In which of the following interval the function \(f(x)=x^x, x>0\) is strictly increasing?

If \(A = \begin{bmatrix} 1 & 0 \\ -1 & 5 \end{bmatrix}\) and \(I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}\), then the value of k so that \(A^2 = 6A + kI\) is given by:

The sum of order and degree of the differential equation \(\frac{\left\{1+\left(\frac{d y}{d x}\right)^2\right\}^{\frac{5}{2}}}{\frac{d^2 y}{d x^2}}= p\) is :

If \(A=\left[\begin{array}{cc}3 & 1 \\ -1 & 2\end{array}\right]\), then \(A^2-5 A+7 I=\)

Two events A and B are independent, if
(A) A and B are mutually exclusive
(B) \(P\left(A^{\prime} \cap B^{\prime}\right)=[1-P(A)][1-P(B)]\)
(C) \(P\left(A^{\prime}\right)=P\left(B^{\prime}\right)\)
(D) P(A) + P(B) = 1
(E) P(A) = P(B)

At what rate will the present value of a perpetuity of Rs.1000 payable at the end of each quarter be Rs.50000?

The solution of the differentiable equation \(2 x \frac{d y}{d x}+y=14 x^3, x>0\), is:

If \(A\) and \(B\) are two events such that \(P(A)=\frac{1}{2}, P(B)=\frac{1}{3}, P(B \mid A)=\frac{1}{4}\), then \(P(A \mid B)\) is :

An example of inverted ecological pyramid is:

Answer the question on the basis of passage given below:
Proteins are the polymers of about twenty different a-amino acids which are linked by peptide bonds. Proteins perform various structural and dynamic functions in the organisms. Proteins which contain only a-amino acids are called simple proteins. The secondary or tertiary structure of proteins get disturbed on change of pH or temperature and they are not able to perform their functions. This is called denaturation of proteins. Enzymes are biocatalysts which speed up the reactions in biosystems. Vitamins are accessory food factors required in the diet. They are classified as fat soluble (A, D, E and K) and water soluble (B group and C). Deficiency of vitamins leads to many diseases. Nucleic acids are the polymers of nucleotides which in turn consist of a base, a pentose sugar and phosphate moiety. Nucleic acids are responsible for the transfer of characters from parents to offsprings. There are two types of nucleic acids DNA and RNA. DNA contains a five carbon sugar molecule called 2-deoxyribose whereas RNA contains ribose.
Which of the following vitamin cannot be stored in our body?

The magnetic field at a distance r from a long wire carrying current I is 0.4 T. The magnetic field at a distance 2r from the wire is

In some plants, the ovary develops into fruit without fertilization. This phenomenon is called:

Arrange the amount of energy in a sequence from the highest trophic level to the lowest trophic level (Pyramid of Energy):
(A). 10,000 J
(B). 1000 J
(C). 10 J
(D). 100 J
Choose the correct answer from the options given below: