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The root(s) of the quadratic equation $x^2-8x-12=0$ is/are

If a line makes an angles $\alpha ,\beta ,\gamma$ with positive axes. Then the range of $\sin \alpha \sin \beta +\sin \beta \sin \gamma +\sin \alpha \sin \gamma$ is:

Find the mean number of heads in three toses of a fair coin.

Evaluate the Given limit:

The equation of tangent to the curve $y=b{e}^{(-x/a)}$ at the point where it crosses the $y-$ axis is

The eccentricity of a hyperbola passing through the points (3, 0),$(3\sqrt{2},2)$ will be

The equation of the normal to the curve $y=|x^2-|x||$ at $x=-2$ is

The length of the perpendicular from the origin to a line is 7 and the line makes an angle of ${150}^{\circ }$ with the positive direction of y-axis. Find the equation of the line.

If $z=x+iy$ and $|z-1{|}^2+|z+1{|}^2=4$, then the locus of $z$ is

Let $X$ represents the absolute value of difference between the number of heads and the number of tails obtained when a coin is tossed $6$ times. Then the possible values of $X$ are:

Integrate x tanx.

If $y=\underset{x^2}{\overset{x^3}{\int }}\frac{1}{\ln t}dt$ $(\text{where}x\in R^{+}-\{1\left\}\right)$, then the value of $\frac{dy}{dx}$ is

Let $f\left(x\right)$ be a function continuous $\forall x\in R-\left\{0\right\}$ such that $f^{\prime }\left(x\right)<0,\forall x\in (-\infty ,0)$ and $f^{\prime }\left(x\right)>0,\forall x\in (0,\infty ).$ If $\underset{x\to 0^{+}}{lim}f\left(x\right)=3,\underset{x\to 0^{-}}{lim}f\left(x\right)=4$ and $f\left(0\right)=5,$ then the image of the point $(0,1)$ about the line, $y\cdot \underset{x\to 0}{lim}f({\cos }^{3}x-{\cos }^{2}x)=x\cdot \underset{x\to 0}{lim}f({\sin }^{2}x-{\sin }^{3}x),$ is

Let $f\left(x\right)=({\sin }^{-1}x{)}^2-({\cos }^{-1}x{)}^2.$ If range of $f$ equals $[\frac{a{\pi }^2}{4},\frac{b{\pi }^2}{4}]$ where $a,b\in Z,$ then the value of $b-a$ is

$\text{If}x+iy=\sqrt{\frac{a+ib}{c+id}},\text{then write the value of}(x^2+y^2{)}^2.$

In $\Delta ABC,a,b$ and $c$ are the lengths of the sides opposite to the angles $A,B$ and $C$ respectively. The bisector of the $\angle A$ meets the side $BC$ at $D$ and the circumscribed circle at $E$. Then $DE$ equals

A tangent is drawn to the circle $2x^2+2y^2–3x+4y=0$ at the point ‘A’ and it meets the line x + y = 3 at B(2, 1), then AB =

If one of the roots of the quadratic equation $x^2+3x+k=0$ is $3$, then find the other root.

ABC is an isosceles triangle. If the coordinates of the base are B (1,3) and C (- 2, 7), the coordinates of vertex

A can be

In a survey, it is found that $63\%$ Americans like cheese and $76\%$ like apple. If $x\%$ Americans like both, then

"10 is 2 times as many as 5"

The given statement is equivalent to,

Which among the following expressions are equivalent (where $n\in I$)

The area enclosed by the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is equal to

If A1, B1, C1 … are the cofactors of the elements a1, b1, c1... of the matrix

$\left[\begin{array}{ccc}a1& b1& c1\\ a2& b2& c2\\ a3& b3& c3\end{array}\right]$ then $\left|\begin{array}{cc}B2& C2\\ B3& C3\end{array}\right|=$

In a hyperbola if the length of conjugate axis is 5 and the length of a latus rectum is 8, then the semi- transverse axis is

If $[.]$ denotes the greatest integer function and $x\in (0,20),$ then the number of points of discontinuity of $f\left(x\right)=[2x+[x\left]\right]$ is

The value of ${\int }_0^2\left(x^2\right]\mathrm{dx}$ is equal to

The area of triangle whose vertices are $(1,2,3),(2,5,-1)$ and $(-1,1,2)$ is

Two newspapers $A$ and $B$ are published in a city. It is known that $25\%$ of the city population reads $A$ and $20\%$ reads $B$ while $8\%$ reads both $A$ and $B$. Further, $30\%$ of those who read $A$ but not $B$ look into advertisements and $40\%$ of those who read $B$ but not $A$ also look into advertisements, while $50\%$ of those who read both $A$ and $B$ look into advertisements. Then the percentage of the population who look into advertisements is :

Let A, B , and C be three independent events with $P\left(A\right)=\frac{1}{3},P\left(B\right)=\frac{1}{2},andP\left(C\right)=\frac{1}{4}.$ . The probability of exactly 2 of these events occurring, is equal to

In $\Delta ABC$, if $a,b$ and $A$ are given and there are two possibilities for the third side $c_1$ and $c_2,$ then the value of $(c_1-c_2{)}^2+(c_1+c_2{)}^2{\tan }^{2}A$ is equal to