Which of the following is the correct equation to find the area of the shaded region, with reference to the figure given below ?

The equation of the normal to the curve \(y=x^4-6 x^3+13 x^2-10 x+5\) at \(x=1\) is:

The corner points of the bounded feasible region determined by a set of constraints (linear inequalities) are \(A(0,5), B(3,5), C(5,0), D(4,1)\) and the objective function is \(z=p x+2 q y\) where \(p, q>0\).
The condition on \(p\) and \(q\) such that the maximum \(z\) occurs at B and D , is

The range of the function \(f(x)=4 x^2+12 x+7, x \in R\) is

Match List-I with List-II

List-I (Inverse Trigonometric Function)	List-II (Principal Value)
(A) \(\sin ^{-1}\left(-\frac{1}{2}\right)\)	(I) \(\pi / 6\)
(B) \(\cos ^{-1}\left(-\frac{1}{2}\right)\)	(II) \(-\pi / 6\)
(C) \(\tan ^{-1}(-\sqrt{3})\)	(III) \(2 \pi / 3\)
(D) \(\cot ^{-1}(\sqrt{3})\)	(IV) \(-\pi / 3\)

Choose the correct answer from the options given below :

Which of the following statements are NOT correct about Standard Normal Distribution?
(A) The probability curve of the Standard Normal Distribution is a bell-shaped curve.
(B) The Standard Normal variate ( Z ) score describes the position of each data point in terms of its distance from the mean, when measured in standard deviation units.
(C) The Z -score is negative if the data point lies above the mean, and positive if it lies below the mean.
(D) There is a \(95.45 \%\) probability of randomly selecting a score between \(\mu-\sigma\) and \(\mu+\sigma\), when \(\sigma\) is standard deviation and \(\mu\) is mean.
Choose the correct answer from the options given below :

If the elementary column transformation \(C_1 \rightarrow 2 C_1\) is carried out on the following matrix equation.
\(\left[\begin{array}{ll}1 & 3 \\ 2 & 4\end{array}\right]\left[\begin{array}{cc}-1 & 2 \\ 5 & 0\end{array}\right]=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]\) Then the transformed equation will be:

A transformer with turns ratio \( \frac{N_1}{N_2} = \frac{100}{1} \) is connected to a 240 V ac supply. If the primary and secondary resistance are \( 1.0 \text{ k}\Omega \) and \( 1 \ \Omega \) respectively, then find the output power ?

An angular magnification of 30 X is desired using an objective lens of focal length 1.25 cm and an eyepiece of focal length 5 cm. What should be the separation between objective and eyepiece when the final image is formed at the near point ?

When a dielectric slab is introduced in between the plates of a charged capacitor with battery connected across the plates, following are the observations. Choose which observation is incorrect?

A wire of length \( L \) meters, carrying a current \( I \) ampere is bent in the form of a circle. The magnitude of its magnetic moment, in SI units, is:

Read the passage carefully and answer the given questions.
DNA Fingerprinting
Polymorphism in DNA sequence is the basis of genetic mapping of the human genome as well as of DNA fingerprinting. DNA fingerprinting involves identification of differences in some specific regions in the DNA sequence called repetitive DNA. It works on the principle of polymorphisms in DNA sequences. The repetitive DNA are separated from bulk genomic DNA. The bulk DNA forms a major peak and the other small peaks are referred to as satellite DNA. These repetitive/satellite DNA sequences show a high degree of polymorphisms and form the basis of DNA fingerprinting.
DNA fingerprinting is meant for:

Which of the following is a transducer?