The solution set of the inequality \(3 x+5 y<15\) is :

A die is thrown again and again until three sixes are obtained. The probability of obtaining third six in sixth throw of the die is:

The function \(f(x)=x+\cot ^{-1} x\) is increasing in the interval:

The value of x given by \(\cos(\tan^{-1} x) = \sin(\cot^{-1} \frac{3}{4})\) is:

Nitin has taken the subjects mathematics, physics and chemistry. The probability of him getting grade A in these subjects are respectively 0.2, 0.3 and 0.9. Getting grades in different subjects are regarded as independent events. The probability of getting A grade by him, either in mathematics or physics, is

Let \(\vec{a}, \vec{b}\) be two vectors such that \(|\vec{a}|=2,|\vec{b}|=3, \vec{a} \cdot \vec{b}=4\). Then \(|\vec{a}-\vec{b}|\) is equal to :

A letter is known to have come either from KOLKATA or TATANAGAR. On the envelope just two consecutive letters TA are visible. The probability that letter has come from TATANAGAR is

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

Let \(f(x)=x|x|\). Then \(f(x)\) is:

\(\text { If } I=\int \frac{x}{x-\sqrt{x^2-4}} d x=\alpha x^3+\beta\left(x^2-4\right)^{\frac{3}{2}}+\gamma\) where \(\gamma\) is a constant of integration, then

If \(A=\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 0 & 2 \\ x & 1 & 1\end{array}\right]\) and \(A^{-1}=\frac{1}{4}\left[\begin{array}{ccc}-2 & 0 & y \\ 5 & -2 & -1 \\ 1 & 2 & -1\end{array}\right]\), then values of \(x\) and \(y\) are:

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.
A reaction is first order in A and second order in B. If the concentration of B is doubled its initial concentration and A is reduced to 3/4th of its initial concentration, the new rate of the reaction is

Let us consider interference between two sources of intensities \( I \) and \( 4I \). What will be the intensity at points where the phase difference is \( \pi \) ?