The eye can be regarded as a single refracting surface. The radius of curvature of this surface is equal to that of cornea \((7.8\, mm)\). This surface separates two media of refractive indices \(1\) and \(1.34\). Calculate the distance from the refracting surface at which a parallel beam of light will come to focus.......\(cm\)

Three conductors of same length having thermal conductivity \(\mathrm{k}_1, \mathrm{k}_2\) and \(\mathrm{k}_3\) are connected as shown in figure.

Area of cross sections of \(1^{\text {st }}\) and \(2^{\text {nd }}\) conductor are same and for \(3^{\text {rd }}\) conductor it is double of the \(1^{\text {st }}\) conductor. The temperatures are given in the figure. In steady state condition, the value of \(\theta\) is _______ \({ }^{\circ} \mathrm{C}\).
(Given : \(\mathrm{k}_1=60 \mathrm{Js}^{-1} \mathrm{~m}^{-1} \mathrm{~K}^{-1}, \mathrm{k}_2=120 \mathrm{Js}^{-1}\mathrm{~m}^{-1}\) \( \mathrm{~K}^{-1}, \mathrm{k}_3=135 \mathrm{Js}^{-1} \mathrm{~m}^{-1} \mathrm{~K}^{-1}\) )

The current sensitivity of moving coil galvanometer is increased by \(25 \%\). This increase is achieved only by changing in the number of turns of coils and area of cross section of the wire while keeping the resistance of galvanometer coil constant. The percentage change in the voltage sensitivity will be \(...........\%\)

For a series \(LCR\) circuit, \(I\) vs \(\omega\) curve is shown \((A)\) To the left of \(\omega_{r}\), the circuit is mainly capacitive. \((B)\) To the left of \(\omega_{r}\), the circuit is mainly inductive. \((C)\) At \(\omega_{r}\), impedance of the circuit is equal to the resistance of the circuit. \((D)\) At \(\omega_{t}\), impedance of the circuit is \(0\). Choose the most appropriate answer from the options given below

The electric field in a region is given by \(\overrightarrow{ E }=\frac{2}{5} E _{0} \hat{ i }+\frac{3}{5} E _{0} \hat{ j }\) with \(E _{0}=4.0 \times 10^{3}\, \frac{ N }{ C } .\) The flux of this field through a rectangular surface area \(0.4 \,m ^{2}\) parallel to the \(Y - Z\) plane is ....... \(Nm ^{2} C ^{-1}\)

A parallel palate capacitor with square plates is filled with four dielectrics of dielectric constants \(K_1, K_2, K_3, K_4\) arranged as shown in the figure. The effective dielectric constant \(K\) will be

Young's moduli of the material of wires \(A\) and \(B\) are in the ratio of \(1: 4\), while its area of cross sections are in the ratio of \(1: 3\). If the same amount of load is applied to both the wires, the amount of elongation produced in the wires \(A\) and \(B\) will be in the ratio of [Assume length of wires \(A\) and \(B\) are same]

At any instant the velocity of a particle of mass \(500\,g\) is \(\left(2 t \hat{ i }+3 t ^2 \hat{ j }\right)\,ms ^{-1}\). If the force acting on the particle at \(t=1 s\) is \((\hat{i}+x \hat{j}) N\). Then the value of \(x\) will be:

A point charge of \(10\,\mu C\) is placed at the origin. At what location on the \(X\)-axis should a point charge of \(40\,\mu\,C\) be placed so that the net electric field is zero at \(x =2\,cm\) on the \(X\)-axis ?

The number of permutations, of the digits \(1,2,3,...7\) without repetition, which neither contain the string \(153\) nor the string \(2467\), is \(........\).

A force \(\overrightarrow{\mathrm{F}}=2 \hat{i}+\mathrm{b} \hat{j}+\hat{k}\) is applied on a particle and it undergoes a displacement \(\hat{i}-2 \hat{j}-\hat{k}\). What will be the value of \(b\), if work done on the particle is zero.

Three masses 200 kg, 300 kg and 400 kg are placed at the vertices of an equilateral triangle with sides 20 m . They are rearranged on the vertices of a bigger triangle of side 25 m and with the same centre. The work done in this process _________ J.

A stone tied to \(180 cm\) long string at its end is making 28 revolutions in horizontal circle in every minute. The magnitude of acceleration of stone is \(\frac{1936}{ x }\,ms ^{-2}\). The value of \(x.........\left(\text { Take } \pi=\frac{22}{7}\right)\)