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There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item?

Evaluate $\underset{0}{\overset{2/\sqrt{3}}{\int }}\frac{dx}{4+9x^2}$

The tangent to the curve $y=e^{kx}$ at a point $(0,1)$ meets the $x-$axis at $(a,0)$ where $a\in [-2,-1]$, then $k\in$ :

The solution set of the inequation $\frac{3}{|x|+2}\ge 1$ is

If $1<x<\sqrt{2}$, then number of solutions of the equation ${\tan }^{-1}(x-1)+{\tan }^{-1}x+{\tan }^{-1}(x+1)={\tan }^{-1}3x$, is

If x and y
are connected parametrically by the equation, without eliminating the
parameter, find.

If the variance of a list containing number $7,9,15,16,18$ is $18$ then the variance of list containing numbers $12,16,28,30,34$ will be

Let E and
F be events with.
Are E and F independent?

Choose the
correct answer.

Let,
where 0 ≤ θ≤ 2π,
then

A. Det
(A) = 0

B. Det
(A) ∈ (2, ∞)

C. Det
(A) ∈ (2, 4)

D. Det
(A)∈ [2, 4]

The range of the function $f\left(x\right)=2|x-1|+|x+2|$, $-1\le x\le 2$ is

The focal chord to $y^2=16x$ is tangent to $(x-6{)}^2+y^2=2$, then the possible values of the slope of this chord are

Let $a,b,c$ be in arithmetic progression. Let the centroid of the triangle with vertices $(a,c),$ $(2,b)$ and $(a,b)$ be $(\frac{10}{3},\frac{7}{3}).$ If $\alpha ,\beta$ are the roots of the equation $a{x}^2+bx+1=0,$ then the value of ${\alpha }^2+{\beta }^2-\alpha \beta$ is

${\int }_0^{\pi /2}\frac{tanx}{1+m^{2}ta{n}^{2}x}dx$

Reduce the following equations to the normal form and find p and $\alpha$ in each case :

$\left(i\right)x+\sqrt{3}y-4=0$ $\left(ii\right)x+y+\sqrt{2}=0$ $\left(iii\right)x-y+2\sqrt{2}=0$ $\left(iv\right)x-3=0$ $\left(v\right)y-2=0$

Discuss
the continuity of the function f,
where f is
defined by

If A and B are two events associated with a random experiment such that $P(A\cup B)=0.8,P(A\cap B)=0.3$ and $P\left(\overline{A}\right)=0.5$, find P(B).

If three lines whose equations are

concurrent,
then show that

If $S_n=\sum _{r=1}^n\sum _{t=0}^{r-1}\left(\frac{1}{6^n}{}^n{C}_r{}^r{C}_t{4}^t\right),$ then the value of $l$ where $l=\sum _{n=1}^{\infty }(1-S_n)$ is

If $r^2=x^2+y^2+z^2$ and ${\tan }^{-1}\frac{yz}{xr}+{\tan }^{-1}\frac{xz}{yr}=\frac{\pi }{2}-{\tan }^{-1}\varphi$ then

If the mean deviation of the data $1,1+d,$ $1+2d,\dots ,1+100d$ from their mean is $255,$ then $d$ is equal to

$\int \frac{si{n}^{6}x+co{s}^{6}x}{si{n}^{2}xco{s}^{2}x}dx=$

A die is thrown 6 times. If ‘getting an odd number’ is a success, then the probability of 4 successes is

If A and B are two events such that ,

[MP PET 1992]

The coefficient of variation of two series are 58% and 69%. If their standard deviations are 21.2 and 15.6, then their A.Ms are

If $\frac{(x^2-1)(x+2)(x+1{)}^2}{(x-2)}<0$ , then x lies in the interval

3x − 2y = a ;
−15x + 10y = −7
In the system of equations above, a and b are constants. If the system has infinitely many solutions, what is the value of a?

What is the greatest integer function and an onto function?How to determine whether a function is an onto function or not?