In the below mentioned demand supply curve, identify the equilibrium point

If \(A=\left[\begin{array}{ccc}a & 4 & -5 \\ d & b & -6 \\ 5 & e & c\end{array}\right]\) is a skew symmetric matrix, then value of \(a+b+c+d+e\) is equal to

For a \(3 \times 3\) matrix \(A=\left[a_{i j}\right]\), whose element \(a_{i j}\) is given by \(a_{i j}=\sqrt{i^2+3 j}\), then what is element \(a_{31}\) ?

If \(A=\left[\begin{array}{cc}3 & 2 a \\ 1 & 5\end{array}\right]\) and \(B=\left[\begin{array}{ll}2 & 3 \\ b & 5\end{array}\right]\) are singular matrices, then \(a+b\) is :

Given that \(\vec{a}=-3 \hat{i}-6 \hat{j}+4 \hat{k}, \quad \vec{b}=9 \hat{i}-\lambda \hat{j}-12 \hat{k}\)
If \(\vec{a} \times \vec{b}=\overrightarrow{0}\), then the value of \(\lambda\) is

The sale of ice creams is higher in summer than in winter is an example of:

If \(f(x)=\left\{\begin{array}{ll}\frac{\tan \left(\frac{\pi}{4}-x\right)}{\cot 2 x}, & x \neq \frac{\pi}{4}, \\ 2 K+1, & x=\frac{\pi}{4},\end{array}\right.\) is continuous at \(x=\frac{\pi}{4}\), then the value of \(K\) is equal to

Sediment left after secondary treatment of sewage/waste is known as:

Consider the following L.P.P minimize \(z=x-7 y+190\) subject to \(x+y \leq 8, x+y \geq 4, x \leq 5, y \leq 5\) and \(x, y \geq 0\). Then which of the following is/are true?
(A) It's feasible region is unbounded
(B) It's feasible region is bounded
(C) It's feasible region has 5 corner polnts
(D) It's feasible region has 6 corner polnts
Choose the correct answer from the options given below :

Read the passage carefully and answer the given questions.
Recombinant DNA Technology Asexual reproduction preserves the genetic information, while sexual reproduction permits variation. Traditional hybridization procedures used in plants and animals breeding very often lead to inclusion and multiplication of undesirable genes along with the desired genes. The techniques of genetic engineering, which include creation of recombinant DNA, use of gene cloning and gene transfer, overcome this limitation and allow us to isolate and introduce only one or a set of desirable genes without introducing genes into the target organism.
Which one of the following techniques is used to amplify a specific DNA sequence?

The components of the ecosystem are seen to function as a unit when you consider the following aspects -
(A) Productivity
(B) Decomposition
(C) Energy flow
(D) Nutrient cycling
Choose the correct answer from the options given below :

Arrange the following events in correct sequence.
A. Formation of zygote
B. Formation of blastocyst
C. Implantation
D. Formation of morula
Choose the correct answer from the options given below:

Electric field at a point due to a uniformly charged infinite plane sheet is