactly one solution.
Reason : The linear equations $2x+ 3y 9 = 0$ and $4x + 6y - 18 = 0$ have a unique solution.
- A
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- ✓
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true
AnswerCorrect option: C. Assertion $(A)$ is true but reason $(R)$ is false.
View full question & answer→MCQ 231 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following :
Assertion : lf the pair of lines are coincident, then we say that pair of linesis consistent and it has a unique solution.
Reason : If the pair of lines are parallel, then the pair has no solution and is called inconsistent pair of equations.
- A
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- ✓
Assertion $(A)$ is false but reason $(R)$ is true
AnswerCorrect option: D. Assertion $(A)$ is false but reason $(R)$ is true
We know that if the lines are coincident, then it has infinite number of solutions
So, Assertion Reason is false We know that if the lines are parallel, then it has no solution.
So, reason is true.
View full question & answer→MCQ 241 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : The slope of the line $2x - y = 0$ is $2$
Reason : The slope of the line which lies in first and third quadrant is positive
- ✓
both assertion and reason are correct and reason is correct explanation for assertion
- B
both assertion and reason are correct but reason is correct explanation for assertion
- C
assertion is correct but reason is false
- D
both assertion and reason are false
AnswerCorrect option: A. both assertion and reason are correct and reason is correct explanation for assertion
View full question & answer→MCQ 251 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R) $ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : $(A) 4x + 3y = 18$ is a line which is parallel to $X -$ axis.
Reason : $(R)$ The graph of linear equation $ax = b,$ where $a \# 0$ is parallel to $Y -$ axis.
- A
$A$ is true, $R$ is true; $R$ is acorrect explanation for $A.$
- B
$A$ is true, $R$ is true; $R$ is not a correct explanation for $A$.
- C
$A$ is true; $R$ is False.
- ✓
$A$ is false; $R$ is true.
AnswerCorrect option: D. $A$ is false; $R$ is true.
View full question & answer→MCQ 261 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : The pairs of equations $x + 2y - 5 = 0$ and $-4x - 8y + 20 = 0$ have infinitely many solution.
Reason : if $\frac{\text{a}_1}{\text{a}_2}=\frac{\text{b}_1}{\text{b}_2}=\frac{\text{c}_1}{\text{c}_2}$ then the pair of equations has infinitely many solutions.
- ✓
both assertion and reason are correct and reason is correct explanation for assertion
- B
both assertion and reason are correct but reason is correct explanation for assertion
- C
assertion is correct but reason is false
- D
both assertion and reason are false
AnswerCorrect option: A. both assertion and reason are correct and reason is correct explanation for assertion
View full question & answer→MCQ 271 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : $(A)$ When $k=-4$, then linear equations $x+(k+1)=5,(k+1) x+9 y=8 k-1$ have infinitely many solutions.
Reason : $(R) a_1 x+b_1 y=c_1$ and $a_2 x+b_2 y=c_2$ have infinitely many solutions, if $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$.
- A
$A$ is true, $R$ is true; $R$ is acorrect explanation for $A$.
- B
$A$ is true, $R$ is true; $R$ is not a correct explanation for $A$.
- C
$A$ is true; $R$ is False.
- ✓
$A$ is false; $R$ is true.
AnswerCorrect option: D. $A$ is false; $R$ is true.
$A$ is false; $R$ is true.
View full question & answer→MCQ 281 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s) \ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : Homogeneous system of linear equations is always consistent.
Reason : $x = 0, y = 0 x = 0, y = 0$ is always a solution of the homogeneous system of equations with unknowns $x$ and $y ,$ then which of the following statements is true
- ✓
both assertion and reason are correct and reason is correct explanation for assertion
- B
both assertion and reason are correct but reason is correct explanation for assertion
- C
assertion is correct but reason is false
- D
both assertion and reason are false
AnswerCorrect option: A. both assertion and reason are correct and reason is correct explanation for assertion
View full question & answer→MCQ 291 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s) \ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : The given pair of linear equations are inconsistent $-3x - 4y - 12 = 0$ and $3x + 4y - 12 = 0$
Reason : if $\frac{\text{a}_1}{\text{b}_2}=\frac{\text{b}_1}{\text{b}_2}\neq\frac{\text{c}_1}{\text{c}_2}$ the the pair of linear equation is inconsistant
- ✓
both assertion and reason are correct and reason is correct explanation for assertion
- B
both assertion and reason are correct but reason is correct explanation for assertion
- C
assertion is correct but reason is false
- D
both assertion and reason are false
AnswerCorrect option: A. both assertion and reason are correct and reason is correct explanation for assertion
View full question & answer→MCQ 301 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s) \ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : The value of $\text{q}=\pm2$, if $x = 3, y=1$ is the solution of the line $2x + y - q^2 - 3 = 0.$
Reason : The solution of the line will satisfy the equation of the line.
- ✓
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: A. Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
As $ x = 3, y = 1$ is the solution of $2x + y - q^2- 3 = 0$
$\therefore2\times3+1-\text{q}^2-3=0$
$\Rightarrow4-\text{q}^2=0$
$\Rightarrow\text{q}^2=4 $
$\Rightarrow\text{q}=\pm2$
So, both $A$ and $R$ are correct and Rexplains $A$.
View full question & answer→MCQ 311 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : If the lines given by $3x + 2ky = 2$ and $2x + 5y + 1 = 0$ are parallel, then the value of $k$ is $\frac{15}{4}$
Reason : For parallel lines $\frac{\text{a}_1}{\text{a}_2}=\frac{\text{b}_1}{\text{b}_2}\neq\frac{\text{c}_1}{\text{c}_2} =\frac{3}{2}=\frac{2\text{k}}{5} =\text{k}=\frac{15}{4}$
- ✓
both assertion and reason are correct and reason is correct explanation for assertion
- B
both assertion and reason are correct but reason is correct explanation for assertion
- C
assertion is correct but reason is false
- D
both assertion and reason are false
AnswerCorrect option: A. both assertion and reason are correct and reason is correct explanation for assertion
View full question & answer→MCQ 321 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s) \ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : A pair of linear equations has no solution $(s)$ if it is represented by intersecting lines graphically.
Reason : If the pair of lines are intersecting, then the pair has unique solution and is called consistent pair of equations.
- A
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ isnot the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- ✓
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: D. Assertion $(A)$ is false but reason $(R)$ is true.
We know that if the lines are parallel, then it has no solution.
So, Assertion is false. We know that if the lines are intersecting, then it has unique solution.
So, Reason is true.
View full question & answer→MCQ 331 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s) \ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : The pairs of equations $9x + 3y + 12 = 0$ and $18x + 6y + 26 = 0$ have no solution.
Reason : $\frac{\text{a}_1}{\text{a}_2}=\frac{\text{a}_1}{\text{a}_2}\neq\frac{\text{c}_1}{\text{c}_2}$ So, the pairs of equations are parallel and the lines never intersect each other at any point, therefore there is no possible solution.
- ✓
both assertion and reason are correct and reason is correct explanation for assertion
- B
both assertion and reason are correct but reason is correct explanation for assertion
- C
assertion is correct but reason is false
- D
both assertion and reason are false
AnswerCorrect option: A. both assertion and reason are correct and reason is correct explanation for assertion
View full question & answer→MCQ 341 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : The two linear equations in the same two variables $X$ and $Y$ are called pair of linear equation in two variable
Reason : The equation of the form $ax + by + c= 0$ where a and b both are not zero is called linear equation in two variable
- A
both assertion and reason are correct and reason is correct explanation for assertion
- ✓
both assertion and reason are correct but reason is correct explanation for assertion
- C
assertion is correct but reason is false
- D
both assertion and reason are false
AnswerCorrect option: B. both assertion and reason are correct but reason is correct explanation for assertion
View full question & answer→MCQ 351 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : The linear equations $x - 2y - 3 = 0$ and $3x + 4y - 20 = 0$ have exactly one solution.
Reason : The linear equations $2x + 3y - 9 = 0$ and $4x + 6y - 18 = 0$ have a unique solution.
- A
both assertion and reason are correct and reason is correct explanation for assertion
- B
both assertion and reason are correct but reason is correct explanation for assertion
- ✓
assertion is correct but reason is false
- D
both assertion and reason are false
AnswerCorrect option: C. assertion is correct but reason is false
View full question & answer→MCQ 361 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following :
Assertion : $(A)$ The graphical represen tation of $2x + y = 6$ and $2x - y + 2 = 0$ will be a pair of parallel lines.
Reason : $(R)$ When $k = -1,$ then linear equations $5x + ky = 4$ and $15x + 3y = 12$ have infinitely many solutions.
- A
$A$ is true, $R$ is true; $R$ is acorrect explanation for $A$.
- B
$A$ is true, $R$ is true; $R$ is not a correct explanation for $A$.
- C
$A$ is true; $R$ is False.
- ✓
$A$ is false; $R$ is true.
AnswerCorrect option: D. $A$ is false; $R$ is true.
View full question & answer→MCQ 371 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s) \ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : The point $(0, 4)$ lies on the graph of the linear equation $4x + 4y = 16$
Reason : $(0, 4)$ satisfies the equation $4x + 4y = 16.$
- ✓
both assertion and reason are correct and reason is correct explanation for assertion
- B
both assertion and reason are correct but reason is correct explanation for assertion
- C
assertion is correct but reason is false
- D
both assertion and reason are false
AnswerCorrect option: A. both assertion and reason are correct and reason is correct explanation for assertion
View full question & answer→MCQ 381 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : If the pair of lines are coincident, then we say that pair of lines is consistent and it has a unique solution.
Reason : If the pair of lines are parallel, then the pair has no solution and is called inconsistent pair of equations.
- A
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- ✓
Assertion $(A)$ is false but reason $(R)$ is true
AnswerCorrect option: D. Assertion $(A)$ is false but reason $(R)$ is true
$[$If the lines are coincident, then it has infinite number of solutions$]$ Reason is clearly true.
View full question & answer→MCQ 391 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : The pair of equations $5x – 15y = 8$ and $3x – 9y = \frac{24}{5}$ has infinitely many solution.
Reason : $\frac{\text{a}_1}{\text{a}_2}=\frac{\text{b}_1}{\text{b}_2}\neq\frac{\text{c}_1}{\text{c}_2}$ it satisfy the condition of infinitely many solution.
- A
both assertion and reason are correct and reason is correct explanation for assertion
- B
both assertion and reason are correct but reason is correct explanation for assertion
- ✓
assertion is correct but reason is false
- D
both assertion and reason are false
AnswerCorrect option: C. assertion is correct but reason is false
View full question & answer→MCQ 401 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : $ (A) x+y-4=0$ and $2 x+k y-3=0$ has no solution if $k=2$.
Reason $(R) a_1 x+b_1 y+c_1=0$ and $a_2 x+b_2 y+c_2=0$ are consistent, if $\frac{ a _1}{ a _2} \neq \frac{ k _1}{ k _2}$.
- A
$A$ is true, $R$ is true; $R$ is acorrect explanation for $A$.
- ✓
$A$ is true, $R$ is true; $R$ is not a correct explanation for $A$.
- C
$A$ is true; $R$ is False.
- D
$A$ is false; $R$ is true.
AnswerCorrect option: B. $A$ is true, $R$ is true; $R$ is not a correct explanation for $A$.
$A$ is true, $R$ is true; $R$ is not a correct explanation for $A$.
View full question & answer→MCQ 411 Mark
Statement $A ($Assertion$) : 4 x+3 y=12$ is a line which is parallel to $8 x+6 y=48$.
Statement $R ($Reason$)$: The graph of linear equation $a x=b$, where $a \neq 0$ is parallel to $x$-axis.
- A
$(a)$ Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is not the correct explanation of assertion $(A).$
- ✓
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: C. Assertion $(A)$ is true but reason $(R)$ is false.
The given system of linear equations is
$4 x+3 y=12\ldots(i)$
$8 x+6 y=48\ldots(ii)$
As $\frac{4}{8}=\frac{3}{6} \neq \frac{12}{48}$
Hence, the given lines are parallel to each other.
Now, $a x=b $
$\Rightarrow x=\frac{b}{a}$, which represents a line parallel to $y-$axis.
So, Assertion is true but Reason is false.
View full question & answer→MCQ 421 Mark
Statement $A \ ($Assertion$)$ : The pair of linear equations $2 x-y-5=0$ and $x-y-3=0$ represent intersecting lines.
Statement $R\ ($Reason$)$ : The linear equations $2 x-y-5=0$ and $x-y-3=0$ meet the $y-$ axis at $(0,-5)$ and $(0,3)$ respectively.
- A
$(a)$ Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A).$
- B
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is not the correct explanation of assertion $(A).$
- ✓
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: C. Assertion $(A)$ is true but reason $(R)$ is false.
The given system of linear equations is
$2 x-y-5=0 \ldots(i)$
$x-y-3=0\ldots(ii)$
Now, $\frac{a_1}{a_2}=\frac{2}{1}, \frac{b_1}{b_2}$
$=\frac{-1}{-1}=1, \frac{c_1}{c_2}$
$=\frac{-5}{-3}=\frac{5}{3}$
So, given equations represent intersecting lines.
$(0,-5)$ satisfy equation $(i)$ but $(0,3)$ does not satisfy equation $(ii)$.
So, Assertion is true but Reason is false.
View full question & answer→MCQ 431 Mark
Statement A (Assertion) : The system of equations $3 x-y-5=0,6 x-2 y-k=0$ has no solution if $k=10$.
Statement $R$ (Reason) : The pair of equations $a_1 x+b_1 y+c_1=0$ and $a_2 x+b_2 y+c_2=0$ has no solution if $\frac{a_1}{a_2}=\frac{b_1}{b_2} \neq \frac{c_1}{c_2}$.
- A
(a) Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
- B
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
- C
Assertion (A) is true but reason ( $R$ ) is false.
- ✓
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: D. Assertion $(A)$ is false but reason $(R)$ is true.
(d) : Given, system of equations is $3 x-y-5=0$ and $6 x-2 y-k=0$
Here, $\frac{a_1}{a_2}=\frac{3}{6}=\frac{1}{2}, \frac{b_1}{b_2}=\frac{-1}{-2}=\frac{1}{2}$ and $\frac{c_1}{c_2}=\frac{-5}{-k}=\frac{5}{k}$
For no solution, $\frac{a_1}{a_2}=\frac{b_1}{b_2} \neq \frac{c_1}{c_2}$
$\therefore \quad \frac{1}{2}=\frac{1}{2} \neq \frac{5}{k} \Rightarrow \frac{5}{k} \neq \frac{1}{2} \Rightarrow k \neq 10$
Hence, for every value of $k$ except 10 , given system has no solution.
So, Assertion is false but Reason is true.
View full question & answer→MCQ 441 Mark
Statement $A\ ($Assertion$)$ : The system of equations are inconsistent: $2 x+4 y=10$
$3 x+6 y=12$
Statement $R\ ($Reason$) : A$ pair of linear equations which has no solution is called an inconsistent pair of linear equations.
- ✓
$(a)$ Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: A. $(a)$ Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
The given system of equations can be written as $2 x+4 y-10=0,$
$3 x+6 y-12=0$
Here, $\frac{a_1}{a_2}=\frac{2}{3}, \frac{b_1}{b_2}$
$=\frac{4}{6}=\frac{2}{3}, \frac{c_1}{c_2}$
$=\frac{-10}{-12}=\frac{5}{6}$
Clearly, $\frac{a_1}{a_2}=\frac{b_1}{b_2} \neq \frac{c_1}{c_2}$.
So, the given system of equations has no solution, i.e., it is inconsistent.
$\therefore $ So, Assertion and Reason both are true and Reason is the correct explanation of Assertion.
View full question & answer→MCQ 451 Mark
Statement A (Assertion) : The system of equations $2 x+3 y+5=0$ and $4 x+k y+7=0$ is inconsistent when $k=6$.
Statement $R$ (Reason): 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 when $\frac{a_1}{a_2}=\frac{b_1}{b_2} \neq \frac{c_1}{c_2}$.
- ✓
(a) Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
- B
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
- C
Assertion (A) is true but reason ( $R$ ) is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: A. (a) Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
(a) : For the given system to be inconsistent, we have
$\frac{2}{4}=\frac{3}{k} \neq \frac{5}{7} \Rightarrow k=6$
So, Assertion and Reason both are true and Reason is the correct explanation of Assertion.
View full question & answer→MCQ 461 Mark
Statement A (Assertion) : If the pair of equations $x+2 y+7=0,3 x+k y+21=0$ represent coincident lines, then the value of $k$ is 6 .
Statement R (Reason) : The pair of linear equations are coincident lines if they have no solution.
- A
(a) Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
- B
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
- ✓
Assertion (A) is true but reason ( $R$ ) is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: C. Assertion (A) is true but reason ( $R$ ) is false.
(c) : The given equations are
$x+2 y+7=0 \text { and } 3 x+k y+21=0 \text {. }$
The given equations will represent coincident lines if they have infinitely many solutions i.e.,
$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2} \Rightarrow \frac{1}{3}=\frac{2}{k}=\frac{7}{21} \Rightarrow k=6$
Hence, the given system of equations will represent coincident lines, if $k=6$.
So, Assertion is true but Reason is false.
View full question & answer→MCQ 471 Mark
Statement A (Assertion) : The system of equations $x+y-6=0$ and $x-y-2=0$ has a unique solution.
Statement R (Reason): The system of equations $a_1 x+b_1 y+c_1=0$ and $a_2 x+b_2 y+c_2=0$ has a unique solution when $\frac{a_1}{a_2}=\frac{b_1}{b_2}$.
- A
(a) Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
- B
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
- ✓
Assertion (A) is true but reason ( $R$ ) is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: C. Assertion (A) is true but reason ( $R$ ) is false.
(c) : The given system of equations is
$x+y-6=0$ and $x-y-2=0$
Here, $\frac{a_1}{a_2}=\frac{1}{1}=1, \frac{b_1}{b_2}=\frac{1}{-1}=-1, \frac{c_1}{c_2}=\frac{-6}{-2}=3$
Since, $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$
$\therefore \quad$ The given system of equations has a unique solution.
So, Assertion is true but Reason is false.
View full question & answer→MCQ 481 Mark
Statement A (Assertion) : The system of equations $x+2 y-5=0$ and $2 x-6 y+9=0$ has infinitely many solutions.
Statement R (Reason) : The system of equations
$a_1 x+b_1 y+c_1=0$ and $a_2 x+b_2 y+c_2=0$ has infinitely many solutions when $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$.
- A
(a) Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
- B
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
- C
Assertion (A) is true but reason ( $R$ ) is false.
- ✓
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: D. Assertion $(A)$ is false but reason $(R)$ is true.
(d): The given system of equations are $x+2 y-5=0$ and $2 x-6 y+9=0$
Here, $\frac{a_1}{a_2}=\frac{1}{2}, \frac{b_1}{b_2}=\frac{2}{-6}=\frac{-1}{3}, \frac{c_1}{c_2}=\frac{-5}{9}$
Since, $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$
$\therefore \quad$ The given system of equations has a unique solution.
So, Assertion is false but Reason is true.
View full question & answer→MCQ 491 Mark
Statement $A \ ($Assertion$)$ : $x=2, y=1$ is a solution of pair of equations $3 x-2 y=4$ and $2 x+y=5$.
Statement $R\ ($Reason$)$ : A pair of values $(x, y)$ satisfying each one of the equations in a given system of two simultaneous linear equations in $x$ and $y$ is called a solution of the system of equations.
- ✓
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: A. Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
$3 x-2 y=4 \ldots(i)$
$2 x+y=5\ldots(ii)$
Putting $x=2$ and $y=1$ in $(i),$ we get
$\text{L.H.S}. =3 \times 2-2 \times 1=4= \text{R.H.S}$.
Putting $x=2$ and $y=1$ in $(ii),$ we get
$\text{L.H.S}. =2 \times 2+1 \times 1=5= \text{R.H.S}$.
Thus, $x=2$ and $y=1$ satisfy both the equations of the given system.
So, Assertion and Reason both are true and Reason is the correct explanation of Assertion.
View full question & answer→