Question
✓
Answer
(i) Distance between bank and hospital $=\sqrt{(-3-9)^2+(-1-5)^2}$
$=\sqrt{180}$ units or $6 \sqrt{5}$ units
(ii) Coordinates of E are $\left(\frac{9+5}{2}, \frac{5+(-5)}{2}\right)=(7,0)$
(iii) (a) Coordinates of D are $\left(\frac{-3+5}{2}, \frac{-1+(-5)}{2}\right)=(1,-3)$
Distance Partha need to cover $=\sqrt{(9-1)^2+(5-(-3))^2}$
$=\sqrt{128}$ units or $8 \sqrt{2}$ units
OR
(iii) (b) P is mid-point of BQ
$
\therefore a=\frac{-1+3}{2}=1
$
Q is mid-point of PA
$
\therefore b=\frac{1+9}{2}=5
$
$=\sqrt{180}$ units or $6 \sqrt{5}$ units
(ii) Coordinates of E are $\left(\frac{9+5}{2}, \frac{5+(-5)}{2}\right)=(7,0)$
(iii) (a) Coordinates of D are $\left(\frac{-3+5}{2}, \frac{-1+(-5)}{2}\right)=(1,-3)$
Distance Partha need to cover $=\sqrt{(9-1)^2+(5-(-3))^2}$
$=\sqrt{128}$ units or $8 \sqrt{2}$ units
OR
(iii) (b) P is mid-point of BQ
$
\therefore a=\frac{-1+3}{2}=1
$
Q is mid-point of PA
$
\therefore b=\frac{1+9}{2}=5
$
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Activities like running or cycling reduce stress and the risk of menta disorders like depression. Running helps build endurance. Childrer develop stronger bones and muscles and are less prone to gain weight The physical education teacher of a school has decided to conduct an inte school running tournament in his school premises. The time taken by group of students to run 100 m , was noted as follows:
Based on the above, answer the following questions:
(i) What is the median class of the above given data ?
(ii) (a) Find the mean time taken by the students to finish the race.
OR
(b) Find the mode of the above given data.
(iii) How many students took time less than 60 seconds?
| Time (in seconds) | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 |
| Number of students | 8 | 10 | 13 | 6 | 3 |
(i) What is the median class of the above given data ?
(ii) (a) Find the mean time taken by the students to finish the race.
OR
(b) Find the mode of the above given data.
(iii) How many students took time less than 60 seconds?
On a Sunday, your parents took you to a fair. You could see lot of toys displayed and you wanted them to buy a RUBIK'S cube and strawberry ice cream for you. Observe the figures and answer the following questions:
(i) The lengtt of the diagonal, if each edge measures 6 cm , is
(a) $3 \sqrt{3} cm$$\quad$ (b) $3 \sqrt{6} cm$$\quad$ (c) $2 \sqrt{3} cm$$\quad$ (d) $6 \sqrt{3} cm$<br>
(ii) Volume of the solid figure, if the length of the edge is 7 cm , is
(a) $256 cm^3$$\quad$ (b) $196 cm^3$$\quad$ (c) $343 cm^3$$\quad$ (d) $434 cm^3$
(iii) What is the curved surface area of hemisphere (ice cream) if the base radius is 7 cm ?
(a) $309 cm^2$$\quad$ (b) $308 cm^2$$\quad$ (c) $803 cm^2$$\quad$ (d) $903 cm^2$
(iv) Slant height of a cone if the radius is 7 cm and the height is 24 cm is
(a) 26 cm$\quad$ (b) 25 cm$\quad$ (c) 52 cm$\quad$ (d) 62 cm
→(i) The lengtt of the diagonal, if each edge measures 6 cm , is
(a) $3 \sqrt{3} cm$$\quad$ (b) $3 \sqrt{6} cm$$\quad$ (c) $2 \sqrt{3} cm$$\quad$ (d) $6 \sqrt{3} cm$<br>
(ii) Volume of the solid figure, if the length of the edge is 7 cm , is
(a) $256 cm^3$$\quad$ (b) $196 cm^3$$\quad$ (c) $343 cm^3$$\quad$ (d) $434 cm^3$
(iii) What is the curved surface area of hemisphere (ice cream) if the base radius is 7 cm ?
(a) $309 cm^2$$\quad$ (b) $308 cm^2$$\quad$ (c) $803 cm^2$$\quad$ (d) $903 cm^2$
(iv) Slant height of a cone if the radius is 7 cm and the height is 24 cm is
(a) 26 cm$\quad$ (b) 25 cm$\quad$ (c) 52 cm$\quad$ (d) 62 cm
Class $X$ students of a secondary school in Krish Nagar have been allotted a rectangular plot of land for gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is a triangular grassy lawn in the plot as shown in the Fig. 6.18. The students are to sow seeds of flowering plants on the remaining area of the plot. Considering $A$ as origin, $A D$ along $x$-axis and $A B$ along $y$-axis answer questions:
(i) What are the coordinates of $A$ ?
(a) $(0,1)$ $\qquad$ $\qquad$ (b) $(1,0)$ $\qquad$ (c) $(0,0)$ $\qquad$ (d) $(-1,-1)$
(ii) What are the coordinates of $P$ ?
(a) $(4,6)$ $\qquad$ (b) $(6,4)$ $\qquad$ (c) $(4,5)$ $\qquad$ (d) $(5,4)$
(iii) What are the coordinates of $R$ ?
(a) $(6,5)$ $\qquad$ (b) $(5,6)$ $\qquad$ (c) $(6,0)$ $\qquad$ (d) $(7,4)$
(iv) What are the coordinates of $D$ ?
(a) $(16,0)$ $\qquad$ (b) $(0,0)$ $\qquad$ (c) $(0,16)$ $\qquad$ (d) $(16,1)$
→(i) What are the coordinates of $A$ ?
(a) $(0,1)$ $\qquad$ $\qquad$ (b) $(1,0)$ $\qquad$ (c) $(0,0)$ $\qquad$ (d) $(-1,-1)$
(ii) What are the coordinates of $P$ ?
(a) $(4,6)$ $\qquad$ (b) $(6,4)$ $\qquad$ (c) $(4,5)$ $\qquad$ (d) $(5,4)$
(iii) What are the coordinates of $R$ ?
(a) $(6,5)$ $\qquad$ (b) $(5,6)$ $\qquad$ (c) $(6,0)$ $\qquad$ (d) $(7,4)$
(iv) What are the coordinates of $D$ ?
(a) $(16,0)$ $\qquad$ (b) $(0,0)$ $\qquad$ (c) $(0,16)$ $\qquad$ (d) $(16,1)$
Read the following text carefully and answer the questions that follow:
$\text{TOWER OF PISA}$ : To prove that objects of different weights fall at the same rate, Galileo dropped two objects with different weights from the Leaning Tower of Pisa in Italy. The objects hit the ground at the same time. An object dropped off the top of Leaning Tower of Pisa falls vertically with constant acceleration. If $s $ is the distance of the object above the ground $($in feet$) \ t$ seconds after its release, then $s$ and $t$ are related by an equation of the form $s=a+b t^2$ where $a$ and $b$ are constants. Suppose the object is $180$ feet above the ground $1$ second after its release and $132$ feet above the ground $2$ seconds after its release.
$i$. Find the constants $a$ and $b$.
$ii$. How high is the Leaning Tower of Pisa?
$iii$. How long does the object fall?
OR
At $t = 2 \sec,$ the object is at what height?
→$\text{TOWER OF PISA}$ : To prove that objects of different weights fall at the same rate, Galileo dropped two objects with different weights from the Leaning Tower of Pisa in Italy. The objects hit the ground at the same time. An object dropped off the top of Leaning Tower of Pisa falls vertically with constant acceleration. If $s $ is the distance of the object above the ground $($in feet$) \ t$ seconds after its release, then $s$ and $t$ are related by an equation of the form $s=a+b t^2$ where $a$ and $b$ are constants. Suppose the object is $180$ feet above the ground $1$ second after its release and $132$ feet above the ground $2$ seconds after its release.
$i$. Find the constants $a$ and $b$.
$ii$. How high is the Leaning Tower of Pisa?
$iii$. How long does the object fall?
OR
At $t = 2 \sec,$ the object is at what height?
Read the following text carefully and answer the questions that follow:
Elpis Technology is a laptop manufacturer. The company works for many branded laptop companies and also provides them with spare parts. Elpis Technology produced $6000$ units in $3^{rd}$ year and $7000$ units in the $7^{th}$ year.
Assuming that production increases uniformly by a fixed number every year.
$i.$ Find the production in the $1^{st}$ year.
$ii.$ Find the production in the $5^{th}$ year.
$iii$. Find the total production in $7$ years.
OR
Find in which year $10000$ units are produced?
→Elpis Technology is a laptop manufacturer. The company works for many branded laptop companies and also provides them with spare parts. Elpis Technology produced $6000$ units in $3^{rd}$ year and $7000$ units in the $7^{th}$ year.
Assuming that production increases uniformly by a fixed number every year.
$i.$ Find the production in the $1^{st}$ year.
$ii.$ Find the production in the $5^{th}$ year.
$iii$. Find the total production in $7$ years.
OR
Find in which year $10000$ units are produced?
In a class the teacher asks every student to write an example of A.P. Two friends Geeta and
Madhuri writes their progressions as -5, -2, 1, 4, ... and 187, 184, 181,.... respectively. Now,
the teacher asks various students of the class the following questions on these two
progressions. Help students to find the answers of the questions.
(i) Find the 34th term of the progression written by Madhuri.
(ii) Find the sum of common difference of the two progressions.
(iii) Find the 19th term of the progression written by Geeta.
OR
Find the sum of first 10 terms of the progression written by Geeta.
Madhuri writes their progressions as -5, -2, 1, 4, ... and 187, 184, 181,.... respectively. Now,
the teacher asks various students of the class the following questions on these two
progressions. Help students to find the answers of the questions.
(i) Find the 34th term of the progression written by Madhuri.
(ii) Find the sum of common difference of the two progressions.
(iii) Find the 19th term of the progression written by Geeta.
OR
Find the sum of first 10 terms of the progression written by Geeta.
Two ships are there in the sea on either side of a light house in such away that the ships and the light house are in the same straight line. The angles of depression of two ships are observed from the top of the light house are 60º and 45º respectively. If the height of the light house is 200m, find the distance between the two ships. $(\text{Use }\sqrt{3}=1.73)$
→London eye is an amusement ride consisting of a rotating upright big wheel with multiple passenger-carrying components (commonly referred to as passenger cars, cabins, tubs, capsules, gondolas or pods) attached to the rim in such a way that as the wheel turns, they are kept upright usually by gravity. After taking a ride in London eye, Anu came out from the crowd and was observing her friends who were enjoying the ride. She was curious about the different angles and measures that the wheel will form. She makes a figure as given below.
(i) In Fig. the measure of $\angle R O Q$ is
(a) $60^{\circ}$ $\qquad$ (b) $100^{\circ}$ $\qquad$ (c) $150^{\circ}$ $\qquad$ (d) $90^{\circ}$
(ii) In Fig. 8.33, The measure of $\angle R Q P$ is
(a) $75^{\circ}$ $\qquad$ (b) $60^{\circ}$ $\qquad$ (c) $30^{\circ}$ $\qquad$ (d) $90^{\circ}$
(iii) In Fig. 8.33, the measure of $\angle R S Q$ is
(a) $60^{\circ}$ $\qquad$ (b) $75^{\circ}$ $\qquad$ (c) $100^{\circ}$ $\qquad$ (d) $30^{\circ}$
(iv) In Fig. 8.33, the measure of $\angle O R P$ is
(a) $90^{\circ}$ $\qquad$ (b) $70^{\circ}$ $\qquad$ (c) $100^{\circ}$ $\qquad$ (d) $60^{\circ}$
→(i) In Fig. the measure of $\angle R O Q$ is
(a) $60^{\circ}$ $\qquad$ (b) $100^{\circ}$ $\qquad$ (c) $150^{\circ}$ $\qquad$ (d) $90^{\circ}$
(ii) In Fig. 8.33, The measure of $\angle R Q P$ is
(a) $75^{\circ}$ $\qquad$ (b) $60^{\circ}$ $\qquad$ (c) $30^{\circ}$ $\qquad$ (d) $90^{\circ}$
(iii) In Fig. 8.33, the measure of $\angle R S Q$ is
(a) $60^{\circ}$ $\qquad$ (b) $75^{\circ}$ $\qquad$ (c) $100^{\circ}$ $\qquad$ (d) $30^{\circ}$
(iv) In Fig. 8.33, the measure of $\angle O R P$ is
(a) $90^{\circ}$ $\qquad$ (b) $70^{\circ}$ $\qquad$ (c) $100^{\circ}$ $\qquad$ (d) $60^{\circ}$
Two schools 'P' and 'Q' decided to award prizes to their students for two games of Hockey ₹$ x$ per student and Cricket ₹ y per student. School 'P' decided to award a total of ₹ 9,500 for the two games to 5 and 4 students respectively; while school 'Q' decided to award ₹ 7,370 for the two games to 4 and 3 students respectively.
(i) Represent the following information algebraically (in terms of $x$ and $y$ ).
(ii) What is the prize amount for hockey?
(iii) Prize amount of which game is more and by how much?
(iv) What will be the total prize amount if there are 2 students each from two games?
→(i) Represent the following information algebraically (in terms of $x$ and $y$ ).
(ii) What is the prize amount for hockey?
(iii) Prize amount of which game is more and by how much?
(iv) What will be the total prize amount if there are 2 students each from two games?
In a pool at an aquarium, a dolphin jumps out of the water travelling at 20 cm per second. Its height above water level after $t$ seconds is given by $h=20 t-16 t^2$.
(i) Find zeroes of polynomial $p(t)=20 t-16 t^2$.
(ii) Which of the following type of graph represents $p(t)$ ?
(iii) What would be the value of $h$ at $t=\frac{3}{2}$ ? Interpret the result.
(iv) How much distance has the dolphin covered before hitting the water level again?
→(i) Find zeroes of polynomial $p(t)=20 t-16 t^2$.
(ii) Which of the following type of graph represents $p(t)$ ?
(iii) What would be the value of $h$ at $t=\frac{3}{2}$ ? Interpret the result.
(iv) How much distance has the dolphin covered before hitting the water level again?