ESE Achiever's plan || Paper 1 || Differential Calculus

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Question 1

Let z = x sin y-y sin x. The partial differential of z = ____.

• A(sin y+y cos x)dx+(x cos y +sin x)dy
• B(sin y-y cos x)dx + (x cos y+sin x)dy
• C(sin y+ y cos x)dx+(x cos y-sin x)dy
• D(sin y- y cos x)dx +( x cos y-sin x)dy

Question 2

The solution of the partial differential equation is

• A
• B
• C
• D

Question 3

The solution of the following partial differential equation is

• Asin (3x – y)
• B3x² + y²
• Csin (3x – 3y)
• D(3y² – x²)

Question 4

Solve the differential equation .

• A 
• B
• C 
• Dnone of these

Question 5

General equation of the differential equation  is

• Alog y = tan^-1x + C
• Blog y = (tan^-1x)²+ C
• Clog y = cot^-1x + C
• Dlog y = (cot^-1x)² + C

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