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While finding the roots of $f\left(x\right)=x^2-4=0$ using Newton - Raphson method, initial value of (x, x₁ = 1). If the value obtained after first iteration is x₂, find [100. x₂], where [ ] is the greatest integer function.

If set $A=\left\{\right(r,s)|r,s\in W\}$, then the number of element(s) in set $A$ such that ${}^5{C}_r\cdot {}^6{C}_s=1$ is

The locus of a point (to the right of $x=2$) whose sum of the distances from the origin and the line $x=2$ is $4$ units, is

Let $X$ be a set containing $6$ elements and $P\left(X\right)$ be its power set. The sets $A$ and $B$ are picked from $P\left(X\right).$ If $n\left(A\right)=n\left(B\right)$ and $A\ne B,$ then total number of ordered pair $(A,B)$ is

[Note $:n\left(A\right)$ represents number of elements in set $A$]

Which of the following represents the condition for a matrix A to be skew hermitian Matrix. Given that the general element of the matrix is aij.

If $p$ be the perpendicular distance of a focal chord $PQ$ of length $l$ from the vertex $A$ of the parabola $y^2=4ax$, then $l$ varies inversely as

The graph of a function $y=a\cos bx+c$ is given below





Then, the function $y$ is

$If|z|=1and\omega =\frac{z-1}{z+1}(where,z\ne -1),thenRe\left(\omega \right)is$

The variance of first 50 even natural numbers is

If $\alpha ={\cos }^{-1}\left(\frac{3}{5}\right),\beta ={\tan }^{-1}\left(\frac{1}{3}\right),$ where $0<\alpha ,\beta <\frac{\pi }{2},$ then $\alpha -\beta$ is equal to:

Number of possible tangents to the curve $y=cos(x+y),-3\pi \le x\le 3\pi$ that are parallel to the line x+2y = 0, is

$\frac{d}{dx}\left(\frac{1}{x\sqrt{x}}\right)=$

For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that the candidate solve any problem is $\frac{4}{5}$, then the probability that he is unable to solve less than two problems is :

The sum of the infinite series $1+\frac{2}{3}+\frac{7}{3^2}+\frac{12}{3^3}+\frac{17}{3^4}+\frac{22}{3^5}+\dots$ is equal to :

For the given expression $\frac{\sqrt{2x-1}}{x-2}<1,x\in$ :

The angle between the pair of tangents drawn from a point P to the circle $x^2+y^2+4x-6y+9$$si{n}^2\alpha +13co{s}^2\alpha =0$ is $2\alpha$. Then the equation of the locus of the point P is

The normal to the circle $x^2+y^2+2x-10y+k$ = 0 which is perpendicular to x-3y+2=0 is

The values of $x$ which satisfying both the equations $\cos x=\frac{-1}{\sqrt{2}}$ and $\tan x=1$ simultaneously is :

If the straight line, $2x-3y+17=0$ is perpendicular to the line passing through the points $(7,17)$ and $(15,\beta )$ then $\beta$ equals:

If $A\equiv (-6,0),B\equiv (3,-3)$ and $C\equiv (5,3)$ are three points, then the locus of the point $P$ such that $|\overline{AP}{|}^2+|\overline{BP}{|}^2=2|\overline{CP}{|}^2$ is

The equation of the curve whose parametric equations are $x=1+4\cos \theta ,y=2+3\sin \theta ,\theta \in R,$ is

Any set $A$ such that $A\cup A=\{11,13,5,6\},$ then $A=$

If z = 3+5i, then $z^3$ + $\overline{z}$ + 198 =

If $x^m.y^n=(x+y{)}^{m+n}$, then $\frac{dy}{dx}$ is

The equation of reflection of $y^2=x$ about $y-$axis is

In a city $20$ percent of the population travels by car, $50$ percent travels by bus and $10$ percent travels by both car and bus. Then the percentage of population travelling by car or bus is

The locus of the midpoints of the focal chords of the parabola $y^2=4ax$ is

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

The standard deviation of 25 numbers is 40. If each of the numbers is increased by 5, then the new standard deviation will be

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are three mutually perpendicular vectors of equal magnitude, then the angle $\theta$ which $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}$ makes with any one of three given vectors is given by

Suppose that the three quadratic equations $a{x}^2-2bx+c=0,b{x}^2-2cx+a=0$ and $c{x}^2-2ax+b=0$ all have only positive roots. Then

Let $T_n$ be the area bounded by $y={\tan }^{n}x,x=0,y=0$ and $x=\frac{\pi }{4}$ where $n$ is a integer greater than $2$, then $T_{100}$ is

The maximum value of $f\left(x\right)=(x+3)(4-x)+3$ is

The area (in sq. units) of the region bounded by the parabola, $y=x^2+2$ and the lines $y=x+1,x=0$ and $x=3,$ is:

The number of solution(s) of the equation $\text{sgn}\left(\ln x\right)=3$ is

(Here, sgn denotes the signum function)

If a directrix of a hyperbola centred at the origin and passing through the point $(4,-2\sqrt{3})$ is $5x=4\sqrt{5}$ and its eccentricity is $e$, then :

The point of intersection of two tangents at the ends of the latus rectum to the parabola $(y+3{)}^2=8(x-2)$ is

If the minimum value of $f\left(x\right)=a{x}^2+2x+5,a>0$ is equal to the maximum value of $g\left(x\right)=3+2x-x^2$, then the value of ${}^{\prime }{a}^{\prime }$ is

The two circles $x^2+y^2+2ax+c=0and{x}^2+y^2+2by+c=0$ touch if $\frac{1}{a^2}+\frac{1}{b^2}=$

If $4\hat{i}+7\hat{j}+8\hat{k},2\hat{i}+3\hat{j}+4\hat{k}$ and $2\hat{i}+5\hat{j}+7\hat{k}$ are the position vectors of the vertices $A,B$ and $C$, respectively of triangle $ABC$, then the position vector of the point where the bisector of $\angle A$ meets $BC$ is

If the angle between the lines represented by the equation $y^2+hxy-x^{2}ta{n}^{2}A=0$ be 2A, then k=

If sixth term of a H.P. is $\frac{1}{61}$ and its tenth term is $\frac{1}{105}$, then first term of that H.P. is

Let f(x+y) = f(x).f(y) for all x and y. Given that f(3) = 3 and f'(0)= 11. Then the value of f'(3) is ___ .

The median of a set of 15 observations is 30.5. If each of the largest 6 observations of the set is increased by 5, then the median of the new set of observations