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Let $z$ is a complex number and $\overline{z}$ is conjugate of $z$. If $(1+i)z=(1-i)\overline{z},$ then the value of $z+i\overline{z}$ is

The probability that out of 10 persons, all born in April, at least two have the same birthday is

The area bounded by the curve $x=a{\cos }^{3}t,y=a{\sin }^{3}t$ is

If the normals at $(x_i,y_i),$ where, $i=1,2,3,4$ on the rectangular hyperbola $xy=c^2$ meet at $(\alpha ,\beta )$, then

If $\alpha ,\beta$ are roots of the equation $6x^2+11x+3=0$ then

The circle passing through three distinct points $(1,t),(t,1)$ and $(t,t)$ for all values of $t$, also passes through the point:

For the following question verify that the given function (explicit or implicit) is a solution of the corresponding differential equation.

y=Ax and xy'=y $(x\ne 0)$

In $\Delta ABC$, if $a=2,b=3$ and $\sin A=\frac{2}{3},$ then $\cos C$ is equal to:

In a football tournament, a team $T$ has to play with each of the $6$ other teams once. Each match can result in a win, draw or loss. The number of ways in which the team $T$ finishes with more wins than losses, is

Let $A=\left(\begin{array}{ccc}[x+1]& [x+2]& [x+3]\\ \left[x\right]& [x+3]& [x+3]\\ \left[x\right]& [x+2]& [x+4]\end{array}\right),$ where $\left[t\right]$ denotes the greatest integer less than or equal to $t.$ If $det\left(A\right)=192,$ then the set of values of $x$ is the interval

Tap on the option which shows the following: $2+2+2+2$

Let the functions $f:R\to R$ and $g:R\to R$ be defined as:

$f\left(x\right)=\{\begin{array}{cc}x+2,& x<0\\ x^2,& x\ge 0\end{array}\text{and}g\left(x\right)=\{\begin{array}{cc}{x}^3,& x<1\\ 3x-2,& x\ge 1\end{array}$

Then, the number of points in $R$ where $\left(fog\right)\left(x\right)$ is non differentiable is equal to :

If a vector making angle α,β and Φ respectively with the x, y and z axis respectively. Then sin² α + sin ² ​​​​​β + sin² Φ = ?

The maximum value of the function f(x) = -|x + 2| + 3 is :

A solution $(x,y)$ of the system of equations $x-y=\frac{1}{3}$ and ${\cos }^2\pi x-{\sin }^2\pi y=\frac{1}{2}$ is given by

1. 1

The total number of solutions of the equation cosx.cos2x.cos3x=$\frac{1}{4}$ in [0, $\pi$] is

Find the area enclosed between sin(x) & cos(x) between x = 0 & $x=\frac{\pi }{2}$.

The minimum point of the function $f\left(x\right)=\left(x^3/3\right)-x$ is at

If $\overrightarrow{u},\overrightarrow{v},\overrightarrow{w}$ are three non-zero and non-coplanar vectors, then $(\overrightarrow{u}+\overrightarrow{v}-\overrightarrow{w})\cdot \left[\right(\overrightarrow{u}-\overrightarrow{v})\times (\overrightarrow{v}-\overrightarrow{w}\left)\right]$ is equal to:

If $0<x<1$, then find the value of $\frac{x}{1-x}(\left(\sin \right({\cot }^{-1}x\left)\sec \right({\cot }^{-1}x){)}^2-1{)}^{\frac{1}{2}}$

Choose the correct answer.
$\int \frac{1}{x^2+2x+2}dx$ equals

$\left(a\right)xta{n}^{-1}(x+1)+C\left(b\right)ta{n}^{-1}(x+1)+C\left(c\right)(x+1)ta{n}^{-1}x+C\left(d\right)ta{n}^{-1}x+C$

The set of all real values of $\lambda$ for which the quadratic equation, $({\lambda }^2+1)x^2-4\lambda x+2=0$ always have exactly one root in the interval $(0,1)$ is:

If the length of the tangent drawn at the point $(1,3)$ on the curve $y=3x^3$ is $a$, then find the value of $9a^2$

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For the matrix $A=\left[\begin{array}{ccc}0& 1& -1\\ 4& -3& 4\\ 3& -3& 4\end{array}\right]$, the inverse of $\frac{A}{2}$ will be

Let $P\left(x\right)=x^2+bx+c$, where $b$ and $c$ are integers. If $P\left(x\right)$ is a facter of both $x^4+6x^2+25$ and $3x^4+4x^2+28x+5$, then value of $P\left(1\right)$ is -

Consider $f:R\to R$ given by f(x)=4x+3. Show that f is invertible. Find the inverse of f.