If \(\left[\begin{array}{cc}2 & 3 \\ 5 & 7\end{array}\right]\left[\begin{array}{cc}1 & -3 \\ -2 & 4\end{array}\right]=\left[\begin{array}{cc}-4 & 6 \\ -9 & x\end{array}\right]\), then the value of \(x\) is:

The solution of the differential equation \(\frac{d y}{d x}=-\frac{x}{y}\) is:

Consider sets A and B, each having 4 elements. If \(f : A \to B\) be a function, then number of functions from A to B are:

If \(A\) is a square matrix of order 3 and \(|A|=5\), then the value of \(\left|-A A^T\right|\) is :

General solution of \(\frac{dy}{dx} + \frac{\sqrt{1-y^2}}{\sqrt{1-x^2}} = 0\) is:

Given that the value of a determinant of order three is zero; which one of the following is not correct?

Let \(f: R \rightarrow R\) be defined as \(f(x)=3 x+4\). Choose the correct answer.

Match List - I with List - II. 

List – I	List – II
(A) SN1 reaction	(I) vic-dibromide
(B) Bromination of alkenes	(II) gem-dibromide
(C) Alkylidene halides	(III) Racemisation
(D) Dehydrohalogenation of haloalkanes	(IV) Saytzeff rule

Choose the correct answer from the options given below :

The demand function for a certain product is represented by the equation: p = 20 + 5x - \(3 x^2\), where \(x\) is the number of units demanded and p is the price per unit (in Rs.), then the marginal revenue when 2 units are sold, is:

If \(\left|\begin{array}{cc}3 x & 7 \\ 4 & x\end{array}\right|=\left|\begin{array}{cc}6 & -2 \\ 4 & 2\end{array}\right|\), then the value of \(x\) is :

Which of the following reactions are disproportionation reactions?
(A) \(2\text{Cu}^+ \rightarrow \text{Cu}^{2+} + \text{Cu}\)
(B) \(3\text{MnO}_4^{2-} + 4\text{H}^+ \rightarrow 2\text{MnO}_4^- + \text{MnO}_2 + 2\text{H}_2\text{O}\)
(C) \(2\text{KMnO}_4 \rightarrow \text{K}_2\text{MnO}_4 + \text{MnO}_2 + \text{O}_2\)
(D) \(2\text{MnO}_4^- + 3\text{Mn}^{2+} + 2\text{H}_2\text{O} \rightarrow 5\text{MnO}_2 + 4\text{H}^+\)
Choose the correct answer from the options given below:"

Answer the question on basis of passage given below :
Lyophobic sols like those of metals (Au, Ag, etc) are unstable and are easily precipitated by addition of electrolytes. However, it is observed that the addition of certain lyophilic colloids like gums, soaps, gelatine, etc. to lyophobic colloids (like a metal sol) render lyophobic colloids difficult to coagulate by the addition of electrolytes. The process is known as 'protection' and the lyophilic colloids are termed as Protective colloids. It is believed that the protective action of the lyophilic colloids is due to the covering up of the particles of the lyophobic colloid by those of the lyophilic colloid.
Evidently, smaller the gold number of a protective colloid, the greater is its protective action.
Which of the following does not form a lyophilic colloid?

The atomic mass unit (1u) is correctly represented by :