The image of the point \((3,-2,1)\) in the plane \(3 x-y+4 z=2\) is:

For \(|x|<1\), if \(x=\cos \left(\frac{1}{a} \log y\right)\), then

For the differential equation \(y d x-\left(x+3 y^2\right) d y=0\), which of the following statements are true?
(A) It is a linear differential equation
(B) It is a homogenous differential equation
(C) Its general solution is \(x=3 y^2+C y: C\) is an arbitrary constant
(D) If \(y(0)=1\), then its particular solution is \(x=3 y^2-1\)
Choose the correct answer from the options given below:

Time reversal test is satisfied by:

Let functions \(f:\{1,3,4\} \rightarrow\{1,2,5\}\) and \(g:\{1,2,5\} \rightarrow\{1,3\}\) be defined as \(f=\{(1,2),(3,5),(4,1)\}\) and \(g=\{(1,3),(2,3),(5,1)\}\) respectively. Then, which one of the following is correct statement for \(g \circ f\)?

A measure of an average yearly growth of an investment over a certain time period when returns are reinvested is

Suppose \(10 \backslash \%\) of men and \(0.5 \backslash \%\) of women have grey hair. A grey haired person is selected at random. If there are equal number of males and females, then the probability of the selected person being a female is :

The drift speed of electrons in a conductor is estimated to be only a few \( \text{mm s}^{-1} \). But on closing a circuit, how current is established almost instantly in an electric circuit?

Read the passage carefully and answer
Carbohydrates are essential for both plants and animals. Some common examples of carbohydrates are glucose, fructose, sucrose, glycogen, cellulose and starch. They form a major portion of our food. Honey has been used for a long time as an instant source of energy in Ayurvedic medicine. Carbohydrates are used as storage molecules in both plants and animals. The cell wall of bacteria and plants is made of cellulose. We use cellulose in the form of wood for making furniture and as cotton fiber for clothing. They also provide raw material for textiles, paper, lacquers, and breweries. Carbohydrates are classified as Monosaccharides, Oligosaccharides and Polysaccharides on the basis of their behavior towards hydrolysis.
Monosaccharides cannot be hydrolyzed further to simpler units whereas oligosaccharides can yield 2-10 units of monosaccharides on hydrolysis. Polysaccharides, which are non-sugars yield a large number of monosaccharide units on hydrolysis.
Answer the following questions about carbohydrates:
Animal starch is popularly known as

Reserpine is an active chemical of which plant?

Match List - I with List - II.

List - I	List - II
(A) The common region determined by all the constraints of LPP is called	(I) objective function
(B) Minimize \(z=c_1 x_1+c_2 x_2+\cdots+c_n x_n\) is	(II) convex set
(C) A solution that also satisfies the non-negative restrictions of a LPP is called	(III) feasible region
(D) The set of all feasible solutions of a LPP is a	(IV) feasible solution

Choose the correct answer from the options given below :

If \(y=5 \cos x-3 \sin x\), then \(\frac{d^2 y}{d x^2}\) is equal to :

Why the Fusion reaction takes place at high temperature among the nuclei, though these experience repulsion between them: