The function \(f(x)=|x-3|, x \in R\) is:

\(\int_0^1 \tan ^{-1}\left(\frac{2 x-1}{1+x-x^2}\right) d x\) is equal to :

if a function \(f: Q \rightarrow R\) defined by \(f(x)=\frac{2 x-1}{2}\) and \(g: Q \rightarrow R\) is defined by \(g(x)=x+2\), then \((g \circ f)\left(\frac{3}{2}\right)\) is :

If \(A =\left(\begin{array}{cc}2 & 3 \\ 5 & -2\end{array}\right)\), be such that \(A ^{-1}=K A\), then the value of \(K\) is :

If \(a, b\) and \(c\) are all different from zero and \(\left|\begin{array}{ccc}1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c\end{array}\right|=0\), then the value of \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\) is :

The shortest distance between the lines \(\vec{r}=(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(2 \hat{i}+3 \hat{j}+4 \hat{k})\) and \(\vec{r}=(2 \hat{i}+4 \hat{j}+5 \hat{k})+\mu(4 \hat{i}+6 \hat{j}+8 \hat{k})\) is equal to

If \(\hat{i}, \hat{j}\) and \(\hat{k}\) are unit vectors along co-ordinates axes \(OX , OY\) and OZ respectively, then which of the following is/are true?
(A) \(\hat{i} \times \hat{i}=\overrightarrow{0}\)
(B) \(\hat{i} \times \hat{k}=\hat{j}\)
(C) \(i \cdot i=1\)
(D) \(\hat{ i } \cdot \hat{ j }=0\)
Choose the correct answer from the options given below:

Which of the following is NOT em wave ?

The atomic numbers and mass numbers of the nuclei of hydrogen, deuterium and tritium, respectively are in the ratio

MONOHYBRID CROSS
The inheritance of flower color in the dog flower (Snapdragon or Antirrhinum sp.) can be understood by crossbreeding between true-breeding red-flowered (RR) and true-breeding white-flowered plants (rr). When they were crossed, F₁ (Rr) was pink. When F₁ was self-pollinated, the F₂ results were Red, Pink and White. Here the genotype ratios were exactly as expected, but the phenotype ratios have been changed. What happened was that R was not completely dominant over r and this made it possible to distinguish Rr as pink from RR (Red) and rr (White).
What will be the percentage of progeny in F₁ generation when RR (red flowered plant) is crossed with rr (white flowered plant) in the above passage?

The area of the region \(\left\{(x, y): x^2+y^2 \leq 1 \leq x+y\right\}\) is

If \(\cos y=x \cos (a+y)\), then \(\frac{d y}{d x}=\)

Read the passage carefully and answer the questions based on the passage:
The number of reacting species (atoms, ions or molecules) taking part in an elementary reaction, which must collide simultaneously in order to bring about a chemical reaction is called molecularity of a reaction. In the rate equation Rate \(=k[\mathrm{~A}]^x[\mathrm{~B}]^y\)
\(x\) and \(y\) indicate how sensitive the rate is to the change in concentration of A and B, respectively. Sum of these exponents, i.e., \(x +y\) gives the overall order of a reaction where \(x\) and \(y\) represent the order with respect to the reactants A and B respectively. Hence, the sum of powers of the concentration of the reactants in the rate law expression is called the order of that chemical reaction. For a first order reaction, the concentration of the reactant varies as \([\mathrm{R}]=[\mathrm{R}]_0 e^{-k t}\)
Which of the following statements is not true for order of a reaction?