If f(a - x) = f(x), then \(\int_0^a x f(x) d x\) is equal to

\(\int \frac{d x}{e^x+e^{-x}}\) is equal to

The value of the integral \(I=\int_{-1}^1|x| d x\) is:

The value of \(\left[\begin{array}{lll}1 & b c & b c(b+c) \\ 1 & c a & c a(c+a) \\ 1 & a b & a b(a+b)\end{array}\right]\) is

The order and degree of differential equation \(\left[1+\left(\frac{d y}{d x}\right)^2\right]^2=\frac{d^2 y}{d x^2}\) respectively, are

Bag I contains 3 black and 2 white balls, Bag II contains 2 black and 4 white balls. A bag is selected at random and then a ball is drawn from it. The probability that the ball drawn is black is :

For the following probability distribution,

X	1	2	3	4
p(x)	\(\frac{1}{10}\)	\(\frac{1}{5}\)	\(\frac{3}{10}\)	\(\frac{2}{5}\)

The value of \(E\left(X^2\right)-[E(X)]^2\)

The area bounded by the y-axis, y = cos x and y = sin x when \(0 \leq x \leq \frac{\pi}{2}\) is :

Which one of the following statements is not correct
A. D (-) fructose exists in furanose structure
B. D (+) glucose exists in pyranose structure
C. In sucrose the two monosaccharides are held together by peptide linkage
D. Maltose is a reducing sugar
E. Pentaacetate of glucose does not react with hydroxylamine
Choose the correct answer from the options given below:

Read the given passage and answer the question given below.
The sex linked recessive disease, which shows its transmission from unaffected carrier female to some of the male progeny has been widely studied. In this disease, a single protein that is a part of the cascade of proteins involved in the clotting of blood is affected. Due to this in an affected individual a simple cut will result in non-stop bleeding. The heterozygous female (carrier) for the disease may transmit it to sons. The possibility of a female becoming a sufferer of disease is extremely rare because mother of such a female has to be at least carrier and the father should be sufferer. The family pedigree of Queen Victoria shows a number of suffering descendents as she was a carrier of the disease.
Man who is sufferer of the disease marries a woman who is a carrier of this disease. What percentage of children born as carrier of this disease?

Let \(f(x)\) satisfies the requirements of Lagrange's mean value theorem in \([0,2]\).
If \(f(0)=0\) and \(f^{\prime}(x) \leq \frac{1}{2}\) for all \(x \in[0,2]\), then :

Suppose \(10 \backslash \%\) of men and \(0.5 \backslash \%\) of women have grey hair. A grey haired person is selected at random. If there are equal number of males and females, then the probability of the selected person being a female is :

Which of the following enzymes are used to clarify the packed juices?
(A) Pectinases
(B) Kinases
(C) Proteases
(D) Nucleases
Choose the correct answer from the options given below: