Consider the LPP,
Maximize \(z=2 x+3 y\), subject to the conditions,
\(\begin{array}{l}x+y \leq 2 \\x \leq 2 \\x \geq 0, y \geq 0\end{array}\)
then maximum value of the objective function is:

At \(6 \%\) converted quarterly, the present value of a perpetuity of ₹ 900 payable at the end of each quarter is :

Mameesh took a loan of Rs 9,00,800 from bank at an interest rate of \(6 \%\) per annum for 10 years. If she has to pay the loan back with the help of equal monthly installments (EMI). Then, the EMI using reduced balance method is (approx) :
(Given: \((1.005)^{-120}=0.5496\))

The remainder, when \(5^{60}\) is divided by 7 , is :

If \(\vec{a}+\lambda \vec{b}\) is perpendicular to \(\vec{c}\), where
\(\vec{a}=-\hat{i}+2 \hat{j}+\hat{k}, \vec{b}=3 \hat{i}+2 \hat{j}+\hat{k}\), and \(\vec{c}=\hat{i}-\hat{j}\),
then :

If \(x=a\left(\cos t+\log \tan \frac{t}{2}\right), y=a \sin t\), then value of \(\frac{d y}{d x}\) at \(t=\pi / 4\) is

If the function \(f(x)=x^2\) is one-to-one and onto, then the domain D and range R of \(f(x)\) are respectively :

Two cells with internal resistances \( r_1 \) and \( r_2 \) are connected across the load resistance R as shown in the figure. The values of \( r_1, r_2 \) and R are (1/2) \( \Omega \), (1/3) \( \Omega \) and (9/5) \( \Omega \), respectively. The current through R is:

The Medical Termination of Pregnancy (Amendment) Act, 2017 was enacted by the government of India with the intension of _________ .

Read the following paragraph and answer the given questions:
In order to link the alien DNA, the vector needs to have very few, preferably single, recognition sites for the commonly used restriction enzymes. Presence of more than one recognition site in the vector will generate several fragments, which will complicate the gene cloning. In order to link the alien DNA, the vector needs to have very few, preferably single, recognition sites for the commonly used restriction enzymes. Presence of more than one recognition sites within the vector will generate several fragments, which will complicate the gene cloning. The ligation of alien DNA is carried out at a restriction site present in one of the two antibiotic resistance genes. The recombinant plasmids will lose tetracycline resistance due to insertion of foreign DNA but can still be selected out from non-recombinant ones by plating the transformants on tetracycline containing medium.
The recombinants will grow in ampicillin containing medium but not on that containing tetracycline. But, non- recombinants will grow on the medium containing both the antibiotics. In this case, one antibiotic resistance gene helps in selecting the transformants, whereas the other antibiotic resistance gene gets 'inactivated due to insertion' of alien DNA, and helps in selection of recombinants. Origin of replication (ori) is a sequence from where replication starts and any piece of DNA when linked to this sequence can be made to replicate within the host cells. This sequence is also responsible for controlling the copy number of the linked DNA. So, if one wants to recover many copies of the target DNA it should be cloned in a vector whose origin support has high copy number.
In cloning vector pBR322, the BamH1 site codes for:

The current and voltage in an ac circuit are given by \( I = 5 \sin(100t - \pi/2) \text{ A} \) and \( V = 200 \sin(100t) \text{ V} \). The power dissipated in the circuit is

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 \([\mathrm{R}]=[\mathrm{R}]_0 e^{-k t}\)
The units of first and zero order rate constant of reactions are respectively:

Products not possible from given reaction is :
\(R - CH _2- C ( O )- CH _2- R ^{\prime} \xrightarrow{[ O ]}\)
(A) RCOOH
(B) \(R ^{\prime} CH _2 COOH\)
(C) \(R - CH _2- COOH\)
(D) \(R ^{\prime}- C ( O )- OCH _3\)
Choose the correct answer from the options given below: