Question 3 :
Suppose we are using stratified sampling for a particular population and have divided it into strata of different sizes. How can we now make sample selection?
Question 5 :
Which sampling is affected the most if there is hidden periodicity in population?
Question 6 :
<span>Under random sampling, each item of population has chance of being chosen for the sample.</span>
Question 7 :
When a population is heterogeneous, it is divided into groups, so that there is homogeneity within the group and heterogeneity between the groups, and some items are selected at random from each group. This is known as ___________.
Question 8 :
If the population is heterogeneous, which one of the following probability sampling methods is more appropriate?<span><br></span>
Question 9 :
If a random variable X takes value $ 0 $ and $1$ with respective probabilities $\dfrac{2}{3}$ and $\dfrac{1}{3}$ , then the expected value of X is<br/>
Question 10 :
The cumulative distribution function of a random variable $x$ is defined as<br/>
Question 11 :
To define probability disribution function we assign to each variable
Question 12 :
 The range of a random variable $\mathrm{X}$ is $\left\{ 0,\quad 1,\quad 2 \right\} $ and $\mathrm{P}(\mathrm{X}=0)=3\mathrm{K}^{3},\mathrm{P}(\mathrm{X}=1)=4\mathrm{K}-10\mathrm{K}^{2}<br/>$<br/>$\mathrm{P}(\mathrm{x}=2)=5\mathrm{K}-1$. Then we have<br/>
Question 13 : A random variable $X$ has the following p.d.f.<table class="wysiwyg-table"><tbody><tr><td>$X$</td><td>$0$</td><td>$1$</td><td>$2$</td><td>$3$</td><td>$4$</td><td>$5$</td><td>$6$</td><td>$7$</td></tr><tr><td>$P(X = x)$</td><td>$0$</td><td>$k$</td><td>$2k$</td><td>$2k$</td><td>$3k$</td><td>$k^{2}$</td><td>$2k^{2}$</td><td>$7k^{2} + k$</td></tr></tbody></table>The value of $k$ is
Question 14 : The probability distribution of $x$ is<table class="wysiwyg-table"><tbody><tr><td>$x$</td><td>$0$</td><td>$1$</td><td>$2$</td><td>$3$</td></tr><tr><td>$P(x)$</td><td>$0.2$</td><td>$k$</td><td>$k$</td><td>$2k$</td></tr></tbody></table>find the value of $k$
Question 15 :
<span>Difference between sample space and subset of sample space is considered as</span>
Question 16 :
In a series of 3 independent trials, the probability of exactly 2 success is 12 times as large as the probability of 3 successes. The probability of a success in each trail is
Question 17 :
Let numbers $1,2,3...4n$ be pasted on $4n$ blocks. The probability of drawing a number is proportional to $r$, then the probability of drawing an even number in one draw is $\left ( n\in N \right )$<br/>
Question 19 :
Pricing strategy which considers setting price after designing marketing program is termed as _______.
Question 20 :
In a call of 100 students there are 70 boys whose average marks in a subject is 75. If the average marks of the complete class is 72 . then the average marks of the girls is 
Question 21 :
<span>The average weight of $A,B,C$ is $45kg$ . If the average weight of $A$ and $B$ be $40kg$ and that of $B$ and $C$ be $43kg$, find the weight of $B$ ?</span>
Question 22 : The cost of living index number from the following data:<br><table class="wysiwyg-table"><tbody><tr><td>Group<br>Commodities</td><td>Weights<br> W</td><td>Group/<br>Commodities<br>Index Number I</td></tr><tr><td>Food</td><td>71</td><td>370</td></tr><tr><td>Clothing </td><td>3</td><td>423</td></tr><tr><td>Fuel etc.</td><td>9</td><td>469</td></tr><tr><td>House rent </td><td>7</td><td>110</td></tr><tr><td>Miscellaneous</td><td>10</td><td>279</td></tr></tbody></table>
Question 23 :
Only element which is the cause of income for company is ______.
Question 24 :
Set price limit from which no more demand is accepted is termed as _______.
Question 27 :
Solution of differential equation $\sin y.\frac{{dy}}{{dx}} + \frac{1}{x}\cos y = {x^4}{\cos ^2}y$ is
Question 31 :
The equation of a curve such that the sum of the co-ordinates of any point on the curve exceeds the slope of the tangent to the curve at that point by $5$ ?<br/>
Question 33 :
A die is thrown 100 times, getting an even number is considered a success. Variance of number of successe, is 
Question 34 :
If X following the Binomial distribution with parameters n=6 and p and 9P (X = 4) = P (X = 2), then p is:
Question 35 :
A random variable $X$ has Poisson distribution with mean $2$ The $\displaystyle P(X>1.5)$ equals<br/>
Question 36 :
A fair coin is tossed $99$ times. Let X be the number of times heads occurs. Then $P(X=r)$ is maximum when r is
Question 37 :
On an average, a submarine on patrol sights $6$ enemy ships per hour. Assuming the number of ships sighted in a given length of time is a Poisson variate, the probability of sighting at least two ships in the next $20$ minutes is
Question 38 :
If $x$ is a random poission variable such that $ B= P\left ( X= 2 \right )= P\:\left ( X= 3 \right ) $, then $ P\left ( X= 4 \right ) $ equals
Question 39 :
Find the area of the closed figure bounded by the following curves y = cos x (0 $\leqslant  x \leqslant  \pi/2)$, y = 0, x = 0, and a straight. line which is a tangent to the curve y = cos x at the point x = $\pi/4$.
Question 40 :
Points of inflexion of the curve<br>$y = x^4 - 6x^3 + 12x^2 + 5x + 7$ are
Question 41 :
A tangent having slope of $-\dfrac{4}{3} $ to the ellipse $\dfrac{x^{2}}{18}+ \dfrac{y^{2}}{32}=1 $ intersects the major and minor axes at points A and B respectively. If C is the center of the ellipse , then area of the triangle ABC is
Question 42 :
The area bounded by the parabolas $y=4x^2,\,y=\dfrac{x^2}{9}$ and line $y=2$ is
Question 43 :
The area bounded by the curves $y=\sqrt{-x}$ and $x=-\sqrt{-y}$, where $x,y\le0$, is equal to
Question 44 :
Area bounded by $y={x}^{2}-2\left| x \right|$ and $y=-1$ is equal to
Question 45 :
The parabolas $y^{2}=4x$ and $x^{2}=4y$ divide the square region bounded by the lines x = 4, y = 4 and the coordinate axes. If $S_{1},S_{2},S_{3}$ are respectively the areas of these parts numbered from top to bottom(Example: $S_1$ is the area bounded by $y=4$ and $x^{2}=4y$ ); then $S_{1},S_{2},S_{3}$ is  <br/>
Question 46 :
The area (in square units) bounded by the curves $x\, =\, -2y^2$ and $x\, =\, 1-3y^2$ is
Question 47 :
The area enclosed between the curves $\mathrm{y}=\mathrm{a}\mathrm{x}^{2}$ and $\mathrm{x}=\mathrm{a}\mathrm{y}^{2} (\mathrm{a}>0)$ is 1 sq. unit, then the value of a is<br/>
