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If the focal chord of the parabola $y^2=axis2x-y-8=0$, then the equation of directrix is.

$\underset{x\to 0}{lim}\frac{\sin 3x}{\sin 5x}$ is equal to

Show that the points (a, 0), (0, b) and (3a, -2b) are collinear. Also find the equation of the line containing them.

Find the equation of a line which makes an angle of 135${}^{\circ }$ with the x-axis and passes through the point (3, 5)

In an Ellipse distance between the foci is 6 and the length of minor axis is 8. Its eccentricity is

If x+iy=$\sqrt{\frac{a+ib}{c+id}}$, then $(x^2+y^2{)}^2$=

If ${\log }_{|sinx|}|cosx|+{\log }_{|cosx|}|sinx|=2$ then |tanx|

Express the following in the form + ib where a, b Є R.

From a bag containing 10 distinct balls, 6 balls are drawn simultaneously and replaced. Then 4 balls are drawn. The probability that exactly 3 balls are common to the drawings is

The number of common terms to the two sequences 17, 21, 25 .......... 417 and 16, 21, 26 ....... 466 is

Find the value of $\cos \frac{32\pi }{3}$

$(p\wedge \sim q)\wedge (\sim p\wedge q)$ is ___.

If sin$\alpha$+sin$\beta$+sin$\gamma$=0= cos$\alpha$+cos$\beta$+cos$\gamma$,

value of $si{n}^2$$\alpha$+$si{n}^2$$\beta$+$si{n}^2$$\gamma$

Three students are standing in a park with signboards 'SAVE ENVIRONMENT', 'DON'T LITTER' and 'KEEP YOUR PLACE CLEAN'. Their positions are marked by the points A(0,7,10), B(-1, 6, 6) and C(-4, 9, 6).

Three students are holdings green colour ribbon together. Does the ribbons form sides or a right angled triangle? Do you feel the need to promote?

What message is given from this question to the society?

If $lo{g}_{a}x,lo{g}_{b}x,lo{g}_{c}x$ be in H.P., then a,b,c are in

If $x^2+ax+10=0$ and $x^2+bx-10=0$ have a common root, then $a^2-b^2$ is equal to

Solve the following inequalities graphically in two dimensional plane:

$x-y\le 2$

If n is a natural number then ${\left(\frac{n+1}{2}\right)}^n$ ≥ n ! is true

when

If $2+i\sqrt{3}$ is a root of the equation $x^2+px+q=0$, where p and q are real, then (p, q) =

The sum of middle terms in the expansion of ${(2a-\frac{a^2}{4})}^9$ is

Find the solution of the inequation 0 < |x-3| $\le$ 1 contains the interval.

Which of the following is the graph of y =$|x+1|$?

What is the probability that a leap year has 53 sundays ?

Team of four students is to be selected from a total of 12 students for a quiz competition. In how many ways it can be selected if two particular students refuse to be together and two particular students wish to be together only in the team. .

If $\overrightarrow{a}-\overrightarrow{b}=2\overrightarrow{c}$, $\overrightarrow{a}+\overrightarrow{b}=4\overrightarrow{c}$ and $\overrightarrow{c}=3\hat{i}+4\hat{j}$, then what are $\overrightarrow{a}$ and $\overrightarrow{b}$?

Find the sum of 10 terms of the series whose $n^{th}$ term is 3.$2^n$.

In how many ways 15 chocolates can be distributed among 6 children such that everyone gets at least one chocolate and two particular children get equal chocolates and another three particular child gets equal chocolates.

The remainder when $2^{2003}$ is divided by 17 is :

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

$y=sin6x+10se{c}^{2}x-cosecxcotx$

If -1,$\alpha$,${\alpha }^3$,${\alpha }^5$,$\overline{\alpha }$,$\overline{{\alpha }^3}$,$\overline{{\alpha }^5}$ are roots of the equation $z^7$ + 1 = 0.Find the value of $\alpha$$\overline{\alpha }$,${\alpha }^3$$\overline{{\alpha }^3}$,${\alpha }^5$$\overline{{\alpha }^5}$,$\alpha$$\overline{\alpha }$ + ${\alpha }^3$$\overline{{\alpha }^3}$ + ${\alpha }^5$$\overline{{\alpha }^5}$.

If z1=a+ib and z1=c+id are complex numbers such that |$z_1$|=|$z_2$|=1 and R($z_1\overline{z_2}$) =0, then the pair of complex numbers w1=a+ic and w2=b+id satisfies

The coordinates of the point P which divides the line segment joining A(1,-2,3) and B(3,4,-5) externally in the ratio 2:3 is

Find the value of $tan\frac{1}{2}[si{n}^{-1}\frac{2x}{1+x^2}+co{s}^{-1}\frac{1-y^2}{1+y^2}]$
$|x|<1,y>0andxy<1$

A $\times$ A $\times$ A has 512 elements. Find the number of elements in A.

The point (4, 1) undergoes the following three transformations successively.
(i) Reflection about the line y = x
(ii) Transformation through a distance 2 unit along the positive direction of x-axis.
(iii) Rotation through an angle of π/4 about the origin in the anti-clockwise direction.
The final position of the point is given by the coordinates

If ${}^n{P}_r$ = 840, ${}^n{C}_r$ = 35, then n is equal to

The number of straight lines that can be drawn through n non collinear points is ____

The range of $f\left(x\right)=\frac{2x}{2+3x}$ is

$|x+1|+|x|>3,xϵR$

The equation of the bisectors of angle between the lines represented by equation $(y-mx{)}^2=(x+my{)}^2$ is

A function f(x) is continuous at a point x = a, then which of the following is incorrect.

Show that the centroid of the triangle with vertices A(x1, y1, z1), B(x2, y2, z2) and C(x3, y3, z3) is
((x1+x2+x3)/3, (y1+y2+y3)/3, (z1+z2+z3)/3).

Find the coefficient of $x^4$ in the expansion of $(1+x{)}^n(1-x{)}^n$. Deduce that $C_2=C_0{C}_4-C_1{C}_3+C_2{C}_2-C_3{C}_1+C_4{C}_0,$ where, $C$ stands for ${}^n{C}_r.$

Prove $(2n+7)<(n+3{)}^2.$