CBSE PYQ 2024 - 2023 || Application of Derivative || Case Study || NCERT Class 12 Chapter 6
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Ex 6.1 Q1 To Q18 NCERT Class 12 Application of Derivative ::https://youtube.com/live/nW1DbS2S7z8?...
Ex 6.2 Q1 To Q6 NCERT Chapter 6 Application of Derivatives :: https://youtube.com/live/I8R3UUDnYWU?...
Ex 6.2 Q7 To Q19 NCERT Chapter 6 Application of Derivatives :: https://youtube.com/live/wup2FXbUOS0?...
Ex 6.3 Q1 To Q15 NCERT Chapter 6 Application of Derivatives :: https://youtube.com/live/2iA45SkEvJ0?...
Ex 6.3 Q15 To Q27 NCERT Chapter 6 Application of Derivatives :: https://youtube.com/live/dPHLQViGPNs?...
Ex 6.4 Q1 To Q9 NCERT Chapter 6 Application of Derivatives ::https://youtube.com/live/3ME-w9jclyA?...
Ex 6.5 Q1 To Q4 NCERT Chapter 6 Application of Derivatives :: https://youtube.com/live/oOhUIqaRrLE?...
Ex 6.5 Q5 To Q16 NCERT Chapter 6 Application of Derivatives :: https://youtube.com/live/eVPG5Zhgyrg?...
Ex 6.5 Q17 To Q22 NCERT Chapter 6 Application of Derivatives ::https://youtube.com/live/uxTrp4KBjJg?...
Ex 6.5 Q23 To Q29 NCERT Chapter 6 Application of Derivatives ::https://youtube.com/live/GsGNAeCeFOo?...
Miscellaneous Ex Q1 To Q8 NCERT Chapter 6 Application of Derivatives ;::https://youtube.com/live/EaOnBVZUuRA?...
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Q) CASE STUDY 01 CBSE 2023
In order to set up a rain water harvesting system, a tank to collect rain water is to be dug. The tank should have a square base and a capacity of 250 𝐦^𝟑. The cost of land is Rs. 5,000 per square metre and cost of digging increases with depth and for the whole tank, it is Rs. 40,000 𝐡^𝟐, where h is the depth of the tank in metres, x is the side of the square base of the tank in metres.
ELEMENTS OF A TYPICAL RAIN WATER HARVESTING SYSTEM
Based on the above information, answer the following questions:
(i) Find the total cost C of digging the tank in terms of x.
(ii) Find 𝐝𝐂/𝐝𝐱
(iii) (a) Find the value of x for which cost C is minimum.
OR
(iii) (a) Check whether the cost of function C(x) expressed in terms of x is increasing or not, where
Q) CASE STUDY O2 CBSE 2023
Sooraj’s father wants to construct a rectangular garden using a brick wall on one side of the garden and wire fencing for the other three sides as shown in the figure. He has 200 metres of fencing wire.
Based on the above information, answer the following questions:
(i) Let ‘x’ metres denote the length of the side of the garden perpendicular to the brick wall and ‘y’ metres denote the length of the side parallel to the brick wall. Determine the relation representing the total length of fencing wire and also write A(x), the area of the garden.
(ii) Determine the maximum value of A(x).
Q12) CASE STUDY 03
Engine displacement is the measure of the cylinder volume swept by all the pistons of piston engine. The piston moves inside the cylinder bore. The cylinder bore in the form of circular cylinder open at the top is to be made from a metal sheet of area 75𝛑 〖𝐜𝐦〗^𝟐.
Based on the above information, answer the following questions:
(i) If the radius of cylinder is r cm and height is h cm, then write the volume V of cylinder in terms of radius r.
(ii) Find 𝐝𝐕/𝐝𝐫
(iii)(a) Find the radius of cylinder when its volume is maximum.
(iii) (b) For maximum volume, h r. State true or false and justify
Q) CASE STUDY 04 CBSE 2023
The equation of the path traced by a roller-coaster is given by the polynomial f(x) = 𝐚(𝐱+𝟗)(𝐱+𝟏)(𝐱−𝟑). If the roller-coaster crossed
y-axis at a point (0, -1) answer the following:
(i) Find the value of ‘a’.
(ii) Find 𝐟"(𝐱) 𝐚𝐭 𝐱=𝟏.
Q) CASE STUDY 05
A volleyball player serves the ball which takes a parabolic path given by the equation 𝐡(𝐭)=−𝟕/𝟐 𝐭^𝟐+𝟏𝟑/𝟐 𝐭+𝟏, where h(t) is the height of the ball at any time t (in seconds), (𝐭≥𝟎).
Based on the above information, answer the following questions:
(i) Is h(t) a continuous function? Justify.
Q) CASE STUDY 06
A tank, as shown in the figure below, formed using a combination of cylinder and a cone, offers better drainage as compared to a flat-bottomed tank.
A tap is connected to such a tank whose conical part is full of water. Water is dripping out from a tap at the bottom at the uniform rate of 2 〖𝐜𝐦〗^𝟑/𝐬. The semi-vertical angle of the conical tank is 45°.
On the basis of given information, answer the following questions:
(i) Find the volume of water in the tank in terms of its radius r.
(ii) Find rate of change of radius at an instant when r = 2√𝟐 cm.
(iii) (a) Find the rate at which the wet surface of the conical tank is decreasing at an instant when radius r = 2√𝟐 cm.
(iii) (b) Find the rate of change of height ‘h’ at an instant when slant height is 4cm.
(ii) Find the time at which the height of the ball is maximum
Ex 6.1 Q1 To Q18 NCERT Class 12 Application of Derivative ::https://youtube.com/live/nW1DbS2S7z8?...
Ex 6.2 Q1 To Q6 NCERT Chapter 6 Application of Derivatives :: https://youtube.com/live/I8R3UUDnYWU?...
Ex 6.2 Q7 To Q19 NCERT Chapter 6 Application of Derivatives :: https://youtube.com/live/wup2FXbUOS0?...
Ex 6.3 Q1 To Q15 NCERT Chapter 6 Application of Derivatives :: https://youtube.com/live/2iA45SkEvJ0?...
Ex 6.3 Q15 To Q27 NCERT Chapter 6 Application of Derivatives :: https://youtube.com/live/dPHLQViGPNs?...
Ex 6.4 Q1 To Q9 NCERT Chapter 6 Application of Derivatives ::https://youtube.com/live/3ME-w9jclyA?...
Ex 6.5 Q1 To Q4 NCERT Chapter 6 Application of Derivatives :: https://youtube.com/live/oOhUIqaRrLE?...
Ex 6.5 Q5 To Q16 NCERT Chapter 6 Application of Derivatives :: https://youtube.com/live/eVPG5Zhgyrg?...
Ex 6.5 Q17 To Q22 NCERT Chapter 6 Application of Derivatives ::https://youtube.com/live/uxTrp4KBjJg?...
Ex 6.5 Q23 To Q29 NCERT Chapter 6 Application of Derivatives ::https://youtube.com/live/GsGNAeCeFOo?...
Miscellaneous Ex Q1 To Q8 NCERT Chapter 6 Application of Derivatives ;::https://youtube.com/live/EaOnBVZUuRA?...
#pyq
#cbsepyq
#casestudy
#cbsecasestudy
#casestudybasedquestions
#casestudybasedquestionsapplicationofderivative
#cbsesamplepaper2024
#cbsepyq2024
#cbsepyq2023
Q) CASE STUDY 01 CBSE 2023
In order to set up a rain water harvesting system, a tank to collect rain water is to be dug. The tank should have a square base and a capacity of 250 𝐦^𝟑. The cost of land is Rs. 5,000 per square metre and cost of digging increases with depth and for the whole tank, it is Rs. 40,000 𝐡^𝟐, where h is the depth of the tank in metres, x is the side of the square base of the tank in metres.
ELEMENTS OF A TYPICAL RAIN WATER HARVESTING SYSTEM
Based on the above information, answer the following questions:
(i) Find the total cost C of digging the tank in terms of x.
(ii) Find 𝐝𝐂/𝐝𝐱
(iii) (a) Find the value of x for which cost C is minimum.
OR
(iii) (a) Check whether the cost of function C(x) expressed in terms of x is increasing or not, where
Q) CASE STUDY O2 CBSE 2023
Sooraj’s father wants to construct a rectangular garden using a brick wall on one side of the garden and wire fencing for the other three sides as shown in the figure. He has 200 metres of fencing wire.
Based on the above information, answer the following questions:
(i) Let ‘x’ metres denote the length of the side of the garden perpendicular to the brick wall and ‘y’ metres denote the length of the side parallel to the brick wall. Determine the relation representing the total length of fencing wire and also write A(x), the area of the garden.
(ii) Determine the maximum value of A(x).
Q12) CASE STUDY 03
Engine displacement is the measure of the cylinder volume swept by all the pistons of piston engine. The piston moves inside the cylinder bore. The cylinder bore in the form of circular cylinder open at the top is to be made from a metal sheet of area 75𝛑 〖𝐜𝐦〗^𝟐.
Based on the above information, answer the following questions:
(i) If the radius of cylinder is r cm and height is h cm, then write the volume V of cylinder in terms of radius r.
(ii) Find 𝐝𝐕/𝐝𝐫
(iii)(a) Find the radius of cylinder when its volume is maximum.
(iii) (b) For maximum volume, h r. State true or false and justify
Q) CASE STUDY 04 CBSE 2023
The equation of the path traced by a roller-coaster is given by the polynomial f(x) = 𝐚(𝐱+𝟗)(𝐱+𝟏)(𝐱−𝟑). If the roller-coaster crossed
y-axis at a point (0, -1) answer the following:
(i) Find the value of ‘a’.
(ii) Find 𝐟"(𝐱) 𝐚𝐭 𝐱=𝟏.
Q) CASE STUDY 05
A volleyball player serves the ball which takes a parabolic path given by the equation 𝐡(𝐭)=−𝟕/𝟐 𝐭^𝟐+𝟏𝟑/𝟐 𝐭+𝟏, where h(t) is the height of the ball at any time t (in seconds), (𝐭≥𝟎).
Based on the above information, answer the following questions:
(i) Is h(t) a continuous function? Justify.
Q) CASE STUDY 06
A tank, as shown in the figure below, formed using a combination of cylinder and a cone, offers better drainage as compared to a flat-bottomed tank.
A tap is connected to such a tank whose conical part is full of water. Water is dripping out from a tap at the bottom at the uniform rate of 2 〖𝐜𝐦〗^𝟑/𝐬. The semi-vertical angle of the conical tank is 45°.
On the basis of given information, answer the following questions:
(i) Find the volume of water in the tank in terms of its radius r.
(ii) Find rate of change of radius at an instant when r = 2√𝟐 cm.
(iii) (a) Find the rate at which the wet surface of the conical tank is decreasing at an instant when radius r = 2√𝟐 cm.
(iii) (b) Find the rate of change of height ‘h’ at an instant when slant height is 4cm.
(ii) Find the time at which the height of the ball is maximum
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