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The solution of $xdx+ydy=x^{2}ydy-x{y}^{2}dy$ is

(where $C_1,C_2,C_3,C_4$ are integration constant)

Given standard equation of ellipse,

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,a>b$,

with eccentricity $e$.

Match the following

$\begin{array}{cc}a)\text{Major axis}& i\left)2a\right(1-e^2)\\ b)\text{Minor axis}& ii)y=0\\ c)\text{Double ordinate}& iii)x=0\\ d)\text{Latus Rectum length}& iv)x=\frac{-a}{e}\\ & v)\sqrt{1-\frac{b^2}{a^2}}\end{array}$

The area of the quadrilateral PQRS whose vertices are P (-5, 7), Q (-4, -5), R (-1, -6) and S (4, 5) is

The value(s) of $x$ satisfying the equation ${\tan }^{-1}\frac{x-1}{x-2}+{\tan }^{-1}\frac{x+1}{x+2}=\frac{\pi }{4}$ is (are)

The equations of the lines through $(-1,-1)$ and making angle ${45}^{\circ }$ with the line $x+y=0$ are given by

Which of the following is/are null sets?

The sum of the mean and variance of a binomial distribution is $15$ and the sum of their squares is $117$. Probability of atmost one success in case of these trials will be:

In an R-L-C circuit v = 20 sin (314t+5$\pi$/6) and i = 10 sin(314 t+2$\pi$/3). The power factor of the circuit is

The reflection of the point $A(1,0,0)$ in the line $\frac{x-1}{2}=\frac{y+1}{-3}=\frac{z+10}{8}$ is:

The equation of line(s) joining the vertex of $y^2=6x$ to the point on it whose abscissa is $24,$ is (are)

A circle $(x-3{)}^2+(y-6{)}^2=r^2$ touches parabola $y^2=4x$ at P(a, b). If the slope of common tangent at P is m, then (b, r > 0)

If the equation of plane passing through the mirror image of a point $(2,3,1)$ with respect to line $\frac{x+1}{2}=\frac{y-3}{1}=\frac{z+2}{-1}$ and containing the line $\frac{x-2}{3}=\frac{1-y}{2}=\frac{z+1}{1}$ is $\alpha x+\beta y+\gamma z=24,$ then $\alpha +\beta +\gamma$ is equal to :

If the distance between the foci fo a hyperbola is 16 its ecentricity is $\sqrt{2}$.then then obtain its equation.

The values of $\lambda$ for which the circle $x^2+y^2+6x+5+\lambda (x^2+y^2-8x+7)=0$ dwindles into a point are

A long straight wire, carrying current $I$, is bent at its midpoint to form an angle of ${45}^{\circ }$. Induction of magnetic field at point $P$, distant $R$ from point of bending is equal to

Calculate APC and MPC:

$\begin{array}{cc}\text{INCOME (Y)}& \text{CONSUMPTION (C)}\\ 0& 4\\ 10& 12\\ 20& 20\\ 30& 28\\ 40& 36\end{array}$

If $A(1,2,3),B(2,3,1)$ and $C(3,1,2$) are the vertices of the triangle. Find the coordinates of its orthocenter $\left(O\right)$ and In center $\left(I\right)$.

Minimize and maximize Z = 5x + 10y subject to constraints are x + 2y $\le$ 120, x + y $\ge$ 60, x - 2y $\ge$ 0 and x, y $\ge$ 0.

1. 6

The area, in square unit, bounded by the curves $y=x^3,y=x^2$ and the ordinates x = 1, x = 2 is

Solution of differential equation $(y+x\sqrt{xy}(x+y\left)\right)dx+\left(y\sqrt{xy}\right(x+y)-x)dy=0$ is

Show that
each of the relation R in the set,
given by

(i)

(ii)

is an
equivalence relation. Find the set of all elements related to 1 in
each case.

Boyle's law may be represented as

1.[dp/dv]T=K/V

2.[dp/dv]T=-K/V

3.[dp/dv]T=-K/V

4.[dp/dv]T=K/V^2

The value of definite integral ${\int }_1^e\sqrt{x}ln\left(x\right)dx$ is

If $\alpha ,\beta$ are the roots of the equation a$x^2$ +2bx +c = 0 and $\alpha +\delta$, $\beta +\delta$ are the roots of A$x^2$ + 2Bx + C= 0 , then $\frac{b^2–ac}{B^2–AC}$ =