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If A = {$xϵC:x^2=1$} and {$xϵC:x^4=1$}, then write A - B and B- A.

By using
properties of determinants, show that:

(i)

(ii)

Find the shortest
distance between the lines whose vector equations are

$\text{The general value of x satisfying the equation}\sqrt{3}sinx+cosx=\sqrt{3}isgivenby$

For any acute angle $\theta ,\cos (\theta -3\pi )=$,$\sin (\theta -3\pi )=$

If ${\log }_2\left(\frac{x-1}{x-2}\right)>0$, then

${\int }_{\pi /2}^{-\pi /2}In\left(\frac{2-sinx}{2+sinx}\right)dx=----$

The equation of the plane which contains the line of intersection of the planes $x+y+z-6=0$ and $2x+3y+z+5=0$ and perpendicular to the $xy-$plane is

Find the second order derivative of the given functions.

$ta{n}^{-1}x$

If $\sec \theta =max(x+\frac{1}{x}),x\in R,$ where $x<0$, then the value of $\theta$

If $l(m,n)={\int }_0^1{t}^m(1+t{)}^{n}dt$, then the expression for $l(m,n)$ in terms of $l(m+1,n-1)$ is

Find the sum to ${}^{\prime }{n}^{\prime }$ terms of the series

$5^2+6^2+7^2+.........+{20}^2$

The differential equation satisfing ${\sin }^{-1}x+{\sin }^{-1}y={\sin }^{-1}c,$ where $c$ is an arbitrary constant, is

The value of x which will satisfy the equation :

x cos (a) cos (${90}^{\circ }$ - a) tan (a) tan (${90}^{\circ }$ - a) sec (a) cosec (a) = 1 is ..............................

If $f\left(x\right)$ is continuous for all real values of $x$, then $\sum _{r=1}^n\underset{0}{\overset{1}{\int }}f(r-1+x)dx$ is equal to,where n is a natural number

The following integral value$\underset{-1/2}{\overset{1/2}{\int }}\cos x\left[\ln \left(\frac{1-x}{1+x}\right)\right]dx$ is

$Aforceof\overrightarrow{F}=3\hat{i}+4\hat{j}isactingonaboxatpoint\overrightarrow{A}whosepositionvectorwithrespecttooriginis<2,3>.Workdoneindisplacingtheparticlefrom\overrightarrow{A}to\overrightarrow{B}whosepositionvectorwithrespecttooriginis<5,6>willbe.......units$

The equation of the tangents to the ellipse $3x^2+4y^2=12,$ which are perpendicular to the line $y+2x=4,$ are

if $x_r$=cos$\left(\frac{\pi }{2^r}\right)$+isin$\left(\frac{\pi }{2^r}\right)$ , then $x_r$, $x_r$, ......$\infty$ is

If the function $f\left(x\right)=\left[\frac{(x-3{)}^2}{a}\right]\sin (x-3)+a\cos (x-3)$ is continuous in $[4,8]$, then the range of $a$ is

($[.]$ denotes the greatest integer function)

If x is real, find the range of y from the equation $x^2(y-1)-2x+(2y-1)$ = 0

The value of $\underset{x\to 0^{-}}{lim}\frac{x\left(\right[x]+|x|)\sin \left[x\right]}{|x|}$ is

(where $[.]$ is greatest integer function)

If A and B are two sets such that n(A) = 115, n(B) = 326, $n(A-B)$ = 47, then writen $(A\cup B)$.

Which among the following can always represent a vector?

Two straight lines are perpendicular to each other. One of them touches the parabola $y^2=4a(x+a)$ and the other touches $y^2=4b(x+b)$. Their point of intersection lies on the line

What is the logical translation of the following statements? "None of my friends are perfect"

The value of $(1+cos\frac{\pi }{6})(1+cos\frac{\pi }{3})(1+cos\frac{2\pi }{3})(1+cos\frac{7\pi }{6})$ is

In a pack of 52 playing cards, three cards are drawn at random with replacement. What is the probability of getting Jack in all 3 draws?

If two distinct chords drawn from the point (p, q) on the circle $x^2+y^2-px-qy=0(wherepq\ne 0)$ are bisected by the x-axis, then