Consider \(f: R ^{+} \rightarrow[4, \infty)\) given by \(f(x)=x^2+4\)
(where \(R ^{+}\)is set of non negative real numbers) then \(f^{-1}(x)\) is :

The value of \(\lambda\) and \(\mu\) if \((2 \hat{i}+6 \hat{j}+27 \hat{k}) \times(\hat{i}+\lambda \hat{j}+\mu \hat{k})=\overrightarrow{0}\) are respectively :

The point estimate of the population standard deviation as per the below mentioned data from a simple random sample 6, 10, 15, 12, 9, 8 will be :-

The values of \(\lambda\) for which the system of equation \(x+2 y+z=14,-x+y+z=10, x+\lambda y+z=2\) has unique solution is :

The order and degree of the differential equation \(x\left(\frac{d y}{d x}\right)^3+\left(\frac{d^2 y}{d x^2}\right)^2-3 \frac{d y}{d x}+y=0\) respectively, are:

The current through a \(4 / 3 \Omega\) external resistance connected to a parallel combination of two cells with emfs of 2 V and 1 V , internal resistances \(1 \Omega\) and \(2 \Omega\) respectively, is :

The water and milk in two vessels are in the ratio 1:1 and 3: 8 respectively. In what ratio, the mixtures in the vessels be mixed to obtain a new mixture containing water and milk in the ratio 4 : 7?

Equipotential surfaces at a great distance from a collection of charges whose total sum is not zero are approximately:

Match List-I with List-II

List-I (Reaction)	List-II (Type of reaction)
(A) Hydrolysis of Ethyl Chloride	(I) Substitution reaction
(B) 2-Propanol is treated with Conc. Sulphuric acid	(II) Addition reaction
(C) Reaction of HCN with Acetone	(III) Degradation reaction
(D) Treatment of acetamide with NaOH and Br2	(IV) Elimination reaction

Choose the correct answer from the options given below:

Which of the following is incorrect about chemical adsorption ?

How many haploid cells will be formed after first meiotic division of one primary spermatocyte ?

Read the passage and answer the following
Microbes are organisms that cannot be seen with the naked eye. They include bacteria, archaea, protists, viruses, prions, and fungi. They account for most of the diversity of life on earth. Far more microbes inhabit a single person's body than there are people on the entire planet. Microbes also dominate in terms of their ability to live and thrive in extreme environments, including clouds, deep-sea volcanoes, springs, ice caps, and animal intestines. Most animals, including humans, exhibit numerous associations with microbes. Our "human microbiome" includes our skin, hair, mouth, and gut.
Match List - I with List - II.

List - I	List - II
(A) Methanobacterium	(I) Swiss cheese
(B) Lactobacillus	(II) Ethanol
(C) Propionibacterium sharmanii	(III) Biogas
(D) Saccharomyces cerevisiae	(IV) Curd

Choose the correct answer from the options given below:

Match List - I with List - II.

List - I	List - II
(A) Down’s syndrome	(I) Inborn error of metabolism
(B) Klinefelter’s syndrome	(II) Absence of one of the X-chromosome
(C) Turner’s syndrome	(III) Presence of an additional copy of X-chromosome
(D) Phenylketonuria	(IV) Presence of an additional copy of chromosome number-21

Choose the correct answer from the options given below :