Read the passage given below and answer these questions: Dev was … - Vidyadip

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Read the passage given below and answer these questions: Dev was doing an experiment to find the radius $r$ of a sphere. For this he took a cylindrical container with radius $R = 7\ cm$ and height $10\ cm$. He filled the container almost half by water as shown in the left figure. Now he dropped the yellow sphere in the container. Now he observed as shown in the right figure the water level in the container raised from $A$ to $B$ equal to $3.40\ cm.$

$i.$ What is the approximate radius of the sphere?
$a. 7\ cm$
$b. 5\ cm$
$c. 4\ cm$
$d. 3\ cm$
$ ii.$ What is the volume of the cylinder?
$a. 700\ cm^3$
$b. 500\ cm^3$
$c. 1540\ cm^3$
$d. 2000\ cm^3$
$iii.$ What is the volume of the sphere?
$a. 700\ cm^3$
$b. 600\ cm^3$
$c. 500\ cm^3$
$d. 523.8\ cm^3$
$ iv.$ How many litres water can be filled in the full container? $($Take $1$ litre $= 1000\ cm^3):$
$a. 1.50$
$b. 1.44$
$c. 1.54$
$d. 2$
$v.$ What is the surface area of the sphere?
$a. 314.3\ m^2$
$b. 300\ m^2$
$c. 400\ m^2$
$d. 350\ m^2$

✓

Answer

$(i)$	$(b)$	$5\ cm$
$(ii)$	$(c)$	$1540\ cm^3$
$(iii)$	$(d)$	$523.8\ cm^3$
$(iv)$	$(c)$	$1.54$
$(v)$	$(a)$	$314.3\ m^2$

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In India, sunlight is available in abundance. Solar panels harness this energy and convert it into electric power. Mr. Krishan installed a triangular shaped solar panel of size 9 m, 9 m and 10 m on the roof of his house. Assuming that in the peak sunlight hours, 1 m² pannel produces 190 watts of electricity per hour, answer the related questions given below (Efficiency of the pannel and other factors are not accountable).

(i) Perimeter of the solar panel is:
(a) 14 m $\quad$(b) 18 m $\quad$(c) 35 m $\quad$(d) 28 m
(ii) Are in $m ^2$ of the solar panel can be calculated using the formula
(a) $\sqrt{s(s-a)(s-b)(s-c)}$
(b) $\sqrt{(s-a)(s-b)(s-c)}$
(c) $\sqrt{s(a-s)(b-s)(c-s)}$
(d)$\frac{1}{2} \sqrt{s(s-a)(s-b)(s-c)}$
where s is the semi-perimeter of the panel and a, b and care its sides.
(iii) Area of solar panel is:
(a) $\sqrt{140}$ sq. m $\quad$(b) $10 \sqrt{14} sq \cdot m$
(c) $14 \sqrt{10}$ sq. m $\quad$(d) $100 \sqrt{14}$ sq. m
(iv) The whole panel will produce: [Take $\sqrt{14}=3.74$ ]
(a) $190 \times 3.7$ watts/hour
(b) $190 \times 37.4$ watts/hour
(c) $190 \times 374$ watts/hour
(d) $190 \times 0.374$ watts/hour

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Read the following text carefully and answer the questions that follow:
Modern curricula include several problem$-$solving strategies. Teachers model the process, and students work independently to copy it. Sheela Maths teacher of class $9^{th}$ wants to explain the properties of parallelograms in a creative way, so she gave students colored paper in the shape of a quadrilateral and then ask the students to make a parallelogram from it by using paper folding.

$i.$ How can a parallelogram be formed by using paper folding?
$ii.$ If $\angle RSP =30^{\circ}$, then find $\angle RQP$.
$iii.$ If $\angle RSP =50^{\circ}$, then find $\angle SPQ$ ?
OR
If $SP =3 cm$, Find the $RQ.$

Read the Source Text given below and answer any four questions:

Chocolate is in the form of a quadrilateral with sides $6\ cm$ and $10\ cm, 5\ cm$ and $5\ cm($as shown in the figure$)$ is cut into two parts on one of its diagonal by a lady. Part$-I$ is given to her maid and part $II$ is equally divided among a driver and gardener.

$i.$ Length of $BD:$
$a. 9\ cm$
$b. 8\ cm$
$c. 7\ cm$
$d. 6\ cm$
Area of $\triangle\text{ABC}:$
$a. 24\ cm^2$
$b. 12\ cm^2$
$c. 42\ cm^2$
$d. 21\ cm^2$
The sum of all the angles of a quadrilateral is equal to:
$a. 180^\circ$
$b. 270^\circ$
$c. 360^\circ$
$d. 90^\circ$
A diagonal of a parallelogram divides it into two congruent:
$a.$ Square.
$b.$ Parallelogram.
$c.$ Triangles.
$d.$ Rectangle.
Each angle of the rectangle is:
$a.$ More than $90^\circ$
$b.$ Less than $90^\circ$
$c.$ Equal to $90^\circ$
$d.$ Equal to $45^\circ$

Hard plastic square shaped sheets are available in the.
The side length of sheets is as per requirement.
The price of a sheet is $z$ per square meter.
Anuj requires two sheets $– a$ smaller sheet with side length $x\ m$ and a larger sheet with side length $y\ m$. He has two choices:
Choice $1 –$ buy two separate sheets of side lengths $x\ m$ and $y\ m$
Choice $2 – $buy a single sheet with side length $(x+ y) m$
$4.$ What is the height of each container?
$5.$ What is the difference in price between the two choices?
$6.$ The area of a rectangle is $\left(3 x^2+x-2\right)$ square units. Its width is $(1+x)$ units. What is the length of the rectangle$?$
$7.$ A polynomial is expressed as $x^3+b x^2+c x+d=0$. The same polynomial can be written in factor form as $x+p x+q x+r=0$.
How is the constant term in the polynomial related to its factors $p, q,$ and $r?$
$A.$ $d=p+q+r$
$B.$ $d=(p+q) \times r$
$C.$ $d=p \times q \times r$
$D.$ $d=p q+q r+p r$
$8.$ A polynomial is divided by $(x-1)$. The quotient obtained is $3 x^3-x^2-x-4$, and the remainder is $-5 .$ Which polynomial meets these conditions$?$
$A.$ $3 x^3-x^2-x-9$
$B.$ $3 x^3-x^2-x-4$
$C.$ $3 x^4-4 x^3-3 x+4$
$D.$ $3 x^4-4 x^2-3 x-1$
9. What is the common factor of $x^3-x^2$ and $-22 x^2+142 x-120 ?$
$A. $ $x$
$B. (x – 1)$
$C. $ $x^2$
$D.$ $1$
$10.$ A polynomial is expressed as: $p (x)=x^3+x^2-x-1$
At what values of $x$ is the polynomial $p (x)=0 ?$

A parking lot for a city mall is shown below. The painted lines that separate the parking spaces are parallel.

$3.$ Parking space number $378$ is inclined at $60^\circ $ to the horizon line. At what angle is parking space $380$ inclined to the horizontal line$?$ Why$?$

Read the following text carefully and answer the questions that follow:
A children's park is in the shape of isosceles triangle said $\text{PQR}$ with $\text{PQ = PR, S}$ and $T$ are points on $\text{QR}$ such that $\text{QT = RS}$.

$i.$ Which rule is applied to prove that congruency of $\ce{\triangle PQS}$ and $\ce{\triangle PRT}$.
$ii.$ Name the type of $\ce{\triangle PST.}$
$iii.$ If $\ce{PQ=6 \ cm}$ and $\ce{QR=7 \ cm}$, then find perimeter of $\ce{\triangle PQR}$.
OR
If $\ce{\angle QPR =80^{\circ}}$ find $\ce{\angle PQR}$ ?

A construction company purchased a big cylindrical vessel to keep some liquid on it. Before using this vessel, the company decided to paint it properly. It costed $₹\ 3300$ to paint the inner curved surface of this $10 \ m$ deep cylindrical vessel at the rate of $₹\ 30$ per $m^2$.

$i.$ Find the inner curved surface area of the vessel,
$ii.$ Find the inner radius of the base and capacity of the vessel.

In the given figure, the isosceles triangle $ABC ≅ EAD.$ The point $E$ is equidistant from both $A$ and $B.$

$4.$ What is the value of $x?$
$A. 40^\circ $
$B. 60^\circ $
$C. 70^\circ $
$D. 80^\circ $
$5.$ What is the value of $y?$
$6.$ What is the value of $\angle BDC?$
$A. 30^\circ $
$B. 40^\circ $
$C. 50^\circ $
$D. 70^\circ $

A company manufactures wooden boxes. Given below is the picture of an open wooden box.

The height of the box is $25\ cm$
7. What is the surface area $($in $cm^2)$ of the box$?$
$A. 3500$
$B. 4700$
$C. 5900$
$D. 30000$
$8.$ A shopkeeper store cubes in it.
The side length of one cube is $9\ cm$
What would be the maximum number of cubes the shopkeeper can store in a box$? ($All cubes should be inside the box.$)$
$9.$ Rajan packs a football into a cubical cardboard box. The radius of the football is $11\ cm.$ Rajan keeps a margin of $1 \ cm$ from all the sides of the box while packing.
What is the side length of the cardboard box$?$
$A. 11\ cm$
$B. 20\ cm$
$C. 22\ cm$
$D. 24\ cm$

Following bar graph represents the sales of cold drinks of two companies A and B from 2015 to 2018.

Read the above bar graph and answer the following questions:
(i) The year in which the difference between the sales of two companies was highest, was
(a) 2018$\quad$ (b) 2015$\quad$ (c) 2016$\quad$ (d) 2017$\quad$
(ii) Total sales of A and B in the year 2016 was
(a) 116,000 units$\quad$ (b) 127,000 units$\quad$ (c) 138,000 units$\quad$ (d) 149,000 units
(iii) The minimum difference between the sales of company A and B in any year in the given period was
(a) 9,000 units$\quad$ (b) 7,000 units$\quad$ (c) 5,000 units$\quad$ (d) 3,000 units
(iv) In which year was the sales of company B more than the sales of company A?
(a) 2015$\quad$ (b) 2016$\quad$ (c) 2017$\quad$ d) 2018
(v) The ratio of the total sales in the year 2017 and that in 2018 was
a) 107:145$\quad$ (b) 29:36$\quad$ (c) 127: 145$\quad$ (d) 107: 127

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