If \(E\) is the amplitude of the electric field of the waves starting from the slits in a double slit experiment and \(\theta\) is the phase difference between the waves reaching a point on the screen, the ratio of the amplitude of the resultant electric field at that point on the screen to the amplitude at one of the slits is

Two slabs are of the thicknesses \(d_1\) and \(d_2\). Their thermal conductivities are \(K_1\) and \(K_2\), respectively. They are in series. The free ends of the combination of these two slabs are kept at temperatures \(\theta_1\) and \(\theta_2\). Assume \(\theta_1>\theta_2\). The temperature \(\theta\) of their common junction is

A calcite crystal is placed over a dot on a paper sheet and the crystal is rotate(d) On viewing through the calcite or sees,

The maximum current that can be measured by a galvanometer of resistance \(40 ~\Omega\), is \(10 \mathrm{~mA}\). It is converted into a voltmeter that can read upto \(50 \mathrm{~V}\). The resistance to be connected in series with the galvanometer (in \(\Omega\) ) is

LCD stands for

A plot of kinetic energy of emitted photoelectrons from a metal versus the frequency of incident radiation gives a straight line, the intercept of which
A. Depends on the nature of the metal used
B. Depends on the intensity of radiation
C. Depends both on the intensity and the nature of metal used
D. Is a constant and is same for all metals which is independent of the intensity of Incident radiation

An uniform sphere of mass \(M\) and radius \(R\) exerts a force of \(F\) on a small mass \(m\) placed at a distance of 3R from the centre of the sphere. A spherical portion of diameter \(R\) is cut from the sphere as shown in the fig. The force of attraction between the remaining part of the disc and the mass \(\mathrm{m}\) is

A candidate is required to answer 7 questions out of 12 questions which are divided into two groups each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. The number of ways in which he can choose the 7 question is

The unit of universal gravitational constant is :

\(\int \tan ^2\left(5-\dfrac{x}{2}\right) d x=\)

Match the names of reactions given in Column I with the appropriate reactions given in Column II.

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No.	Name of reaction	No.	Equations representing reactions
A	Sandmeyer	P	\(2C_6H_5Cl + Na\) (dry ether) \(\to\) Diphenyl
B	Fittig	Q	\(CH_3 - CHBr - CH_3 + AgF \to CH_3 - CHF - CH_3 + AgBr\)
C	Swarts	R	\(CH_3 - CH_2 - Br + NaI\) (Acetone) \(\to CH_3 - CH_2 - I + NaBr\)
D	Finkelstein	S	\(C_6H_5N_2^+ Cl^- + Cu_2Br_2/HBr \to C_6H_5Br + N_2\)

A transformer which steps down \(330 \mathrm{~V}\) to \(33 \mathrm{~V}\) is to operate a device having impedance \(110 \Omega\). The current drawn by the primary coil of the transformer is :

Match the reactions in Column I with the correct products given in Column II:
\(\begin{array}{|l|l|l|l|} \hline \text{S.N.} & \text{Column I} & \text{S.No.} & \text{Column II} \\ \hline \text{A} & 1- \text{Chloropropane} + (\mathrm{Zn} / \mathrm{HCl}) \rightarrow & \text{P} & \text{Propanone + Methanal} \\ \hline \text{B} & n- \text{Hexane + (anh.} \left.\mathrm{AlCl}_3 / \mathrm{HCl}_{(\mathrm{g})}\right) \rightarrow & \text{Q} & \text{Propanone} \\ \hline \text{C} & 2- \text{Methylpropene} + ( \left.\mathrm{O}_3 ~\&~ \mathrm{Zn} / \mathrm{H}_2 \mathrm{O}\right) \rightarrow & \text{R} & \text{Propane} \\ \hline \text{D} & \text{Propyne} +\left(\mathrm{HgSO}_4 / \mathrm{H}_2 \mathrm{SO}_4\right. at 333 K) \rightarrow & \text{S} & \text{2-Methylpentane + 3-Methylpentane} \\ \hline \end{array}\)