Question 1 :
<span>Cost of one apple is 3 times the cost of an orange. </span>This is an example of linear equation in ..... variables.
Question 2 :
In the given equation<br><span>$\displaystyle a=\frac { 2 }{ 3 } b+5$<br></span>It is linear equation in ....... variables.
Question 4 :
<span>Cost of one apple is 3 times the cost of an orange. </span>This is an example of linear equation in ..... variables.
Question 6 : <span>Write of the following equation in the form $ax + by + c = 0$ and indicate the values of $a, b $ and $c$.</span><div>$2x + 3y = 9.35$</div>
Question 7 :
In the given equation<br><span>$\displaystyle a=\frac { 2 }{ 3 } b+5$<br></span>It is linear equation in ....... variables.
Question 8 : <span>Write a linear equation in two variables to represent each of the following statement.</span><div><span>5 books and 7 pens together cost Rs 79.</span></div>
Question 9 :
The condition that the equation $ax + by + c = 0$ represent a linear equation in two variables is :<br>
Question 10 : <div>Is the following equation linear in two variables?</div>$\displaystyle \frac{4}{x} + 3y = 14$
Question 11 :
Which of the following is a linear equation in one variable?
Question 15 : <span>Frame simultaneous linear equations in two variables representing the following information:</span><div>Sum of the ages of Monali and Sonali is 29 years. Monali is younger than Sonali by 3 years. </div>
Question 17 :
A class has total $60$ students with $x$ girls and $y$ boys. The number of girls is twice the number of boys. Express these statement in the linear equations form.
Question 18 :
A bag with total $10$ balls contains $x$ blue and $y$ red balls. If the number of blue balls is four times the number of red, then write the two equations.
Question 19 :
Which equation represents the line that passes through the point $(1, 3)$ and is parallel to the $x$-axis?<br/>
Question 20 :
A class has total $60$ students with $x$ girls and $y$ boys. The number of girls is twice the number of boys. Express these statement in the linear equations form.
Question 21 : <span>Express the given information in mathematical form using two variables:</span><div>One number is 5 more than seven times the other number.</div>
Question 22 :
Which of the following is a linear equation in $2$ variables?
Question 23 :
Which of the equation given below have graphs parallel to the X-axis and which ones have graphs parallel to the Y-axis?
Question 24 :
The number of values of z which satisfies both the equation $\left|x-1-i \right|=\sqrt{2}$ and $\left|x-1-i \right|={2}$, is
Question 27 :
Use the identity $ (a+b)(a-b) = a^2-b^2$ to evaluate:<br/>$21\times 19 $.
Question 28 :
If $(x-1)$ is a factor of $x^2 + 2x - k$, then find $k$.
Question 29 :
If x -a is a factor of $x^3 -3x^2a + 2a^2x + b$, then the value of b is
Question 30 :
Use the identity $ (a+b)(a-b) = a^2-b^2$ to evaluate:<br/>$33\times 27 $.
Question 32 :
The value of p for which $(x-2)$ is a factor of polynomial $x^4 - x^3 + 2x^2 - px +4$ is:<br/>
Question 34 :
If x+2 is a factor of $ \displaystyle \left \{ \left ( x+1 \right )^{5}+(2x+k)^{3} \right \} $, then the value of 'k' is 
Question 35 :
Consider the following statements:<br/>1. x-2 is a factor of $ \displaystyle x^{3}-3x^{2}+4x-4    $<br/>2. x+1 is a factor of $ \displaystyle 2x^{3}+4x+6    $<br/>3. x-1 is a factor of $ \displaystyle x^{6}-x^{5}+x^{4}-x^{3}+x^{2}-x+1    $<br/>of these statements<br/><br/>
Question 36 :
<span>Using $(x + a) (x + b) = x^2+(a+b)x+ab$, find </span>$5.1 \times 5.2$.
Question 38 :
If $(x+2)$ is a factor of $2x^3+5x^2-x-k$, then value of $k$ is :
Question 39 :
Find the remainder when $x^{3} + 3x^{2} + 3x + 1$ is divided by $x$.
Question 42 :
If $(3x^{3} - 2x^{2}y - 13xy^{2} + 10y^{3})$ is divided by $(x - 2y)$, then what is the remainder?
Question 45 :
If $7+3x$ is factor of $3x^3+7x$, then the remainder is :
Question 47 : <p>Find the missing term in the following problem:</p><p>$\left(\displaystyle \frac{3x}{4}\, -\, \displaystyle \frac{4y}{3} \right )^2\, =\, \displaystyle \frac{9x^2}{16}\, +\, ..........\, +\, \displaystyle \frac{16y^2}{9}$.</p>
Question 48 :
Which of the following is a factor of the polynomial $-2{x}^{2}+7x-6$?
Question 49 : <table class="wysiwyg-table"><tbody><tr><td>$x$</td><td>$f(x)$</td></tr><tr><td>$0$</td><td>$3$</td></tr><tr><td>$2$</td><td>$1$</td></tr><tr><td>$4$</td><td>$0$</td></tr><tr><td>$5$</td><td>$-2$</td></tr></tbody></table>The function $f$ is defined by a polynomial. Some values of $x$ and $f (x)$ are shown in the table above. Which of the following must be a factor of $f (x)$?
