The integral \(\int e^x\left(1+\frac{1}{x}+\log x\right) d x\) is equal to:

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

A box contains 10 balls, each marked with one of the digits 0 to 9 .
If four balls are drawn successively with replacement from the box,
then the probability that none is marked with the digit \(0\) is :

If \(y=(x+1)\left(x^2+1\right)\left(x^4+1\right)\left(x^8+1\right)\) then \(\frac{d y}{d x}\) at \(x = -1\) is

The function \(y=f(x)\) has extreme values at the points where ___________ .

\(\cos \left(\frac{\pi}{6}-\cos ^{-1}\left(-\frac{\sqrt{3}}{2}\right)\right)\) is equal to:

If the direction ratios of two lines are \(a, b, c\) and \((b-c),(c-a),(a-b)\) respectively, then the angle between these lines is :

Read the given passage and answer the following questions:
Secondary treatment or biological treatment: The primary effluent is passed into large tanks where air is pumped into it. This allows vigorous growth of aerobic microbes. While growing, these microbes consume the major part of the organic matter in the effluent. This significantly change the BOD (biochemical oxygen demand) of the effluent. The effluent in then passed into a tank a small part of the sludge is pumped back into the aeration tank to serve as the inoculum. The remaining major part of the sludge is pumped into large tanks called sludge digesters. Here, other kinds of bacteria grow anaerobically in the sludge. The biogas produced can be used source of energy as it is inflammable. The effluent from the secondary treatment plant is generally released into natural water bodies like rivers and streams.
Steps in primary treatment does not include:

The menstrual flow results due to:
A. Increased estrogen levels
B. When released ovum is not fertilized
C. When pregnancy occurs
D. Breakdown of the endometrial lining of the uterus and its blood vessels

Read the following passage carefully and answer the given questions.
Theory of Evolution
The evolution of life is a gradual process through which simple organisms are transformed into complex life forms over billions of years. It involves genetic changes, adaptation to the environment, and the emergence of diversity in species. Fossil records provide evidence of extinct life forms and transitional stages. Evolution is influenced by factors such as mutation, genetic recombination, and environmental pressure, shaping the biodiversity we see today. Charles Darwin and Alfred Russel Wallace were pioneering naturalists who developed the theory of evolution by natural selection.
Which one of the following statements is not a connotation of the theory of special creation?

Any feasible solution which optimizes the objective function is called:

Sex chromosomes of female in chicken are:

Which of the following are the products of electrolysis of aqueous solution of sodium chloride?