Let \(A=\left[\begin{array}{ccc}1 & \sin \theta & 1 \\ -\sin \theta & 1 & \sin \theta \\ -1 & -\sin \theta & 1\end{array}\right]\), where \(0 \leq \theta \leq 2 \pi\), then which of the following are true?
(A) \(|A|=2+2 \sin ^2 \theta\)
(B) \(|A|=2+\sin ^2 \theta\)
(C) minimum value of \(|A|\) is 1
(D) maximum value of \(|A|\) is 4.
Choose the correct answer from the options given below:

If \(A=\left[\begin{array}{cc}3 & 1 \\ -1 & 2\end{array}\right]\) and \(I=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]\), then the value of \(A^2-5 A+6 I\) is

A machine costing Rs. \(2,00,000\) has a useful life of 5 years. The estimated scrap value is Rs. 20,000 . By using straight line method, the annual depreciation is

The general solution of the differential equation \(\frac{d y}{d x}=e^{a x+b y}\) is : (Here \(C\) is an arbitrary constant)

Direction ratios of the line perpendicular to the lines \(\frac{x+2}{1}=\frac{y+3}{2}=\frac{z-5}{-2}\) and \(\frac{x-3}{2}=\frac{y+7}{-3}=\frac{z-2}{1}\) are:

For the linear programming problem (LPP),
Maximize \(Z=4 x+y\)
Subject to:
\(x+y \leq 5\)
\(3 x+y \leq 9\)
\(x, y \geq 0\)
Which of the following are NOT true?
(A) The given LPP has unbounded feasible region.
(B) The corner points of the feasible region are \((0,0),(0,5),(3,2)\) and \((3,0)\).
(C) The optimal value of the objective function is 12.
(D) The given LPP has a unique optimal solution.
Choose the correct answer from the options given below:

The number of all possible matrices of order 2 × 2 with each entry 0 or 1 is:

An aqueous solution of urea has a freezing point of \(\text{– } 0.52^{\circ}\text{C}\). Predict the osmotic pressure of the solution at \(37^{\circ}\text{C}\) [\(K_f = 1.86\), assuming that the molar concentration and molality are numerically equal]

Answer the question on the basis of passage given below :
All transition elements display typical metallic properties like high melting point, boiling point, tensile strength, high malleability and ductility, luster, etc. Their metallic character increases down the group and elements of 4d and 5d series exhibit higher metallic characters. They show variable oxidation states and forms a number of coloured compounds due to the presence of unpaired electrons which shows d-d transitions and makes them paramagnetic.
Which out of the following coordination compounds are colourless in nature?
A. \(\left[ Cr \left( NH _3\right)_6\right] Cl _3\)
B. \(\left[ Co \left( NH _3\right)_6\right] Br _3\)
C. \(K _3\left[ Fe ( CN )_6\right]\)
D. \(\left[ MnCl _2(e n)_2\right]^{+}\)
E. \(\left[ Ni ( CO )_4\right]\)
Choose the correct answer from the options given below :

ELISA is based on the principles of:

Arrange the given steps of 'Recombinant DNA Technology' in correct sequence.
A. Transfer of recombinant plasmid into host cell for cloning.
B. Ligation of desired DNA to plasmid.
C. Selection of desired DNA and plasmid.
D. Cutting of desired DNA and plasmid using same restriction enzyme.
Choose the correct answer from the options given below:

Choose the correct dimension of \(\varepsilon_0 \frac{d \phi_{ E }}{ dt }\) from the following :
In the given expression symbols have their usual meaning.

Which of the following compounds can be prepared by Sandmeyer's reaction?
(A) Chlorobenzene
(B) Bromobenzene
(C) Cyanobenzene
(D) Fluorobenzene
Choose the correct answer from the options given below: