The function \(f : R \rightarrow R\) defined by \(f(x)=\left\{\begin{array}{ll}x^2, & x \geq 1 \\ x, & x<1\end{array}\right.\) is

Which of the following statements are correct?
(A) If elements of a row (or column) of a determinant are multiplied with cofactors of any other row (or column), then their sum is zero.
(B) The value of determinant is equal to the sum of the product of elements of any row (or column) with their corresponding cofactors.
(C) If any two rows (or columns) of a determinant are interchanged, their sign of determinant does not change.
(D) The value of determinant remains unchanged if its rows and columns are interchanged.
(E) A square matrix A has inverse if and only if A is singular.
Choose the correct answer from the options given below:

The value of the integral \(\int\left(x^6+x^4\right) d\left(x^2\right)\) is equal to:

Match List-I with List-II

List-I (Differential Equations)	List-II (Order and degree)
(A) \(\frac{d y}{d x}+e^y=0\)	(I) order 2, degree not defined
(B) \(\frac{d^2 y}{d x^2}=\left[1+\left(\frac{d y}{d x}\right)^2\right]^{3 / 2]}\)	(II) order 2, degree 1
(C) \(\left(\frac{d^2 y}{d x^2}\right)^2+e^{\left(\frac{\text { 临 })}{}\right.}=0\)	(III) order 1, degree 1
(D) \(\frac{d^2 y}{d x^2}+x \frac{d y}{d x}-2 y=\log x ; x>0\)	(IV) order 2, degree 2

Choose the correct answer from the options given below:

A specific characteristic of a sample is known as a:

The number of all possible matrices of order \(2 \times 2\) with each entry \(0,1,2\), and 3 is:

The number of all possible matrices of order \(2 \times 2\) with each entry ' \(a\) ', ' \(b\) ' or ' \(c\) ' is :

Identify the correct statements from the following in the context of electromagnetic waves.
(A) X-rays are not electromagnetic waves.
(B) Electromagnetic waves are transverse in nature.
(C) Electromagnetic waves can not be polarised.
(D) Electromagnetic waves travel with the speed of light in vacuum.
Choose the correct answer from the options given below:

The following statements describe various properties of a Mercury cell :
(A) It converts energy of combustion into electrical energy
(B) It is rechargeable
(C) The cell reaction involved is Zn(Hg) + HgO(s) \(\rightarrow\) ZnO(s) + Hg(l)
(D) It is a low current device used in hearing aids
Choose the correct answer from the options given below :

The point at which the maximum value of \(x+y\), subject to constraints \(x+2 y \leq 70,2 x+y \leq 95, x \geq 0, y \geq 0\) is obtained, is :

The construction of first rDNA was done using plasmid of :

Read the passage carefully and answer the Questions
The term vitamin was coined from the word vital +amine since the earlier identified compounds had amino groups. Later work showed that most of them didn't contain amino groups. They are very essential for the body. They has to be taken various diet or in the form of medicines also.
Vitamins are classified into two groups depending upon their solubility in water or fat.
Fat soluble vitamins are soluble in fat and oils but insoluble in water. Thhey are stored in liver and adipose (fat storing) tissues Water soluble vitamins are soluble in water. These must be supplied regularly in diet because they are readily excreted in urine and cannot be stored in our body.
Which among the following is not a fat soluble vitamin?

\(\int \frac{x+e^{2 z}}{x^2+e^{2 x}} d x=\)