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Mechanical Engineering - Practice Test - 14

Q1:

Find the value of log(-6).

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Q2:

Represent ii in terms of e.

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Q3:

Modulus of 4+3i is

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Q4:

Find the value of (3-5i)-(-5+11i)+(9+6i)

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Q5:

Find the general solution to y′′ − 4y′ + 8y = 0

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Q6:

Meaning of f’(c)  

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Q7:

Find the value of c by Lagrange’s theorem function f(x)=(x-1)(x-2) in [0,4]

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Q8:

By Cauchy’s mean value theorem find value of c function  f(x)=3x+2 and g(x)=x2+1 in [1,4]

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Q9:

nth derivative ofeax

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Q10:

The value of ∫0∞∫x∞e-y/y dydx by changing the order of integration is _

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Q11:

The area bounded by the curve y=Ψ(x), x-axis and the lines x=l, x=m(l<m) is given by

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Q12:

∫0π/2∫0π/2sin⁡(x+y)  dxdy is _ 

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Q13:

Find the gradient of a function V if V= xyz.

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Q14:

The equation   has _______number of roots

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Q15:

Find the value of log2(-3)

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Q16:

∫1log⁡8∫0log⁡yex+y  dydx is equal to 

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Q17:

The value of 
∫01∫0x∫0x+y(x+y+z) dzdydx is 
 

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Q18:

What is the divergence of the vector field f ⃗=3x2 i ̂+5xy2 j ̂+xyz3 k ̂ at the point (1, 2, 3)?

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Q19:

Curl of f ⃗(x,y,z)=2xyi ̂+(x2+y2 ) j ̂+2yzk ̂ is ____________.

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Q20:

A vector field which has a vanishing divergence is called as ____________.

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Q21:

The curl of vector field f ⃗(x,y,z)=x2 i ̂+2zj ̂-yk ̂ is _________

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Q22:

A zero of x3 + 64 is

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Q23:

A polynomial equation in x of degree n always has

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Q24:

The polynomial x3 + 2x + 3 has

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Q25:

If x3 +12x2 +10ax +1999 definitely has a positive zero, if and only if

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