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Which of the following function is identity function?

Let $T_r$ be the $r^{th}$ term of an A.P. for 1, 2, 3, - - - - -. If $T_3=18$ nd $T_6=39$, find $T_{18}$.

How many three-digit numbers are there with no digit repeated ?

If ${\theta }_1$ and ${\theta }_2$ are two value lying on [0, 2$\pi$] for which tan$\theta$ = $\lambda$ then tan $\frac{{\theta }_1}{2}$.tan $\frac{{\theta }_2}{2}$ is

The locus of the point of intersection of the lines bxt-ayt=ab and bx+ay=abt is

If the lengths of the tangents from the point (1, 2) to the circles $x^2+y^2+x+y-4=0$ and $3x^2+3y^2-x-y-\lambda =0$ are in the ratio 4:3 then $\lambda =$

The condition for (a - 2) $x^2$ + 2ax + (a + 3) = 0 to have both roots to be real is

The tangent at A (2, 4) on $y=x^3-2x^2+4$ cuts the x axis at T then AT =

The equation of the curve passing through the origin and satisfying the differential equation ${\left(\frac{dy}{dx}\right)}^2=(x-y{)}^2$, is

If n(A)=2, n(B)=2 . What is the total number of relations from A to B?

If $2^{x+y}=6^y$, then the value of $\frac{x}{y}$ is

Three distinct points $P(3u^2,2u^3);Q(3v^2,2v^3)andR(3w^2,2w^3)$ are collinear and equation $a{x}^3+b{x}^2+cx+d=0$ has roots u, v and w, then which of the following is true

Three poles $A,B$ and $C$ are in a straight line, apart by $10$ metres each. The height of pole $A$ is $20$ metres and the angle of depression from the top of pole $A$ to the top of pole $B$ is ${60}^{\circ }$ and the angle of elevation from the top of pole $B$ to the top of pole $C$ is ${30}^{\circ }.$ The height (in metres) of pole $C$ is

If $y=\sqrt{(a-x)(x-b)}-(a-b)ta{n}^{-1}\sqrt{\left(\frac{a-x}{x-b}\right),}$ then $\frac{dy}{dx}$ is equal to

Let $z_1$ and $z_2$ be two complex numbers such that $\left|\frac{z_1-2z_2}{2-z_1\overline{z_2}}\right|=1$ and $|z_2|\ne 1$. Then the value of $|z_1|$ is

Let $P(asec\theta ,btan\theta )$ and $Q(asec\varphi ,btan\varphi )$, where $\theta +\varphi =\frac{\pi }{2}$, be two points on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$.
If (h, k) is the point of the intersection of the normals at P and Q, then k is equal to

Show that the surface area of a closed cubiod with square base and given volume is minimum,when it is a cube.

If $x=-1$ and $x=2$ are extreme points of $f\left(x\right)=\alpha \log |x|+\beta x^2+x$ then :

The locus of the point p(x,y) satisfying the relation $\sqrt{(x-3{)}^2+(y-1{)}^2}+\sqrt{(x+3{)}^2+(y-1{)}^2}=6$ is

The equation of the straight line whose perpendicular distance from origin is $3\sqrt{2}$ units and this perpendicular makes an angle of ${75}^{\circ }$ with the positive direction of x-axis, is

How to open mod and cocept of mod and mod inequality please tell

The derivative of $y=lo{g}_{e}sin\left(e^x\right)$ with respect to x will be

The symmetric difference of A = {1,2,3 } and {3,4,5} is ___.

A particle is projected from a horizontal plane (x-z plane) such that its velocity vector at time t is given by $\overrightarrow{V}=a\hat{i}+(b-ct)\hat{j}$. Its range on the horizontal plane is given by :

The coefficient of x^5 in ${(\frac{x}{2}-\frac{3}{x^2})}^{10}$ is

If (-3, 2) lies on the circle $x^2+y^2+2gx+2fy+c=0$ which is concentric with the circle $x^2+y^2+6x+8y-5=0$, then c=

Solve the following quadric equations by factorization method only $x^2+x+1=0$

The correct conclusion that can be drawn from these figures is

The sum of all the solution(s) of the equation ${\sin }^{-1}\left(2x\right)={\cos }^{-1}x$ is

The number of solution(s) of $y=|x^2-3|$ and $y=1,$ is

If a variable chord $PQ$ of the parabola $y^2=4ax$ is drawn parallel to $y=x,$ then the locus of point of intersection of normals at $P$ and $Q$ is

Find the maximum and minimum values, if any, of the following functions given by

$f\left(x\right)=(2x-1{)}^2+3$

$f\left(x\right)=9x^2+12x+2$

$f\left(x\right)=-(x-1{)}^2+10$

$g\left(x\right)=x^3+1$

A survey shows that in a city, $45$% citizens like tea, whereas $65$% citizens like coffee. If $x$% like both tea and coffee, then

A second order determinant is written down at random using the numbers $1,-1$ as elements. The probability that the value of the determinant is non zero is

A balloon which remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the radius is 10 cm.

Let A denotes the area bounded by $y=(lnx{)}^2$ and lines y = 0 and $x=e^2$ then -