A metallic disc is being heated. Its area (in `m^(2)`) at any time t (in sec) is given by `A=5t^(2)+4t`. Calculate the rate of increase in area at `t=3sec`.
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`d/(dx)sqrt((1-sin2x)/(1+sin2x))i se q u a lto,(0<x<pi/2),` `sec^2x` (b) `-sec^2(pi/4-x)` `sec^2(pi/4+x)` (d) `sec^2(pi/4-x)`
`y=sqrt((1-sin 2x)/(1+ sin 2x))=(cos x - sin x)/(cos x + sin x)=(1-tan x)/(1+ tan x)=tan ((pi)/(4)-x)` `therefore (dy)/(dx)=-sec^(2)((pi)/(4)-x)`
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Find the ratio of magnetic dipole moment and magnetic field at the centre of a disc. Radius of disc is `R` and it is rotating at constant angular spee
Correct Answer - `[(piR^(3))/(2mu_(0))]`
2 Answers 1 views
1. Concepts related to population growth Birth rate, Death rate, Survival rate, Interest rate.
1. Interest rate 2. Expansion of industrial sector
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(i) The radius of a circle is increasing at the rate of 5 cm/sec. Find the rate of increasing of its perimeter. (ii) If the area of a circle increases
Correct Answer - `10 pi cm//sec`
2 Answers 2 views
The length of a rectangle is decreasing at a rate of 3 cm/sec and breadth is increasing at a rate of 4 cm/sec. Find the rate of change of its (a) peri
Correct Answer - `(a) 2 cm//sec (b) 4 cm^(2)//sec`,Increase
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A particle is projected vertically upwards from the earth. It crosses the same point at t=2 sec and t=8 sec. Find out `[g=10 ms^(-2)]` (i) the time fo
Correct Answer - (i) 10 sec (ii) 50 m//s (iii) 125 m (iv) 80 m
2 Answers 2 views
A rocket of mass 20000 kg is ejecting the gases at the rate of 50 kg/sec with speed of 20 m/sec in gravity free space. Find the acceleration of rocket
Correct Answer - `a=(10)/(19)m//s^(2)`
2 Answers 1 views
The side of a square in increasing at the rate of 0.2 cm/sec. Find the rate of increase of the perimeter of the square.
Correct Answer - `(dP)/(dt) = 0.8 cm//s`
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A liquid occupies a volume of 2 × 10^-4 m^3 at 0 °C. Calculate the increase in its volume If It is heated to 80 °C.
Given: V0 = 2 × 10-4 m3, T0 = 0°C,T = 80°C, γr = 4 × 10-4 K-1, T – T0 = 80 – 0 = 80°C To find: Increase in volume (∆V) Formula: ∆V = V0γr(T – T0) Calculation: From formula. ∆V =...
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A disc has an area of 0.32 m^2 at 20 °C, what will be its area at 100 °C? (α = 2 × 10^-6/ °C)
Correct option is: (B) 0.32 m2
2 Answers 9 views