The value of \(\left|\begin{array}{lll}265 & 240 & 219 \\ 240 & 225 & 198 \\ 219 & 198 & 181\end{array}\right|\) is

The direction ratios of the line perpendicular to the lines \(\frac{x-5}{2}=\frac{y+11}{-3}=\frac{z+3}{1}\) and \(\frac{x-7}{1}=\frac{y+2}{2}=\frac{z-4}{-2}\) are proportional to :

The following data shows the percentage of rural and urban Indian households who have a high speed internet connection.

Year(x)	Rural Household \((y \%)\)	Urban Household\((y \%)\)
2020	2	6
2021	3	7
2022	3	9
2023	4	15
2024	5	20

Based on the above data, which of the following statements are correct?
(A) A straight line trend by the method of least squares for rural Indians \(y_t=3.4+0.7(x-2022)\)
(B) A straight line trend by the method of least squares for urban Indians is \(y_t=11.4+4.3(x-2022)\)
(C) The forecast for the year 2025 for urban group using the trend equation is \(22.2 \%\)
(D) The forecast for the year 2025 for rural group using the trend equation is \(5.5 \%\)
Choose the correct answer from the options given below :

Match List-l with List-ll

List-l	List-ll
(A) Angle between \(\hat{i}\) and \(-\hat{j}\) is	(I) \(\frac{\pi}{6}\)
(B) Angle between \(2 \hat{i}+\hat{k}\) and \(10 \hat{i}+5 \hat{k}\) is	(II) \(\frac{\pi}{4}\)
(C) Angle between \(\hat{i}\) and \(\hat{i}+\hat{j}\) is	(III) \(2 \pi\)
(D) Angle between \(\sqrt{3} \hat{j}-\hat{k}\) and \(\hat{j}\) is	(IV) \(\frac{\pi}{2}\)

Choose the correct answer from the options given below :

For any two matrices A and \(B , AB + BA\) is a possible matrix, then :

\(\int_0^{\frac{\pi}{2}} \sin ^2 x d x\) is equal to:

A box contains 2 black and 4 red balls and another box contains 4 black and 3 red balls. If a ball is drawn at random from one of the two boxes, then the probability of getting a black ball is

Read the passage carefully and answer the Questions
Alcohols and phenols are obtained when a hydrogen atom in aliphatic and aromatic hydrocarbons respectively, is replaced by \(OH\) group. These compounds find wide applications in industry as well as in our daily life. You may notice that ordinary spirit is used for polishing wooden furniture which is chiefly a compound containing hydroxyl group. An alcohol contains one or more hydroxyl \((OH)\) group(s) directly attached to carbon atom(s), of an aliphatic system \((CH_3OH)\) while a phenol contains \(OH\) group(s) directly attached to carbon atom(s) of an aromatic system \((C_6H_5OH)\). Alcohols are prepared by the hydration of alkenes, fermentation of glucose, and reduction of carbonyl compounds. Alcohols produce alkenes upon dehydration whereas alkenes on acid catalyzed hydration convert into alcohols.
Which of the following compounds lacks phenolic group?

\(\int e^{-x}\left(\cot x+\mid \operatorname{cosec}^2 x\right) d x\) =

Arrange the given stages involved in embryo development in a dicot angiosperm in correct sequence
(A) Globular embryo
(B) Proembryo
(C) Zygote
(D) Heart shaped embryo
Choose the correct answer from the options given below:

Diameter of the objective lens of a telescope is 250 cm. For light of wavelength 600 nm, coming from a distant object, the limit of resolution of the telescope is close to :

For the brown ring test, the correct order of the steps in the experiment is :
(A) Pour conc. \(H_2SO_4\) very slowly along the side of the test tube, very few drops of the acid should be poured.
(B) Take half spatula of the given salt in a dry test tube.
(C) Add 2 - 3 mL of freshly prepared ferrous sulphate solution to the test tube.
(D) Make a solution of the given salt.
Choose the correct answer from the options given below:

Read the passage carefully and answer the given questions.
DNA Fingerprinting
Polymorphism in DNA sequence is the basis of genetic mapping of the human genome as well as of DNA fingerprinting. DNA fingerprinting involves identification of differences in some specific regions in the DNA sequence called repetitive DNA. It works on the principle of polymorphisms in DNA sequences. The repetitive DNA are separated from bulk genomic DNA. The bulk DNA forms a major peak and the other small peaks are referred to as satellite DNA. These repetitive/satellite DNA sequences show a high degree of polymorphisms and form the basis of DNA fingerprinting.
Which one of the following techniques is involved in DNA fingerprinting?