Consider the following hypothesis test.
\(H _0: \mu \leq 12\)
\(H _a: \mu>12\)
If a sample of 25 is taken with sample mean 15 and a sample standard deviation of 6, then the value of t-test statistic is:

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

The value of the integral \(\int_{-1}^1|x| d x\) is :

If \(r_{e f f}=\) effective rate of interest, \(r=\) nominal rate of interest and \(m=\) number of conversion periods per year, the relationship between nominal rate and effective rate of interest is :

If the line \(\vec{r}=(\hat{i}+\hat{j}+\hat{k})+\lambda(2 \hat{i}+\hat{j}+2 \hat{k})\)
is parallel to the plane \(\vec{r} \cdot(3 \hat{i}-2 \hat{j}+a \hat{k})=11\), then \(a\) is equal to :

If \(\int_0^a 3 x^2 d x=8\), then the value of \(a\) is:

Area (in sq. units) of the region bounded by curves \(y^2=x\) and \(x=4\) is

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:
Identify a component of starch from among the following.

Match List - I with List - II

List - I	List - II
(A) The number of possible matrices of order 3 × 3 with each entry 1 or 0	(I) \(2^4\)
(B) The number of possible matrices of order 2 × 3 with each entry 1 or 0	(II) \(2^9\)
(C) The number of possible matrices of order 2 × 3 with each entry 0, 1, 2	(III) \(2^6\)
(D) The number of possible matrices of order 2 × 2 with each entry 1 or 0	(IV) \(3^6\)

Choose the correct answer from the options given below:

Which one of the given assisted reproductive technologies (ART) involves transfer of fertilized egg into the fallopian tube?

Let \(A\) and \(B\) be independent events such that \(P(A)=0.3\) and \(P(B)=0.4\), then
Match List-l with List-ll

List-I	List-II
(A) \(P(A \cap B)\)	(I) 0.3
(B) \(P(A \cup B)\)	(II) 0.4
(C) \(P(A \mid B)\)	(III) 0.12
(D) \(P(B \mid A)\)	(IV) 0.58

Choose the correct answer from the options given below :

The velocity of light in diamond, glass and water decreases in the following order :

Why does a microwave oven heat up a food item containing water molecules efficiently?