The ratio of the speeds of a motor boat and that of the current of water is \(26: 4\). The boat goes certain distance against the current in 6 hrs . The time taken by the boat to come back is ___________

Year (t)	2010	2011	2012	2013	2014	2015	2016
Sales (in Rs. crores) (y)	6	8	9	11	13	17	20

In reference to the above data, which of the following statements are correct?
(where \(x=t-2013\) )
(A) If the equation of the straight line trend is \(y=12+2.29 x\), then the trend value for the year 2017 is 21.16.
(B) If the equation of the straight line trend is \(y=12+2.29 x\), then the trend value for the year 2013 is 11.
(C) If the equation of the straight line trend is \(y=12+2.29 x\), then the trend value for the year 2015 is 17.
(D) If \(\left(t_1, y_1\right),\left(t_2, y_2\right), \ldots,\left(t_n, y_n\right)\) denote the time series and \(y_t\) are the trend values of \(y\), then \(\sum\left(y-y_t\right)=0\).
Choose the correct answer from the options given below :

The simplest form of \(\tan ^{-1}\left(\frac{x}{\sqrt{a^2-x^2}}\right)\) is, where \(-a < x < a\).

The degree of the differential equation \(\left(\frac{d y}{d x}\right)^3+\left(\frac{d^2 y}{d x^2}\right)^2=0\) is:

The point on the curve \(y^2=x\), where the tangent makes an angle of \(\frac{\pi}{4}\) with x-axis is:

If \(\mathbf{A}=\left[\begin{array}{ccc}0 & 0 & \sqrt{7} \\ 0 & \sqrt{7} & 0 \\ \sqrt{7} & 0 & 0\end{array}\right]\), then \(|\operatorname{adj} \mathbf{A}|\) is equal to

The value of \(\sin ^{-1}\left(\frac{8}{17}\right)+\sin ^{-1}\left(\frac{3}{5}\right)\) is :

Which reagent will distinguish Benzophenone from acetone ?

The conductivity of an ionic solution depends on:
A. The nature of the electrolyte added
B. The Volume of the container
C. The size of the ions and their solvation
D. Pressure
E. Concentration of the electrolytes
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Ferro-magnetic materials used in transformer core must have :

Insulin used in earlier times caused some patients to develop allergies because
(A). It was extracted from the pancreas of slaughtered cattle.
(B). It was a foreign protein for the body of the patient.
(C). It was a foreign lipid molecule for the body of the patient
(D). It consists of two polynucleotide chains held together by disulphide bridges
Choose the correct answer from the options given below:

The function \(f(x)=\left\{\begin{array}{ll}\frac{x^2+2 x-3}{x-1}, & \text { if } x \neq 1 \\ 0, & \text { if } x=1\end{array}\right.\) is

Arrange the following alkyl halides in order of increasing reactivity towards \(S_N^1\) reaction.
(A) \(\left( CH _3\right)_3 C - I\)
(B) \(\left( CH _3\right)_3 C - F\)
(C) \(\left( CH _3\right)_3 C - Br\)
(D) \(\left( CH _3\right)_3 C - Cl\)
Choose the correct answer from the options given below: