For the following probability distribution:

X	-4	-3	-2	-1	0
p(x)	0.1	0.2	0.3	0.2	0.2

The function \(f(x)=k x^3+6 k x^2+18 x+17\) is increasing on \(R\) (set of real numbers) if:

Match List - I with List - II.

LIST-I (Equation of curves)	LIST-II (Slope of tangent at \(x=2\))
(A) \(y=x^3-x\)	(I) 8
(B) \(y=(x-2)^2\)	(II) \(frac{2}{3}\)
(C) \(y=2 x^2+3\)	(III) \(11\)
(D) \(y=\sqrt{4 x+1}-7\)	(IV) \(0\)

Choose the correct answer from the options given below :

The amount to which ₹ 5000 will accumulate at the effective rate of 4% for 4 years and 5% for 2 years is:

The greatest possible value of \(a\) such that the function\(f(x)=x^2+a x+1\) is always decreasing in the interval \([1,2]\), is:

For the given five values 3.6, 4.3, 4.3, 3.4, 4.4, the three years moving averages are:

The shortest distance between the lines \(\vec{r}_1=\hat{i}+\hat{j}+\lambda(2 \hat{i}-\hat{j}+\hat{k})\) and \(\vec{r}_2=2 \hat{i}+\hat{j}-\hat{k}+\mu(4 \hat{i}-2 \hat{j}+2 \hat{k})\) is :

Which of the following is TRUE for gel electrophoresis ?
(A) It is used to separate DNA fragments.
(B) Separation of DNA occurs on the basis of the fragment size.
(C) Separation of DNA fragments occurs on the basis of charge.
(D) Separated DNA fragments can be visualised without staining.
Choose the correct answer from the options given below:

Read the Passage carefully and answer the the questions
The DNA fragments can be separated by a technique known as gel electrophoresis. Since DNA fragments are negatively charged molecules, they can be separated by forcing them to move towards the anode under an electric field through a medium/matrix. The separated DNA fragments can be visualised only after staining the DNA with a compound known as ethidium bromide followed by exposure to UV radiation. The repeated amplification of DNA is achieved by the use of a thermostable DNA polymerase (isolated from a bacterium, Thermus aquaticus). After completion of the biosynthetic stage, the product has to be subjected through a series of processes before it is ready for marketing as a finished product. The downstream processing and quality control testing vary from product to product. The convention for naming restriction enzymes is the first letter of the name comes from the genus and the second two letters come from the species of the prokaryotic cell from which they were isolated.
In agarose gel electrophoresis, DNA fragments move towards _______ under an electric field through a medium.

Cellulose is a __________ polymer composed of __________ .

If \(e^y(x+2) = 10\), then \(\frac{d^2y}{dx^2}\) is equal to :

The current in a device varies with time 't' as I = 6 t, where I is in mA and t is in s. The amount of charge that passes through the device during t = 0 s to t = 3 s is

The unit of rate constant for first order reaction is: