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A thin uniform rod of length l and mass m is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $ω$. Its centre of mass rises to a maximum height of

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Two coaxial solenods are made by winding thin insulated wire over a pipe of cross sectional area A = $10cm_{2}$ and length = 20 cm. If one of the solenoids has 300 turns and the other 400 turns, their mutual inductance is $(μ_{0}=4π×10_{−7}TmA_{−1})$

If (2, 3, 5) is one end of a diameter of the sphere $x_{2}+y_{2}+z_{2}−6x−12y−2z+20=0$, then the coordinates of the other end of the diameter are

A value of C for which the conclusion of Mean Value Theorem holds for the function $f(x)=(g)_{e}x$on the interval [1, 3] is

A capillary tube (A) is drooped in water. Another identical tube (B) is dipped in a soap water solution which of the following shows the relative nature of the liquid columns in the two tubes ?

Let $f(x)={(x−1)sin(x−11 ),ifx=10,ifx=1}$ . Then which one of the following is true?

A liquid was mixed with ethanol and a drop of concentrated $H_{2}SO_{4}$ was added. A compound with a fruity smell was formed. The liquid was:

Standard entropy of $X_{2},Y_{2}andXY_{3}$ are 60, 40 and 50 $JK_{−1}mol_{−1}$, respectively. For the reaction,

The perpendicular bisector of the line segment joining P (1, 4) and Q (k, 3) has y-intercept $−4$. Thena possible value of k is