Question 11 Mark
By Changing one variable in to another variable in solving pair of linear equations is called method of substitution. (Creamer rule, Elimination, Substitution)
Question 21 Mark
The linear equations in two variables has infinite solutions if lines are ____________ (coincident, parallel, intersecting)
Question 31 Mark
Normally, the condition that $a$ and $b$ both equally zero can be described by ___________$\left(a^2-b^2 \neq 0, a^2+b^2 \neq 0,-a^2+b^2 \neq 0\right)$
View full question & answer→Question 41 Mark
The sum of $5$ chairs and $2$ tables is $₹ 4850$, then from it the linear equations in two variables will be __________$(5 x-2 y=4850,2 x+5 y=4850,5 x+2 y=4850)$
View full question & answer→Question 51 Mark
By which number have to multiply the equation $x+2 y=5$ into equation $(i)$ and $2 x+3 y=7$ from equation (ii) to eliminate $y ? \quad\left(\frac{-3}{3}, \frac{2}{3}, \frac{3}{2}\right)$
View full question & answer→Question 61 Mark
The sum of $1 kg$ tea and $7 kg$. sugar is $₹ 480$, then from it the linear equation in two variables will be _______________ $(x-7 y=480, x+7 y=480,7 x+y=480)$
View full question & answer→Question 71 Mark
The graph of $2 x+y=3$ and $4 x+2 y=6$ is _____________ (line, ray, line segment)
View full question & answer→Question 81 Mark
The sum of the present age of Shashin and Hitesh is 58 years. Then, the pair of linear equations in two variables is __________ $(x-y=58, x+y=58,2 x-y=58)$
View full question & answer→Question 91 Mark
In standard form the equation $\frac{x}{2}-\frac{y}{3}=1$ can be written as _________$(3 x+2 y+6=0,-3 x+2 y-6=0,3 x-2 y-6=0)$
View full question & answer→Question 101 Mark
For pair of linear equations in two variables when $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$, then we get _______ solutions. (infinite, consistent, inconsistent)
View full question & answer→Question 111 Mark
Two lines are intersecting in one point, then this type of pair is_________ (inconsistent, consistent, infinity)
Question 121 Mark
The general form of pair of linear equations in two is______ $\left(a x-b y-c=0\right.$ where $a \neq 0, b \neq 0, a^2+b^2 \neq 0 ; a x_1+b y+c=0$ where $a \neq 0, b \neq 0, a^2+b^2 \neq 0 ; a x-$ $b y+c=0$ where $a \neq 0 \quad b \neq 0, a^2+b^2=0$ )
Answer$a x+b y+c=0$, where $a \neq 0, b \neq 0$ and $a^2+b^2 \neq 0$
View full question & answer→Question 131 Mark
Shilpa went to the stationary shop and purchased $3$ pencils and $2$ pens and pays $₹ 25$, then pair of linear equations in two variables is________ $(3 x-2 y=25,3 x+2 y=-25,3 x+2 y=25)$
View full question & answer→Question 141 Mark
Point $(8,-2)$ is of ______ quadrant. (First, Third, Fourth)
View full question & answer→Question 151 Mark
If one of the solution of $8 x+5 k=18$ is $(1,0)$ then $k=$_________ $(2,-2,6)$
View full question & answer→Question 161 Mark
The present age of father and his son is $x$ years and y years respectively. After $8$ years, father's age will be $\frac{5}{2}$ times the age of his son. It is represented by______$x+8=\frac{5}{2}(y+8), x-8=\frac{5}{2}(y-8), x+8=\frac{5}{2}(y-8))$
Answer$x+8=\frac{5}{2}(y+8)$
View full question & answer→Question 171 Mark
The sum of a two digit number and the number formed by interchanging its digit is always divisible by_____ $(10,11,101)$
View full question & answer→Question 181 Mark
In a two digit number, the unit's digit is $(a-1)$ and the ten's digit is $(a+1)$ Then this number is_______ $(11 a-9,9 a+11,11 a+9)$
View full question & answer→Question 191 Mark
The present age of mother and her daughter is $x$ years and $y$ years respectively. The difference of their reciprocal is$\left(\frac{x y}{x-y}, \frac{x-y}{x y}, \frac{x+y}{x y}\right)$
View full question & answer→Question 201 Mark
$\frac{5}{x}+\frac{3}{y}=24$ and $\frac{3}{x}+\frac{5}{y}=16$ then $\frac{1}{x}+\frac{1}{y}=\ldots \ldots . .(x \neq 0, y \neq 0)(10,15,5)$
View full question & answer→Question 211 Mark
If the graph of the equation $2 x+3 y=p$ is passing through the origin then $p=\ldots \ldots \ldots . .(0,1,2)$
View full question & answer→Question 221 Mark
The sum of two numbers is $10$ and their difference is $2$ . Then the larger number is ......... $(6,8,10$ )
View full question & answer→Question 231 Mark
$\quad \frac{x}{6}=\frac{y}{6}=\frac{1}{6}$ then $x+y=\ldots \ldots \ldots . .(2,1,0)$
View full question & answer→Question 241 Mark
$\quad \frac{x}{2}=\frac{8}{y}=4$ then $x-y=\ldots \ldots \ldots . . \quad(8,2,6)$
View full question & answer→Question 251 Mark
If the solution of the equations $3 a+2 b=13$ and $a+3 b=9$ is $(3, k)$ then $k=\ldots \ldots \ldots . .(2,4,6)$
View full question & answer→Question 261 Mark
$\quad 51 x+49 y=150$ and $49 x+51 y=50$ then $x-y=$ (Without finding $x, y)(100,150,50)$
View full question & answer→Question 271 Mark
$\quad 0.4 x+0.3 y=2.5$ and $0.5 x-0.3 y=1.1$ then $x=\ldots \ldots . .(8,4,2)$
View full question & answer→Question 281 Mark
$2$ tube and $3$ value to gather cost $₹ 350$, where as $3$ tube and $2$ value together cost $₹ 500$ The cost of one tube and one value together is_______ $(170,180,190)$
View full question & answer→Question 291 Mark
If $2 x+3 y=7$ and $3 x+2 y=3$ then $x-y=$_________ (Without finding $x, y)(4,2,-4)$
View full question & answer→Question 301 Mark
If $5 x+3 y=24$ and $3 x+5 y=8$ then $x-y=$_______ (Without finding the vlues of $x, y$ )
$(12,8,4)$
View full question & answer→Question 311 Mark
If the solution of the equations $3(k-1) x+4 y=24$ and $15 x+20 y=8(k+13)$ is infinite then $k=$_______ $(2,-2,1)$
View full question & answer→Question 321 Mark
If the pair of linear equations $a_1 x+b_1 y+c_1=0$ and $a_2 x+b_2 y+c_2=0$ has unique solution then $\frac{y}{x}$=______
$\left(\frac{ a _1 b _2- a _2 b _1}{1}, \frac{ b _1 c _1- b _2 c _1}{ a _1 b _2- a _2 b _1}, \frac{ c _1 a _1- c _2 a _1}{ b _1 c _2- b _2 c _1}\right)$
Answer$\frac{c_1 a_2-c_2 a_1}{b_1 c_2-b_2 c_1}$
View full question & answer→Question 331 Mark
If the pair of linear equations $a_1 x+b_1 y+c_1=0$ and $a_2 x+b_2 y+ c _2=0$ has unique solution then $y=$_________
${\left[\frac{ c _1, a _2- c _2 a _1}{ a _1, b _2- a _2 b _1}, \frac{ b _1 c _1- b _2 c _1}{ a _1 b _2- a _2 b _2} \text {, where } a_1 b_2-a_2 b_1 \neq 0 \text {, where } a, b_2-a_2 b_1 \neq 0 \frac{ a _1 b _2- a _2 b _1}{1}\right]}$
Answer$=\frac{b_1 c_2-b_2 c_1}{a_1 b_2-a_2 b_1}, a_1 b_2-a_2 b_1 \neq 0$
View full question & answer→Question 341 Mark
If the pair of linear equations $a_1 x+b_1 y+c_1=0$ and $a_2 x+ b _2 y+ c _2=0$ has unique solution then $x=$___________
${\left[\frac{ c _1, a _2- c _2 a _1}{ a _1, b _2- a _2 b _1}, \frac{ b _1 c _1- b _2 c _1}{ a _1 b _2- a _2 b _2}, \text { where } a_1 b_2-a_2 b_1 \neq 0 \text {, where } a, b_2-a_2 b_1 \neq 0 \frac{ a _1 b _2- a _2 b _1}{1}\right]}$
Answer$\frac{b_1 c_2-b_2 c_1}{a_1 b_2-a_2 b_1}, a_1 b_2-a_2 b_1 \neq 0$
View full question & answer→Question 351 Mark
If the pair of linear equations $a_1 x+b_1 y+c_1=0$ and $a_2 x+b_2 y+ c _2=0$ has unique solution then $\frac{x}{y}=$________$
\left(\frac{ b _1 c _1- b _2 c _1}{ b _1 b _2- b _2 b _1}, \frac{ c _1 a _1- c _2 a _1}{ a _1 b _2- a _2 b _1}, \frac{ a _1 b _2- a _2 b _1}{1}\right)
$
Answer$\frac{b_1 c_2-b_2 c_1}{c_1 a_2-c_2 a_1}$
View full question & answer→Question 361 Mark
If the equations $3 x+y=1$ and $(2 k-1) x+(k-1) y=2 k+1$ are inconsistent then $k=$________$(-2,2,1)$
View full question & answer→Question 371 Mark
If the graph of the linear equations $3 x+2 k y=2$ and $2 x+5 y+1=0$ represents parallel lines then $k=$ _____________$\left(\frac{15}{4}, \frac{4}{15}, \frac{3}{5}\right)$
View full question & answer→Question 381 Mark
If $2 x+3 y=13$ and $5 x-4 y=-2$ then $a_1 b_2-a_2 b_1=$_______ $(23,-23,7)$
View full question & answer→Question 391 Mark
If the solution of the pair of the linear equations $a x+2 y=7$ and $2 x+3 y=8$ is unique then $a \neq$ ____________$\left(\frac{3}{4}, \frac{4}{3}, \frac{2}{3}\right)$
View full question & answer→Question 401 Mark
If $(5,3)$ is the solution of the equation $2 x+3 y+k=0$ and $(m, 5)$ is also the solution of it then $m$ $=$_______$(2,-2,5)$
View full question & answer→Question 411 Mark
If one of the solution of $x+2 y-4=0$ is $(2, k)$ then find the value of $k=$___________ $(0,1,-1)$
View full question & answer→Question 421 Mark
The solution is $(1,4)$ of $x+y=14$ and $x-y=4$.
View full question & answer→Question 431 Mark
The graph represents $y$-axis if $y=0$
View full question & answer→Question 441 Mark
The graph of equation $3 x=7$ is parallel to $x$-axis.
View full question & answer→Question 451 Mark
The graph of equation $5 x-4 y=0$ is passed the line from origin.
View full question & answer→Question 461 Mark
For pair of linear equations two variables $a_1 x+b_1 y$ $+c_1=0$ and $a_2 x+b_2 y=c_2=0, \frac{a_1}{a_2} \neq \frac{b_1}{b_2}$, then pair of equation has one and only one solution.
View full question & answer→Question 471 Mark
The graph of pair of linear equations x + 2y - 4 = 0 and 2x + 4y - 12 = 0 is parallel lines.
Question 481 Mark
The solution is $(1,4)$ of $x+y=14$ and $x-y=4$.
View full question & answer→Question 491 Mark
For pair of linear equations two variables $a_1 x+b_1 y$ $+c_1=0$ and $a_2 x+b_2 y=c_2=0, \frac{a_1}{a_2} \neq \frac{b_1}{b_2}$, then pair of equation has one and only one solution.
View full question & answer→Question 501 Mark
The graph represents $y$-axis if $y=0$
View full question & answer→