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Find the Derivation of $f\left(x\right)=x^2.atx=0$

A number is randomly selected from the first 40 natural numbers. What is the probability that the selected number is divisible by 5 or 7?

Find the cube root of 126 to 5 places of decimals.___

Let $A$ be a $3\times 3$ matrix such that $det\left(A\right)=a=3$ and $B=adj\left(A\right)$ such that $det\left(B\right)=b.$ Then the value of $(3b^2+9b+1)S,$ where $\frac{1}{2}S=\frac{a}{b}+\frac{a^2}{b^3}+\frac{a^3}{b^5}+\cdots \text{upto}\infty ,$ is

If $\int g\left(x\right)dx=g\left(x\right)$, then $\int g\left(x\right)\left\{f\right(x)+f^{\prime }(x\left)\right\}dx$ is equal to

Let $y=a{x}^2+bx+c(a\ne 0)$ and $a,b,c\in R$. If $abc>0$, then which of the following graph(s) satisfy the given condition?

If $Z$ represents a set of all Integers and $T$ is a set of all Irrational numbers, $R$ is the set of all Real numbers, then select the correct representation of these sets.

The incentre of the triangle whose vertices are $(1,\sqrt{3}),(0,0)$ and $(2,0)$ is

The differential equation of the family of curves $y^2=4a(x+a)$, where a is an arbitrary constant, is

The locus of the foot of perpendicular from the centre upon any normal to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is

Equation of circle whose parametric equations are $x=5-5\sin t$ and $y=4+5\cos t$ is

Find the equation of a family of circles touching the lines $x^2-y^2+2y-1=0$. (where $h$ and $k$ are parameters)

Coordinates of parametric point on the parabola, whose focus is $(\frac{-3}{2},-3)$ and the directrix is $2x+5=0$ is given by

If [.] denotes the greatest integer function, then which of the following is/are ture?

The equation of the median through the vertex $A$ of triangle $ABC$ whose vertices are $A(2,5),B(-4,9)$ and $C(-2,-1)$ is

If the lines $2x-py+1=0,3x-qy+1=0$ and $4x-ry+1=0$ are concurrent, then $p,q,r$ are in

Total number less than $3\times {10}^8$ and can be formed using the digits $1,2,3$ is equal to $\frac{a}{b}\left(\right[a+2b]\cdot a^7-1)$, then

If $z_1\ne 0$ and $z_2$ be two complex numbers such that $\frac{z_2}{z_1}$ is a purely imaginary number, then the value of $\left|\frac{2z_1+3z_2}{2z_1-3z_2}\right|$ is

A set $Y$ containing all elements $x$ such that $x$ is a whole number less than $10$ can be represented in Set-builder form as:

The area (in sq. units) of the region $\left\{\right(x,y)\in R^2|4x^2\le y\le 8x+12\}$ is :

If $F\left(x\right)=f\left(x\right).g\left(x\right)and{f}^{\prime }\left(x\right)g^{\prime }\left(x\right)=c$ , where ‘c’ is a constant then $\frac{f‘‘}{f}+\frac{g‘‘}{g}+\frac{2C}{fg}$=

The locus of the mid points of the chords of the circle $x^2+y^2-ax-by=0$ which subtend a right angle at $(\frac{a}{2},\frac{b}{2})$ is :

$x^2-11x+a$ and $x^2-14x+2a$ will have a common factor, if a =

The incentre of the triangle with vertices (1, $\sqrt{3}$), (0, 0) and (2, 0) is

If $4$ integers are to be selected from {$1,2,3,......20$} such that the sum of the integers should be the multiple of $4$, then number of ways to select the numbers are

Acute angle between the lines represented by $(x^2+y^2)\sqrt{3}=4xy$ is

The equation of the ellipse, whose axes are coincident with the co-ordinates axis and which touches the straight lines $3x-2y-20=0$ and $x+6y-20=0,$ is

Solve for $x$:

$lo{g}_3\left(\frac{x}{3}\right)+lo{g}_{1/9}\left(x\right)<1$

Find the locus of the point P if $A{P}^2-B{P}^2=18$, where A ≡ (1, 2, –3) and B ≡ (3, –2, 1)

The sum of roots of ${\sin }^{2}x-5\sin x\cos x+2=0$, where $x\in [0,2\pi ]$ is

Football teams $T_1$ and $T_2$ have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of $T_1$ winning, drawing and losing a game against $T_2$ are $\frac{1}{2},\frac{1}{6}$ and $\frac{1}{3}$, respectively. Each team gets 3 points for a win, 1 point for a draw and 0 points for a loss in a game. Let $X$ and $Y$ denote the total points scored by teams $T_1$ and $T_2$, respectively, after two games.



$P(X=Y)$ is

The range of $x$ for which $x^2-|x+2|+x>0$ is

A fair coin is tossed repeatedly until the outcomes of both types have been obtained. The probability that the coin will be tossed exactly 5 times, is equal to:

If a ray of light along the line $y=4$ gets reflected from a parabolic mirror whose equation is $(y-2{)}^2=4(x+1)$, then equation of reflected ray will be

Which one is the graph of $q=\mathrm{xcos}\left(x\right)$?

Find the Derivative of Sin x.

The sum of coefficients of intergral power of $x$ in the binomial expansion ${(1-2\sqrt{x})}^{50}$is:

If the latus rectum of an ellipse is equal to half of its minor axis, then its eccentricity is

According to LMVT, if a function f(x) is continuous on [a, b] and differentiable on the interval (a, b) then which of the following option should be correct for some value c from the interval (a,b)?( c can take any value from the interval (a,b) )

A man alternately tosses a coin and throws a dice beginning with the coin. The probability that he gets a head in the coin before he gets a 5 or 6 on the die is:

Let $x^k+y^k=a^k,(a,k>0)$ and $\frac{dy}{dx}+{\left(\frac{y}{x}\right)}^{\frac{1}{3}}=0$, then $k$ is

If $\tan \alpha =\frac{1}{\sqrt{x(x^2+x+1)}},\tan \beta =\frac{\sqrt{x}}{\sqrt{x^2+x+1}}$

and $\tan \gamma =\sqrt{x^{-3}+x^{-2}+x^{-1}}$, where $x\ne 0$, then $\alpha +\beta$ is

If the tangent to the curve $y=\frac{x}{x^2-3},x\in R,(x\ne \pm \sqrt{3},)$ at a point $(\alpha ,\beta )\ne (0,0)$ on it is parallel to the line $2x+6y-11=0,$ then :

Find the equation of the circle circumscribing the triangle formed by the lines $x+y=0,2x+y=4$ and $x+2y=5$

The sum of the series $1+2.2+{3.2}^2+{4.2}^3+{5.2}^4+\cdots +{100.2}^{99}$ is

The solution of $x^2\frac{dy}{dx}-xy=1+\cos \frac{y}{x}$ is