Question:medium

Two thin wires, Wire-1 of diameter 0.650 mm and Wire-2 of unknown diameter $d$ are given. To obtain the value of $d$, the diameters of the two wires are measured with a screw gauge. The screw gauge has a pitch of 0.5 mm and there are 100 divisions on the circular scale (CS). The smallest division on the linear scale (LS) is 0.5 mm. The table shows the readings of LS and CS for the measurements. The value of $d$ (in µm) is:

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Always remember: True Value = Observed Value - Zero Error. If the observed value of a standard object is greater than its actual value, the instrument has a positive zero error, which must be subtracted from all subsequent readings.

Updated On: May 22, 2026

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Correct Answer: 1915

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A thin uniform rod of length L and certain mass is kept on a frictionless horizontal table with a massless string of length L fixed to one end (top view is shown in the figure). The other end of the string is pivoted to a point O. If a horizontal impulse P is imparted to the rod at a distance x = L/n from the mid-point of the rod (see figure), then the rod and string revolve together around the point O, with the rod remaining aligned with the string. In such a case, the value of n is _____.
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Let $P$ be the point on the parabola $y=x^2$ such that the slope of the tangent to the parabola at the point $P$ is $4$. Let $Q$ be the point in the first quadrant lying on the circle \[ x^2+y^2=2 \] such that the slope of the tangent to the circle at the point $Q$ is $-1$. Let $R$ be the point in the first quadrant lying on the ellipse \[ x^2+4y^2=8 \] such that the slope of the tangent to the ellipse at the point $R$ is $-\frac12$. Then the radius of the circle passing through the points $P$, $Q$ and $R$ is:

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Correct Answer: 1915

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