Question 11 Mark
The difference between the ages of two sisters Leela and Yamini is a variable.
AnswerFalse.Solution:
Difference between the ages of two sisters Leela and Yamini is not a variable because Leela’s and Yamini’s ages are fixed. But the value of a variable is not fixed. So, the statement false.
View full question & answer→Question 21 Mark
If $x$ is a negative integer, $-x$ is a positive integer.
AnswerIf at is a negative integer, then positive integer $= -(x) = -x$
So, the statement is true.
View full question & answer→Question 31 Mark
An auto rickshaw charges $Rs .10$ for the first kilometre then $Rs .8$ for each such subsequent kilometre. The total charge (in Rs) for d kilometres is .
AnswerAn auto rickshaw charges $Rs .10$ for the first kilometre then $Rs. 8$ for each such subsequent kilometre.
The total charge (in Rs) for d kilometres is $8d + 2$.
Solution:
Given, autorickshaw charges for first $km = Rs. 10$
After that, each such subsequent $\ km$ charge $= Rs. 8$
Total distance $= d \ km$
$\therefore$ Total charge $= 10 + (d - 1) 8 = 10 + 8d - 8 = Rs. 8d + 2$
View full question & answer→Question 41 Mark
In an equation, the $LHS$ is equal to the $RHS.$
AnswerIn an equation, the $LHS$ is equal to the $RHS$. So, the statement is true.
View full question & answer→Question 51 Mark
Price of petrol was Rs p per litre last month. Price of petrol now is $Rs (p - 5)$ per litre.
AnswerThe price of petrol per litre is decreased this month by $Rs. 5$ than its price last month.
View full question & answer→Question 61 Mark
The equations $x + 1 = 0$ and $2x + 2 = 0$ have the same solution.
AnswerGiven equations,
$\Rightarrow x + 1 = 0 $
$\Rightarrow 2x + 2 = 0$ From Eq. $(i), x + 1 = 0 $
$\Rightarrow x = -1$ From Eq. $(ii), 2x + 2 = 0 $
$\Rightarrow 2x = -2$
$\Rightarrow\text{x}=\frac{-2}{2}$
$\Rightarrow x = -1$ Clearly, the solution of both the equations are same.
So, the statement is true.
View full question & answer→Question 71 Mark
If the present age of Ramandeep is n years, then her age after $7$ years will be .
AnswerIf the present age of Ramandeep is $n$ years,
then her age after $7$ years will be $(n + 7)$ years.
Given, present age of Ramandeep $= n$ years.
Age after $7yr =$ (Present age $+ 7)$ years $= (n + 7)$ years.
View full question & answer→Question 81 Mark
The number of girls enrolled in a school last year was g. The number of girls enrolled this year in the school is $3g - 10.$
AnswerThe number of girls enrolled this year was $10$ less than $3$ times the girls enrolled last year.
View full question & answer→Question 91 Mark
Annual salary at r rupees per month alongwith a festival bonus of $Rs 2000$ is .
AnswerAnnual salary at r rupees per month alongwith a festival bonus of $Rs 2000$ is $12r + 2000$
Given, bonus $= Rs. 2000$
Total months in one year $= 12$
Per months salary $= Rs. r $
$\therefore$ Annual salary $= Rs. (12r + 2000)$
View full question & answer→Question 101 Mark
The variable used in the equation $2p + 8 = 18$ is .
AnswerThe variable used in the equation $2p + 8 = 18$ is not fixed.Solution:
Given equation is $2p + 8 = 18.$
Here, variable $p$ is used in the equation $2p+ 8 = 18$
Note Value of $p$ is not fixed.
View full question & answer→Question 111 Mark
The two digit number whose ten’s digit is $‘t’$ and units’s digit is $‘u’$ is .
AnswerThe two digit number whose ten’s digit is $‘t’$ and units’s digit is $‘u’$ is $10t + u.$
The number is $10 t + u.$
Here, ten’s digit $= t,$
unit digit $= u$
$\therefore$ Required number $= 10 \times $ Ten’s digit $+ 1 \times $ Unit digit $= 10 \times t + u = 10t + u$
View full question & answer→Question 121 Mark
The height of Mount Everest is $20$ times the height of Empire State building.
AnswerLet height of Empire State be h metre.
Then, height of Mount Everest $= 20 \times h = 20h$ metre
Hence, the required expression is $20h.$
View full question & answer→Question 131 Mark
$0$ is a solution of the equation $x + 1 = 0$
AnswerGiven, equation $x + 1 = 0 $
$\Rightarrow x = -1$ [transposing $+1$ to $RHS]$
So, $-1$ is the solution of the given equation. Hence, the given statement is false.
View full question & answer→Question 141 Mark
t minutes are equal to $60t$ seconds.
AnswerWe know that, $1$ minute $= 60$
seconds [transposing $+2$ to $RHS$] minutes $= 60 \times f$ seconds $= 601$ seconds
So, the statement is true.
View full question & answer→Question 151 Mark
$20^\circ$C less than the present temperature.
AnswerLet the present temperature be$ f ^\circ C.$
$\therefore$ Required expression = Present temperature $-20^\circ C = (f-20)^\circ C$
View full question & answer→Question 161 Mark
John planted t plants last year. His friend Jay planted $2t + 10$ plants that year.
AnswerLast year, Jay planted $10$ more plants than twice the number of plants planted by John.
View full question & answer→Question 171 Mark
In the equation $7k - 7 = 7$, the variable is $7.$
AnswerEquation is $7k - 7 = 7$
Here, variable is $k.$
So, the statement is false.
View full question & answer→Question 181 Mark
‘One third of a number added to itself gives $8’$, can be expressed as $\frac{\text{x}}{3}+8=\text{x}$
AnswerLet the number be $x.$
$\therefore$ One-third of the number $=\frac{1}{3}\times\text{x}=\frac{\text{x}}{3}$
Now, according to the given statement is $\frac{\text{x}}{3}+\text{x}=8$
But given equation is $\frac{\text{x}}{3}+8=\text{x}$
So, the statement is false.
View full question & answer→Question 191 Mark
$‘8$ more than three times the number $x’$ can be written as .
Answer$‘8$ more than three times the number $x’$ can be written as $3x + 8$
Given, number $= x$
Now, three times of $x = 3x$
Then, according to the question $= 3x + 8$
View full question & answer→Question 201 Mark
Number of pencils bought for $Rs .x$ at the rate of $Rs. 2$ per pencil is .
AnswerNumber of pencils bought for $Rs. x$ at the rate of $Rs 2$
per pencil is $\frac{\text{x}}{2}$.Solution:
Given, total cost of pencils $= ₹ x$
Cost per pencil $= ₹ 2$
Number of pencils $=\frac{\text{Total cost of pencils}}{\text{Cost per pencil}}$ $= \ ₹ \ \frac{\text{x}}{2}$
View full question & answer→Question 211 Mark
$‘x$ exceeds y by $7’$ can be expressed as .
Answer$‘x$ exceeds $y$ by $7′$ can be expressed as $x = y + 7.$
View full question & answer→Question 221 Mark
$x$ metres = __________ centimetres.
AnswerWe know that, $1$ metre $= 100\ cm$
So, $x$ metres $= 100 \times x = 100x \ cm$
View full question & answer→Question 231 Mark
A pencil costs $Rs. p$ and a pen costs $Rs. 5p.$
AnswerThe cost of a pen is $5$ times the cost of a pencil.
View full question & answer→Question 241 Mark
The distance between New Delhi and Bhopal is not a variable.
AnswerTrue.Solution:
Distance between New Delhi and Bhopal is fixed. Clearly, it is not a variable, so the statement is true.
View full question & answer→Question 251 Mark
$a = 3$ is a solution of the equation $2a - 1 = 5$
AnswerGiven equation is $2a - 1 = 5 $
$\Rightarrow 2a = 5 + 1 $
$\Rightarrow 2a = 6$
$\Rightarrow\frac{2\text{a}}{2}=\frac{6}{2} a = 3$
Clearly, $a = 3$ is the solution of the given equation.
So, the statement is true.
View full question & answer→Question 261 Mark
Translate each of the following statements into an equation: The diameter $(d)$ of a circle is twice its radius $(r).$
AnswerGiven,
Diameter of a circle $= d$
Radius of a circle $= r$
Twice of radius, $r = 2r$
Then, according to the question, $d = 2r$
View full question & answer→Question 271 Mark
Translate each of the following statements into an equation:
The perimeter $(p)$ of an equilateral triangle is three times of its side $(a).$
AnswerGiven, Perimeter of an equilateral triangle $= p$
Side of an equilateral triangle $= a$
Then, three times of side $(a) = 3a$
Then, according to the question, $p = 3a$
View full question & answer→Question 281 Mark
$2x - 5 > 11$ is an equation.
Answer$2x - 5 > 11$ is not an equation because it has no equality $(=)$ sign.
So, the statement is false.
View full question & answer→Question 291 Mark
The number of lines that can be drawn through a point is a variable.
Answer True. Solution:
Because infinite number of lines can be drawn through a point. View full question & answer→Question 301 Mark
The distance (in km) travelled in h hours at a constant speed of $40\ km$ per hour is .
AnswerWe know that, $\text{Speed}=\frac{\text{Distance}}{\text{Time}}$
$\therefore$ Distance = Speed $\times $ Time
Here, Speed $= 40km/h$ Time $= h$
$\therefore$ Distance $= 40 \times h = 40h/km$
View full question & answer→Question 311 Mark
If $7x + 4 = 25$, then the value of $x$ is .
AnswerGiven, $7x + 4 = 25 $
$\Rightarrow 7x = 25 - 4 $
$\Rightarrow 7x = 21$
$\Rightarrow\frac{7\text{x}}{7}=\frac{21}{7}$
$\Rightarrow\text{x}=\frac{21}7{}$
$\Rightarrow x = 3$
Hence, the value of $x$ is $3.$
View full question & answer→Question 321 Mark
The number of days in w weeks is .
AnswerWe know that, number of days in $1$ week $= 7$
So, number of days in $W$ weeks $= 7 \times W = 7W$
View full question & answer→Question 331 Mark
Khader’s monthly salary was $Rs. P$ in the year $2005$. His salary in $2006$ was $Rs (P + 1000).$
AnswerKhader’s monthly salary is increased by $Rs. 1000$ in the year $2006$ than in $2005.$
View full question & answer→Question 341 Mark
Translate each of the following statements into an equation: Amount $(a)$ is equal to the sum of principal $(p)$ and interest $(i).$
AnswerGiven, amount $= Rs. a$ Principal $= Rs. p$ Interest $= Rs.$ Then, according to the question, $ a = p + i$
View full question & answer→Question 351 Mark
Leela contributed Rs $y$ towards the Prime Minister’s Relief Fund. Leela is now left with $Rs (y + 10000).$
AnswerAmount left with Leela is $Rs. 10000$ more than the amount she contributed towards Prime Minister’s Relief Fund.
View full question & answer→Question 361 Mark
If m is a whole number, then $2m$ denotes a multiple of $2$.
AnswerGiven, m is a whole number.
Put $m = 0, 1, 2, 3, … 2m $
$= 2 \times 0 = 0, 2m $
$= 2 \times 1 = 2 2m $
$= 2 \times 2 = 4, 2m $
$= 2 \times 3 = 6$
Clearly, $2m$ is the multiple of $2.$
So, multiples of $2$ are $2, 4, 6, …$
Hence, the statement is true.
View full question & answer→Question 371 Mark
If I spend f rupees from $100$ rupees, the money left with me is rupees.
AnswerGiven, total money $= Rs. 100$
Spend money $= Rs. f$
Left money with me $=$ Total money - Money spent $= Rs. (100 - f)$
View full question & answer→Question 381 Mark
The solution of the equation $3x + 7 = -20$ is .
AnswerGiven, $3x + 7 = -20 $
$\Rightarrow 3x = -20 - 7$ [transposing $+7$ to $RHS] $
$\Rightarrow 3x = -27$
$\Rightarrow\frac{3\text{x}}{3}=\frac{-27}{3}$ [dividing both sides by $3] $
$\Rightarrow x = -9$
Hence, the solution of equation $3x + 7 = -20$ is $-9$
View full question & answer→Question 391 Mark
$x = 5$ is the solution of the equation $3x + 2 = 20$
AnswerGiven equation is $3x + 2 = 20$
$\Rightarrow 3x = 20 - 2$ [transposing $+2$ to $RHS]$
$\Rightarrow 3x = 18$
$\Rightarrow\frac{3\text{x}}{3}=\frac{18}{3}$ [dividing both sides by $3]$
$\Rightarrow x = 6$
So, the solution of the given equation is $x = 6$.
But according to question, $x = 5$ is the solution of the given equation.
So, the statement is false.
View full question & answer→Question 401 Mark
Translate each of the following statements into an equation: The selling price (s) of an item is equal to the sum of the cost price (c) of an item and the profit (p) earned.
AnswerGiven, selling price of an item $= Rs. s$
Cost price of an item$ = Rs. c$
Profit $= Rs. p$
Then, according to question, $s = c + p$
View full question & answer→Question 411 Mark
The number of students dropping out of school last year was m. Number of students dropping out of school this year is m-$30.$
AnswerThe number of students dropping out of school this year is $30$ less than the number of students dropped last year.
View full question & answer→Question 421 Mark
The maximum temperature on a day in Delhi was $p ^\circ C$. The minimum temperature was $(p - 10)^\circ C.$
AnswerThe difference between maximum and minimum temperature on a day in Delhi was $10^\circ C.$
View full question & answer→Question 431 Mark
What is the area of a square whose side is m cm?
AnswerGiven, Side of a square $= m \ cm$
$\therefore$ Area of a square $=$ Side $\times $ Side $= m \times msq \ cm$
View full question & answer→Question 441 Mark
$r$ rupees = __________ paise
AnswerWe know that, $1$ rupee $= 100$ paise.
So, r rupees $= 100 \times $ r paise $= 100r$ paise.
View full question & answer→Question 451 Mark
Sharad used to take p cups tea a day. After having some health problem, he takes $p-5$ cups of tea a day.
AnswerSharad reduced the consumption of tea per day by $5$ cups after having some health problem.
View full question & answer→Question 461 Mark
The additive inverse of an integer $x$ is $2x.$
AnswerGiven, integer $= x$
Additive inverse of $x = -x$
Then, the sum of integer and its additive inverse $= x + (-x) = x - x = 0$
But according to question, additive inverse is $2x.$
So, the statement is false.
View full question & answer→Question 471 Mark
p \ kg of potatoes are bought for $Rs 70.$ Cost of $1\ kg$ of potatoes (in Rs) is .
AnswerCost of pkg potatoes $= Rs. 70$ Cost of $1\ kg$ potatoes $= Rs. 70/p$
View full question & answer→Question 481 Mark
$p$ litres = __________ millilitres.
AnswerWe know that, $1$ litre $= 1000$ millilitres.
So, p litres $= 1000 \times p$ millilitres $= 1000p$ millilitres.
View full question & answer→Question 491 Mark
Kartik is n years old. His father is $7n$ years old.
AnswerAge of Kartik’s father is seven times the age of Kartik.
View full question & answer→