Consider the following data

Year (X)	2014	2016	2018	2020	2022	2024
Profit(in Rs. Thousand) (Y)	7	9	10	12	14	14

Then for the above data the equation of straight line trend by method of least square is given by:

If P and Q are non-singular square matrices of the same order, then \(\left(P Q^{-1}\right)^{-1}\) equals

If the total cost and total revenue of a company that produces and sells \(x\) units of a particular product are \(C(x)=5 x+350\) and \(R(x)=50 x-x^2\) respectively, then which of the following is/are the breakeven values:
(A) \(x=10\)
(B) \(x=25\)
(C) \(x=45\)
(D) \(x=30\)
Choose the correct answer from the options given below:

If A is a square matrix of order \(3 \times 3\) such that \(A^2 = A\) and I is the unit matrix of order \(3 \times 3\), then the value of \((I - A)^3 + A^2 + I\) is:

If \(a, b, c\) are in A.P., then the value of determinant \(\left|\begin{array}{lll}x+2 & x+3 & x+2 a \\ x+3 & x+4 & x+2 b \\ x+4 & x+5 & x+2 c\end{array}\right|\) is:

Match List-I with List-II

List-I	List-II
(A) The equation of the line passing through the points \((-1,0,2)\) and \((3,4,6)\) is	(I) \(\vec{r}=(-\hat{i}+2 \hat{k})+\lambda(4 \hat{i}+4 \hat{j}+4 \hat{k})\)
(B) The vector equation of the line \(\frac{x-1}{2}=\frac{y+1}{3}=\frac{4-z}{5}\) is	(II) \(\vec{r}=(\hat{i}+3 \hat{j}+2 \hat{k})+\lambda(2 \hat{i}+\hat{j}+3 \hat{k})\)
(C) The equation of the line passing through \((1,3,2)\) and parallel to \(\frac{x+1}{2}=\frac{y-1}{1}=\frac{z+1}{3}\) is	(III) \(\vec{r}=(-\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(2 \hat{i}+\hat{j}+4 \hat{k})\)
(D) The equation of the line along \(2 \hat{i}+\hat{j}+4 \hat{k}\) and passing through \((-1,2,3)\) is	(IV) \(\vec{r}=(\hat{i}-\hat{j}+4 \hat{k})+\lambda(2 \hat{i}+3 \hat{j}-5 \hat{k})\)

where \(\lambda\) is an arbitrary constant.
Choose the correct answer from the options given below:

A doctor is to visit a patient.
The probabilities that he comes by train, bus, scooter or other means are
\(\frac{3}{10}, \frac{1}{5}, \frac{1}{10}\) and \(\frac{2}{5}\) respectively.
The probabilities that he will be late are
\(\frac{1}{4}\) if he comes by train,
\(\frac{1}{3}\) if he comes by bus,
\(\frac{1}{12}\) if he comes by scooter.
If he comes by other means of transport, he will not be late.
When he arrives, he arrives late.
The probability that he comes by bus is:

The sensitivity of a moving coil galvanometer can be increased by decreasing

Electron and Photon have same de Broglie wavelength, which of the following is true for their momentum :

When a potential difference is applied across a copper wire, the drift velocity of the electrons is v. If the same potential difference is applied across another copper wire of the same length but twice the diameter, the drift velocity of electrons will be

Identify the tools for recombinant DNA technology:
A. Restriction enzymes and hostorganism
B. Ligases and vectors
C. Ribosome
D. Polymerase enzyme
Choose the correct answer from the options given below:

Which of the following defects are shown by \(\text{KCl}\) Crystal?
(A) Schottky defect
(B) Frenkel defect
(C) Metal excess defect
(D) Metal deficiency defect
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.
In Recombinant DNA Technology, what is the role of the "selectable marker gene"?