Question
A funfair has activities for both children and adults. Activities can have group or pair or individual
participation. The winner in an activity is decided on the basis of scores. For some activities there
are penalties. Penalty points are subtracted from the scores.
This table below shows the details about the games and their scoring.Image
$1.$ Rohan and Samar compete in the car race.
Rohan’s car knocked down ive lags and Samar’s car knocked down one lag. Rohan reached the finish line faster than Samar.
Who is the winner and how many points did he score$?$

Answer

$1.$ Either Samar or $50$ points

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Given below is the map of a society park.
Image

The park has four grass patches of equal area.
The dotted line represents the path for running and jogging.
$1.$ What is the perimeter of grass patch $1?$
$A. 191\ m$
$B. 382\ m$
$C. 800\ m$
$D. 1528\ m$
$2. $What is the area of the running and jogging path$?$
$A. 3519\ m^2$
$B. 3600\ m^2$
$C. 8495.25 \ m^2$
$D. 37,500\ m^2$
$3.$ Two sitting benches are installed in the grass patches. The seat of each bench is of the length $1.2 m$ and width $0.7 m.$ How much area $($in $m^2)$ is reserved for sitting in the park$?$
$A. 0.84$
$B. 1.68$
$C. 3.36$
$D. 6.72$
$4.$ The patch $2$ is divided diagonally into two triangles of equal areas. Tulips are planted in one triangular area. What is the area in which the tulips are planted?
$A. 2831.75\ m^2$
$B. 4247.625\ m^2$
$C. 8495.25\ m^2$
$D. 18,750\ m^2$
$5.$ Inside the grass patch $4,$ lily lowers are planted to make a $1.25 m$ wide bed. The length of the bed is same as the length of the patch. What is the area $($in $m^2$ covered by lillies$)?$
$A. 88.125$
$B. 150.625$
$C. 243.5$
$D. 8645.875$
$6.$ Swings are installed for kids at the centre of grass patch $3.$ The area reserved for the swings is square in shape with a width of $40\ m.$ What is the remaining area of grass patch 3 after the swing installation$?$
$7$. One room in Joseph’s house has a circular glass roof. The diameter of the roof is $2.8\ m. $ What is the area of the glass roof?
$8.$ The circular frame of the glass roof is made of wire. What is the length of the wire$?$
$A. 6.16\ m$
$B. 8.8\ m$
$C. 17.6\ m$
$D. 12.32\ m$
Prabhat runs a typing company that processes the manuscripts obtained from publishing companies. There are two processes in this work—typing and typesetting. He owns one team for each of the two processes. He received a manuscript of 3960 pages from a publishing company ABD. He knows that his team of 24 typists can type 264 pages in a day and his team of 6 typesetters can typeset 360 pages in 4 days.
Q.1. How many days will Prabhat's team take to type the manuscript?
(a) 14 days$\quad$(b) 15 days$\quad$(c) 16 days$\quad$(d) 18 days
Q.2. If Prabhat employs 6 more typists in his team, in how many days will he be able to finish the typing work?
(a) $18 \frac{3}{4}$ days$\quad$(b) 15 days$\quad$(c) 12 days$\quad$(d) 10 days
Q.3. In how many days will Prabhat's team of typesetters finish typesetting the work?
(a) 48 days$\quad$ (b) 44 days$\quad$(c) 66 days$\quad$(d) 64 days
Q.4. If typesetting work begins only after the typing work is finished, what is the least number of days Prabhat needs to get the work done with his team of 30 typists and 6 type setters?
(a) 56 days $\quad$(b) 78 days$\quad$(c) 81 days$\quad$(d) 59 days
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$?$
$A. 200$
$B. 20$
$C. 2$
$D. 0.2$
A shelf with a triangular frame is ixed on a wall as shown below.
Image

The lengths of the rods used in the shaded triangular frame are $48\ cm, 55\ cm$ and $73\ cm.$
$1.$ What is the type of the shaded triangle$?$
$A.$ Obtuse triangle
$B.$ Isosceles triangle
$C.$ Equilateral triangle
$D. $ Right-angled triangle
$2.$ What can be the height of the shelf$?$
Mr Tiwari has two choices of investing his money. If he invests in a bank, he gets 10% simple interest. If he invests in his friend's company SIB, he gets 15% simple interest.
Q.1. If Mr Tiwari invests ₹6,00,000 with the bank, the interest that he receives after 2 years will be 
(a) ₹1,10,000$\quad$(b) ₹1,20,000$\quad$(c)₹ 60,000$\quad$(d) ₹₹80,000
Q.2. What sum invested in SIB company will amount to 6,65,000 in 6 years?
(a) ₹3,50,000$\quad$(b)₹4,00,000$\quad$(c)₹4,25,000$\quad$(d)₹4,50,000
Q.3. How long will it take the money invested in SIB company to become four times of itself?
(a) 12 years(b) 15 years(c) 20 years(d) 24 years
Q.4. Mr Tiwari wishes to invest ₹6,00,000 partly in the bank and partly in SIB company such that after 2 years, he receives the same interest from both. Find the sum that he should invest in the bank.
(a) ₹3,00,000$\quad$(b) ₹3,30,000$\quad$(c) ₹3,60,000$\quad$(d) ₹2,40,000
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.
In an equilateral triangle $ABC,$ the length of $AC = 10\ cm$ and altitude $AD = 6\ cm.$ $P$ is a point on $AB.$Image

The length of $BP = 4x – 1.$ The length of $PA = 3x+ 4$
$1.$ What is the length of $BP?$
$A. 1\ cm$
$B. 3\ cm$
$C. 5\ cm$
$D. 10\ cm$
$2.$ What is the length of the median on $BC?$
$A. 3\ cm$
$B. 5\ cm$
$C. 6\ cm$
$D. 10\ cm$
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 $1\ yr?$
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$?$