Engineering Mathematics GATE-1998

Q 1: The Laplace transform of the function e^{-at}  has the form:

A) \frac1{s+a}
B) \frac1{s\left(s+a\right)}
C) \frac as
D) s+a

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Q 2: The unit normal to the plane 2x + y + 2z = 6 can be expressed in the vector form:

A) i3+j2+k2
B) i\frac23+j\frac13+k\frac23
C) i\frac13+j\frac12+k\frac12
D) -i\frac23+j\frac13-k\frac23

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Q 3: \lim\limits_{x\rightarrow0}\frac{x-\sin2x}{x+\sin3x}  has the value:

A) 1
B) -1/4
C) 0
D) ∞

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Q 4: The differential equation ... will have a solution of the form

NOTE: C1 and C2 are constant

A) C_1e^{3t}+C_2e^{2t}
B) C_1e^{-2t}+C_2e^{-t}
C) C_1e^{-3t}+C_2e^{-2t}
D) C_1e^{-5t}

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Q 5: The integral \int_0^1\frac{dx}{x^p}  is convergent for

A) no value of p
B) p > 1
C) p < 1
D) all values of p

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