The amusement park is divided into three regular-shaped sections for rides, ticket room and car parking respectively. 1. What is the perimeter of the amusement park? A. 6P B. 8P C. 9P D. 11P 2. What area of the amusement park is occupied by the parking space?

The amusement park is divided into three regular-shaped sections …

Liqueied gas is a type of fuel used in cars and other vehicles. After petrol and diesel, liqueied gas is the third most popular fuel in the world. For the past two decades, it has been used as an
alternative for petrol worldwide.
$1.$ In the year $2019,$ worldwide consumption of liqueied gas was $27$ million tonnes, whereas in India, its consumption was $0.42$ million tonnes.
What is the ratio of consumption of liqueied gas in India to worldwide$?$
$2.$ In the year $2019,$ India consumed $28.3$ million tonnes of petrol and $83.5$ million tonnes of diesel.
Is it correct to say that in the year $2019,$ the consumption of diesel was less than three times the
consumption of petrol in India? Give reasons.
$3.$ The cost of per litre petrol in New Delhi on $11$ August, $2021$ was $Rs. 101.84.$ On the same day, the cost of one litre of liqueied gas was $60\%$ less than the cost of petrol in New Delhi.
Which of the following could be the cost of liqueied gas?
$A. Rs. 38.56$
$B. Rs. 61.27$
$C. Rs. 142.58$
$D. Rs. 162.94$
$4.$ Liqueied gas contains gases like butane and propane. The percentage of both butane and propane in liqueied gas varies from 100% of propane to $20\%$ of propane.
One litre of liqueied gas weighs $510\ g$ in which the mass of propane gas is $357\ g.$
Which of the following shows the percentage of propane gas present in $1\ L$ of the liqueied gas$?$
$A. 20\%$
$B. 30\%$
$C. 70\%$
$D. 100\%$
$5.$ Parvez wants to use liqueied gas in his car. He needs to install a liqueied gas kit in his car. The kit costs $Rs. 50,000.$ To install the kit, he paid $Rs. 5000$ and has availed a loan of $Rs. 45,000$ at a rate of $10\%$ per annum using simple interest. The repayment period for him is $1\ yr.$
What is the total sum of money (in rupees) Parvez has to pay in $1\ yr?$

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Here is a picture of a car wheel.

1. Awhat is the order of rotational symmetry for this wheel?

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Insulin is a hormone made by the pancreas in the human body. It helps to regulate blood sugar level and absorbs glucose to get energy. The number of required units of insulin varies according to the individual.
In some cases, an individual body is not able to produce suficient amount of insulin. For those
individuals, supplementary units of insulin are injected into the body.
$1.$ A doctor uses this formula to calculate the daily insulin units required for Prakhar’s body.
Daily insulin requirement $($units$) = 0.55 ×$ Total body mass $($kilograms$)$
$2.$ Insulin also helps in disposing of carbohydrates in the human body.
In Prakhar’s body, $14.5$ insulin units dispose of $290$ grams of carbohydrate.
How many grams of carbohydrates are disposed of by $1$ insulin unit$?$
$A. 200$
$B. 20$
$C. 2$
$D. 0.2$

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Nanoscience is the study of structures and materials of an ultra-small scale. The widely used
units to measure length in nanoscience are nanometre and micrometre.
The relations between different units of length are given below.
$10^3$ nanometre $(nm) = 1$ micrometre $(µm)$
$10^6$ nanometre $(nm) = 1$ millimetre $(mm)$
$10^7$ nanometre $(nm) = 1$ centimetre $(cm)$
$10^9$ nanometre $(nm) = 1$ meter $(m)$
$1.$ Electron microscopes are used to see very small particles. These microscopes can enlarge an image up to $106$ times. A laboratory developed a switch that is $1$ nanometre wide. How wide will the switch look when seen under an electron microscope$?$
$A. 1$ nanometre
$B. 1$ micrometre
$C. 1$ millimetre
$D. 1$ centimetre
$2.$ Asha measures the thickness of one sheet of newspaper. A stack of $100$ sheets of newspaper is $1\ cm$ thick. What would be the thickness of the newspaper when expressed in nanometres?
$3.$ Scalpel is an instrument used by surgeons in surgery. During an experiment it was found that the size of tip of scalpel can affect the recovery rates of patients.
Two scalpels of tip sizes $0.8$ micrometre and $12.5$ micrometre were tested.
Patients on whom the scalpel with tip radius $0.8$ micrometre was used healed faster.
What is the difference between the radii of the two tips in millimetres$?$
$A. 1.6 \times 10^{-4}$
$B.0.8 \times 10^{-3}$
$C. 1.17 \times 10^{-2}$
$D. 4.5 \times 10^{-2}$
$4.$ Deoxyribonucleic acid $(DNA)$ is found in every cell of almost all living beings including humans. One strand of human $DNA $ is $2.5$ nanometres in diameter. What is the diameter of the strand of $DNA$ in meters$?$
$A. 2.5 \times 10^{-10}$
$B. 1 \times 10^{-9}$
$C. 2.5 \times 10^{-9}$
$D. 2.5 \times 10^9$
$5$. Research says, “Human fingernail grows one nanometre in one second.”
What would be the approximate growth of the fingernail (in cm) in $24$ hours?
$A. 8.64 \times 10^{-3}$
$B.8.64 \times 10^{-2}$
$C. 8.64 \times 10^3$
$D. 8.64 \times 10^{11}$
$6.$ Rajat claims, “A negative number raised to a power is always less than the number itself.” Give an example that proves that Rajat is incorrect.
$7.$ Simplify the following.
$\{(92)^4× 9^5\} ÷ 9^8$
$8.$ Assume x and y are two negative numbers. ‘The result of the multiplication of $x$ and $y$ with the same positive power is greater than the multiplication of $x$ and $y$ with the same negative power.’
Give an example to support this statement.

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Carat $(K)$ is a unit to measure the purity of gold. The higher the carat, the purer the gold. $24K$ gold is considered as the purest gold with no traces of any other metal in it.
$22K$ gold has $2$ parts other metals present in it.
$1.$ Puneet is a jeweller. He wants to make $18K$ gold jewellery from $22K$ gold.
What percent of other metals are to be added to the $22K$ gold$?$
$2.$ Countries have their own minimum acceptance standard for an item to be called a gold item.
The minimum accepted standard of gold is $10$ carat in the $US$ and $8$ carat in Denmark.
What is the difference in percentage of gold between the standards set by the two countries$?$
Round your answer to the nearest whole number.

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Jacob and Mariya participated in Archery.
Jacob’s scores for ive shots are given below.

First shot	Second shot	Third shot	Fourth shot	Fifth shot
$0$	$4$	$8$	$10$	$6$

Mariya’s scores for three shots are given below.

First shot	Second shot	Third shot
$0$	$4$	$8$

Mariya won the competition.
$1.$ How much she did score in her fourth and fifth shots$?$
$2.$ Team Alpha and Beta played the Paint Ball game. Each team had $6$ members and each member shot the paint ball three times.
Team Alpha hit the opponent team $12$ times. Team Beta hit the opponent team $15$ times.
Which team got more penalty points and how many penalty points did they get$?$
$3.$ In another match, each member of team Alpha got hit $3$ times.
$4$ members hit back $5$ times each and the rest hit back $2$ times each.
Which calculation shows the team’s score$?$
$A. 6 × [3 + (-10)] + 4 × (5 + 20) + 2 × (2 + 20)$
$B. 6 × [3 × (-10)] + 4 × (5 × 20) + 2 × (2 × 20)$
$C. 6 + [3 + (-10)] + 4 + (5 + 20) + 2 + (2 + 20)$
$D. 6 + [3 + (-10)] + 4 + (5 + 20) + 2 + (2 + 20)$

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Anand runs a computer repair service company. For a Lenovo laptop, he charges ₹450 for diagnosis and ₹60 per hour for repairs. For an Acer laptop, he charges ₹360 for diagnosis and ₹90 per hour for repairs.
Q.1. Anand repaired Mr Sharma's Lenovo laptop. He charged ₹810 for the work. How long did he take to complete the repair work?
(a) 5 hours$\quad$(b) 6 hours$\quad$(c) 7 hours$\quad$ (d) 8 hours
Q.2. Anand repaired Mr Singh's Acer laptop. The total charges were ₹1170. How long did he take to complete the repair work?
(a) 9 hours$\quad$(b) 8 hours$\quad$(c) 7 hours$\quad$(d) 6 hours
Q.3. What were the total service charges that Mr Dev had to pay for both the laptops?
(a) ₹ 630 $\quad$(b) ₹810$\quad$ (c) ₹1260$\quad$(d) ₹1620

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During the $HC$ game, players can spin the wheel to earn points.

$1.$ What is the probability that she earns $6$ points$?$

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The Bureau of Indian Standards $(BIS),$ certiies the purity of gold jewellery using hallmark codes.
The $BIS$ hallmark codes for gold jewellery are given below.

Hallmark code	Purity of gold jewellery (Carats)
$22K916$	$22$
$18K750$	$18$
$14K585$	$14$

$1.$ Riya purchased a gold necklace weighing $20 g$ hallmarked $18K750.$ How many grams of pure gold are in the necklace$?$

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In the triangle $XYZ,$ the median $XP$ is half the length of the side $YZ.$
In the triangle, $XZQ, XZ = ZQ.$

$1.$ What is the measure of $\angle ZXQ?$

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