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Is the function, f(x) = min {x,x²} ᵿx ϵ R continuous?

acos∆ - bsin∆=c.prove that asin∆+bcos∆= ±√(a^2 +b^2-c^2)

If the coefficient of x in ${(x^2+\frac{k}{x})}^5$ is 270, then k =

If $L=\underset{x\to 0}{lim}{\left(\frac{\tan x}{x}\right)}^{1/x^2},$ then the value of $L$ is

If $A=\left[\begin{array}{cc}3& -2\\ 4& -2\end{array}\right]andI=\left[\begin{array}{cc}1& 1\\ 0& 0\end{array}\right]$, then find k so that $A^2=kA-2I.$

If the equation ${\sin }^2(\theta -\alpha )\cos \alpha ={\cos }^2(\theta -\alpha )\sin \alpha =m\sin \alpha \cos \alpha$ has solution for all permissible value of $\theta ,\alpha \in R$ then

The sum of all three digit numbers, formed using non zero digits, with all the digits perfect square of a natural number, is

Verify Mean Value Theorem, if

in the interval,
where
and.

$\int \frac{co{s}^{n-1}x}{si{n}^{n+1}x}dx,n\ne 0$ is

Let $f\left(x\right)=\left|\begin{array}{ccc}{\omega }^3& {\omega }^4& {\omega }^5\\ \sin (m-1)x& \sin mx& \sin (m+1)x\\ \cos (m-1)x& \cos mx& \cos (m+1)x\end{array}\right|$,

where $m\in N$ and $\omega$ is the cube root of unity.
If $\underset{0}{\overset{\pi /2}{\int }}f\left(x\right)dx=a\omega +b{\omega }^2,$ then $(a,b)=$

Match the following :

If $A\times B\subseteq C\times D$ and $A\times B\ne \varphi ,$ prove that $A\subseteq CandB\subseteq D.$

Number of circular permutations of n distinct objects is

Let $2si{n}^{2}x+3sinx-2$ >0 and $x^2-x-2$ < 0 (x is measured in radians). Then x lies in the Interval

Let the function $f:R\to R$ be defined by $f\left(x\right)=cosx,\forall x\in R$. Show that $f$ is neither one-one nor onto.

If a sequence is given by $9,12,15,18,\cdots$, then the value of ${16}^{th}$ term is

For hyperbola $\frac{x^2}{co{s}^2\alpha }-\frac{y^2}{si{n}^2\alpha }=1$, which of the following remains constant with change in ${}^{\prime }{\alpha }^{\prime }$ ?

$\int \frac{\sqrt{x}}{\sqrt{a^3-x^3}}dx=$

The entries in a $2X2$ determinant $\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|$ are integers chosen randomly and independently, and for each entry, the probability that the entry is odd is $p$. If the probability that value of determinant is even is$\frac{1}{2}$, then find the value of $p$

Two point charges repel each other with a force of $100\text{N}$. One of the charges is increased by $10\%$ and the other is reduced by $10\%$. The new force of repulsion at the same distance would be

If $c$ is a value of $x$ for which Rolle's theorem holds for the function $f\left(x\right)=\sin x-\sin 2x$ on the interval $[0,\pi ],$ then the value of $\cos c$ is

${lim}_{x\to \frac{\pi }{4}}\frac{cose{c}^{2}x-2}{cotx-1}$