Question 1 :
If x=b-c, y=c-a, z=a-b then the value of $\displaystyle x^{2}-y^{2}+z^{2}+2xz$ is
Question 2 : <div><div><span>Do the following pair of linear equations have no solution ? </span><br/></div></div>x = 2y ;<br/>y = 2x<br/>
Question 5 :
A boat takes 3 hours to travel 30 km downstream and takes 5 hours to return to the same spot upstream. Find the speed of the boat in still water. (km/hr)
Question 7 :
If $\displaystyle a + b = 7$ and $\displaystyle ab = 10$; find $\displaystyle a - b$
Question 8 :
Carina has $100$ ounces of coffee divided into $5-$ and $10-$ ounce packages. If she has $2$ more $5-$ ounce packages than $10$-ounce packages, how many $10$-ounce packages <span>does she have?</span>
Question 9 :
If the point $(3,4)$ lies on the equation $3y=ax+7$, then the value of $a$ is
Question 10 :
If $x+y=0$, which of the following must be equivalent to $x-y$?
Question 11 :
<span>In a two digit number, the units digit is x and the tens digit is y. Then the number is </span>
Question 13 :
Given equations are $\displaystyle x+3y=42$ and $\displaystyle 3x-y=8$<br/>In the system of equations above, how many points of intersection do the equations share and find their relationship, if any.
Question 14 : <div>State True or False.</div>If the total cost of $2$ apples and $3$ mangoes is Rs. $22$, then the cost of each apple and each mango must be Rs. $5$ and Rs. $4,$ respectively, (where the cost of each apple and mango is an integer).
Question 15 :
If $\dfrac {x}{3} = \dfrac {16}{y} = 4$ then $x + y =$ ______.
Question 16 :
A mans age is now four times that of his son and it is also three times that of his daughter In six years time it will be three times that of his son How old was he when his daughter was born?
Question 17 :
If $\displaystyle \frac{(\sqrt{a}-\sqrt{b})^{2}+4\sqrt{ab}}{a-b}=\frac{5}{3}$ then the value of a : b is
Question 18 :
Given equations are $\begin{array}{l}3x - 6y = 15\\ - 2y + 4y = - 10\end{array}$<br/>How many solution $\left( {x,y} \right)$ are there to the system of equations above?
Question 19 :
$(2p - 1, p)$ is a solution of equation $10x - 9y = 15$, find the value of $p$.
Question 20 :
When the square of a number and the cube of a small number are added the result is $593$. If the square of the smaller number exceeds the bigger number by $55$. Find the difference between two numbers.
Question 21 :
The pair of equations $x = a$ and $y = b$ graphically represents lines which are<br>
Question 22 :
A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?
Question 24 :
Rohit's revenue $R$ in dollars, as a result of selling cards for $x$ days, that is given by the function $\displaystyle R(x)=250x-20$. If Rohit earned $ $1230$, how many days has he sold cards?
Question 26 :
If $217x+131y=913$ and $131x+217y=827$, then the value of $x+y$ is __________?
Question 27 :
<span>A solution $(x, y)$ of the system of equations $x-y=\dfrac 13$ and $x^2-y^2=4$ is given by,</span>
Question 28 :
Consider the following statements. The system of equations<br/>$2x-y=4$<br/>$px-y=q$<br/>1. has a unique solution if $p\neq2$<br/>2. has infinitely many solutions if $p=2,q=4$<br/>Of these statement
Question 29 :
If $x=6$, and $c=5$, which of the following has the value $32$?
Question 30 : <div><span>Say true or false.</span><br/></div>The pair of linear equations $3x-y=3$ and $9x-3y=9$ have infinite solutions.
Question 31 :
The simplest algebraic expression of $4st (s - t) - 6s^{2} (t - t^{2}) - 3t^{2}(2s^{2} - s) + 2st (s - t)$ is _________.
Question 32 :
The value of m if :<br>$\displaystyle 4^{2m} = (3 \sqrt {16})^{- \frac {6}{n}} = (\sqrt 8)^2$ is $\displaystyle m = \frac {3}{4}$<br>If true then enter $1$ and if false then enter $0$<br>
Question 33 :
The cost of a notebook $(y)$ is twice that of a pen $(x)$.<br/>Write a linear equation to represent this statement.
Question 34 :
If the temperature is 95$^o$ F, what is the temperature in Celsius?
Question 35 :
The sum of the present ages of father and his son is 60 years 6 years ago father's age was five times the age of the son After six years son's age will be
Question 37 : <span>Write the following equation in the form $ax + by + c = 0$ and indicate the values of $a, b$ and $c$. </span><div>$y - 2 = 0$</div>
Question 38 :
In a class the number of students is 84. If there were six boys more and six girls less then the ratio of boys and girls is 5 : 2. Find the number of boys in the class.
Question 40 :
Find the value of $m$, if $x= 2,y= 1$ is a solution of the equation $2x+3y= m$.
Question 41 :
The cost of a note book is twice the cost of a pen. If the cost of a note book is $x$ and that of a pen is $y$ then a linear equation in two variable to represent is
Question 42 :
Choose the correct answer which satisfies the linear equations: $2a + 5b = 13$ and $a + 6b = 10$
Question 45 : <span>Write a linear equation in two variables to represent the following statement.</span><div>Two numbers are such that $2$ times of one <span>is same as $3$ times of the other.</span></div>
Question 46 :
If $\dfrac {x}{2} = \dfrac {y}{3}$, then $\left [\dfrac {4}{5} + \dfrac {y - x}{y + x}\right ]$ equals.
Question 47 : <span>Write the following equations in the form ax + by + c = 0 </span><div>$x - 4 = \sqrt 3 y$</div>
Question 48 :
$(- 3, - 2)$ is point, which belongs to the graph of the equation :<br>
Question 49 :
The value of $\frac{3}{a + b}$ when a = $4$ and b = $-4$ is:
Question 50 : <div><span>If we write $\displaystyle 3x-7y=10$ in form of $\displaystyle ax+by+c=0,$ then $a=$</span><span>?</span></div>
Question 51 :
The solution of the simultaneous linear equations $2x + y = 6$ and $3y = 8 + 4x$ will also be satisfied by which one of the <span>following linear equations?</span>
Question 52 :
The difference of two numbers is $3$ and the difference of their square is $69$. Find the numbers.
Question 53 :
A certain number of men are twice as many women and thrice as many boys, earn Rs. $5100$ <span>in $6$ days</span>. A woman earns one and a half times as a boy and a man as much as a woman and a boy earn together per day. How many women were there if a boy earned Rs. $25$ daily ?
Question 55 :
Mohan's mother is six times as old as Mohan now, Five years after, she will be $20$ years older than Mohan. What are their present ages?
Question 56 :
If the sum of two numbers is $640$ and their difference is $280$, then the numbers are
Question 57 :
A certain two digits number is equal to five times the sum of its digits. If $9$ were added to the number, its digits would be reversed. The sum of the digits of the number is :
Question 59 : <span>If $x$ and $y$ are $+$ve integers, then find the solution of the following equation:</span><div><span>$\displaystyle 7x+12y= 220$</span></div>
Question 60 :
The equation $x=7$ can be written in two variables $x,\,y$ as
Question 61 :
Which of the following is not a solution of the pair of equations $3x - 2y = 4$ and $9x - 6y = 12$
Question 62 :
The blade of a rotor rotates at $1,000$ rotations per second when the mixer is empty. The rate at which the blade slows is four rotations per second less than three times the square of the height of the liquid. If h is the height of liquid in the mixer, which of the following represents $R(h)$, the rate of rotation?
Question 63 :
The marks obtained by a student in a mathematics test is 8 more than two-third of $x$. If $x=60$, then marks obtained by the student is
Question 64 :
A boat goes $24$ km upstream and $28$ km downstream in $6$ hours. It goes $30$ km upstream and $21$ km downstream in $6$ hours and $30$ minutes. The speed of the boat on still water is
Question 65 :
If three times the larger of the two numbers is divided by the smaller one, we get $4$ as the quotient and $3$ as remainder. Write a linear equation in two variables to represent this statement.
Question 66 :
If $x = a, y = b$ is the solution of the equations $x - y = 2$ and $x + y = 4$, then the values of $a$ and $b$ are respectively:<br/>
Question 67 :
The coach of a cricket team buys $7$ bats and $6$ balls for Rs. $3,800$. Later he buys $3$ bats and $5$ balls for Rs. $1,750$. The cost of each bat and each ball is
Question 69 :
$x = 5, y = 2$ is a solution of the linear equation<br>
Question 70 :
The sum of the heights of $A$ and $B$ is $320\: cm$ and the difference of heights of $A$ and $B$ is $20\: cm$. The height of $B$ can be _____
Question 71 :
Two number are in the ratio $3:5$ if the sum numbers is $144$, then the smaller numbers is
Question 72 :
If $99x + 101y = 400$ and $101x + 99y = 600$ then $x + y$ is _____
Question 73 :
The number of non-negative integer solutions of the equations $6x+4y+z = 200$ and $x+y+z = 100$ is
Question 74 :
The number of states that joined the United States between $1776$ and $1849$ is twice the number of states that joined between $1850$ and $1900$. If $30$ states joined the United States between $1776$ and $1849$ and x states joined between $1850$ and $1900$, which of the following equations is true?
Question 75 :
All buys $10$ burgers and $7$ chocolate milkshakes for $ $50.95$. If the price of a chocolate milkshake is $ $0.25$ cheaper than the price of a burger, what is the price of a chocolate milkshake? <br/>
Question 76 : <div><span>A machine takes $2$ litres of petrol to start and then $3$ litres per hour while running. </span><span>What will no. of hours for which machine will run if $2$ litres of petrol is used?</span></div>
Question 77 : <div><span>Father's age is $10$ more than twice age of his son. </span><span>What is the difference in the age of father and son, if son's age is $21$?</span></div>
Question 78 : <div><span>Cost of one apple is $3$ times the cost of an orange. </span><span>If price of one apple is Rs. $30$, then price of orange will be Rs. _____</span></div>
Question 80 :
At a convenience store, two candy bars and two bags of potato chips cost $\$4.00$, and three candy bars and two bags of potato chips cost $\$4.75$. What is the price of one bag of potato chips?
Question 81 :
In a zoo, there are rabbits and pigeons. If their heads are counted, these are $90$ while their legs are $224$. Find the number of pigeons in the zoo.
Question 82 :
When the positive integer $m$ is divided by $5$, the remainder is $3$. What is the remainder when $20m$ is divided by $25$?
Question 84 :
Suppose $x$ and $y$ are positive real numbers such that $x\sqrt {x} + y \sqrt {y} = 183$ and $x\sqrt {y} + y\sqrt {x} = 182$ then value of $\dfrac {18}{5}(x + y)$ is :
Question 85 :
If Arshad earns $Rs. x$ per day and spends $Rs. y$ per day, then his saving for the month of
Question 86 :
Points $A$ and $B$ are $90km$ apart from each other on a highway. A car starts from $A$ and another from $B$ at the same time. If they go in the same direction, they meet in $9hrs$ and if they go opposite directions, they meet in $\cfrac{9}{7}hrs$. Find their speeds.
Question 87 : Solve the following system of Simultaneous Linear Equations to determine the value of $p$:<div>$\displaystyle \frac { p }{ 3 } +\frac { q }{ 2 } =1$, $\displaystyle p-3q=1$<br/></div>
Question 88 :
The price of a certain type of cherry can range from $\$2.50$ to $\$3.00$ per pound, and the price of a certain type of roll can range from $\$0.80$ to $\$1.10$<span> per dozen.To be sure of having enough money to buy $c$ pounds of these cherries and $r$ dozen of these rolls, a person </span><span>needs at least how many dollars, in terms of $c$ and $r$?</span>
Question 90 :
If $41 x + 31y = 18$ and $31x + 47y = 60$ then find the value of $x + y$.
Question 91 :
A machine takes $2$ litres of petrol to start and then $3$ litres per hour while running. <span>If the equation thus formed is of the form $ax+by+c=0$. </span>What is the value of $c$, if x denotes the number of hours machine had run?
Question 92 : Solve the equations simultaneously to find the value of $h$.<div><span>$\displaystyle 3h-j=7$ and </span><span>$\displaystyle 2h+3j=1$</span><br/></div>
Question 93 :
For which value of K the system of equations 3x+ y -1 and (2k-1)x+ (k-1)y=(2k +1) has no solution <span><br></span>
Question 94 :
Sharon celebrated her $16^{th}$ birthday $\displaystyle x$ years ago. How old would she be in $\displaystyle z$ years time ?
Question 95 :
The sum of the digits of a two-digit number is $13$.If $27$ is added to the number ,the digits get interchanged.What is the number ?
Question 96 :
A stream flows from $A$ to $B$ at a distance of $15$ km . A man who can row in still water at $4$ km in an hour and can row up and down in $8$ hours. The rate of stream is
Question 98 : <span>From the following figure, we can say: </span><div>$\displaystyle \frac{x}{3}+\frac{y}{4}=4; \, \, \frac{5x}{6}-\frac{y}{8}=4 $</div>
Question 99 :
<span>Perry and Katy are both saving money from their summer jobs to buy a car</span><span>. If Perry had $\$150$ less, she would have exactly $\displaystyle \frac { 1 }{ 3 } $ as much as Katy. And if Katy had twice as much, she would have exactly $3$ times as much as Perry. How much money have they saved together?</span>
Question 100 :
An English word consists of $9$ alphabets. The sum of twice the number of vowels and three times the number of consonants present in the word is equal to four more that four times the total numbers of vowels in the English alphabets. The product of the number of vowels and consonants present in the word is
Question 101 :
If $331a + 247b = 746$ and $247a + 331b = 410$ then find $a$.
Question 102 :
In a fraction, if the numerator is decreased by $1$ and the denominator is increased by $1$, then the resulting fraction is $\dfrac14$. Instead if the numerator is increased by $1$ and the denominator is decreased by $1$, then the resulting fraction is $\dfrac23$. Find the absolute difference of the numerator and the denominator of the fraction.
Question 103 :
Find two numbers whose sum is $26$ and whose product is $165$
Question 104 :
The ratio of monthly incomes of Mr. $X$ and Mr. $Y$ is $3: 4$ and the ratio of their monthly expenditures is $5: 7$. If the ratio of their monthly savings is $3: 2$ and Mr X saves Rs. $500$ more than Mr. $Y$ per month, then find the monthly income of Mr. $Y$ [in Rs. ]
Question 105 :
If $\dfrac{1}{x}+y=2$ and $x+\dfrac{1}{y}=3$, then the ratio of $x$ to $y$ is
Question 107 :
The ratio of two nubers is $\displaystyle \frac{2}{3}$. If $2$ is subtracted from the first and $8$ from the second, the ratio becomes the reciprocal of the original ratio. Find the numbers.
Question 108 :
Henry drives 150 miles at 30 miles per hour and then another 200 miles at 50 miles per hour. What was his average speed, in miles per hour, for the entire journey, to the nearest hundredth?
Question 109 :
Total cost of $15$ erasers and $25$ pencils is Rs. $185$ and the total cost of $9$ erasers and $x$ pencils is Rs. $106$. Which of the following cannot be the value of $x$?
Question 110 :
The sum of the ages of $X$ and $Y$ $12$ years ago was $48$ years and the sum of the ages of $X$ and $Y$ $12$ years hence will be _____ years.
Question 112 :
A man buys $m$ articles at Rs. $x$ each and another $n$ articles for Rs. $y$. If he sells all the articles at Rs. $z$ per article. Frame an equation to find his profit.
