Question 1 : The total mark in the fourth class interval is _____<br><table class="wysiwyg-table"><tbody><tr><td>class interval<br></td><td>30-40<br></td><td>40-50<br></td><td>50-60<br></td><td>60-70<br></td><td>70-80<br></td><td>80-90<br></td></tr><tr><td>mark<br></td><td>1<br></td><td>2<br></td><td>4<br></td><td>5<br></td><td>6<br></td><td>7<br></td></tr></tbody></table><br>
Question 2 :
Find the arithmetic mean of $1, 3, \displaystyle 3^{2}, ...,\displaystyle 3^{n-1}$.
Question 3 :
Solve the systems of equations : $y=3x-1 ; -9x + 3y=4$<br>
Question 4 :
Find the value of $m$, if $x= 2,y= 1$ is a solution of the equation $2x+3y= m$.
Question 5 :
<span>Write the following equations in the form $ax + by + c = 0 $, </span><span>where $a= -2,b=3$ and $c=-6$</span>
Question 7 :
The total cost of $2$ shirts and $3$ pants is $Rs.1000$ which of the following equation represent the above statement ?<br/>
Question 9 :
The cost of a notebook $(y)$ is twice that of a pen $(x)$.<br/>Write a linear equation to represent this statement.
Question 12 :
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 14 :
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 16 :
Which of the following is a solution of the equation 4x + 3y = 16?
Question 17 :
The solution set of the pair of equations $2x=8$ and $3y=15$ is -<br>
Question 18 :
Solve x + 4y = 14 & 7x - 3y = 5
Question 19 :
If the temperature is 95$^o$ F, what is the temperature in Celsius?
Question 20 :
If x=b-c, y=c-a, z=a-b then the value of $\displaystyle x^{2}-y^{2}+z^{2}+2xz$ is
Question 21 : <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 22 :
Total expenses of a boarding house are partly fixed and partly varying linearly with the number of boarders. The average expense per boarder is Rs. $700$ when there are $25$ boarders and Rs. $600$ when there are $50$ boarders. What is the average expense per boarder when there are $100$ boarders?
Question 23 :
If $x=6$, and $c=5$, which of the following has the value $32$?
Question 24 : Check if this is solution of equation x-2y=4 <div>$\displaystyle \left(\sqrt 2, 4\sqrt 2\right)$</div>
Question 25 :
A linear equation in two variables has how many solutions ?
Question 26 :
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 27 : <div><span>If we write $\displaystyle 3x-7y=10$ in form of $\displaystyle ax+by+c=0,$ then $a=$</span><span>?</span></div>
Question 28 : <div><span>Say true or false.</span><br/></div>Every solution of the equation is a point on the line representing it.
Question 31 :
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 32 :
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 33 :
For what value of $c$, the linear equation $2x + cy = 8$ has equal values of $x$ and $y$ for its solution.<br/>
Question 34 :
The solution of equations $\displaystyle \frac{m}{3}+\frac{n}{4}=12\: \: and\: \: \frac{m}{2}-\frac{n}{3}=1$ is
Question 35 :
If $\displaystyle \frac{(\sqrt{a}-\sqrt{b})^{2}+4\sqrt{ab}}{a-b}=\frac{5}{3}$ then the value of a : b is
Question 36 :
Which of the following is not a solution of the pair of equations $3x-2y=4$ and $6x-4y=8$ ?<br/>
Question 38 :
If $217x+131y=913$ and $131x+217y=827$, then the value of $x+y$ is __________?
Question 39 :
The pair of equations $x = a$ and $y = b$ graphically represents lines which are<br>
Question 40 :
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 41 : <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 42 :
Which of the following is a solution of $2p + 3q = 5$?
Question 43 : <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 44 :
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 45 : <span>Check if this is the solution of the equation x - 2y = 4 </span><div>(2, 0)</div>
Question 46 :
If the point $(3,4)$ lies on the equation $3y=ax+7$, then the value of $a$ is
Question 47 :
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 49 :
If $\displaystyle a + b = 7$ and $\displaystyle ab = 10$; find $\displaystyle a - b$
Question 50 :
The simplest algebraic expression of $4st (s - t) - 6s^{2} (t - t^{2}) - 3t^{2}(2s^{2} - s) + 2st (s - t)$ is _________.
Question 51 : <div><div><span>Do the following pair of linear equations have no solution ? </span><br/></div></div>x = 2y ;<br/>y = 2x<br/>
Question 53 :
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 54 :
If $7x + 4y = 18$ and $3x + y = 3$, what is the value of $x + y$?
Question 56 : <div><span>Rakesh went to a stationary shop to purchase a total of $38$ pens, erasers and sharpeners. He purchased at least 11 items of each. He purchased more sharpeners than erasers and more erasers than pens. </span><span>If each pen cost Rs. $2$ each eraser cost Rs. $3$ and each sharpener cost Rs. $4$. find the minimum expenditure be could have incurred on the items (in Rs.)</span></div>
Question 57 :
The equation $x=7$ can be written in two variables $x,\,y$ as
Question 58 :
Snehal can row $28$ km downstream and $12$ km upstream in $5$ hours. He can row $21$ km downstream and $10$ km upstream in $4$ hours. Find the speed of Snehal in still water (in km/hr)
Question 59 :
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 60 :
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 61 :
Charu's phone company charges <b>35 cents</b> each minute of use during peak hours and <b>15 cents</b> each minute of use during non-peak hours. If Charu's phone company charged her <b>$7.90</b> for a half hour phone call, what is the greatest number of minutes charged at peak hour rates?
Question 62 :
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 63 :
Find the value of m and n the equation have infinitely many solutions:<br>$20x+12y=m$ and $-2nx+2y=10$
Question 64 :
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 65 :
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 66 :
If $99x + 101y = 400$ and $101x + 99y = 600$ then $x + y$ is _____
Question 67 :
If two real numbers x and y satisfy the equation x/y = x- y, then:
Question 68 :
Theo bakery sells red velvet cakes and cheese cakes in boxes of $12$ at a cost of $\$15$ per box of red velvet and $\$9$ per box of cheese cakes. On Monday and Tuesday, the shop earned $\$396$ by selling a total of $46$ boxes of these two items. If $r$ and $l$ represent the number of boxes of red velvet and cheese cakes respectively, which of the following systems of equations could be used to find the number of boxes of each type of item sold?<br/>
Question 69 :
The number of non-negative integer solutions of the equations $6x+4y+z = 200$ and $x+y+z = 100$ is
Question 70 :
If 5 is a solution of variable x in the equation $\dfrac{5x - 7}{2}$= y, then the value of y is 18.
Question 71 :
If $x = 1, y = 1$ is a solution of equation $9ax + 12ay = 63$ then, the value of a is
Question 72 :
If the sum of two integers is $12$ and their difference is $4$ then the greater number is ________.
Question 73 :
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 74 :
If the sum of two numbers is $640$ and their difference is $280$, then the numbers are
Question 75 :
$x = 5, y = 2$, is a solution of a linear equation<br>
Question 76 :
A three-digit number $N$ leaves the same remainder upon dividing $68488$ and $67516$. How many possible values does $N$ have?
Question 77 :
Syed took out a cash advance of $d$ dollars from a financing company. The company deducts a fee of $\displaystyle\frac{1}{3}$ of the original advanced amount along with a written transfer fee of $\$ 30.00$. Which of the following represents the final advanced amount that Syed receives after all applied fees, in dollars?
Question 78 : <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 79 :
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 80 :
What was the initial amount of fuel, in gallons, if there are now $x$ gallons, $y$ gallons were pumped into a storage tank, and then $50$ gallons were added to the tank?
Question 81 :
$20$ years ago, Ram was five times as old as his son who will be $41$ years old $16$ years after, then present age of Ram?
Question 83 :
A fraction becomes $\displaystyle \frac {4}{5}$ when 1 is added to each of the numerator and denominator. However, if we subtract 5 from each then it becomes $\displaystyle\frac {1}{2}$. The fraction is<br>
Question 85 :
Once a certain plant begins to grow, its height increases at a linear rate. After six weeks, the plant is $54$ centimetres tall. Which of the following functions best models the relationship between $h(w)$, the height in centimetres, of the plant and $w$, the number of weeks that the plant has been growing?
Question 86 :
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 88 :
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 89 :
The sum of two positive numbers is 24. If their product is maximum , then the numbers are :
Question 90 :
If $\left| {4x - 4} \right| = 8$ and $\left| {5y + 10} \right| = 15$, what is the smallest possible value of $xy$?
Question 93 : <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 94 :
If Arshad earns $Rs. x$ per day and spends $Rs. y$ per day, then his saving for the month of
Question 95 :
<span>Suppose you are given two natural numbers and are asked to multiply them followed by adding 4 to the result. The result of this operation is 40. Which of the following could NOT be the sum of the two numbers?</span>
Question 97 :
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 98 :
Choose the correct answer from the alternatives given.<span><br>2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can finish it in 8 days. Number of days taken by 2 men and I boy to finish it will be</span>
Question 99 :
Which of the following is not a linear equation in two variables?<br/>
Question 100 :
If $41 x + 31y = 18$ and $31x + 47y = 60$ then find the value of $x + y$.
Question 101 :
A two digit number x is the digit at units place and y is the digit at tens place, then the number is.
Question 103 :
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 104 :
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 106 :
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 107 :
If $331a + 247b = 746$ and $247a + 331b = 410$ then find $a$.
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 :
Find two numbers whose sum is $26$ and whose product is $165$
Question 110 :
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 111 :
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.
Question 114 :
If $\dfrac{1}{x}+y=2$ and $x+\dfrac{1}{y}=3$, then the ratio of $x$ to $y$ is
Question 115 :
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.
