The solution of the differential equation \(\frac{d y}{d x}=\frac{x+y}{x-y}\) is

A machine has been producing steel tubes of mean inner diameter of 2 cm.
A sample of 10 tubes gives an inner diameter of 2.01 cm and a standard deviation of 0.063 cm.
Test the hypothesis that the machine is working in the proper order at 5% level of significance and answer, which of the following statements are correct?
[Given that \(t_{0.05}=2.262\)]
(A) The value of the test statistic is t = 0.476
(B) The null hypothesis is rejected at \(5 \%\) level of significance.
(C) The null hypothesis is accepted at \(5 \%\) level of significance.
(D) The degree of freedom is 10
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Irregular variations in a time series are not caused by:

If the lines \(\frac{x-5}{7}=\frac{y+2}{-5}=\frac{z}{\lambda}\) and \(\frac{x}{1}=\frac{y}{2 \lambda}=\frac{z}{3}\) are perpendicular to each other, then \(\lambda\) is equal to

\(\int \frac{d x}{\left(1+5 \sin ^2 x\right)}\) is equal to

If \(A\) is a square matrix of order 3 and \(\operatorname{det}(A)=1\). If \(B=2 A\) is another matrix, the value of \(\operatorname{det}(B)\) is:

If \(y=\sin ^{-1}\left(\frac{1-x^2}{1+x^2}\right)\) then \(\frac{d y}{d x}=\)

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The concentration dependence of the rate of a reaction is called the differential rate equation. It is not always convenient to determine the instantaneous rate, as it is measured by calculating the slope of the tangent at point 't' in the concentration vs time plot. This makes it difficult to determine the rate and hence the order of the reaction. This difficulty is overcome by integrating the differential rate equation. This integrated rate equation gives a direct relation between concentrations at different times and the rate constant. The integrated rate equations are different for the reactions having different reaction orders.
The rate constant of a reaction is 2.1 mol L-'s-¹. What is the order of the reaction?

The current through a \(4 / 3 \Omega\) external resistance connected to a parallel combination of two cells with emfs of 2 V and 1 V , internal resistances \(1 \Omega\) and \(2 \Omega\) respectively, is :

Three identical polaroid sheets \(P_1, P_2, P_3\) are oriented so that pass axis of \(P_2\) and \(P_3\) are inclined to \(P_1\) at 60° and 90° respectively. A monochromatic source of intensity \(I_0\) is used to pass through \(P_1, P_2, P_3\). Intensities after passing through \(P_1, P_2, P_3\) will be respectively :
(A) \(I_0, \frac{I_0}{2}, \frac{I_0}{8}\)
(B) \(\frac{I_0}{2}, \frac{I_0}{8}, \frac{I_0}{32}\)
(C) \(\frac{I_0}{2}, \frac{I_0}{8}, \frac{3 I_0}{32}\)
(D) \(I_0, \frac{I_0}{2}\), zero
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Read the passage carefully and answer the questions
Sodium dichromate \(Na _2 Cr _2 O _7\) and Potassium dichromate \(K _2 Cr _2 O _7\) are strong oxidizing agents; in acidic solution, its oxidising action can be represented as follows :
\(Cr _2 O _7^{2-}+14 H ^{+}+6 e^{-} \rightarrow 2 Cr ^{3+}+7 H _2 O \left( E ^{\circ}=1.33 V\right)\)
The chromates and dichromates are interconvertible in aqueous solution depending upon pH of the solution.
The chromate ion is tetrahedral whereas the dichromate ion consists of two tetrahedra sharing one corner with \(Cr - O - Cr\) bond angle of \(126^{\circ}\)
Potassium permanganate is prepared by fusion of \(MnO _2\) with an alkali metal hydroxide and an oxidising agent like \(KNO _3\).
This produces the dark green \(K _2 MnO _4\) which disproportionates in a neutral or acidic solution to give permanganate. It is a strong oxidizing agent. Hydrogen ion concentration of the solution plays
an important part in the reduction of permanganate to manganate, manganese dioxide and manganese(II) salt.
Potassium permanganate forms dark purple (almost black) crystals which are isostructural with those of \(KClO _4\).
The salt is not very soluble in water \((6.4 g / 100 g\) of water at 293 K ), but when heated it decomposes at 513 K .
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In the formation of a Leclanche cell, the space between electrodes is filled with:
(A) \(ZnCl _2\)
(B) \(NH _4 Cl\)
(C) \(AlCl _3\)
(D) ZnS
(E) \(NH _4 NO _3\)
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Following are the steps involved in Hershey and Chase experiment to prove DNA as the genetic material.
(A) Blending the cells
(B) Centrifugation of the cells was performed
(C) Growing some bacteriophages on a medium containing radioactive phosphorus and other on radioactive sulfur.
(D) Cells were infected with virus
(E) Observation and established the inference.
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