If the feasible region of a system of linear inequalities can be enclosed within a circle then it is called

There are 50 telephone lines in an exchange. The probability that any one of them will be busy is 0.1, then the probability that all the lines are busy?

If \(A=\left[\begin{array}{ll}2 & 3 \\ 1 & 4\end{array}\right]\) and \(B=\left[\begin{array}{cc}1 & -2 \\ 1 & 3\end{array}\right]\), then which of the following are incorrect?
(A) \(|A|=5\)
(B) \(\operatorname{Adj} A=\left[\begin{array}{ll}4 & 3 \\ 1 & 2\end{array}\right]\)
(C) \(A(\operatorname{Adj} A)=25 I\)
(D) \(|3 B|=45\)
(E) \((A B)^{-1}=B^{-1} A^{-1}\)
Choose the correct answer from the options given below:

\(\int \frac{\left(x^4-x\right)^{1 / 4}}{x^5} d x\) is equal to

The probability distribution of a random variable X is given by

X	0	1	2
P(X)	\(1-7 a^2\)	\(\frac{1}{2} a+\frac{1}{4}\)	\(a^2\)

If \(a>0\), then \(P(0<X \leq 2)\) is equal to

Bag A contains 2 unbiased and 3 biased coins whereas Bag B contains 3 unbiased and 2 biased coins. A bag is selected at random and 2 coins are taken out simultaneously. The probailty, that both coins are unbiased is :

The integral \(\int e^x\left(\frac{x-1}{2 x^2}\right)\)dx is equal to

Select the hormone which is not secreted by human placenta:

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 phenotypic ratio in F₂ generation when F₁ (Rr) was self-pollinated?

Which constraint correctly represents the situation "Mixture of x and y must be at least 8 units"?

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?

Consider the function \(f: R \rightarrow R\) defined by \(f(x)=\frac{x}{x^2+1}\) then

In gel electrophoresis, the separated DNA fragment can be visualized -