Test: Rate of Change of Quantities and Approximation(13 Sep) - JEE MCQ

Let V be the instantaneous volume of the cube.
dV/dt = 3 cm³/s
Let x be the side of the cube.
V = x³
dV/dt = 3x² * (dx/dt)
3 = 3*(5²)*(dx/dt)
So, dx/dt = 1/25 cm/s

C(x) = 5x² + 14x + 6
Marginal Cost M(x) = C’(x)
M(x) = 10x +14
So, M(5) = 50 + 14
= 64 Rs

Tan(z) = ^h⁄_x

Rate of increase of radius dr/dt = 2 cm/s
Area of circle A = πr²
dA/dt = π*(2r)*(dr/dt)
= π*(24)*2
= 48π cm²/s
Rate of increase of area is 48π cm²/s (increasing as it is positive).

Let x=4, Δx=0.01

y=x^½ = 2

y+Δy = (x+ Δx)^½ = (4.01)^½

Δy = (dy/dx) * Δx

Δy = (x^(-1/2))/2 * Δx

Δy = (½)*(½) * 0.01

Δy = 0.25 * 0.01

Δy = 0.0025

So, (4.01)^½ = 2 + 0.0025 = 2.0025

f(x) = 5x² +6x + 3
f(10.01) = 5*(10.01)² + 6*(10.01) + 3
To find (10.01)²
Let p=10, Δp=0.01
y=p2 = 100
y+Δy = (p+ Δp)² = (10.01)²
Δy = (dy/dp) * Δp
Δy = 2*p* Δx
Δy = 2*10* 0.01
Δy = 20 * 0.01
Δy = 0.2
So, (10.01)² = y + Δy
= 100.2
So,
f(10.01) = 5*(100.2) + 6*(10.01) + 3
= 501 + 60.06 + 3
= 564.06

Comprehension for Testing Writing Skills: Writing comprehension has also been included in the writing test. The comprehension skills namely, recognition, inference, recreation, and reorganization have been tested through the comprehension test on writing.

• The comprehension framed for testing writing skill was mainly based on the testing of the items and aspects of writing such: 
• Comprehensibility skills for writing include understanding that writing is communicating messages or information.
• Comprehension depends upon grasping word meanings, which involves grasping the relation between the words in sentences, between sentences in paragraphs, and between paragraphs in larger wholes. 
• Comprehending a text involves actively creating meaning by building relationships among ideas in a text, and between the text and one’s knowledge, beliefs, and experiences. 
• Writing about a text should enhance comprehension because it provides students with a tool for visibly and permanently recording, connecting, analyzing, personalizing, and manipulating key ideas in a text.

Hence, we conclude that If you are testing your students' comprehension of written English, you are testing their understanding of what they have just 'Written'.