CASE BASED
1. In a class the teacher asks every student to write an example of
AP. Two boys Aryan andRoshan writes their progressions as
-5,-2, 1,4 …… and 187, 184, 181,….. respectively. Now the
teacher asks the various students of the class the following
questions on this progression. Help students to find the answers
of the following.
(i) Find the sum of common difference of the two progressions.
(ii)Find the 34th term of the progression written by Roshan.
(iii) Find the sum of first 10 terms of the progression written by Aryan.
(iv) Which term of the two progressions will have the same value?
2.
(i) What is the height of the tower?
(ii) What is the height of Ajay’s house?
(iii) What will be the length of the shadow of the tower when Vijay’s house
casts a shadow of 12m?
(or)
(iv)When the tower casts a shadow of 40m, same time what will be the
length
of the shadow of Vijay’s house?
, 3. 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 questions-:
(i) Find the length of the diagonal if each
edge measures 6cm ?
(ii)Find the volume of the solid figure if the length of the edge is 7cm?
(iii)What is the surface area of hemisphere (ice cream) if the base radius is
7cm?
(or)
(iv)If the slant height of the conical part is 5 cm, and its radius is 4 cm, find its
height.
4. Ms. Sheela visited a store near her house and found that the glass jars
are arranged one above the other in a specific pattern.
On the top layer there are 3 jars. In the next layer there are 6 jars. In the
3rd layer from the top there are 9 jars and so on till the 8th layer.
On the basis of the above situation answer the following questions.
(i) Write an A.P whose terms represent the number of jars in different
layers starting from top . Also, find the common difference.
(ii) Is it possible to arrange 34 jars in a layer if this pattern is continued?
Justify your answer.
(iii) (a) If there are ‘n’ number of rows in a layer then find the expression
for finding the total number of jars in terms of . Hence find .
OR
(iii) (b) The shopkeeper added 3 jars in each layer. How many jars are
there in the 5th layer from the top?
5. A girl of height 90 cm is walking away from the base of a lamp-post for 4
seconds at a speed of 1.2 m/s. If the lamp is 3.6 m above the ground, then
(i) From which criteria ∆ ABE and ∆ CDE are similar?
(ii) What is the ratio of length AE to length AC?
1. In a class the teacher asks every student to write an example of
AP. Two boys Aryan andRoshan writes their progressions as
-5,-2, 1,4 …… and 187, 184, 181,….. respectively. Now the
teacher asks the various students of the class the following
questions on this progression. Help students to find the answers
of the following.
(i) Find the sum of common difference of the two progressions.
(ii)Find the 34th term of the progression written by Roshan.
(iii) Find the sum of first 10 terms of the progression written by Aryan.
(iv) Which term of the two progressions will have the same value?
2.
(i) What is the height of the tower?
(ii) What is the height of Ajay’s house?
(iii) What will be the length of the shadow of the tower when Vijay’s house
casts a shadow of 12m?
(or)
(iv)When the tower casts a shadow of 40m, same time what will be the
length
of the shadow of Vijay’s house?
, 3. 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 questions-:
(i) Find the length of the diagonal if each
edge measures 6cm ?
(ii)Find the volume of the solid figure if the length of the edge is 7cm?
(iii)What is the surface area of hemisphere (ice cream) if the base radius is
7cm?
(or)
(iv)If the slant height of the conical part is 5 cm, and its radius is 4 cm, find its
height.
4. Ms. Sheela visited a store near her house and found that the glass jars
are arranged one above the other in a specific pattern.
On the top layer there are 3 jars. In the next layer there are 6 jars. In the
3rd layer from the top there are 9 jars and so on till the 8th layer.
On the basis of the above situation answer the following questions.
(i) Write an A.P whose terms represent the number of jars in different
layers starting from top . Also, find the common difference.
(ii) Is it possible to arrange 34 jars in a layer if this pattern is continued?
Justify your answer.
(iii) (a) If there are ‘n’ number of rows in a layer then find the expression
for finding the total number of jars in terms of . Hence find .
OR
(iii) (b) The shopkeeper added 3 jars in each layer. How many jars are
there in the 5th layer from the top?
5. A girl of height 90 cm is walking away from the base of a lamp-post for 4
seconds at a speed of 1.2 m/s. If the lamp is 3.6 m above the ground, then
(i) From which criteria ∆ ABE and ∆ CDE are similar?
(ii) What is the ratio of length AE to length AC?
