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

Consider the LPP, \(\operatorname{Max} Z=2 x+y\), subject to the conditions
\(\begin{array}{l}3 x+2 y \leq 6 \\4 x+y \leq 4\end{array}\)
\(x \geq 0, y \geq 0\), then the maximum value of the objective function is:

Consider the following L.P.P.
Max. \(z=5 x+2 y\), subject to \(-2 x-3 y \leq-6, x-2 y \leq 2,3 x+2 y \leq 12,-3 x+2 y \leq 3\) and \(x, y \geq 0\) then

For \(x>0\), the minimum value of \(\frac{x}{\log _e x}\) is

The general solution of the differential equation \(\left(1+x^2\right) d y-x d x=0\) is :

Which of the following are correct about equated monthly installments (EMI)?
(A) The EMI depends on principal borrowed, rate of interest and tenure of the loan.
(B) It is a fixed amount made by borrower to the lender every month.
(C) The interest remains constant for every EMI in reducing balance method.
(D) As we pay off our loan, the outstanding principal amount decreases with every EMI in reducing balance method.
Choose the correct answer from the options given below :

Which of the following is not correct?

Read the Passage carefully and answer the Questions
Kinetic studies not only help us to determine the rate of a chemical reaction but also describe the conditions by which the reaction rates can be altered.
The factors such as concentration, temperature, pressure and catalyst affect the rate of a reaction.
The speed of a reaction or the rate of a reaction can be defined as the change in concentration of a reactant or product in unit time.
Rate \(=k[A]^x[B]^y\)
Here \(k\) is the rate constant
\(x+y\) gives the overall order of a reaction, whereas \(x\) and \(y\) represent the order with respect to the reactants \(A\) and \(B\), respectively.
The order of a reaction which does not exist is

A reaction is 2nd order w.r.t A and 1st order w.r.t B. When the concentrations of both A and B are doubled the rate of reaction will become:

Match the properties given in List-l with the metals given in List-ll

List-l (Property)	List-II (Metal)
(A) An element which can show +8 oxidation state	(I) V
(B) 3d block element that can show upto +7 oxidation state	(II) Cr
(C) 3d block element with the highest melting point	(III) Os
(D) 3d block element with the highest enthalpy of atomization	(IV) Mn

Choose the correct answer from the options given below:

Let \(A\) and \(B\) are square matrices of order 3 such that \(A+B=\left[\begin{array}{ccc}2 & -2 & -4 \\ -1 & 3 & 4 \\ 1 & -2 & -3\end{array}\right]\). If \(A\) is a symmetric matrix, then the value of \(|B|\) is:

Choose the correct statement(s)
A. In photo electric effect, the minimum negative potential to the plate A for which photocurrent is zero is called saturation potential.
B. Maximum kinetic energy of photoelectrons is directly proportional to intensity of incident radiation.
C. \(K_{\text {max }}=e V_o\)
D. Photocurrent becomes zero at stopping potential.
E. For different intensities of light, stopping potential is different.
Choose the correct answer from the options given beow:

Read the passage carefully and give the answers to the question .
India was amongst the first countries in the world to initiate action plans plans and programmes at a national level to attain total reproductive health as a social goal.
These programmes called 'family planning' were initiated in 1951 and were periodically assessed over the past decades. Improved programmes covering wider reproduction-related areas are currently in operation. Creating awareness among the people about various reproduction-related aspects and providing facilities and support for building up a reproductively healthy society are the major tasks under these programmes.
Which of the following methods of contraception is not meant for females?