Match List-I with List-II
The function \(f(x)=(x-1)(x+1)^2\) has

List-I	List-II
(A) A local maxima at \(x=\) __________	(I) \(\frac{1}{3}\)
(B) A local minima at x = __________	(II) \(0\)
(C) The local minimum value of \(f(x)=\) __________	(III) \(-1\)
(D) The local maximum value of \(f(x)=\) __________	(IV) \(-\frac{32}{27}\)

Choose the correct answer from the options given below :

The area of region bounded by the curves
\(y=x^2+2, y=-x, x=0\) and \(x=1\) is

Out of the given statement, choose the correct statement.
(A) The direction ratios of the vector \(\vec{a}=3 \hat{i}-\hat{j}+4 \hat{k}\) is \(3,-1,4\).
(B) If \(\theta\) is the angle between two vectors \(\vec{a}\) and \(\vec{b}\), then their cross product is given as \(\vec{a} \times \vec{b}=|\vec{a}||\vec{b}| \cos \theta\).
(C) The unit vector in the direction of vector \(\vec{a}=\hat{i}+2 \hat{j}-2 \hat{k}\) is \(\hat{a}=\frac{1}{3}(\hat{i}+2 \hat{j}-2 \hat{k})\).
(D) If \(\vec{a}=3 \hat{i}\) and \(\vec{b}=4 \hat{j}\) then \(\vec{a} \cdot \vec{b}=12\).
(E) If \(\vec{a}\) and \(\vec{b}\) represent the adjacent sides of a triangle then its area is given of \(\frac{1}{2}|\vec{a} \times \vec{b}|\).
Choose the correct answer from the options given below :

If \(\left[\begin{array}{ll}x-y & 0 \\ x+y & 1\end{array}\right]\) is an identity matrix and \(\left[\begin{array}{ll}x & y \\ x & x\end{array}\right]\) is a singular matrix then :

The area of the region enclosed between the two circles \(x^2+y^2=1\) and \((x-1)^2+y^2=1\) is

If \(A\) and \(B\) are square matrices of the same order, then which of the following statements are correct?
(A) \(\left|A^{-1}\right|=|A|^{-1}\)
(B) \(\operatorname{adj}(A)=|A| A^{-1}\)
(C) \((A+B)^{-1}=B^{-1}+A^{-1}\)
(D) \((A B)^{-1}=B^{-1} A^{-1}\)
Choose the correct answer from the options given below :

Match List - I with List - II

List - I (Time series component)	List - II (Example)
(A) Secular Variation	(I) Pandemic
(B) Seasonal Variation	(II) Recession in business
(C) Cyclic Variation	(III) Monthly sale of woolen clothes
(D) Irregular Variation	(IV) Data regarding National income

Choose the correct answer from the options given below:

"Arrange the following in decreasing order of basic strength:
(A)\(\text{C}_6\text{H}_5\text{NH}_2\)
(B) \(\text{C}_6\text{H}_5\text{N(CH}_3\text{)}_2\)
(C) \((\text{C}_2\text{H}_5\text{)}_2\text{NH}\)
(D) \(\text{CH}_3\text{NH}_2\)
Choose the correct answer from the options given below:"

Arrange the given steps of DNA fingerprinting in sequence.
(A) Transferring of separated DNA fragments on nitrocellulose membrane
(B) Isolation of DNA and digestion by restriction endonuclease
(C) Hybridisation using VNTR Probe
(D) Separation of isolated DNA fragments by Gel Electrophoresis
Choose the correct answer from the options given below :

The radius of a nucleus varies with its mass number A as:

Which of the following are autosomal recessive trait/ disorder?
(A) Thalassemia
(B) Haemophilia
(C) Sickle cell anaemia
(D) Phenylketonuria
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.
When \(1 mol CrCl _3 \cdot 6 H _2 O\) is treated with excess of \(AgNO _3, 3 mol\) of AgCl are obtained. The formula of the complex is:

Which of the following is a stop codon?