The area of the region bounded by the lines x = 2y + 3, x = 0, y = 1 and y = - 1 is:

The area of the smaller region bounded by the ellipse \(\frac{x^2}{16}+\frac{y^2}{9}=1\) and the straight line \(3 x+4 y=12\) is :

If \(\frac{d}{d x}\left[a x^3+a x^2+a x+1\right]=9 x^2+6 x+3\), then \(a\) is equal to :

If \(A=\left[\begin{array}{ll}5 & 2 \\ 4 & 3\end{array}\right]\) is a given matrix, then which statements are correct?
(A) \(|A|=7\)
(B) minor of \(3=-5\)
(C) co-factor of \(2=-4\)
(D) \(\operatorname{adj}(A)=\left[\begin{array}{cc}3 & -2 \\ -4 & 5\end{array}\right]\)

The range of the function \(f(x)=4 x^2+12 x+7, x \in R\) is

The function \(f(x)=\left|\begin{array}{cc}x^2 & x \\ 3 & 1\end{array}\right|, x \in R\) has a:

The corner points of the bounded feasible region determined by the system of linear constraints are (0,10), (5, 5), (15, 15), (0, 20). Let \(z=p x+q y\) where \(p, q>0\). Then the condition on p and q so that the maximum value of z occurs at (15, 15) and (0, 20) is

The direction cosines of z-axis are:

Three pipes A, B and C are installed to fill a tank. Pipes A and B opened together can fill the tank in the same time in which \(C\) can alone fill the tank. If pipe \(B\) can fill the tank 15 minutes faster than pipe \(A\) and 5 minutes slower than pipe \(C\), then the time required by pipe \(A\) to fill the tank alone is:

In a Wheatstone Bridge, all the four arms have equal resistance r. If the resistance of the galvanometer arm is also equal to r, the equivalent resistance of the combination will be

50,000 different strains of rice are example of:

If \(A=\left[\begin{array}{ccc}2 & -1 & 0 \\ 1 & 2 & 1 \\ -1 & 0 & 1\end{array}\right]\), then which of the following statement(s) is/are correct?
(A) A is singular matrix
(B) |3A |= 135
(C) |adj A| = 125
(D) \(\left|A^{-1}\right|=\frac{1}{5}\)
Choose the correct answer from the options given below:

Read the passage carefully and answer the questions
The transition metals and their compounds are known for their catalytic activity. This activity is ascribed to their ability to adopt multiple oxidation states and to form complexes. Vanadium(V) oxide (in Contact Process), finely divided iron, and nickel (in Catalytic Hydrogenation) are some of the examples. Catalysts at a solid surface involve the formation of bonds between reactant molecules and atoms of the surface of the catalyst (first row transition metals utilise 3d and 4s electrons for bonding). This has the effect of increasing the concentration of the reactants at the catalyst surface and also weakening of the bonds in the reacting molecules (the activation energy is lowering). Also because the transition metal ions can change their oxidation states, they become more effective as catalysts.
Which of the following is incorrect about the ability of catalytic action of transition metals?