Which of the following statements are true?
(A) The function \(f(x)=\frac{x^4}{4}-\frac{4}{3} x^3+\frac{x^2}{2}+6 x\) has 3 critical points.
(B) The function \(f(x)=|x|+3\) has no minimum value.
(C) A local maximum value is always the absolute maximum value.
(D) \(f(x)=x^2\) has minima at \(x=0\).
Choose the correct answer from the options given below :

Area bounded by \(x=\frac{y^2}{4}\) and its latus rectum is:

Ram invested Rs. 20,000 in a mutual fund in the year 2012.
The value of the mutual fund increased to Rs. 32,000 in the year 2017.
The compound annual growth rate (CAGR) of his investment is (Given : \((1.6)^{\frac{1}{5}}=1.098\))

For the given five values 16, 25, 19, 34, 46, the three years moving averages are:

A container is full of pure milk. From this container, one third of milk is taken out and then an equal amount of water is poured into the container to fill it. This operation is repeated four times. The final ratio of milk and water in the container is :

\(\int \frac{d x}{x^3 \sqrt{\left(1+x^4\right)}}=\)

Mrs Rathna invested Rs. 2 lakh in an enterprise for 5 years. Her compound annual growth rate (CAGR) turned out to be 20.5%. The end balance would be (given \((1.205)^5=2.54\) ):

Which of the following statements are correct ?
(A) Electrostatic field lines form closed loops.
(B) In an electric dipole, the direction from charge to q is the direction of the dipole.
(C) Water molecule is an example of polar molecule.
(D) The electric field due to a uniformly charged thin shell is zero at some points inside the shell.
(E) Electrostatic force is conservative in nature.
Choose the correct answer from the options given below :

Read the following paragraph carefully and answer the given questions.
In the year 1963 the two enzymes responsible for restricting the growth of bacteriophage in E. coli were isolated. The first restriction endonuclease - Hind II, whose functioning depended on a specific DNA nucleotide sequence was characterized five years later. It was found that Hind II always cut DNA molecules at a particular point by recognizing a specific sequence of six base pairs. This specific base sequence is known as the recognition sequence for Hind II. Besides Hind II, today we know more than 900 restriction enzymes that have been isolated from over 230 strains of bacteria, each of which recognize different recognition sequences.
In EcoR I the latter 'R' is derived from the -

A wire has a resistance of \( 3.0 \Omega \) at \( 30^{\circ}C \) and a resistance of \( 4.5 \Omega \) at \( 100^{\circ}C \). The temperature coefficient of resistance of the wire is

The correct expression for osmotic pressure of the solution involving dissociation of the solute is

Let \(f: R \rightarrow R\) defined by \(f(x)=2 x^3-7\) for \(x \in R\). Then :
(A) \(f\) is one-one function
(B) \(f\) is many to one function
(C) \(f\) is bijective function
(D) \(f\) is into function
Choose the correct answer from the options given below:

A long wire with a small current element of length 1 cm is placed at the origin and carries a current of 10 A along the x-axis. The magnitude of the magnetic field, due to the element, on the y-axis at a distance \( r = 0.5 \, m \) from it, would be