1
WB JEE 2010
+1
-0.25

If the displacement, velocity and acceleration of a particle at time t be x, v and f respectively, then which one is true?

A
$$f = {v^3}{{{d^2}t} \over {d{x^2}}}$$
B
$$f = - {v^3}{{{d^2}t} \over {d{x^2}}}$$
C
$$f = {v^2}{{{d^2}t} \over {d{x^2}}}$$
D
$$f = - {v^2}{{{d^2}t} \over {d{x^2}}}$$
2
WB JEE 2010
+1
-0.25

The displacement x of a particle at time t is given by x = At2 + Bt + C, where A, B, C are constants and v is velocity of a particle, then the value of 4Ax $$-$$ v2 is

A
4AC + B2
B
4AC $$-$$ B2
C
2AC $$-$$ B2
D
2AC + B2
3
WB JEE 2010
+1
-0.25

The displacement of a particle at time t is x, where x = t4 $$-$$ kt3. If the velocity of the particle at time t = 2 is minimum, then

A
k = 4
B
k = $$-$$4
C
k = 8
D
k = $$-$$8
4
WB JEE 2011
+1
-0.25

The general solution of the differential equation $${{{d^2}y} \over {d{x^2}}} + 8{{dy} \over {dx}} + 16y = 0$$ is

A
$$(A + Bx){e^{5x}}$$
B
$$(A + Bx){e^{ - 4x}}$$
C
$$(A + B{x^2}){e^{4x}}$$
D
$$(A + B{x^4}){e^{4x}}$$
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