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Which of the following is correct about the function f(x)=0?

Graph of f(x) is given. Draw the graph of y=f({x})

The locus of the mid-point of the line segment joining the focus to a moving point on the parabola $y^2=4ax$ is another parabola with directrix

The slope(s) of the common tangent(s) to the two hyperbolas $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ and $\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$ is/are

If n is positive integer and three consecutive coefficients in the expansion of $(1+x{)}^n$ are in the ratio 6 : 33 : 110, then n =

Let R be a relation from N to N defined by $R=\left\{\right(a,b):a,bϵN$ and $a=b^2$}. Are the following true?

(i) $(a,a)ϵR$ for all $aϵN$

(ii) $(a,a)ϵR$ implies $(b,a)ϵR$

(iii) $(a,b)ϵR,(b,c)ϵR$ implies $(a,c)ϵR$

Justify your answer in each case.

A chord of contact of a point P(k, 2k) is drawn with respect to the circle $x^2+y^2+2x+2y-9=0$. What is the value of 'k' if the chord passes through the origin?

The solution set of ${\log }_{|\sin x|}(x^2-8x+23)>\frac{3}{{\log }_2|\sin x|}$ contains

On the set Z of integers define a relation R by a R b if $|a-b|\le 3$.Then R is

$(1+\frac{3}{1})(1+\frac{5}{4})(1+\frac{7}{9})\cdots (1+\frac{(2n+1)}{n^2})=(n+1{)}^2$

For all values of $\theta$, the lines represented by the equation

$(2cos\theta +3sin\theta )x+(3cos\theta -5sin\theta )y-(5cos\theta -2sin\theta )=0$

xy plane divides the line joining the points $(2,4,5)$and$(-4,3,-2)$ in the ratio

The value of $\frac{1}{2-3i}+1+i$ is .

If $\tan A-\tan B=x$ and $\cot B-\cot A=y$, where $x,y\ne 0$, then $\cot (A-B)$ is

A person goes to office either by car, scooter, bus or train, the probability of which being $\frac{1}{7},\frac{3}{7},\frac{2}{7}and\frac{1}{7}$ respectively. The probabilities that he reaches the office late, if he takes a car, scooter, bus or train are $\frac{2}{9},\frac{1}{9},\frac{4}{9}and\frac{1}{9}$, respectively. Given that he reaches the office on time, then what is the probability that he travelled by car?

Find the angle made by the line x cos ${30}^{\circ }$ + y sin ${30}^{\circ }$ + sin ${120}^{\circ }$ = 0 with the positive direction of the x-axis

Find the Slope of the transverse common tangent to the circles $x^2+y^2-4x+6y-12=0$ and $x^2+y^2+6x+18y+26=0$

Consider the point $A\equiv (0,1)$ and $B\equiv (2,0).{}^{\prime }{P}^{\prime }$ be a point on the line $4x+3y+9=0.$ Coordinate of the point $P$ such that $|PA-PB|$ is maximum, is

5 students of a class have an average height $150\text{cm}$ and variance $18{\text{cm}}^2$. A new student, whose height is $156\text{cm}$ joined them. The variance $\left(\text{in}{\text{cm}}^2\right)$ of the height of these six students is:

If the function

$f\left(x\right)=\{\begin{array}{cc}(1+|sinx|{)}^{\frac{a}{|sinx|,}},& -\frac{\pi }{6}<x<0\\ b,& x=0\\ e^{\frac{tan2x}{tan3x}},& 0<x<\frac{\pi }{6}\end{array}$, is continuous at x = 0, then

Find the multiplicative inverse of each of the complex numbers

$\sqrt{5}+3i$

If the product of the roots of equation 2$x^2$ + ax + 4 sin a = 0 is 1, then roots will be imaginary if :

If $f\left(x\right)=\underset{n\to \infty }{lim}(2x+4x^3+\dots +2^n{x}^{2n-1})$, where $x\in (0,\frac{1}{\sqrt{2}}),$ then $\int f\left(x\right)dx$ is equal to

The equation of the directrix of the parabola $y^2+4y+4x+2=0$ is

For the given distinct values $x_1,x_2,x_3,.....x_n$ occurring with frequencies $f_1,f_2,f_3,...f_n$ respectively. The mean deviation about mean where $\overline{x}$ is the mean and N is total number of observations would be

Let $S=C_0^2+1.\frac{C_1^2}{C_0}+2.\frac{C_2^2}{C_1}+3.\frac{C_3^2}{C_2}+.........+n.\frac{C_n^2}{C_{n-1}}$ Where $C_r={}^n{C}_r$ then which of the following is wrong

1. 0

The $6^{\text{th}}$ term in the expansion of ${(2x^2-\frac{1}{3x^2})}^{10}$ is

The axis of the parabola $9y^2-16x-12y-57-0$ is

Let $f_k\left(x\right)=\frac{1}{k}({\sin }^{k}x+{\cos }^{k}x)$ where $x\in R$ and $k\ge 1$. Then $f_4\left(x\right)-f_6\left(x\right)$ equals:

Find the equation of chord joining the two parametric points of the $P\left(t_1\right)\&P\left(t_2\right)$ of the hyperbola $xy=c^2$.

If $x$ satisfies the inequality ${\log }_{(x+3)}(x^2-x)<1,$ then

Which of the following is/are the solution(s) of the inequality $\frac{1}{\left(x\right|-3}\ge \frac{1}{2}$?

If $(a+bx)e^{\frac{y}{x}}$=x then$x^3\frac{d^{2}y}{d{x}^2}$ equals

Let a, b, x and y be real numbers such that $a-b=1$ and $y\ne 0$. If the complex numbers $z=x+iy$ satisfies Im $\left(\frac{az+b}{z+1}\right)=y$, then which of the following is/are possible value(s) of x?

For any three positive real numbers a, b and c, if $9(25a^2+b^2)+25(c^2-3ac)=15b(3a+c)$, then

Tickets numbered from 1 to 12 are mixed up together and then a ticket is withdrawn at random. Find the probability that the ticket has a number which is a multiple of 2 or 3.

5 girls and 5 boys are to be seated around a circular table such that no 2 girls will sit together. The number of ways in which they can be seated around the table is

Let the harmonic mean and the geometric mean of two positive numbers be in the ratio $4:5.$ Then the two numbers are in the ratio

If $x^2$ + 2(a - 1)x + a + 5 =0 has real roots belonging to the interval (1, 3) then a$ϵ$

The value of ${\int }_{-1}^{2}f\left(x\right)\mathrm{dx},\mathrm{where}f\left(x\right)=\left(x+1\right|+\left(x\right|+\left(x-1\right|$ is

Which of the following is an inference that could be drawn from central tendency?

Let $Q(acos\theta ,bsin\theta )$ be a point on the auxiliary circle. Then the corresponding point with respect to Q on the ellipse when a line drawn perpendicular to major axis AA' will be.