Let \(\vec{a}\) and \(\vec{b}\) be two unit vectors. If the vectors \(\vec{c}=5 \vec{a}-4 \vec{b}\) and \(\vec{d}=\vec{a}+2 \vec{b}\) are perpendicular to each other, then the angle between \(\vec{a}\) and \(\vec{b}\) is :

If \(\left|\begin{array}{lll}a & b & 0 \\ 0 & a & b \\ b & 0 & a\end{array}\right|=0\) then :

If \(|\vec{a}|=3\) and \(|\vec{b}|=4\), then a value of \(\lambda\) for which \(\vec{a}+\lambda \vec{b}\) and \(\vec{a}-\lambda \vec{b}\) are perpendicular is :

The smaller area between the ellipse \(\frac{x^2}{4}+\frac{y^2}{36}=1\) and the line \(\frac{x}{2}+\frac{y}{6}=1\) is given by:

The differential equation of the family of lines through the origin is:

If the maximum value of the function \(f(x)=\frac{\log _e x}{x}, x>0\) occurs at \(x=a\), then \(a^2 f^{\prime \prime}(a)\) is equal to:

The value of the determinant \(\left|\begin{array}{ccc}a+1 & b & c \\ a & b+1 & c \\ a & b & c+1\end{array}\right|\) is :

If the minimum value of the objective function \(Z=a x+b y\) of an LPP occurs at two points \((3,5)\) and \((5,3)\), then

If a moneylender charges interest at the rate of 10 rupees per 100 rupees per half year, payable in advance, then the effective rate of interest per annum is :

Match List-I with List-II.

List-I	List-II
A. Reimer - Tiemann reaction	I. Benzene
B. Kolbe's reaction	II. Picric acid
C. Nitration of phenol with conc. \(HNO _3\)	III. Salicylic acid
D. Reaction of phenol with zinc dust	IV. Salicyaldehyde

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Read the passage carefully and answer the questions given along
Our immune system plays the major role in preventing diseases when we are exposed to disease-causing agents. Immunity is of two types: (i) Innate immunity and (ii) Acquired immunity. The human immune system consists of lymphoid organs, tissues, cells and soluble molecules like antibodies. The immune system also plays an important role in allergic reactions, auto-immune diseases and organ transplantation. The primary lymphoid organs are bone marrow and thymus. The secondary lymphoid organs are spleen, lymph nodes, tonsils, Peyer's patches of small intestine and appendix. There is lymphoid tissue also located within the lining of the major tracts (respiratory, digestive and urogenital tracts) called mucosa associated lymphoid tissue (MALT). It is important to note that HIV/AIDS is not spread by mere touch or physical contact; it spreads only through body fluids. AIDS has no cure, prevention is the best option. Adolescence is accompanied by several biological and behavioural changes and surveys and statistics show that use of drugs and alcohol has been on the rise especially among the youth. Factors associated with drug and alcohol abuse among adolescents are a child's natural curiosity, stress, the perception among youth that it is 'cool' or progressive to smoke, media exposure and an unstable or unsupportive family structures and peer pressure. It is best to identify the situations that may push an adolescent towards use of drugs or alcohol, and to take remedial measures well in time.
Which one of the following structures is not an example of a cellular barrier in innate immunity?

A cell of emf 1.1 V and internal resistance \(0.5 \Omega\) is connected to a \(0.5 \Omega\) wire. Another cell of same emf is added in series, but current remains unchanged. The second cell's internal resistance is :

Match List I with List II

LIST - I	LIST - II
A. \(\left( CH _3\right)_3 N, CH _3 CH _2 CH _2 NH _2\)	I. Tollen's test
B. \(HCOOH , CH _3 COOH\)	II. Lucas test
C. \(CH _3- C (= O )- CH _2- CH _2- CH _3, CH _3- CH _2- C (= O )- CH _2-CH _3\)	III. Carbylamine test
D. \(CH _3- CH _2- CH _2- CH _2- OH , CH _3- C \left( CH _3\right)( OH )- CH _3\)	IV. lodoform test

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