The integrating factor of the differential equation \(\left(x \log _e x\right) \frac{d y}{d x}+y=2 \log _e x\) is:

A bag contains 6 red balls, 4 green balls and 10 blue balls. Three balls are drawn with replacement. Find the probability of getting at least one green ball

Maximum value of \(z=5 x+4 y\) subject to the constraints \(x-y \leq 0, x+y \leq 4, x \geq 0, y \geq 0\) occurs at the point \((a, b)\). Then \(4 a+5 b=\) \(\_\_\_\_\) ,

For the given \(5\) values, \(15, 18, 21, 27, 39;\) the three year moving averages are:

\(\int_{0}^{1} (x^3 + 3x^2)e^x dx =\)

\(\int(x-1) e^{-x} d x=\)

If \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\), then \(\frac{d^2 y}{d x^2}\) is equal to

The molecule with largest \(C - X\) bond length is

A charged particle is moving in a cyclotron. What is the effect on time for one revolution of this charged particle, when its radius of the orbit is doubled?

Read the passage and answer the question : There are thousands of varieties of rice in India alone. The diversity of rice in India is one of the richest in the world. Basmati rice is distinct for its unique aroma and flavour and 27 documented varieties of Basmati are grown in India. There is reference to Basmati in ancient texts, folklore and poetry, as it has been grown for centuries. Several attempts have also been made to patent uses, products and processes based on Indian traditional herbal medicine, e.g. turmeric, neem. There has been growing realisation of the injustice, inadequate compensation and benefit sharing between developed and developing countries. The Indian Parliament has recently cleared a Bill that takes such issues into consideration, including patent terms emergency provisions and research and development initiative.
One of the classical example of biopatent controversy is of -

Which of the following microbe serves as an important biofertiliser in paddy field?

Solution of the differential equation \(\log \left(\frac{d y}{d x}\right)=3 x+4 y\) given that y = 0 when x = 0 :

The charge flowing in a conductor varies with time as \(q(t) = (8t^2 - 4t + 5)C\). Then the current changes at the rate of :