Which of the following statements are true
A. \(\vec{a}\) and \(-\vec{a}\) are always collinear.
B. Two collinear vectors are always equal in magnitude.
C. Two vectors having the same magnitude are equal.
D. Two collinear vectors having the same magnitude are equal.
E. If \(\hat{p}\) is a unit vector along line \(l\) then the projection of vector \(\vec{a}\) on line \(l\) is given by \(\vec{a} \cdot \hat{p}\)
Choose the correct answer from the options given below:

500 g of jaggery syrup has 30% jaggery in it.
The quantity of jaggery that should be added to make it 50% of syrup is:

The function \(f(x)=2 \log _e(x-2)-x^2+4 x+1,(x>2)\) is increasing on the interval :

The feasible region associated with the inequality \(2 x+3 y>4\) is

A square board of side 36cm is made into a box without top by cutting a square from each corner and folding up the flaps to form a box then maximum volume of the box is

The area (in sq. units) of the region bounded by the curve \(x^2 = 250y, y = 0\) and \(x = 50\) is

Five dice are thrown simultaneously. If the occurrence of an even number in a single dice is considered a success, then the probability of at most 3 successes is:

The value of the determinant \(\left|\begin{array}{lll}a-b & b+c & a \\b-c & c+a & b \\c-a & a+b & c\end{array}\right| \text { is : }\)

Read the passage carefully and answer the Questions
Werner in 1898, propounded his theory of coordination compounds. In coordination compounds metals show two types of linkages (valences)-primary and secondary. The primary valences are normally ionisable and are satisfied by negative ions. The secondary valences are non-ionisable. These are satisfied by neutral molecules or negative ions. The secondary valence is equal to the coordination number and is fixed for a metal. The ions or group bound by the secondary linkages to the metal have characteristic spatial arrangements corresponding to the different coordination numbers. Both double salts as well as complexes are formed by the combination of two or more stable compounds in stoichiometric ratio. However, they differ in the fact that double salts such as carnallite, Mohr's salt, potash alum etc. dissociate into simple ions completely when dissolved in water. But complex ions do not dissociate completely into simple ions.
Which of the following is a double salt?

What is the IUPAC name of the product of hydration of propene in the presence of dilute sulphuric acid?

A cylindrical bar magnet is kept along the axis of circular coil. If the magnet is rotated about its axis, then :

The current in a circuit having constant resistance is tripled. The power dissipation will become :

Match List I with List II

LIST - I (compound)	LIST - II (Hybridization & Geometry)
A. \(X e F_6\)	I. \(sp^3d^3 \text{ distorted octahedral}\)
B. \(XeO _3\)	II. \(sp^3d^2 \text{ square planar}\)
C. \(X e O F_4\)	III. \(sp^3\text{ pyramidal }\)
D. \(X e F_4\)	IV. \(sp^3d^2 \text{ square pyramidal}\)

Choose the correct answer from the options given below