If the straight lines \(x=1+s, y=-3-\lambda s, z=1+\lambda s\) and \(x=\frac{t}{2}, y=1+t, z=2-t\) with parameters s and \(t\) respectively, are coplanar, then \(\lambda\) is equal to :

If \(f(x)=|2 x+5|\), then \(f(x)\) is :

If \(A=\left[\begin{array}{ll}1 & 0 \\ 0 & 0\end{array}\right], B=\left[\begin{array}{ll}0 & 0 \\ 3 & 0\end{array}\right]\) then

Area (in sq. units) of the region bounded by the curve \(y^2=4 x\) y-axis and the line y = 3 is

The function \(f:[0,1] \rightarrow R\) given by \(f(x)=\alpha x^3\) has:

Match List-I with List-II

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

Choose the correct answer from the options given below :

A boat covers a distance of 24 km upstream and returns to the same point in a total time of 4 hours. If the speed of the boat in downstream is twice its speed in upstream, then the speed of boat in upstream is:

Two coherent light beams of intensities I and 4 I are superimposed. The maximum and minimum possible intensities in the resulting pattern are :

The person with karyotype 44+XXY is suffering from:

Read the passage carefully and answer the questions given along
Our immune system plays the major role in preventing diseases when we are exposed to disease-causing agents. Immunity is of two types: (i) Innate immunity and (ii) Acquired immunity. The human immune system consists of lymphoid organs, tissues, cells and soluble molecules like antibodies. The immune system also plays an important role in allergic reactions, auto-immune diseases and organ transplantation. The primary lymphoid organs are bone marrow and thymus. The secondary lymphoid organs are spleen, lymph nodes, tonsils, Peyer's patches of small intestine and appendix. There is lymphoid tissue also located within the lining of the major tracts (respiratory, digestive and urogenital tracts) called mucosa associated lymphoid tissue (MALT). It is important to note that HIV/AIDS is not spread by mere touch or physical contact; it spreads only through body fluids. AIDS has no cure, prevention is the best option. Adolescence is accompanied by several biological and behavioural changes and surveys and statistics show that use of drugs and alcohol has been on the rise especially among the youth. Factors associated with drug and alcohol abuse among adolescents are a child's natural curiosity, stress, the perception among youth that it is 'cool' or progressive to smoke, media exposure and an unstable or unsupportive family structures and peer pressure. It is best to identify the situations that may push an adolescent towards use of drugs or alcohol, and to take remedial measures well in time.
Find the incorrect statement about human health and disease.

These structures represent which particular kind of halides :

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 :

The solubility of the gas in a liquid :
(A) Increases with increase in pressure
(B) Decreases with increase in pressure
(C) Increases with increase in temperature
(D) Decreases with increase in temperature
Choose the correct answer from the options given below :