In the interval [-5, -3], the function f(x) = (x + 1)(x - 3) is:

The value of the determinant \(\left|\begin{array}{cc}a \cos \theta & a \sin \theta \\ -a \sin \theta & a \cos \theta\end{array}\right|\) is:

If \(x = at^2, y = 2at\) then \(\frac{d^2y}{dx^2} =\)

If \(A=\left[\begin{array}{cc}\alpha & \beta \\ \gamma & -\alpha\end{array}\right]\) is such that \(A^2=I\), then:

If \(A\) is a square matrix of order 2 , then \(|\operatorname{adj} A|\) is equal to:

The function \(f : R \rightarrow R\) defined by \(f(x)=\left\{\begin{array}{ll}x^2, & x \geq 1 \\ x, & x<1\end{array}\right.\) is

The function \(f: R \rightarrow[-1,1]\) defined by f(x) = cos x 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.
When DNA from different sources is cut by the same restriction enzymes, the resultant DNA fragments have the :

In the context of linear programming, Match List I with List II

List - I	List - II
(A) Z = 250x +75y	I. non-trivial constraints
(B) \(5 x+y \leq 100, x-y \leq 4\)	II. feasible solution
(C) \(x, y \geq 0\)	III. objective function
(D) points within and on the boundary of shaded region	IV. Trivial constraints

The probability of guessing correctly atleast 8 out of 10 answers on a true false type examination is :

The corner points of the bounded feasible region determined by the system of linear constraints are (0,0), (5,0), (6,5), (6,8), (4,10), (0,8).
Let \(z=3 x-4 y\) be the objective function. Then the minimum value of z occurs at :

Which of the following is not the correctly matched pair of organism and its respective cell wall degrading enzyme

The interval on which the function \(f(x)=x^4-\frac{x^3}{3}\) is strictly decreasing, is :