Two persons A and B throw a die alternately till one of them gets a 'three' and wins the game. The probability of A's winning if A starts first is :

The probability of a shooter hitting a target is \(\frac{2}{3}\)
Minimum how many number of times must the shooter fire so that the probability of hitting the target at least once is more than 0.98.

Given that the value of a determinant of order three is zero; which one of the following is not correct?

If \(P(A)=\frac{2}{5}, P(B)=\frac{3}{10}\) and \(P(A \cap B)=\frac{1}{5}\), then \(P\left(A^{\prime} / B^{\prime}\right) \cdot P\left(B^{\prime} / A^{\prime}\right)\) is equal to :

If \(A\) and \(B\) are invertible matrices of same order, then which one of the following is NOT true?

Which of the following statements are true?
(A) The vector equation of the line through the point (5, 2, -4) and parallel to the vector \(3 \hat{i}+2 \hat{j}-8 \hat{k}\) is \(\vec{r}=(5 \hat{i}+2 \hat{j}-4 \hat{k})+\lambda(3 \hat{i}+2 \hat{j}-8 \hat{k})\)
(B) Vector form of the equation of line \(\frac{x-5}{3}=\frac{y+4}{7}=\frac{z-6}{2}\) is \(\vec{r}=(5 \hat{i}-4 \hat{j}+6 \hat{k})+\lambda(3 \hat{i}+7 \hat{j}+2 \hat{k})\)
(C) The direction cosines of z-axis are (1, 1, 0).
(D) If a line has direction ratios 2, -1, -2, then its direction cosines are \(-2 / 3,-1 / 3,-2 / 3\).
Choose the correct answer from the options given below:

The probability that X can take the values \(x_i\) has the following form:
\(P\left(X=x_i\right)=\left\{\begin{array}{ll}0.2 & \text { if } x_i=0 \\ k x_i & \text { if } x_i=1 \text { or } 2 \\ k\left(5-x_i\right) & \text { if } x_i=3 \\ 0 & \text { otherwise }\end{array}\right.\)
The value of P(X = 2) is:

Mischmetall consists of a lanthanoid metal (95\(\%\)) and Iron (~5\(\%\)) and traces of S, C, Ca \(\&\) Al. Mischmetall used for producing bullets contains:

A group 14 element is converted into n-type semiconductor by doping it with :

Read the paragraph given below and answer the question.
Insulin used for diabetes was earlier extracted from slaughtered cattle and pigs. Insulin from an animal source, though caused some patients to develop allergy or other type of reactions. Insulin consists of two short polypeptide chains: chain A and chain B, that are linked bridges. In mammals, including human, insulin is synthesised as a pro-hormone.
Proinsulin is made up:
(A) Peptide A
(B) Free peptide
(C) Peptide B
(D) Peptide C
Choose the correct answer from the options given below :

Arrange in increasing order of number of species to represent global biodiversity?
(A) Molluscs
(B) Crustaceans
(C) Insects
(D) Other animal groups
Choose the correct answer from the options given below:

An astronomical telescope uses two lenses of power 10 D and 2 D. The distance between the objective and the eye lens in normal adjustment would be

Let \(f: R \rightarrow R\) be defined as \(f(x)=10 x\). Then (Where R is the set of real numbers):