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Given that the event A and B ar esuch that $P\left(A\right)=\frac{1}{2}P(A\cup B)=\frac{3}{5}andP\left(B\right)=p.$ Find p, if they are
mutually exclusive
independent

The area bounded by the curve $4y^2=x^2(4-x)(x-2)$ is equal to :

If $a={\pi }^{3e},b=3^{\pi e}andc=e^{3\pi },$ then

A = $\left|\begin{array}{ccc}ka& kb& kc\\ kd& ke& kf\\ kg& kh& ki\end{array}\right|$
B = $\left|\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right|$

Whats the value of A/B = ?

The ratio in which the line joining$(2,-4,3)and(-4,5,-6)$ is divided by the plane $3x+2y+z-4=0$ is

AC is an abbreviation for_________.

A horse runs along a circle with a speed of 20 km/hr. A lantern is at the centre of the circle. A fence is along the tangent to the circle at the point at which the horse starts. The speed with which the shadow of the horse move along the fence at the moment when it covers $\frac{1}{8}$ of the circle in km/hr is

Find the length of the perpendicular from the point $(x^1,y^1)$ to the straight line Ax + By + C = 0, the axes being inclined at an angle $\omega$, and the equation being written such that C is a negative quantity.

Let f be a function defined on an interval I and there exists a point “c” in I such that f(c) $\le$ f(x) for all x $\in$ I , then

The locus of mid-points of the line segments joining $(-3,-5)$ and the points on the ellipse $\frac{x^2}{4}+\frac{y^2}{9}=1$ is

If $f_n\left(x\right)=e^{f_{n-1}\left(x\right)}\forall n\in N$ and $f_0\left(x\right)=x,$ then $\frac{d}{dx}\left\{f_n\right(x\left)\right\}$ is equal to

Tangents are drawn from any point on the line $x+4a=0$ to the parabola $y^2=4ax$. Then the angle subtended by the chord of contact at the vertex will be .

The range of $f\left(x\right)=\frac{x^2+14x+9}{x^2+2x+3},x\in R$ is

The set of exhaustive values of $x$ which satisfying the equation $|x^2-5x+4|+|x^2-7x+10|=2|x-3|$ is given by

If the line $x=\alpha$ divides the area of region $R=\left\{\right(x,y)\in R^2:x^3\le y\le x,0\le x\le 1\}$ into two equal parts, then

In
the matrix,
write:

(i) The
order of the matrix (ii) The number of elements,

(iii) Write
the elements a₁₃,
a₂₁,
a₃₃,
a₂₄,
a₂₃

The sum of the tangents of the interior angles of a triangle formed by the lines $L_1:2x+3y+3=0;L_2:y-x-2=0$ and $L_3:2x-3y-3=0$, is

A curve is given as $y=x^3+3x^2+7$. The rate of change of abscissa at a certain point is equal to $\frac{1}{9}$ of the rate of change of ordinate. Which of the following denotes that point , if it is known to lie in $1^{st}$ Quadrant.

Mettez au négatif.



(1) Vous avez des bonbons.

(2) J'achète un crayon.

(3) Ils ont des cahiers.

(4) Je suis étudiant.

(5) Il y a une table.

(6) Ils regardent le tableau.

(7) Ils commencent la leçon.

(8) Le professeur donne des stylos.

(9) Je mange des chocolats.

(10) Ce sont des glaces au chocolat.

Find the locus of the point P if $A{P}^2–B{P}^2=18$, where A ≡ (1, 2, –3) and B ≡ (3, –2, 1)

If $4\hat{i}+7\hat{j}+8\hat{k},2\hat{i}+3\hat{j}+4\hat{k}$ and $2\hat{i}+5\hat{j}+7\hat{k}$ are the position vectors of the vertices $A,B$ and $C$, respectively of triangle $ABC$, then the position vector of the point where the bisector of $\angle A$ meets $BC$ is

The product of 5 geometric means inserted between 2 and 72 is

Find the equation of a line drawn perpendicular to the line $\frac{x}{4}+\frac{y}{6}=1$ through the point where it meets the y-axis.

If in the expansion of ${(\frac{1}{x}+x\tan x)}^5,$ the ratio of $4^{\text{th}}$ term to the $2^{\text{nd}}$ term is $\frac{2}{27}{\pi }^4,$ then the smallest positive value of $x$ is

If the angle between two lines is $\frac{\pi }{3}$ and the slope of one of the lines is $\frac{1}{2}$,
then the slope of the other line is/are:

The number of proper divisors of $2160$ is

If ${(1+x-2x^2)}^6=1+a_{1}x+a_2{x}^2+a_3{x}^3+\cdots +a_{12}{x}^{12},$ then the value of
$a_2+a_4+a_6+\cdots +a_{12}$ will be

If $si{n}^{-1}x+ta{n}^{-1}x=\frac{\pi }{2}$ , then $2x^2+1=$

Find locus of z if Re(1/z)<1/2

Find
for
,
x in quadrant II

Coefficeint of $x^{40}$ in the expansion $(1+x^2{)}^{40}{(x^2+2+\frac{1}{x^2})}^{-5}$ is :

General solution of the equation
${\cos }^{3}x\sin x-{\sin }^{3}x\cos x=\frac{\sqrt{2}}{8}$, is (where $n\in I$ )

If $l,m,n$ denote the sides of pedal triangle opposite to the vertices $A,B,C$ respectively of triangle$ABC.$ Then the value of $\frac{l}{a^2}+\frac{m}{b^2}+\frac{n}{c^2}$ is :