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Find the equation of the ellipse, with major axis along the X-axis and passing through the points (4,3) and (-1,4)

Or

Find the equation of the circle pasing through the points (-3, 4), (-2, 0) and (1,5)) find the coordinates of the centre and radius of the circle.

If the equations $x^2+2x+3=0$ and $a{x}^2+bx+c=0,a,b,c\in R$, have a common root, then $a:b:c$ is

The solution(s) of the equation $(3|x|-3{)}^2=|x|+7$ which belong to the domain of $\sqrt{x(x-3)}$ is/are

In a triangle ABC, a = 3, b = 5, c = 7. Find the angle opposite to C.

If $\tan A=\frac{1}{3}$ and $\sec B=\frac{13}{5}$ where $\pi <A<\frac{3\pi }{2}$, $\frac{3\pi }{2}<B<2\pi$, then $\cot (A+B)$ is equal to

The condition for 2 sets A and B to be disjoint is

In a certain city only two newspapers A and B are published, it is known that 25% of the city population reads A and 20% reads B, while 8% reads both A and B. It is also known that 30% of those who read A but not B look into advertisements and 40% of those who read B but not A look into advertisements while 50% of those who read both A and B look into advertisements. If a person is chosen at random from the population, what is the percentage probability that he/she reads advertisements?

In a group of $70$ people, $37$ like coffee, $52$ like tea and each person like atleast one of the two drinks. The number of persons liking both coffee and tea is

Let $S_1$ = ${}^n{C}_0$ + ${}^n{C}_1$ + ${}^n{C}_2$.............${}^n{C}_n$ and $S_2$ = ${}^n{C}_0$ - ${}^n{C}_1$ + ${}^n{C}_2$ ..............+ $(-1{)}^n$ ${}^n{C}_n$

Find the value of $\frac{S_1}{S_1+S_2}$ is ___.

The origin of the co-ordinate axes is shifted to (-1,3) and the axes is rotated through an angle of ${90}^{\circ }$ in anti-clockwise direction. If (a,b) is the new coordinates of (2,3) in the new coordinate system, then find the value of $2a^2+3b^2$

Find the set of values of $\lambda$ for which the
line $3x-4y+\lambda =0$ intersects the ellipse
$\frac{x^2}{16}+\frac{y^2}{a}=1$ at 2 distinct point.

The number of ways in which a volleyball team of $6$ can be selected out of $10$ players so that $2$ particular players are always included, is

Sum of the common roots of $z^{2006}+z^{100}+1=0$

and $z^3+2z^2+2z+1=0$ is

If a set $A$ is a subset of another set $B,$ then , which means

If $\omega$ is imaginary cube root of unity, then arg(i $\omega$) + arg(i ${\omega }^2$) =

The locus of the middle points of chords of hyperbola $3x^2-2y^2+4x-6y=0$ parallel to $y=2x$ is :

If cos (A-B) = $\frac{3}{5}$ and tanAtanB = 2,then

A spiral is made up of successive semicircles, with centres alternately at $A$ and $B,$ starting with centre at $A$. If the radii are in sequence, $0.5\text{cm},1.0\text{cm},1.5\text{cm},2.0\text{cm},\dots$ as shown in figure below.





Then the total length of the spiral made by thirteen consecutive semicircles is

$(\text{Take}\pi =\frac{22}{7})$

${\left(\frac{1+cos\varphi +isin\varphi }{1+cos\varphi -isin\varphi }\right)}^n$ =

The value of is equal to

The equation $x^2-3xy+\lambda y^2+3x-5y+2=0$ When $\lambda$ is a real number, represents a pair of straight lines.If $\theta$ is the angle between the lines, then $cose{c}^2\theta =$ [EAMCET 1992]

The angle between the lines represented by the equation $a{x}^2+xy+b{y}^2=0$ will be ${45}^{\circ }$, if

Find the sum of the series $\frac{1^3}{1}+\frac{1^3+2^3}{1+3}+\frac{1^3+2^3+3^3}{1+3+5}+------------------------------------12terms$

A, B, C, D are four trees, located at the vertices of a square. Wind blows from A to B with uniform speed. The ratio of times of flight of a bird from A to B and from B to A is 'n'. At what angle should the bird fly from the direction of wind flow, in order that it starts from A and reaches C.Let

Which of the following options has (have) the correct combination of the function and its graph?

$\underset{x\to 0}{lim}{x}^5\left[\frac{1}{x^3}\right]$ where [.] denotes the greatest integer function.

Let $f\left(x\right)=\frac{x-\left[x\right]}{1+x-\left[x\right]},xϵR$, where [ x] denotes the greatest integer function. Then, the range of f is

Two sets A and B have p and q elements respectively. Then the number of relations from B to A is

An n-digit number is a positive number with exactly n digits. Nine hundred distinct n-digit numbers are to be formed using only the three digits 2, 5 and 7. The smallest value of n for which this is possible is

$6^{th}$ term in expansion of $(2x^2-\frac{1}{3x^2}{)}^{10}$ is

Let $f\left(\theta \right)=\sin \theta (\sin \theta +\sin 3\theta )$, then $f\left(\theta \right)$ is

Which of the following numbers has the positive value?

${10}^{(2n-1)}+1$ is divisible by

If the integers m and n are chosen at random between 1 and 100, then the probability that a number of the form $7^m+7^n$ is divisible by 5 equals

If the sum of the series $1+2r+3r^2+4r^3+\cdots \infty$ is $\frac{9}{4},$ then the value of $r$ is

What is the value of cos x in second quadrant if sin x = 3/5 in II quadrant

$$\begin{array}{cc}column1& column2\\ a& p)x\\ b& q)-x\\ c& r)x^2\\ d& s)x^4\end{array}$$

Match the graphs with their corresponding functions.

If $z_1,z_2,z_3$ are complex numbers such that $|z_1|=|z_2|=|z_3|=|\frac{1}{z_1}+\frac{1}{z_2}+\frac{1}{z_3}|=1$, then $|z_1+z_2+z_3|$ is

Find the Integral of the given function w.r.t x

$Y=3x^2-\frac{1}{\sqrt{x}}$

The numerical value of $\text{cosec}\theta [\frac{1-\cos \theta }{\sin \theta }+\frac{\sin \theta }{1-\cos \theta }]-2{\cot }^2\theta$ is