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If Z is a complex number such that $\left|z\right|$ greater than or equal to 2, then the minimum value of $|z+\frac{1}{2}|$.

The correct statement concerning the following data set:

$2,5,9,3,4,7,3,8,11,15,10$ is

The lines represented by the equation $9x^2+24xy+16y^2+21x+28y+6=0$ are

The equation of one of the lines represented by the pair of lines $12x^2-10xy+2y^2+11x-5y+2=0$ is/are

The ratio in which $yz-$plane divides the line segment joining $(-3,4,2),(2,1,3)$ is:

Suppose $A_1,A_2,...,A_{30}$ are thirty sets each having 5 elements and $B_1,B_2,...,B_n$ are n sets each having 3 elements. Let each element of S belongs to exactly 10 of $A_i^{\prime }$ s and exactly 9 of $B_i^{\prime }$ s. Then, find the value of n.

Let S and T be the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{8}=1$. If P(x,y) is any point on the ellipse, then the maximum area of the triangle PST (in square units) is ___

Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from $(n+1{)}^{th}to(2n{)}^{th}$term is $\frac{1}{r^n}$

A set of parallel chords of the parabola $y^2=4ax$ have their mid points on

How many real numbers satisfy the relation [x] = $\frac{3}{2}$ {x}.

If atoms of a metal having radius 166 pm are arranged in ABCABC fashion then what is the surface area of each unit cell?

The product of three geometric mean between $\frac{1}{4}$ and $4$ is

If $co{t}^{2}x=cot(x-y).cot(x-z)$ where $x\ne \pm \frac{\pi }{4}$, then $cot2x=$

No. Of ways in which 12 identical balls can be put in 5 different boxes in a row, if no box remains empty is

Solve the following systems of inequalities graphically:

$x\ge 3,y\ge 2$

Find the square root of $-1+2\sqrt{2}i$

If A = [($x,y$): $x^2+y^2=25$] And B = [($x,y$): $x^2+9y^2=144],$ then $A\cap B$ contains

If $C_r={}^n{C}_r$, then $C_0{C}_4-C_1{C}_3+C_2{C}_2-C_3{C}_1+C_4{C}_0=$

The length of the latus rectum of the parabola $9x^2-6x+36y+19=0$

The co-ordinate axes are rotated through an angle of ${60}^{\circ }$ anti-clockwise. Find the vector corresponding to 1+i in new co-ordinate axes.

The multiplicative inverse of a non-zero complex number $z$ is

The coefficient of $x^2{y}^3$ in the expansion of $(1-x+y{)}^{20}$ is

A bag contains $30$ white balls and $10$ red balls. $16$ are drawn one by one randomly from the bag with replacement. If $X$ be the number of white balls drawn, then $\left(\frac{\text{mean of X}}{\text{standard deviation of X}}\right)$ is equal to :

If ${}^{2n}{C}_3:{}^n{C}_2$ = 44:3, then for which of the following values of r, the value of ${}^n{C}_r$ will be 15

If the eccentricity of the hyperbola$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is$\frac{5}{4}$ and $2x+3y–6=0$ is a focal chord of the hyperbola, then the length of transverse axis is equal to ____________

If normal at $P(2,\frac{3\sqrt{3}}{2})$ meets the major axis of the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$ at $Q$ and $S,S^{\prime }$ are foci of given ellipse along positive and negative directions of axes, then the ratio $SQ:S^{\prime }Q$ is

If a+b = $\alpha$,ab = $\beta$,and a,$H_1$,$H_2$,b form H.P,then $\frac{1}{H_1}$ + $\frac{1}{H_2}$ equals to

If $n>1$, the values of the positive integer $m$ for which $n^m+1$ divides $a=1+n+n^2+\dots \dots +n^{63}$ is/are

Find the function corresponding to the graph given below, 1 $\le$ x < 3 ( The function which closely describes the graph )

The total number of divisors of the form $4n+2(n\ge 0)$ of integer $240$ is

The distance of the point (9,12,5) from the x-axis is ___.

$\text{The value of}\underset{x\to 1}{lim}\frac{x^n+x^{n-1}+x^{n-2}+.......+x^2+x-n}{x-1}$

The number of ways in which we can get a sum of $11$ by throwing three dice is :

Express $(1+i{)}^{10}$ in the standard form a + ib.

Find the distance between the parallel lines $15x+8y-34=0$ and $15x+8y+31=0$

The value of ${\sin }^{2}6{}^{\circ }+{\sin }^{2}12{}^{\circ }+{\sin }^{2}18{}^{\circ }+\cdots +{\sin }^{2}84{}^{\circ }+{\sin }^{2}90{}^{\circ }$

is

If $a,b,c$ are different real numbers and $x$ is a variable then a factor of the determinant

$\left|\begin{array}{ccc}0& x^2-a& x^3-b\\ x^2+a& 0& x^2+c\\ x^4+b& x-c& 0\end{array}\right|$ is

If $a_r=(\cos 2r\pi +i\sin 2r\pi {)}^{\frac{1}{9}}$, then the value of $\left|\begin{array}{ccc}{a}_1& a_2& a_3\\ a_4& a_5& a_6\\ a_7& a_8& a_9\end{array}\right|$ is:

Find the value of $\frac{{1.2}^2+{2.3}^2+{3.4}^2+-------nterms}{1^2.2+2^2.3+3^2.4+-------nterms}$.

If a, b, x, y are positive, then (ab + xy) (ax + by) is

The equation of a circle whose radius is $7$ units and $x-$coordinate of the centre is $-2$ and also touches the $x-$axis, is

Find the ratio in which the line segment joining points (2, -1, 3) and (-1, 2, 1) is divided by the plane x + y + z = 5.

There are two die $A$ and $B$ both having six faces. Die $A$ has three faces marked with $1$, two faces marked with $2$, and one face marked with $3$. Die $B$ has one face marked with $1$, two faces marked with $2$, and three faces marked with $3$. Both dices are thrown randomly once. If $E$ be the event of getting sum of the numbers appearing on top faces equal to $x$, let $P\left(E\right)$ be the probability of event $E$, then

When $x=4$, then $P\left(E\right)$ is equal to

If $-\frac{\pi }{2}<x<\frac{\pi }{2}$ and the sum to infinite number of terms of the series$cosx+\frac{2}{3}cosxsi{n}^{2}x+\frac{4}{9}cosxsi{n}^{4}x+.....$ is finite, then $x$ lies in the set