For \(y \neq 0\), the particular solution of the differential equation \(2 y e^{x / y} d x+\left(y-2 x e^{x / y}\right) d y=0\) at the point \((1,1)\) is

If \(e^y=\log x\), then which of the following is true?

If the total cost and total revenue of a company that produces and sells \(x\) units of a particular product are \(C(x)=5 x+350\) and \(R(x)=50 x-x^2\) respectively, then which of the following is/are the breakeven values:
(A) \(x=10\)
(B) \(x=25\)
(C) \(x=45\)
(D) \(x=30\)
Choose the correct answer from the options given below:

In the context of linear programming, Match List I with List II

List - I	List - II
(A) Z = 250x +75y	I. non-trivial constraints
(B) \(5 x+y \leq 100, x-y \leq 4\)	II. feasible solution
(C) \(x, y \geq 0\)	III. objective function
(D) points within and on the boundary of shaded region	IV. Trivial constraints

The following system of equations \(2 x-y+3 z=5,3 x+2 y-z=7,4 x+5 y-\lambda z=\mu\) is consistent. Then

If \(a+b+c=\pi\), then the value of \(\left|\begin{array}{ccc}\sin (a+b+c) & \sin (a+c) & \cos b \\ -\sin b & 0 & \tan a \\ \cos (a+c) & \tan (b+c) & 0\end{array}\right|\) is:

The area bounded by the curve \(y=x^2|x|, x\)-axis and the ordinates \(x=-1\) and \(x=0\) is given by :

The function \(f(x)=x^3, x \in R\), has:

Read the passage carefully and answer the questions
The speed at which a chemical reaction takes place is called the rate of reaction. The rate of reaction depends on various factors like concentration of the reactants, temperature, etc. The relation between the rate of reaction and the concentration of reacting species is represented by the equation r = k[A]^x[B]^y, where x and y are the order of the reaction with respect to the reactants A and B, respectively. The overall order of the reaction is x + y. The rate of reaction can also be increased by the use of a catalyst which provides an alternate pathway of lower activation energy. It increases the rate of forward and backward reaction to an equal extent. It does not alter the Gibbs energy of the reaction.
If the rate of reaction becomes twenty-seven times upon increasing the concentration of reactant by three times, the order of this reaction is

Which of the following statements is INCORRECT?

Arrange in increasing order of number of species to represent global biodiversity?
(A) Molluscs
(B) Crustaceans
(C) Insects
(D) Other animal groups
Choose the correct answer from the options given below:

'Species richness contributes to the well being of an ecosystem' was explained through an analogy the rivet popper hypothesis'. The hypothesis was given by :

A dietician wishes to mix two types of food in such a way that the vitamin contents of the mixture contains atleast 8 units of Vitamin A and 10 units of Vitamin C. Food 'I' contains 2 units/kg of Vitamin A and 1 unit/kg of Vitamin C while food 'II' contains 1 unit/kg of Vitamin A and 2 units/kg of Vitamin C. It costs ₹5 per kg to purchase food I and ₹7 per kg to purchase food II. If 'x' kg of food I is mixed with 'y' kg of food II, then the constraint pertaining to vitamin C contents will be: