Q.1
For which value of k the pair of linear equations $x+2y=5$ and $3x+ky+15=0$ has no solution ?

Q.2
The equations of two sides of a right angled $\Delta$ are $y=x$ & $y=0$ which of the following equations can not represent the 3rd side ?

Q.3
What is the area of $\Delta$ formed b a co-ordinate axes and $ax+by=c$ (where a, b are two positive real numbers)

Q.4
If $\left(x-3\right),$ is a factor of ${k}^{2}{x}^{3}-k{x}^{2}+3kx-k$ then the value of k is :

Q.5
If $ab<0$ and point $\left(a,b\right)$ is in 2nd quadrant then $\left(-a,-b\right)$ will be in :?

Q.6
Area of the $\Delta$ (in sq. m) formed by the graphs of three equations $x=4,y=3$ and $3x+4y=12$ is : ?

Q.7
The circumradius of that $\Delta$ which is formed by x-axis, y-axis and $4x+3y=12;$ is : ?

Q.8
Two simple linear equations ${a}_{1}x+{b}_{1}y+{c}_{1}=0$ and ${a}_{2}x+{b}_{2}x+{b}_{2}y+{c}_{2}=0$ has an infinite number of solutions if -

Q.9
If  the equations of two parallel lines are $2x+3y=k$ and $4x+6y=8$, which of the following is correct ?

Q.10
If straight line $3x+5y=24$ intersects x-axis at any point then co-ordinates of that point is ?

Q.11
If graph of the equation $4x+3y=12$ intersect the coordinate axes at the points A and B then the length of hypotenuse of $\Delta AOB$ is :

Q.12
The area of $\Delta$ formed by y-axis, $x-y=1$ and $2x+y=8$ is :

Q.13
For which value of k, the polynomial $2{x}^{4}+3{x}^{3}+2k{x}^{2}+3x+6$is completely divisible by $x+2$?

Q.14
If point $\left(3,4\right)$ is situated on the graph of equation $3y=ax+7$ then the value of a is :

Q.15
What will be the area of that $\Delta$ which is formed by x-axis and lines of equations $2x+y=6$$2x-y+2=0$ .

Q.16
For which value of a; $\left(x-a\right)$ is a factor of polynomial $f\left(x\right)={x}^{5}-{a}^{2}{x}^{3}+2x+a-3$ ?

Q.17
Area of the $\Delta$formed by $A\left(2,0\right),B\left(6,0\right)&C\left(4,6\right)$ is :

Q.18
One factor of polynomial $f\left(x\right)={x}^{3}+{x}^{2}-17x+15$ is :

Q.19
For which value of x the distance between points $\left(x,-1\right)$ and $\left(3,2\right)$ will be 5 ?

Q.20
The co-ordinates of points P, Q and S are $\left(a{t}^{2},2at\right),$ $\left(\frac{a}{{t}^{2}},\frac{2a}{t}\right)$ and $\left(a,0\right)$ respectively then $\frac{1}{SP}+\frac{1}{SQ}=?$

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