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 \(x=t^2\) and \(y=t^3\), then \(\frac{d y}{d x}=6\) at \(t=\)

Using the concept of differentials,\(\sqrt{36.6}\) is approximately equal to:

If \(\hat{a}\) is a unit vector perpendicular to both the vectors \(\vec{b}=\hat{j}+2 \hat{k}\) and \(\vec{c}=\hat{i}+2 \hat{j}\), then \(\hat{a}\) is equal to :

If \(P(A)=\frac{3}{5}, P(B)=\frac{1}{2}\) and \(P(A \cap B)=\frac{1}{4}\), then \(P(\bar{A} \mid \bar{B})\) is

Which of the following statements are correct?
(A) Direction ratios of the line \(\frac{x-1}{2}=\frac{y+2}{3}=\frac{z-3}{4}\) are 2, 3, 4
(B) Direction ratios of the line \(\frac{x-1}{2}=\frac{2-y}{7}=\frac{2 z-1}{6}\) are 2, -7, 3
(C) Direction cosines of z axis are 0, 1, 0
(D) Direction ratios of the line joining the point (1, 2, -3) and (4, 5, 6) are 1, 1, 3
(E) Direction cosines of a line which makes equal angles with the coordinate axes are \(\frac{1}{3}, \frac{-1}{3}, \frac{1}{3}\)
Choose the correct answer from the options given below:

If \(A=\left[\begin{array}{ccc}2 & -3 & 4 \\ -3 & 5 & x \\ 4 & 3 & 0\end{array}\right]\) is a symmetric matrix and \(B=\left[\begin{array}{ccc}0 & 2 & -10 \\ -2 & z & 6 \\ y & -6 & 0\end{array}\right]\) is a skew-symmetric matrix, then the value of \((x y+y z+z x)\), is:

A boat covers a distance of 24 km upstream and returns to the same point in a total time of 4 hours. If the speed of the boat in downstream is twice its speed in upstream, then the speed of boat in upstream is:

Which of the following statements are correct?
A. The number of photoelectrons emitted per second is directly proportional to the intensity of incident radiation.
B. The minimum value of photoelectric current is called saturation current.
C. For a given frequency, stopping potential is independent of its intensity.
D. The stopping potential is same for all frequencies.

Light from a point source in air falls on a spherical glass surface. If \(\mu = 1.5\) and radius of curvature \(= 20\) cm. The distance of light source from the glass surface is 100 cm, at what position will the image be formed?

Arrange the following compounds in increasing order of their acidic strength ?

Ferric oxide in blast furnace's upper half is mainly reduced by :

Read the following paragraph carefully and answer the given questions.
Certain types of leukocytes (WBC) of our body like polymorpho-nuclear leukocytes (PMNL-neutrophils) and monocytes and natural killer (type of lymphocytes) in the blood as well as macrophages in tissues can phagocytose and destroy microbes. For determining the cause of allergy, the patient is exposed to or injected with very small doses of possible allergens, and the reactions studied. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Heroin, commonly called smack is chemically diacetylmorphine which is a white, odourless, bitter crystalline compound. This is obtained by acetylation of morphine. Techniques like radiography (use of X-rays), CT (computed tomography) and MRI (magnetic resonance imaging) are very useful to detect cancers of the internal organs. Different species of Plasmodium (P. vivax, P. malaria and P. falciparum) are responsible for different types of malaria. Of these, malignant malaria caused by Plasmodium falciparum is the most serious one and can even be fatal.
Which of the following technique is not very useful to detect the cancers of internal organs?