Consider the curves, \(x^2+y^2=1\) and \((x-1)^2+y^2=1\).
Points of intersection of two curves are :

If \(C(x)=x^3-5 / 2 x^2+10\) represents the total cost of producing \(x\) units by a car manufacturing company. The slope of the marginal cost curve at \(x = 3\), will be:

The interval on which the function \(f(x) = 2x^3 + 12x^2 + 18x - 7\) is decreasing, is:

Vector in the direction of \(\hat{i}+\hat{j}+\hat{k}\) with magnitude 5 units is :

The increase in the sale of shawls during winters is an example of :

A and \(B\) throw a pair of dice alternately. A wins the game if he gets a total of 6 and \(B\) wins if he gets a total of 7 . If \(A\) starts the game, the probability of winning the game by \(A\) in the third throw of the pair of dice is:

If \(e^x+e^y=e^{x+y}\), then \(\frac{d y}{d x}=\)

Read the following passage carefully and answer the given questions.
Productivity in the Ecosystem The flow of energy through a terrestrial ecosystem starts with the harnessing of sunlight by autotrophs. The radiant energy is converted by photosynthesis to organic compounds is known as productivity. The productivity is expressed in units of energy per unit of area per unit time. The amount of organic matter present at any given time is biomass. The productivity of any ecosystem is affected by many parameters like weather conditions, nutrient availability etc. The productivity of any ecosystem does vary seasonally and yearly.
The Net Primary Productivity of an ecosystem are represented by:

Identify the statements which hold true with respect to origin of life.
(A) Louis Pasteur demonstrated that life comes only from pre-existing life.
(B) Big Bang theory attempts to explain the origin of universe.
(C) Oparin and Haldane proposed first form of life came from pre-existing non-living organic molecules.
(D) Miller's experiment was unable to prove chemical evolution.

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

Arrange the following complexes in increasing order of their magnetic mome
(A) \(\left[\mathrm{NiCl}_4\right]^{2-}\)
(B) \(\left[\mathrm{Fe}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+}\)
(C) \(\left[\mathrm{Cr}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{3+}\)
(D) \(\left[\mathrm{Co}\left(\mathrm{C}_2 \mathrm{O}_4\right)_3\right]^{3-}\)
Choose the correct answer from the options given below:

A pair of dice is thrown, getting a total of 7 is considered a success. Then the probability of success in a single throw is:

The resistance of a galvanometer is G = 30 \( \Omega \). It gives full scale deflection for \( I_g = 2 \text{ mA} \). It is to be converted into an ammeter to measure current I = 0.3 A. The value of the shunt required is approximately