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Let $f,g:R\to R$ be two functions defined as $f\left(x\right)=|x|+x$ and $g\left(x\right)=|x|-x,\forall x\in R$. Then $(f\circ g)\left(x\right)$ for $x<0$ is

$\underset{x\to 1}{lim}\frac{\sqrt{1-cos2(x-1)}}{x-1}$

Find the lengths of the major and minor axes; coordinates of the vertices and the foci; the eccentricity and length of the latus rectum of the ellipse.

$4x^2+9y^2=144.$

Let $A(9,-6),B(1,2)$ and $C(4,4)$ be three points on the parabola $y^2=4x.$ The equation of the circumcircle formed by the point of intersections of the tangents at $A,B$ and $C$ is $x^2+y^2+kx-ky+h=0.$ Then the value of $k+h$ is
(correct answer + 1, wrong answer - 0.25)

Number of ways of selecting none or more of $10$ identical things is

Find the locus of the points which are equidistant from the points (1, 2, 3) and (3, 2, -1).

For each binary operation $\ast$ defined below, determine whether $\ast$ is binary, communtative or associative.
(v) On $Z^{+}$, define $a\ast b=a^b$

Sum of n terms of an Ap is 3n^2+5n and mth term is 164,m=?

Could you please solve it. It waa on your app.

I am unable to understand it..

Thank you

What's the equation of the line joining 2 points with eccentric angles ${30}^{\circ }$ and ${60}^{\circ }$ in the hyperbola $\frac{x^2}{16}-\frac{y^2}{9}=1$?

I am not able to understand this chapter.

In a $△ABC,2casin\left(\frac{A-B+C}{2}\right)$ is equal to

What is value of power factor if ⏀ = 90^o

Let * be any binary operation on the set R defined by a * b = a + b – ab, then the binary operation * is

If the line $x+2y+4=0$ cutting the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ in points whose eccentric angles are ${30}^{\circ }$ and ${60}^{\circ }$ subtends a right angle at the origin then its equation is

If the product of distances of the point (1, 1, 1) from the origin and the plane x - y + z + k = 0 be 5, then k =

If $f\left(x\right)={\int }_0^x(1+t^3{)}^{\frac{-1}{2}}$ and g (x) is the inverse of f, then the value of $\frac{g"\left(x\right)}{g^2\left(x\right)}$ is

The ${17}^{th}$ term from the end of the A.P. $-36,-31,-26,...,79$ is

Let M be 2 $\times$ 2 symmetric matrix with integer entries. Then M is invertible if

If $|z_1+z_2|=|z_1-z_2|$ then $arg{z}_1-arg{z}_2=$

If $P=\frac{\sin {300}^{\circ }\cdot \tan {330}^{\circ }\cdot \sec {420}^{\circ }}{\tan {135}^{\circ }\cdot \sin {210}^{\circ }\cdot \sec {315}^{\circ }}$ and $Q=\frac{\sec {480}^{\circ }\cdot \text{cosec}{570}^{\circ }\cdot \tan {330}^{\circ }}{\sin {600}^{\circ }\cdot \cos {660}^{\circ }\cdot \cot {405}^{\circ }},$ then the value of $P$ and $Q$ are respectively

If $0<\alpha <\frac{\pi }{6}$,

then $\alpha$.$cosec\alpha$ is

The range of $f\left(x\right)=\frac{x^2}{x^4+1}$ is

Foot of the perpendicular of (1, 1) on the line x + 2y = 8 is (2, 3). Find the image of (1, 1) in the line x + 2y = 8.

The striaght lines whose direction cosines satisfies $al+bm+cn=0,fmn+gnl+hlm=0$ are perpendicular or parallel if

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

Let the random variable $X$ have a binomial distribution with mean $8$ and variance $4.$ If $P(X\le 2)=\frac{k}{2^{16}},$ then $k$ is equal to:

Find the image of the point $P(2,-3,1)$ about the line
$\frac{x+1}{2}=\frac{y-3}{3}=\frac{z+2}{-1}$

$P=\left\{\right(x,y):x,yϵR,x^2+y^2=1\},thenPis$

Find the solution to the following system of linear equations:
2x-5y+4=0
2x+y-8=0

If $\frac{\pi }{3}\le \arg \left[\frac{(z+1)}{(z-1)}\right]\le \frac{2\pi }{3}$, represented by

then $z$ lies in

The sum of all positive integers n for which $\frac{1^3+2^3....+(2n{)}^3}{1^2+2^2+...n^2}$ is also an integer is.

Integrate (log x²)/x