If \(e^y(x+2) = 10\), then \(\frac{d^2y}{dx^2}\) is equal to :

The sides of an equilateral triangle are increasing at the rate of \(5 cm / sec\). The rate at which the area increases when the side is 20 cm , is

If \(\frac{d}{d x}\left(2 \frac{d^2 y}{d x^2}\right)^3=7\), then the sum of order and degree of the differential equation is:

The value of \(|\text{adj}(2A)|\), if \(A = [a_{ij}]_{3 \times 3}\) and \(|A| = 2\) is:

The solution of a LPP with basic feasible solutions (0,0), (10,0), (0,20), (10, 15) and objective function Max Z = 2x + 3y is:

For what value of \(\alpha\), the function \(f\) defined by \(f(x)=\left\{\begin{array}{ll}\alpha\left(x^2-2 x+1\right), & \text { if } x \leq 0 \\ 2 x+1, & \text { if } x>0\end{array}\right.\) is continuous at \(x=0\) ?

Which of the following is not the specification of the Sinking Fund?

Match List-l with List-II

List-l	List-II
(A) Ambident nucleophiles	(I) Symmetrical object
(B) Plane polarized light	(II) Saytzeff rule
(C) Superimposable mirror image	(III) Cyanides and nitrites
(D) β-elimination reaction	(IV) Nicol Prism

Choose the correct answer from the options given below :

The area enclosed between the curves \(y=x^2\) and \(x=y^2\) is

Question based on following passage :
Adsorption is the process of attracting and retaining the adsorbate molecules on the surface of adsorbent. It is of two types i.e. Physisrption and chemisorption. To increase the rate of reaction, the substance called 'catalyst' is added. Promotors enhance the activity of catalyst while poison decrease the catalyst activity. Solutions may be true solution, suspension and colloids. Colloids are heterogenous but quite stable. On the basis of nature of interaction, colloids may be Lyophilic or Lyophobic. On the basis of type of dispersed phase particles, there may be multimolecular colloids, macromlecular colloids and associated colloids. The congulation of colloids may be done by boiling, dialysis or by mixing oppositely charged sols.
The substances which behave as normal electrolyte at low concentration but become colloids at higher concentration, are known as :

The equation of the tangent line to \(y=2 x^2+7\) , which is parallel to the line \(4 x-y+3=0\) is

If \(a_{i j}\) represents the element of \(i^{\text {th }}\) row and \(j^{\text {th }}\) column and \(A_{i j}\) is the corresponding cofactor, then for the matrix \(A=\left[\begin{array}{ccc}1 & -1 & 0 \\ 2 & 0 & 1 \\ 3 & 4 & 2\end{array}\right]\) the value of \(a_{11} A_{21}+a_{12} A_{22}+a_{13} A_{23}\) is:

A man rows 15 km upstream in 5 hours and 25 km downstream in 5 hours each time, then the speed of the stream is