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Maths-

General

Easy

Question

Let z = 1 – t + i $square root of t to the power of 2 end exponent plus t plus 2 end root$ , where t is a real parameter. The locus of z in the Argand plane is

a straight line
a hyperbola
an ellipse
None of these

The correct answer is: a hyperbola

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For all complex number z₁, z₂ satisfying $open vertical bar z subscript 1 end subscript close vertical bar$ = 12 and $open vertical bar z subscript 2 end subscript minus 3 minus 4 i close vertical bar equals 5$ , the minimum value of $open vertical bar z subscript 1 end subscript minus z subscript 2 end subscript close vertical bar$ is -

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Blocks A and B in the figure are connected by a bar of negligible weight. If mass of A and B are 170 kg each and $mu subscript A end subscript equals 0.2$ and $mu subscript B end subscript equals 0.4 comma$ where $mu subscript A end subscript$ and $mu subscript B end subscript$ are the coefficient of limiting friction between blocks and plane, calculate the force in the bar. $open parentheses g equals 10 m divided by s to the power of 2 end exponent close parentheses$

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Two spheres of equal masses are attached to a string of length 2 m as shown in figure. The string and the spheres are then whirled in a horizontal circle about O at a constant rate. The value of the ratio
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