If the points \(A, B, C\) with position vectors \(20 \hat{i}+\lambda \hat{j}, 5 \hat{i}-\hat{j}\) and \(10 \hat{i}-13 \hat{j}\) respectively are collinear, then the value of \(\lambda\) is:

Match List-1 with List-2

List-1	List-2
(A) A fire in a factory causing production delay for some time is	(I) Secular trend
(B) Technological progress is	(II) Seasonal trend
(C) The rise in prices before big festival is example of	(III) Irregular trend
(D) Rise and fall of share market is	(IV) Cyclic trend

Choose the Correct answer from the options given below :-

If the system of equation
\(x-y+z=4\)
\(x-2 y-2 z=9\)
\(2 x+y+\lambda z=1\)
has a unique solution, then

The value of derivative of the function \(\cot ^{-1}\left\{(\cos 2 x)^{1 / 2}\right\}\) at \(x=\frac{\pi}{6}\) is

The inverse of the matrix \(A=\left[\begin{array}{cc}a & b \\ c & \frac{1+b c}{a}\end{array}\right]\) is:

Consider the following hypothesis test.
\(H _0: \mu \leq 12\)
\(H _a: \mu>12\)
If a sample of 25 is taken with sample mean 15 and a sample standard deviation of 6, then the value of t-test statistic is:

Which of the following is NOT correct?

Identify the correct statements among the following:
(A) The value of the electrostatic force constant, k depends on the medium between the two charges and on the choice of system of units.
(B) For two positively charged bodies, one more highly charged than the other, the force between them may be attractive.
(C) The charge on a body does change with its velocity.
(D) An electric dipole is a pair of two equal and similar charges placed at a very small distance.

Two point charges \(+3 \mu C\) and \(-8 \mu C\) attracts each other with a force of 40 N , when separated by finite distance d . If a charge of \(+5 \mu C\) is added to each of them, then the force between them will become:

If the sum of the lengths of the hypotenuse and one of the other two sides of a right angled triangle is fixed, then the area of the triangle is maximum, when the angle between them is :

Choose the wrong statement from the following :

What will happen during the electrolysis of aqueous solution of \(CuSO_4\) by using platinum electrodes?
A. Copper will deposit at cathode.
B. Copper will deposit at anode.
C. Oxygen will be released at anode.
D. Copper will dissolve at anode.
Choose the correct answer from the options given below:

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 statement is correct as per Werner theory?