If \(\vec{a}\) and \(\vec{b}\) are two vectors such that \(|\vec{a}|=10,|\vec{b}|=2\) and \(\vec{a} \cdot \vec{b}=12\), then \(|\vec{a} \times \vec{b}|\) is equal to

Which one of the following set of constraints represents the shaded region given below?

Match List - I with List - II

LIST-I (Differential Equations)	LIST-II ( Degree)
(A) \(\left(\frac{d y}{d x}\right)^3+y x=0\)	(I) 2
(B) \(e^{\frac{d y}{d x}}+y^2+y^{\prime \prime}=0\)	(II) 1
(C) \(x y y^{\prime \prime}+x\left(y^{\prime}\right)^2-y y^{\prime}=0\)	(III) Not defined
(D) \(\left(y^{\prime \prime}\right)^2+y=0\)	(IV) 3

Choose the correct answer from the options given below :

The corner points of the feasible region determined by the system of linear inequalities are \((0, 0), (0, 4), (4, 0), (2, 4)\) and \((0, 5)\). If the maximum value of \(Z = ax + by\) where \(a, b > 0\) occurs at both \((2, 4)\) and \((4, 0)\), then

The feasible region of the linear programming problem is represented below :

The constraints of this LPP are

The maximum value of the objective function \(z=2 x+3 y\) of an L.P.P. subjected to the constraints \(x-y \leq 1, x+y \leq 3, x, y \geq 0\), is

If \(A^2-A+I=0\), then \(A^{-1}\) is equal to :

The following reaction of benzene with carbon monoxide and hydrogen chloride in the presence of aluminum trichloride to give benzaldehyde is known as

The sum of the minor and the cofactor of the element 6 in the determinant \(\Delta=\left|\begin{array}{lll}2 & 3 & 1 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{array}\right|\) is:

Two point charges \( q_1 = 36 \text{ }\mu\text{C} \) and \( q_2 = -9 \text{ }\mu\text{C} \) are placed at a distance of 30 cm. The distance from \( q_1 \) where the net electric field is zero, will be :

A square of side L m lies in the XY plane in a region where the magnetic field is \( \vec{B} = B_0(2\hat{i} + 3\hat{j} + 4\hat{k}) \text{ T.} \) The magnitude of magnetic flux through the square is:

Read the following passage carefully.
Restriction enzyme
Restriction enzymes cut the strand of DNA a little away from the center of the palindrome sites, but between the same two bases on the opposite strands. This leaves single stranded portions at the ends. There are overhanging stretches called sticky ends on each strand. These are named so because they form hydrogen bonds with their complementary cut counterparts. This stickiness of the ends facilitates the action of the enzyme DNA ligase. The word palindromes refer to group of letters that forms the same words when read both forward and backward. Restriction endonucleases are used in genetic engineering as molecular scissors.
Which one of the following option is correct about restriction enzyme?

If \(2 P(A)=P(B)=\frac{5}{13}\) and \(P(A \mid B)=\frac{2}{5}\), then \(P(A \cap B)\) is