Which of the following are NOT correct about "Sinking Fund"?
(A) It does not have any specific purpose.
(B) It can be used in any emergency.
(C) Any amount, any time can be deposited in it.
(D) It is set up for a particular upcoming expense.
Choose the correct answer from the options given below:

Match List - I With List - II

List - I	List - II
(A) The area of parallelogram determined by vectors \(2 \hat{i}\) and \(3 \hat{j}\)	(I) 2
(B) The value of \((\hat{i} \times \hat{j}) \cdot \hat{k}+(\hat{j} \times \hat{k}) \cdot \hat{i}\)	(II) 4
(C) The value of a for which the vectors \(2 \hat{i}-3 \hat{j}+4 \hat{k}\) and \(a \hat{i}-6 \hat{j}+8 \hat{k}\) are collinear.	(III) 0
D. The value of \(\lambda\) for which the vectors \(2 \hat{i}+\hat{j}+\hat{k}\) and \(2 \hat{i}-4 \hat{j}+\lambda \hat{k}\) are perpendicular.	(IV) 6

Choose the correct answer from the options given below.

The corner points of the feasible region determined by the system of linear inequalities are \((0, 0), (0, 4), (4, 0), (2, 4)\) and \((0, 5)\). If the maximum value of \(Z = ax + by\) where \(a, b > 0\) occurs at both \((2, 4)\) and \((4, 0)\), then

For \(\ x \in R -\{-1,0,1\} \), \(\int \frac{1}{x-x^5} d x\) is equal to:

If \(\left[\begin{array}{cc}2 & -1 \\ 1 & 0 \\ -3 & 4\end{array}\right] A=\left[\begin{array}{ccc}-1 & -8 & -10 \\ 1 & -2 & -5 \\ 9 & 22 & 15\end{array}\right]\), then matrix \(A\) is equal to:

(A) \(\frac{d}{d x} a^x=\frac{a^x}{\log _e a}\)
(B)\(\frac{d}{d x} e^{a x}=a e^{a x}\)
(C) \(\frac{d}{d x} x^x=x \cdot x^{x-1}\)
(D) \(\frac{d}{d x} x^a=a x^{a-1}\)
(E) \(\frac{d}{d x} a^a=0\)
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

Read the passage carefully and answer the questions based on the passage:
Species diversity on earth is not uniformly distributed. It is generally highest in the tropics and decreases towards the poles. Earth's fossil history reveals the incidences of mass extinctions in the past. Earth's rich biodiversity is vital for the very survival of mankind. It is believed that communities with high diversity tend to be less variable and more productive. The reasons of conserving biodiversity are narrowly utilitarian, broadly utilitarian and ethical. Biodiversity conservation may be in-situ as well as ex-situ.
Which of the following hot spots does not cover India's biodiversity regions?

Answer the question on basis of passage given below:
Organic compounds containing carbon -oxygen double bonds ( \(C = O\) ) are called carbonyl compounds. These are highly polar molecules. Hence, their boiling points are higher than hydrocarbons and ethers. Aldehydes can be prepared from dehydrogenation or oxidation of alcohols and by reduction of acylhalides. Ketones are prepared by oxidation of secondary alcohols or by hydration of alkynes etc. Aldehydes and ketones undergo nucleophilic addition reaction with the number of nucleophiles such as HCN , NaHSO3 ammonia derivatives. Carboxylic acids are prepared by the oxidation of primary alcohols, aldehydes and alkenes, by hydrolysis of nitriles. Carboxylic acids are more acidic than alcohols and phenols.
Which of the following is most reactive towards nucleophilic addition reaction ?

Which of the following is male sex hormone ?

A transmitting antenna at the top of a tower has a height 18 m and the height of the receiving antenna is 32 m. What is the maximum distance between them for satisfactory communication in line-of-sight mode? Given radius of earth is \( 6.4 \times 10^6 \text{ m} \)

The relation R = {(1, 1), (2, 2), (3, 3)} on the set {1, 2, 3} is :

Read the following passage carefully and answer the given questions.
Insulin consists of two short polypeptide chains- chain A and chain B, that are linked together by disulphide bridges. Some strains of Bacillus thuringiensis produce proteins that kill certain insects such as lepidopterans, coleopterans and dipterans. Bt toxin protein is converted into an active form of toxin due to the alkaline pH of the gut which solubilise the crystals. Transgenic animals that produce useful biological products can be created by the introduction of the portion of DNA (or genes) which codes for a particular product such as human protein (alpha-1-antitrypsin) used to treat emphysema. Plants, bacteria, fungi and animals whose genes have been altered by manipulation are called Genetically Modified Organisms (GMO). GM plants have been useful in many ways. Genetic modification has: (i) made crops more tolerant to abiotic stresses. (ii) reduced reliance on chemical pesticides (pest-resistant crops). (iii) helped to reduce post harvest losses. (iv) increased efficiency of mineral usage by plants (this prevents early exhaustion of fertility of soil). (v) enhanced nutritional value of food.
Transgenic animals that produce useful biological products such as human protein (alpha-1-antitrypsin) used to treat the disorder: