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If $|z-2|=min\{|z-1|,|z-5|\}$, where $z$ is a complex number, then possible value(s) of $Re\left(z\right)$ is/are

The maximum value of $4si{n}^{2}x+3co{s}^{2}x+sin\frac{x}{2}+cos\frac{x}{2}$ is

Find the value of $si{n}^2\frac{\pi }{16}$ + $si{n}^2\frac{2\pi }{16}$ + $si{n}^2\frac{3\pi }{16}$ +.....$si{n}^2\frac{16\pi }{16}$

If $S$ be the sum, $P$ the product and $R$ the sum of reciprocals of $n$ terms in G.P., then the value of ${\left(\frac{S}{R}\right)}^n$ is

The angle between the pair of straight lines $x^2+4y^2-7xy=0,$ is

Find the radius of the circle $x^2+y^2-2x+4y-11=0$

If $m$ is the arithmetic mean of two distinct real numbers $l$ and $n(l,n>1)$ and $G_1,G_2$ and $G_3$ are three geometric means between $l$ and $n,$ then $G_1^4+2G_2^4+G_3^4$ equals

What is the first order predecate calculus statement equivalent to the following ? Every teacher is likes by some student

Find the value of $\frac{{\sec }^{2}x-{\text{cosec}}^{2}x}{{\tan }^{2}x-{\cot }^{2}x}$,

$(x\in (0,\frac{\pi }{2}),x\ne \frac{\pi }{4})$

Equation of the hyperbola with focus (-3,4) directrix 3x-4y+5=0 and e = $\frac{5}{2}$ is

The solution of the differential equation $x\frac{dy}{dx}=y(logy-logx+1)$ is

Find equation of the line passing through the point (2, 2) and cutting off intercepts on the axis whose sum is 9.

If ${}^5{C}_r=r\cdot {}^5{C}_{r-1}$, then the number of value(s) of $r$ is

In a group of $400$ people, $160$ are smokers and non-vegetarian; $100$ are smokers and vegetarian and the remaining $140$ are non-smokers and vegetarian. Their chances of getting a particular chest disorder are $35\%,20\%$ and $10\%$ respectively. A person is chosen from the group at random and is found to be suffering from the chest disorder. The probability that the selected person is a smoker and non-vegetarian is:

If the 4th, 7th and 10th terms of aq G.P. be a, b, c respectively, then the relation between a, b, c is

The domain of the function $f\left(x\right)=\frac{1}{\sqrt{x+|x|}},$ is

The letter's of the word $LABOUR$ are permuted in all possible ways and the words thus formed are arranged as in a dictionary. The rank of the word $LABOUR$ will be

Let $f\left(x\right)=\{\begin{array}{cc}1+x,& 0\le x\le 2\\ 3-x,& 2<x\le 3\end{array}$ then $f\left\{f\right(x\left)\right\}=$

A line segment joining (1, 0, 1) and the origin (0, 0, 0) is revolved about the x-axis to form a right circular cone. If (x, y, z) is any point on the cone other than the origin, then it satisfies the equation

If $(10{)}^9+2(11{)}^1(10{)}^8+3(11{)}^2(10{)}^7+\dots \dots +10(11{)}^9=k(10{)}^9$, then k is equal to

$If\frac{2sin\alpha }{1+cos\alpha +sin\alpha }=y,then\frac{1-cos\alpha +sin\alpha }{1+sin\alpha }isequalto$

Let $y=f\left(x\right)$ be a parabola, having its axis parallel to $y-$axis, which is touched by the line $y=x$ at $x=1$, then

Graph of $y=|x-2|-5$ is

Each of the circles $|z-1-i|=1$ and $|z-1+i|=1$ where $z=x+iy,$ touches internally a circle of radius $2$ units. The equation of the circle touching all the three circles can be

If $3+{\log }_{5}x=2{\log }_{25}y$, then the value of $x$ is

Find the general solutions of $3tan\frac{x}{2}+3=0$

The sum of the series $6+13+22+33+\dots \dots$ upto $20$ terms is

If $x_1,x_2,x_3,x_4$ are roots of the equation $x^4-x^{3}sin2\beta +x^{2}cos2\beta -xcos\beta -sin\beta =0$ then $ta{n}^{-1}{x}_1+ta{n}^{-1}{x}_2+ta{n}^{-1}{x}_3+ta{n}^{-1}{x}_4=$

$Rangeofthefunctionf\left(x\right)=\frac{x^2+x+2}{x^2+x+1};xϵRis$

The number of positive real roots for any degree of equation f(x) is given by________.

If $\theta$ = $\frac{\pi }{3}$ + $\frac{\pi }{3^2}$ + $\frac{\pi }{3^3}$ + $\frac{\pi }{3^4}+\dots \dots -\infty$ , Find the vvalue of $e^{i\theta }$ .

In a class of $80$ students numbered $1$ to $80$, all odd numbered students opt for cricket, students whose numbers are divisible by $5$ opt for football and students whose numbers are divisible by $7$ opt for hockey. The number of students who do not opt any of the three games, is -

If $A=\{1,2\}andB=\{3,4\}$ how many subsets will $A\times B$

Write the following sets in the set-builder form:

(i) {3, 6, 9, 12} (ii) {2, 4, 8, 16, 32}

(iii) {5, 25, 125, 625} (iv) {2, 4, 6,........}

(v) {1, 4, 9,........,100}

A person draws a card from a pack, replaces it shuffles the pack, again draws a card, replace it and draws again. This process he does until he draw a heart card. The probability that he will have to make at least four draws is

A straight line $L_1:\frac{x}{a}+\frac{y}{b}=1$ intersects the $x$-axis and $y$-axis at $P$ and $Q$ respectively and a straight line $L_2$ perpendicular to $L_1$ cuts the $x$-axis and $y$-axis at $R$ and $S$ respectively. The locus of the point of intersection of the lines $PS$ and $QR$ is