If \(y=38.85+7.64(x-2020)\) is the equation of the straight line trend for the following data:

Year(x)	2017	2018	2019	2020	2021	2022	2023
Profit( Rs. '000) (y)	14	30	26	44	38	56	64

The trend value for the year 2021 by least square method is :

The variance of the number of heads in two tosses of a coin is :

In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is:

If \(\left[\begin{array}{ll}3 & 1 \\ 2 & 1\end{array}\right] A\left[\begin{array}{ll}2 & 1 \\ 1 & 1\end{array}\right]=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]\), then matrix ' \(A\) ' is

\(\int \frac{d x}{e^x+e^{-x}}\) is equal to

The interval in which \(f(x)=2 x^3-9 x^2+12 x+1\) is decreasing is:

The value of \(\int_{-5}^5|x+3|\) \(dx\) is

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 one of the following is not the cellular barrier of innate immunity?

The factors that affect the Hardy-Weinberg equilibrium are:
(A) Gene migration or gene flow
(B) Natural selection
(C) Mutation
(D) Genetic drift
Choose the correct answer from the options given below:

A resistor and a capacitor are connected in series with an alternating current source. The potential difference across resistor and capacitor are 90 V and 120 V respectively and rms value of current is 3 A. What is the power factor of the circuit?

Which of the following process is used in the extractive metallurgy of magnesium?

The statement "all tax payers above 60 years in India" is an example of
(A) Sample
(B) Finite population
(C) Infinite population
(D) Statistical Interference

If A and B are independent events, then which of the following is not true?