Which of the following are examples of irregular trends in a time series?
(A) Decrease in production due to a sudden strike.
(B) The rise in prices before festivals.
(C) Unusual rise in income of the printing press due to the announcement of an election.
(D) Fall in crop yield due to floods.
Choose the correct answer from the options given below :

Match List-I with List-II

List-I (Function f(x))	List-II (Interval)
(A) \(f(x)=x|x|\)	(I) Decreases on \((0, \infty)\)
(B) \(f(x)=x^2+2 x-5\)	(II) Increases on \((3, \infty)\)
(C) \(f(x)=x^2-6 x+9\)	(III) Decreases on \((-\infty,-1)\)
(D) \(f(x)=-x^2\)	(IV) Increases on \((-\infty, \infty)\)

Choose the correct answer from the options given below:

If the function \(f(x)=x^4-62 x^2+a x+9\) attains its local maximum value at \(x=1\), then \(a\) is equal to :

Which of the following are correct?
(A) If \(a \equiv b(\bmod n)\), then \(-a \equiv-b(\bmod n)\)
(B) If \(a+b=c\), then \(a(\bmod n)+b(\bmod n) \equiv(a+b+c)(\bmod n)\)
(C) If \(a \equiv b(\bmod n)\), then \(k a \equiv k b(\bmod n), \forall k \in I\)
(D) If \(a \equiv b(\bmod n)\), then \((a+k) \equiv(b+k)(\bmod n), \forall k \in I\)
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If \(A=\left[\begin{array}{ll}1 & 0 \\ 0 & 0\end{array}\right], B=\left[\begin{array}{ll}0 & 0 \\ 3 & 0\end{array}\right]\) then

If \(A=\left[\begin{array}{ccc}1 & 2 & 3 \\ -4 & -5 & -6\end{array}\right], \quad B=\left[\begin{array}{cc}2 & -3 \\ 4 & -5 \\ 2 & -1\end{array}\right]\) and \(B A=\left[b_{i j}\right]\), then \(\left(b_{23}-b_{31}\right)\) is equal to

The equation of tangent to the curve \(y=\sqrt{3 x-2}\) which is parallel to the line \(4 x-2 y+5=0\) is :

Inner orbital complex among the following is :
(A) \(\text{[Co(NH}_3)_6\text{]}^{3+}\)
(B) \(\text{[CoF}_6\text{]}^{3-}\)
(C) \(\text{[Ni(CN)}_4\text{]}^{2-}\)
(D) \(\text{[MnCl}_6\text{]}^{3-}\)
(E) \(\text{[FeF}_6\text{]}^{3-}\)
Choose the correct answer from the options given below :

The menstrual flow results due to:
A. Increased estrogen levels
B. When released ovum is not fertilized
C. When pregnancy occurs
D. Breakdown of the endometrial lining of the uterus and its blood vessels

Actinoid contraction is of greater extent then lanthanide contraction because

Match List-l with List-II

List-l (Terms)	List-ll (Features)
(A) IgE	(I) Formed by yeast
(B) IgA	(II) Cellular barrier
(C) Hepatitis B vaccine	(III) Antibodies due to allergens
(D) Polimorpho- nuclear leucocytes	(IV) Present in colostrum

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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 :

Which of the following mico-organism is used to produce statins, a blood-cholesterol lowering agent ?