A shelf with a triangular frame is ixed on a wall as shown below. 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?

7. D. Right-angled triangle 8. Accept any of the two lengths, either 48 or 55 ● 48 cm ● 55 cm

A shelf with a triangular frame is ixed on a wall as shown below.…

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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Pratibha made a paper lag by pasting an isosceles right triangle on a stick.

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

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An online game has $50$ levels. A gamer is in the Gold team until he cross of the $\frac{3}{4}$ total levels. After that he is in the Platinum team.
This table shows the rewards unlocked after completing various levels.

Levels completed	Rewards
More than or equal to $\frac{4}{5}$ levels	Jeep
More than $\frac{3}{5}$ levels but less than $\frac{4}{5}$ levels	Dress
More than $\frac{2}{5}$ levels but less than $\frac{3}{5}$ levels	Face mask
More than $\frac{1}{5}$ levels but less than $\frac{2}{5}$ levels	Badge

$1.$ Mita completed $37$ levels.
Which reward would she get$?$ Justify your answer.
$2.$ Mayank is at level $15$ in the game. In which team, would he play$?$

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Gaming apps allow users to download and play games in online or offline mode. A play store data shows 20 million downloads of 6 popular games. The table below shows the number of daily active users of the games

Game	Active users (in million)
KC	2.07
RJ	1.99
CM	1.82
SN	1.56
CR	1.34
HC	1.20

(i) Around 50% of those who downloaded the games are active users. Is the statement correct? Give reason to justify your answer.
(ii) Every fourth person who downloaded the games spends more than an hour a day playing them.
What percentage of active players play more than an hour a day?

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Sunder is a fruit seller. Today he bought plums to sell. He purchased them at the rate of 9 for 100 from the wholesale market.
Q.1. How many plums should he sell for ₹40 if he wishes to gain 20%?
(a) 3$\quad$ (b) 4$\quad$(c) 5$\quad$(d) 8
Q.2. He found that another fruit seller Kishan was selling plums at the rate of 6 for ₹90. Find the gain per cent of Kishan. (Assume that the wholesale rate is the same for all fruit sellers.
(a) 15%$\quad$(b) 20%$\quad$(c) 25%$\quad$(d) 35%
Q.3. Sunder decided to sell his plums at the rate of 7 for₹ 100. Find his gain per cent.
(a) $15 \frac{5}{9} \%$$\quad$(b) $17 \frac{7}{9} \%$$\quad$(c) $21 \frac{1}{9} \%$$\quad$(d) $22 \frac{2}{9} \%$
Q.4. In a box of 180 plums, he found that 28 were rotten and he had to throw them away. He sold the remaining plums at the rate of 8 for 100. Find his gain or loss per cent on this box.
(a) 2% gain$\quad$(b) 5% gain$\quad$(c) 2% loss$\quad$(d) 5% loss

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A diagram of a see-saw is given below.

$1.$ State all the pairs of vertically opposite angles in the given figure.
$2.$ Which of the following is a pair of alternate exterior angles?
$A. \angle 1$ and $\angle 4$
$B. \angle 2$ and $\angle 8$
$C. \angle 3$ and $\angle 8$
$D. \angle 4$ and $\angle 6$

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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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Given below is a piece of cardboard.

$1.$ What is its area$?$
$2.$ Jatin placed another cardboard of same size along the $12\ cm$ long edge.
What is the perimeter of the combined shape$?$

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Gaming apps allow users to download and play games in online or ofline mode. A play store data
shows $20$ million downloads of $6$ popular games. The table below shows the number of daily active users of the games:

Game	Active users (in millions)
$KC$	$2.07$
$RJ$	$1.99$
$CM$	$1.82$
$SN$	$1.56$
$CR$	$1.34$
$HC$	$1.20$

$1.$ Around $50\%$ of those who downloaded the games are active users.
Is the statement correct? Give reason to justify your answer.
$2.$ Every fourth person who downloaded the games spends more than an hour a day playing them.
What percentage of active players play more than an hour a day?

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An ice-cream cart has an ice-candy drawn on all sides, except the top and the bottom.

$1.$ Which geometric shape does the ice-cream container resemble$?$
$A.$ Cuboid
$B.$ Cylinder
$C.$ Cone
$D. $ Pyramid
$2.$ How many ice-candies are drawn on the cart$?$
$A. 1$
$B. 2$
$C. 4$
$D. 6$

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