If \(\vec{a}, \vec{b}, \vec{c}\) are vectors such that \(\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}\) and \(|\vec{a}|=1,|\vec{b}|=2,|\vec{c}|=5\), then the expression \(\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}\) equals

The total cost \(C(x)\) associated with the production of \(x\) units of an item is given by \( C(x)=0.001 x^3+0.06 x^2+20 x+500\)
The marginal cost when 10 units are produced is:

If \(|\vec{a}|=10,|\vec{b}|=2\) and \(\vec{a} \cdot \vec{b}=12\), then value of \(|\vec{a} \times \vec{b}|\) is :

If \(\vec{a}=2 \hat{j}-\hat{k}, \vec{b}=2 \hat{i}-3 \hat{j}+\hat{k}\) and \(\vec{c}=-\hat{i}+\hat{k}\) are three vectors, then the area (in sq, units) of the parallelogram whose diagonals are \((\vec{b}+\vec{c})\) and \((\vec{a}+\vec{c})\) is

The solution set of the inequation \(|2 x-3| \leq 4\) is

Suppose \(10 \backslash \%\) of men and \(0.5 \backslash \%\) of women have grey hair. A grey haired person is selected at random. If there are equal number of males and females, then the probability of the selected person being a female is :

Match \(List - I\) with \(List - II\)

\(List - I\)	\(List - II\)
General solution	Differential Equation
(A) \(y=c x\)	(I) \(y^{\prime}=\frac{1}{2 \sqrt{x}}-1\)
(B) \(y=e^{-3 x}+c\)	(II) \(y^{\prime}+3 y=0\)
(C) \(x+y=\sqrt{x}+c\)	(III) \(y^{\prime}=\frac{y^2}{1-x y}(x y \neq 1)\)
(D) \(x y=\log y+c\)	(IV) \(x y^{\prime}=y\)

(c is an arbitrary constant and \(y^{\prime}=\frac{d y}{d x}\) )
Choose the correct answer from the options given below:

Rakshita plans to buy a house for Rs. 1,00,00,000 with down payment of 20% of the value of the house paid by her mother. Rest of the amount she wishes to pay in 25 years by equal monthly instalments at an interest of 9% per annum compounded monthly Then the EMI paid by her is \(\left(\right.\) Given \(\left.(1.0075)^{300}=9\right)\) :

Three varieties A, B and C of rice are mixed together in the ratio 1:1:3 respectively. The price of rice A is Rs 127 per kg and that of rice B is Rs 135 per kg. If the price of the mixture is Rs. 152 per kg, then the price per kg of rice of type C is :

According to Bohr's Model :
(A) The radius is directly proportional to 'n'.
(B) The speed is directly proportional to \(\frac{1}{n} \) .
(C) The magnitude of total energy is directly proportional to \(\frac{1}{n^2} \).
(D) The radius is directly proportional to \(n^2\)

Which of the following equation correctly describes 'Net primary productivity'?

Which of the following structures produces both eggs and hormones in human females?

Read the passage carefully and answer the questions
Carbohydrates are naturally formed organic compounds from various plants. The common chemical formula, \(C _x\left( H _2 O \right)_y\), was considered as hydrates of carbon to derive the various carbohydrates. For instance, the general formula for glucose ( \(C _6 H _{12} O _6\) ) easily fits into the above formula. Carbohydrates also called saccharides are classified on the basis of their behavior towards hydrolysis. Monosaccharides cannot be hydrolyzed further to simpler units of polyhydroxy aldehyde or ketones. About 20 monosaccharides are known to occur in nature. Carbohydrates that yield large number of monosaccharide units are called polysaccharides. Amino acids contain ( \(- NH _2\) ) and ( - COOH ), which can be classified in various forms. Proteins are polymers of alpha amino acids which are connected to each other by a peptide bond or peptide linkage. When a native protein is subjected to physical change, its globules unfold and helix get uncoiled and the protein loses its biological activity. The protein is said to be denaturated.
The two monosaccharides units are joined together through which linkage ?