Let \(F(z)\) be the cumulative density function of the standard normal variate \(Z\), then which of the following are correct?
(A) \(F(z)=\frac{1}{\sqrt{2 \pi}} \int_{-\infty}^z e^{-t^2 / 2} d t,-\infty<Z<\infty\)
(B) \(F(-Z)=1-F(Z)\)
(C) \(F(0)=0\)
(D) \(F(\infty)=1\)
Choose the correct answer from the options given below:

If A and B are independent events, then which of the following is/are true?
(A) \(\bar{A}\) and B are independent events
(B) \(P(A \cap B)=0\)
(C) \(\bar{A}\) and \(\bar{B}\) are independent events
(D) \(P(A \cap B)=P(A)+P(B)\)
Choose the correct answer from the options given below:

For the given values 8, 10, 12, 14, 16, the three-year moving averages are:

Three college graduates Asha, Babita and Cyrus enter into partnership to run an online tea business. After a bumper turnover they divide profits as 80,000, 60,000 and 1 lakh respectively. Which of the following was correct ratio of their investments?

If \(\vec{a}=4 \hat{i}-2 \hat{j}+5 \hat{k}\) and \(\vec{b}=\hat{i}-2 \hat{j}-2 \hat{k}\) represent, both in magnitude and direction, two adjacent sides of a parallelogram, then a unit vector parallel to the diagonal, which is coinitial with \(\vec{a}\) and \(\vec{b}\), is :

Which of the following statements are correct?
(A) If \(E\) and \(F\) are independent events then \(P(E \cap F)=P(E) P(F)\)
(B) If \(E\) and \(F\) are mutually exclusive events, then \(P(E \cup F)=P(E)+P(F)-P(E) P(F)\)
(C) The conditional probability of an event \(E\), given the occurrence of the event \(F\) is given by \(\frac{P(E \cap F)}{P\left(F^{\prime}\right)}, P(F) \neq 0\)
(D) If \(E\) and \(F\) be the events associated with the sample space \(S\) of an experiment, then \(P(\bar{E} \mid F)=2-P(E \mid F)\)
Choose the correct answer from the options given below:

Let * be a binary operation defined on \(Q ^{+}\)(the set of positive rational numbers) by the rule \(a * b=\frac{a b}{7}\) for all \(a, b \in Q ^{+}\). Then inverse of \(2 * 7\) is:

The area of a triangle with vertices \((0,-3),(0,3)\) and \((k, 0)\) is 27 sq. units. The value of \(k\) is:

If \(A=\left[\begin{array}{ccc}-1 & 2 & 3 x \\ 2 y & 4 & -1 \\ 6 & -1 & 0\end{array}\right]\) is a symmetric matrix, then the value of 22 - y is:

A strong magnetic field is applied on a stationary electron :

The internal resistance of a cell of emf 2 V is 0.1 \( \Omega \). It is connected to an external resistance of 3.9 \( \Omega \). The terminal potential difference across the cell will be

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.
Which one of the followings cannot cause cancer:

If A is a square matrix of order 3, B = kA and |B| = x|A| then,