Based on the data available for the production ( \(y_i\) in thousand tons) of a cloth factory for 7 years (\(x_i\)) using the method of least squares, the straight line trend is given by \(y=a+b x\) with \(\sum y_i=608, \sum x_i=0, \sum x_i y_i=116, \sum x_i^2=28\). Then, the increase in production per year is :

Let \(x\) denote the number of heads in a simultaneous toss of three coins, then \(P(0 < x \leq 3)\)

Given \(A=\left[\begin{array}{ll}2 & 3 \\ 1 & 4\end{array}\right]\) and \(B=\left[\begin{array}{ll}x & y \\ 1 & 4\end{array}\right]\), If \(A=B\), then \(x\) and \(y\) are :

A machine has been producing steel tubes of mean inner diameter of 2 cm.
A sample of 10 tubes gives an inner diameter of 2.01 cm and a standard deviation of 0.063 cm.
Test the hypothesis that the machine is working in the proper order at 5% level of significance and answer, which of the following statements are correct?
[Given that \(t_{0.05}=2.262\)]
(A) The value of the test statistic is t = 0.476
(B) The null hypothesis is rejected at \(5 \%\) level of significance.
(C) The null hypothesis is accepted at \(5 \%\) level of significance.
(D) The degree of freedom is 10
Choose the correct answer from the options given below:

The value of \(\left[\begin{array}{lll}1 & b c & b c(b+c) \\ 1 & c a & c a(c+a) \\ 1 & a b & a b(a+b)\end{array}\right]\) is

A bag contains 3 white, 4 black and 2 red balls. If 2 balls are drawn at random (without replacement), then the probability that both the balls are white is:

A lot of \(50\) watches is known to have \(10\) defective watches. If \(8\) watches are selected one by one with replacement at random, then the probability that there will be at least one defective watch is:

The area (in sq. units) bounded by the parabola \(y^2=4 a x\), its latus rectum and the \(x\)-axis in the first quadrant is:

If \(A=\left[\begin{array}{cc}\sin \alpha & -\cos \alpha \\ \cos \alpha & \sin \alpha\end{array}\right]\), and \(A+A^{\prime}=I\), then the value of \({ }^{\prime} \alpha^{\prime}\) is :

Answer the question on the basis of passage given below :
Adsorption is a surface phenomenon which can be expressed by means of an empirical relationship know as Freundlich Adsorption isotherm. The relationship given by \(\frac{x}{m} = Kp^{\frac{1}{n}}\ (n > 1)\)
x = Mass of the gas adsorbed
m = Mass of adsorbent
p = Pressure at which adsorption takes place
K and n are constant
Choose the incorrect statement with reference to physical adsorption:

Read the following passage carefully and answer the given questions.
Cancerous cells just continue to divide giving rise to masses of cells called tumors. Benign tumors normally remain confined to their original location and do not spread to other parts of the body and cause little damage. The malignant tumors, on the other hand are a mass of proliferating cells called neoplastic or tumor cells. Transformation of normal cells into cancerous neoplastic cells may be induced by physical, chemical or biological agents. Ionising radiations like X-rays and gamma rays and non-ionizing radiations like UV cause cancer. Cancer-causing viruses are called oncogenic viruses which have viral oncogenes. The substances to which an immune response is produced are called allergens. The antibodies produced to these are of IgE type. Common examples of allergens are mites in dust, pollens, animal dander, etc. The primary lymphoid organs are bone marrow and thymus. The secondary lymphoid organs provide the sites for interaction of lymphocytes with the antigen, which then proliferate to become effector cells.
Cancer cells divide without any control due to:

Ambidentate ligand among the following is
A. NCS
B. \(\text{C}_2\text{O}_4^{2-}\)
C. SCN
D. \(\text{H}_2\text{NCH}_2\text{CH}_2\text{NH}_2\)
E. \(\text{NO}_2\)
Choose the correct answer from the options given below :

What is the refractive index of the material of a prism if the angle of minimum deviation for the prism of angle \( \frac{\pi}{3} \) is \( \frac{\pi}{6} \)?