If \(\left[\begin{array}{cc}2 a+b & a-2 b \\ 5 c-d & 4 c+3 d\end{array}\right]=\left[\begin{array}{cc}4 & -3 \\ 11 & 24\end{array}\right]\), then the value of \(a+2 b-3 c+4 d\) is equal to

If \(y=\log \left(x+\sqrt{x^2+a^2}\right)\) then \(\frac{d y}{d x}\) =

If the matrix \(\left[\begin{array}{ccc}-3 & x-y & 5 \\ 1 & 0 & z \\ x+y & 4 & 7\end{array}\right]\) is symmetric, then the correct option of the following, is :

On simplifying \(\cot \left(2 \tan ^{-1} x\right)\) where \(|x|<1\), we get:

The value of c in Rolle's theorem for the function \(f(x)=x^3-3 x\) in the interval \([0, \sqrt{3}]\) is :

Maximize \(z=2 x-y\)
Subject to constraints
\(x+y \leq 4, \quad x+3 y \leq 6, \quad x \geq 0, \quad y \geq 0 .\)
The corner points of the feasible region are:

If the matrix A = \(\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]\), then \(A ^2\) is equal to:

While charging the lead storage battery......

The rate of change in area of a triangle having sides 10 cm and 12 cm when the variable angle between them is \(\theta=60^{\circ}\), is :

The reaction of two molecules of 1-chlorobenzene with sodium metal in the presence of dry ether to form diphenyl is known as

Read the following paragraph carefully and answer the given questions.
In the year 1963 the two enzymes responsible for restricting the growth of bacteriophage in E. coli were isolated. The first restriction endonuclease - Hind II, whose functioning depended on a specific DNA nucleotide sequence was characterized five years later. It was found that Hind II always cut DNA molecules at a particular point by recognizing a specific sequence of six base pairs. This specific base sequence is known as the recognition sequence for Hind II. Besides Hind II, today we know more than 900 restriction enzymes that have been isolated from over 230 strains of bacteria, each of which recognize different recognition sequences.
In EcoR I the latter 'R' is derived from the -

Which one of the following drugs can not quickly reduce the symptoms of allergy?

From the below-mentioned graph of shaded feasible region of a linear programming problem (LPP) with objective function
\(z=1.50 x+1.00 y\), the maximum value of \(z\) will be;-