If \(y=x^{x \sin x}\) then \(\frac{d y}{d x}=\) ?

If \(\left(t_1, y_1\right),\left(t_2, y_2\right),\left(t_3, y_3\right), \ldots,\left(t_n, y_n\right)\) denote the time series and \(y_t\) are the trend values of the variable \(y\), then \(\sum\left(y-y_t\right)\), the sum of deviations of \(y\) from their corresponding trend value is equal to :

Rakshita plans to buy a house for Rs. 1,00,00,000 with down payment of 20% of the value of the house paid by her mother. Rest of the amount she wishes to pay in 25 years by equal monthly instalments at an interest of 9% per annum compounded monthly Then the EMI paid by her is \(\left(\right.\) Given \(\left.(1.0075)^{300}=9\right)\) :

The solution of the differential equation xdy - ydx = 0 represents

If \(A\) is a square matrix of order 3 and \(|A|=5\), then the value of \(\left|-A A^T\right|\) is :

Consider the line \(\frac{x-2}{2}=\frac{2 y-5}{-3}, z=-1\).
Then which of the following is/are true?
(A) It has Direction ratios \((2,-3,-1)\)
(B) It has Direction cosines \(\left(\frac{4}{5},-\frac{3}{5},-\frac{1}{5}\right)\)
(C) It has Direction ratios \(\left(2,-\frac{3}{2}, 0\right)\)
(D) It has Direction cosines \(\left(\frac{4}{5},-\frac{3}{5}, 0\right)\)
Choose the correct answer from the options given below :

The values of \(b\) for which \(y=2 x^2-b x+2\) touches the \(x\)-axis are:

Match List-I with List-II

List-I (Name of Compound)	List-II (Application)
(A) Neutral Ferric Chloride	(I) Anaesthetic
(B) Methanol	(II) Detection of Phenolic group
(C) Diethylether	(III) Wood Spirit
(D) Acetylsalicylic acid	(IV) Analgesic

Choose the correct answer from the options given below:

Read the passage carefully and answer the Questions
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.
For an integrated first order reaction, a straight line graph is plotted. The incorrect co-ordinates and resulting slope of the graph are

If \(y=\left(x+\sqrt{x^2+1}\right)^m\), then \(\frac{d y}{d x}\) is

What is the coordination number of Ni in \([Ni(NH_{3})_{4}]\) complex?

If \(y=7 \sqrt{x}+3 e^x\), then \(\frac{d^2 y}{d x^2}\) is :

A rod of 20 cm lying along the horizontal East-West direction falls freely from the roof of a building of height 3 m. If the horizontal component of the Earth's magnetic field is 0.36 G over the region, find the magnitude of Induced emf when it reaches the bottom of the building (take \( g = 10 \text{ m/s}^2 \) at that place)