Category solved model papers

Solve (x^2 + y^3 + 6x)dx + y^2xdy = 0

6. A) Solve (x2 + y3 + 6x)dx + y2xdy = 0 Answer:-

Solve p^3 + 2xp^2 + y^2p^2 – 2xy^2 p = 0

5. C) Solve p3 + 2xp2 + y2p2 – 2xy2p = 0 Answer:-

Water at a temperature of 10°𝐶 takes 5 min to warm to 20°𝐶 at a room temp of 40°𝐶. Find the temp of the water after 20 min

5. B) Water at temperature 10°𝐶 takes 5 minutes to warm up to 20°𝐶 at a roomtemperature of 40°𝐶. Find the temperature of the water after 20 minutes. Answer:-

Solve dy/dx+ y tan x = y^3sec x

5. A) Solve dy/dx+ y tan x = y3sec x Answer:-

Find the extreme values of x3+y3-3axy , a>=0

4. C) Find the extreme values of x3+y3-3axy , a>=0

If u = f(y-x/xy, z-x/xz), show that x² ∂u/∂x + y2 ∂

4.A] Evaluate

(i) lim 𝑥→0 (𝑎𝑥 + 𝑥)1/𝑥 (ii) lim 𝑥 𝜋 →𝜋/2 (tan 𝑥)tan2𝑥

If 𝑢 = 𝑦𝑧/x, 𝑣 = 𝑧𝑥/y, 𝑤 = 𝑥𝑦/z, show that 𝛛(𝑢,𝑣,𝑤)/𝛛(𝑥.𝑦,𝑧) = 4

If 𝑢 = 𝑡𝑎𝑛−1 (𝑦/𝑥) ,𝑤ℎ𝑒𝑟𝑒 𝑥 = 𝑒𝑡 − 𝑒−𝑡𝑎𝑛𝑑 𝑦 = 𝑒𝑡 + 𝑒−𝑡, find the total derivative (𝑑𝑢/𝑑𝑡) using partial differentiation.

If 𝑢 = 𝑡𝑎𝑛−1 (𝑦/𝑥) ,𝑤ℎ𝑒𝑟𝑒 𝑥 = 𝑒𝑡 − 𝑒−𝑡𝑎𝑛𝑑 𝑦 = 𝑒𝑡 + 𝑒−𝑡, find the total derivative (𝑑𝑢/𝑑𝑡) using partial differentiation. Answer:-

Expand √1 + 𝑠𝑖𝑛2𝑥 by Maclaurin’s series up to the term containing 𝑥5

3.A. Expand √1 + 𝑠𝑖𝑛2𝑥 by Maclaurin’s series up to the term containing 𝑥5