If \(A=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]\), then the value of \(A^{20}\) is :

The function \(f(x)=x^2-x+1\) is

The approximate volume of a cube of side a meters on increasing the side by 4% is:

The value of parameter k for which the function \(f(x)=1+k x, k \neq 0\) is the inverse of itself is:

Which of the following statements are true?
(A) The vector equation of the line through the point (5, 2, -4) and parallel to the vector \(3 \hat{i}+2 \hat{j}-8 \hat{k}\) is \(\vec{r}=(5 \hat{i}+2 \hat{j}-4 \hat{k})+\lambda(3 \hat{i}+2 \hat{j}-8 \hat{k})\)
(B) Vector form of the equation of line \(\frac{x-5}{3}=\frac{y+4}{7}=\frac{z-6}{2}\) is \(\vec{r}=(5 \hat{i}-4 \hat{j}+6 \hat{k})+\lambda(3 \hat{i}+7 \hat{j}+2 \hat{k})\)
(C) The direction cosines of z-axis are (1, 1, 0).
(D) If a line has direction ratios 2, -1, -2, then its direction cosines are \(-2 / 3,-1 / 3,-2 / 3\).
Choose the correct answer from the options given below:

If \(y=\sin x+e^x\), then \(\frac{d^2 x}{d y^2}\) is equal to:

The equation of the tangent, to the curve \(y=x^2-2 x-3\) which is perpendicular to the line x + 2y + 3 = 0, is:

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.
Hind II is a restriction endonuclease because

Consider the LPP, optimize \(Z=x+5 y\) subject to \(x+y \geq 5 ; 2 x-5 y \geq 10, x \leq 2 ; x \geq 0, y \geq 0\), then which of the following is correct?

The first clinical gene therapy was given to treat :

Kirchhoff's second law for an electric network is based on:

Nitration of aniline with nitric acid and sulphuric acid gives major product as

A concave mirror of focal length 6 cm is placed at a distance 'd' from the convex lens of focal length 8 cm. A beam of light coming from infinity and falling on this convex lens-concave mirror combination returns to infinity. The distance 'd' must be equal to: