If \(\vec{a}, \vec{b}, \vec{c}\) are unit vectors such that \(\vec{a} \cdot \vec{b}=\vec{a} \cdot \vec{c}=0\), and the angle between \(\vec{b}\) and \(\vec{c}\) is \(\frac{\pi}{6}\), then

Match List-I with List-II
[.] denotes the greatest integer function.

List-I	List-II
(A) \(\int_0^3[x] d x\)	(I) \(\frac{1}{2}\)
(B) \(\int_0^1[2 x] d x\)	(II) 1
(C) \(\int_0^1[3 x] d x\)	(III) \(\frac{3}{2}\)
(D) \(\int_0^1[4 x] d x\)	(IV) 3

Choose the correct answer from the options given below :

In a LPP , if the objective function \(Z=a x+b y\) has the same maximum value at two corner points of the feasible region, then the number of points at which \(Z_{\max }\) occurs is:

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 \((a+k) \equiv(b+k)(\bmod n), \forall k \in I\)
Choose the correct answer from the options given below :

Match List I with List II

LIst - I	List - II
(A) The present value of an immediate perpetuity of ₹R payable at end of any year forever at rate of i per period is:	(I) \(\frac{R}{i}(1+i)^m\)
(B) Present value of deferred perpetuity is	(II) \(\frac{A i}{(1+i)^n-1}\)
(C) Periodic payment R in a sinking fund is given by formula (for Amount A)	(III) \(A(1+i)^{-n}\)
(D) The present value of redemption price A of a bond is given by	(IV) \(\frac{R}{i}\)

The range of the function \(f(x)=4 x^2+12 x+7, x \in R\) is

The value of \(\cot \left(\cos ^{-1} \frac{7}{25}\right)\) is

Arrange the following PCR steps in the correct sequence.
A. Extension of Primers
B. Amplification of DNA
C. Annealing of Primers
D. Denaturation of DNA fragment
Choose the correct answer from the options given below:

In the given circuit when steady current flows, the potential drop across the capacitor is:

Read the following passage carefully and answer the given questions.
Immune System in the Body
The human immune system consists of lymphoid organs, tissues, cells and soluble molecules like antibodies. The primary lymphoid organs are bone marrow and thymus where immature lymphocytes differentiate into antigen-sensitive lymphocytes. After maturation the lymphocytes migrate to secondary lymphoid organs like spleen, lymph nodes, tonsils, Peyer's patches of small intestine and appendix. The secondary lymphoid organs provide the sites for interaction of lymphocytes with the antigen, which then proliferate to become effector cells. The bone marrow is the main lymphoid organ where all blood cells including lymphocytes are produced. Each antibody molecule has four peptide chains, two small called light chains and two longer called heavy chains. Hence, an antibody is represented as H2L2. Different types of antibodies are produced in our body. IgA, IgM, IgE, IgG are some of them. Techniques like radiography (use of X-rays), CT (computed tomography) and MRI (magnetic resonance imaging) are very useful to detect cancers of the internal organs.
Maturation of lymphocytes takes place in:

The following statements predict the temperature dependence on the rate of reaction:
(A) Increase in temperature increases the rate of reaction.
(B) Increase in temperature decreases the rate of reaction.
(C) Increase in temperature by \(10 \,^\circ C\) doubles the reaction rate.
(D) An increase in temperature by \(10 \,^\circ C\) triples the rate of reaction.
Choose the correct answer from the options given below:

Match List-I with List-II

List-I (Lines)	List-II (Direction Ratios)
(A) \(\frac{x-1}{2}=\frac{2-y}{1}=z\)	(I) \((1,3,-1)\)
(B) \(\frac{2 x-1}{2}=\frac{y+1}{3}=\frac{1-z}{1}\)	(II) \((2,-2,0)\)
(C) \(\frac{x+1}{2}=\frac{3-y}{2}=z=2\)	(III) \((2,-1,1)\)
(D) \(\frac{2 x-3}{4}=\frac{1-2 y}{2}=\frac{z}{5}\)	(IV) (2, -1, 5)

Choose the correct answer from the options given below:

Match List I with List II.

List-I	List-II
A. Insulin	I. Female hormone
B. Thyroxine	II. Male sex hormone
C. Testosterone	III. Thyroid
D. Estradiol	IV. Blood glucose level

Choose the correct answer from the options given below :