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If $y=f\left(x\right)=\frac{ax-b}{bx-a},x\ne \frac{a}{b},|a|\ne |b|,$ then $f\left(y\right)=$

The lines tangent to the curve $x^3+2y^3+3x^{2}y-2y{x}^2+3x-2y=0\text{and}{x}^7-y^4+2x+3y=0$ at the origin intersect at an angle $\theta$, then the value of $\theta$ is equal to

Find
the middle terms in the expansions of

The number of numbers of 4 digits which are not divisible by 5 are

The number of value(s) of $x$ for which ${\cot }^{-1}(x^2-1)+{\tan }^{-1}\left(\frac{1}{x^2-1}\right)=\frac{\pi }{2}$ is

Let

Find each
of the following

(i) (ii) (iii)

(iv) (v)

The statement P(n) = $4^n-1\ge 3^n$ is true for which of the following options?

A function f such that $f\left(a\right)=f^{\prime \prime }\left(a\right)=......f^{2n}\left(a\right)=0$ and f has a local maximum value b at x = a, if f (x) is

Maximize Z = x + y, subject to constraints are x - y $\le$ - 1, - x + y $\le$ 0 and x, y $\ge$ 0.

If $f^{\prime }\left(x\right)={\tan }^{-1}(\sec x+\tan x),-\frac{\pi }{2}<x<\frac{\pi }{2},$ and $f\left(0\right)=0$, then $f\left(1\right)$ is equal to :

Let $a_1,a_2,a_3\dots ,a_n$ be in A.P. and $a_3,a_5,a_8,b_1,b_2,b_3,\dots ,bn$ be in G.P. If $a_9=40,$ then

The number of pairs (x,y) satisfying the equation $sinx+siny=sin(x+y)$, $\left|x\right|+\left|y\right|=1$is

If $y=2\left[x\right]+30,y=3[x-2]+15$, then $[x+y]$ is equal to

(where [.] denotes greatest integer function)

For every positive integer $m$ and $n$ such that

$m+10<n+1,$ both the mean and median of the set $\{m,m+4,m+10,n+1,n+2,2n\}$ are equal to $n.$ The value of $m+n$ is equal to

if e,f are the roots of the equation 2x²+6x+b=0(b<0) then (e/f)+(f/e) is less then

Answer :- -2

When I solved the given expression I got (18/b)-2 but I am unable to show that it is less than -2.

If ${}^n{C}_{r-1}=36,{}^n{C}_r=84$ and ${}^n{C}_{r+1}=126$ then the value of ${}^n{C}_8$ is

Find the equation of the line whose perpendicular distance from the origin is 4 units and the angle which the normal makes with the positive direction of x-axis is ${15}^{\circ }.$

In the figure, $ABCD$ is a unit square. A circle is drawn with centre $O$ on the extended line $CD$ and passing through $A$ . If the diagonal $AC$is tangent to the circle, then the area of the shaded region is

What are distributive quantities

The number of common tangents to the following pairs of circles $x^2+y^2+4x-6y-3=0$ and $x^2+y^2+4x-2y+4=0$ is

If x = 1 is a common root of the equation x² + ax - 3 = 0 and bx² - 7x + 2 = 0 then ab =

Find the relationship between a
and b so
that the function f
defined by

is
continuous at x =
3.

Let $a,r,s,t$ be nonzero real numbers. Let $P(a{t}^2,2at),Q,R(a{r}^2,2ar)\text{and}S(a{s}^2,2as)$ be distinct points on the parabola $y^2=4ax$. Suppose that $PQ$ is the focal chord and lines $QR$ and $PK$ are parallel, where $K$ is the point $(2a,0).$

The value of $r$ is

Let $a_1,a_2,a_3$ be the first three terms of an A.P. such that $a_1+a_2+a_3=-12$ and $a_1{a}_2{a}_3=80$. Then the value of $a_1^2+a_2^2+a_3^2$ is equal to

Find
the inverse of each of the matrices, if it exists.

Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0) focus (–2, 0)

The value of $\underset{x\to 1}{lim}\frac{1-\sqrt{x}}{({\cos }^{-1}x{)}^2}$ is

If the tangent at the point P(2, 4) to the parabola $y^2=8x$ meets the parabola $y^2=8x+5$ at Q and R,

then the midpoint of QR is