If \(A=\left[\begin{array}{ll}1 & 0 \\ 0 & 0\end{array}\right], B=\left[\begin{array}{ll}0 & 0 \\ 3 & 0\end{array}\right]\) then

The feasible region represented by the constraints \(x+y \leq 50,3 x+y \leq 90, x \geq 0, y \geq 0\) of an LPP is

The value of the determinant \(\left|\begin{array}{ccc}a+1 & b & c \\ a & b+1 & c \\ a & b & c+1\end{array}\right|\) is :

Angle between the line \(\frac{x-1}{3}=\frac{y+1}{5}=\frac{z-2}{4}\) and the plane \(2 x+2 y-z=3\) is:

The point on the curve \(y=(x-2)^2\) at which the tangent is parallel to the chord joining the points \((2,0)\) and \((4,4) \) is :

If the curves \(x=y^2\) and \(x y=k\) meet at right angles, then the value of \(k\) is:

If \(f(x)=\left\{\begin{array}{ll}\frac{\tan \left(\frac{\pi}{4}-x\right)}{\cot 2 x}, & x \neq \frac{\pi}{4} \\ k, & x=\frac{\pi}{4}\end{array}\right.\)
is continuous at \(x=\frac{\pi}{4}\), then the value of \(k\) is:

Which of the following statement(s) is/are correct?
(A) The power of a lens is the ability of the lens to converge or diverge the incident rays.
(B) S.I unit of the power of a lens is dioptre while focal length is in centimetres
(C) For a lens of larger focal length, power is smaller
(D) In any combination of lenses, the power of combination is not algebraic addition of power of combined lenses
Choose the correct answer from the options given below:

Which statement is not true for a detergent molecule ?

An ammeter of resistance 5 \( \Omega \) reads up to 1 A. The value of the shunt required to increase its range to 5 A will be

Read the passage carefully and answer the questions
The chemical reactions proceed at different rates which depend on various factors like concentration, temperature, etc. Rate law is an expression which relates the rate of reaction with concentration of various reacting species in the reaction. For a first order reaction, the concentration of the reactant after time \(t\) is related with its initial concentration by the relation, \(C=C_0 e^{-k t}\). The rate constants for different orders have different expressions. For a first order reaction, \(k=\frac{2.303}{t} \log \frac{a}{a-x}\), where \(a\) is the initial concentration and \(x\) is the extent of reaction.
A first order reaction is one-fifth completed in 40 minutes. Calculate the time required for its 100 % completion

The average power associated with an ideal capacitor of capacitance \( 5 \ \mu\text{F} \) connected to an alternating emf \( E = 200 \sin 100\pi t \) is:

Read the passage carefully and answer the given questions.
Recombinant DNA Technology
Asexual reproduction preserves the genetic information, while sexual reproduction permits variation. Traditional hybridization procedures used in plants and animals breeding very often lead to inclusion and multiplication of undesirable genes along with the desired genes. The techniques of genetic engineering, which include creation of recombinant DNA, use of gene cloning and gene transfer, overcome this limitation and allow us to isolate and introduce only one or a set of desirable genes without introducing genes into the target organism.
In Recombinant DNA Technology, what is the role of the "selectable marker gene"?