Which of the following is the range of the principal value of \(\sec ^{-1} x\) ?

There is a Building which is tilted and equations of two different walls are \(2 x-y+z=4\) and \(x+y+2 z=3\). Angle between the walls is :

If \(\left|\begin{array}{ccc}1 & -2 & 5 \\ 2 & a & -1 \\ 0 & 4 & 2a\end{array}\right|=86\), then product of all values of \(a\) is :

If a random variable \(x\) follows Polseon's distribution such that \(P(x=2)=9 P(x=4)+90 P(x=6)\), them sum of the mean and variance of \(x\) is

The value of the determinant \(\left|\begin{array}{ccc}\cos ^2 \theta & \cos \theta \sin \theta & 0 \\ -\sin \theta & \cos \theta & 0 \\ 0 & 0 & 1\end{array}\right|\) is equal to

If \(A\) and \(B\) are independent events such that \(P(A \mid B)=\frac{1}{3}\) and \(P(B)=\frac{1}{2}\), then the value of \(P(A \cap B)\) is equal to :

For any vector \(\vec{a}\), the value of \(|\vec{a} \times \hat{i}|^2+|\vec{a} \times \hat{j}|^2+|\vec{a} \times \hat{k}|^2\) is equal to :

If the objective function for an L.P.P. is \(z=3 x-4 y\) and the corner points for the bounded feasible region are \((0,0),(5,0),(6,5),(6,8),(4,10)\) and \((0,8)\), then the minimum value of \(z\) occurs at :

Identify the incorrect statements from the following.
(A) A charged particle of charge e is moving through a magnetic field, work will be done by the magnetic field on the charge.
(B) A conductor with free electrons is placed in a magnetic field. No current is flowing through the conductor. No magnetic force acts on the conductor.
(C) A charged particle is moving perpendicular to the magnetic field. The magnetic force does not change the speed of the particle but changes its direction.
(D) A charged particle is moving in a straight direction without any change of direction. It shows that no magnetic field is there.
Choose the correct answer from the options given below:

Which of the following is incorrect with reference to drug abuse?

The current in a wire varies with time according to the relationship; I = (2 + 2 t) A, where t is time in seconds. The charge passing through a cross-section of the wire in the time interval between t = 0 s to t = 4 s is

Match List-I with List-II

List-I (Terms)	List-II (Explanation)
(A) Secondary productivity	(I) The amount of biomass or organic matter produced per unit area over a time period by plants
(B) Net primary productivity	(II) The rate of formation of new organic matter by consumers
(C) Gross primary productivity	(III) The available biomass for the consumption to heterotrophs (herbiviores and decomposers)
(D) Primary production	(IV) The rate of production of organic matter during  photosynthesis

Choose the correct answer from the options given below:

The linear constraints, for which the shaded area in the figure is the feasible region of an LPP, are: