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The given graph shows a function representing the speed of a car with time. Find the domain where the speed is constant.

Prove
that

The lengths of the intercepts made by any circle on the coordinates axes are equal if the centre lies on the line(s) represented by

The largest value of a third-order determinant whose elements are $0$ or $1$ is

There are $m$ men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by $84$, then the value of $m$ is :

If X Y means X is the father of Y; X * Y means X is the mother of Y; X / Y means X is the brother Y; and X # Y means X is the sister of Y, then which of the following shows that P is the maternal uncle of Q?

If $A_1,A_2;$ $G_1,G_2$ and $H_1,H_2$ are arithmetic mean, geometric mean and harmonic mean between two numbers, then the value of $\frac{G_1{G}_2}{H_1{H}_2}\times \frac{H_1+H_2}{A_1+A_2}$ is

${lim}_{x\to 0}\frac{1-cos2x}{cos2x-cos8x}$

If

$P={\log }_2(\cos 1^{\circ }\cdot \cos 2^{\circ }\cdot \cos 4^{\circ }\cdot \cos 8^{\circ }\dots \cos {1024}^{\circ }\cdot \cos {2048}^{\circ })$

$Q={\log }_2\left((1+\tan {23}^{\circ })(1+\tan {22}^{\circ })\right)$

$R={\log }_2\left(\sin 1^{\circ }\right)$

and $S={\log }_2\left(\cos {46}^{\circ }\right),$

then the value of $|(P+Q+R)-S|$ equals

In the relation $P=\frac{\alpha }{\beta }{e}^{-\frac{\alpha Z}{k\theta }}$, $P$ is pressure, $Z$ is the distance, $k$ is Boltzmann constant and $\theta$ is the temperature. The dimensional formula of $\beta$ will be

The $7^{\text{th}}$ term in ${(\frac{1}{y}+y^2)}^{10},$ when expanded in descending power of $y,$ is

If the locus of the middle point of chords of an ellipse $\frac{x^2}{3}+\frac{y^2}{4}=1$ passing through $(2,0)$ is another ellipse $A,$ then the length of latus rectum of the ellipse $A$ is

If the tangent to the conic, $y–6=x^2$ at $(2,10)$ touches the circle, $x^2+y^2+8x–2y=k$ (for some fixed$\left(k\right)$ at a point $(\alpha ,\beta )$; then $(\alpha ,\beta )$ is :

If the matrices $A=\left[\begin{array}{ccc}1& 1& 2\\ 1& 3& 4\\ 1& -1& 3\end{array}\right],B=\text{adj}A$ and $C=3A$, then $\frac{|adjB|}{|C|}$ is equal to :

If $1,\omega ,{\omega }^2$ are the three cube roots of unity, then for $\alpha ,\beta ,\gamma ,\delta ϵR$, the expression $\left(\frac{\alpha +\beta \omega +\gamma {\omega }^2+\delta {\omega }^2}{\beta +\alpha {\omega }^2+\gamma \omega +\delta \omega }\right)$ is

If the equation $a{x}^2+bx+c=0,$ where $a,b,c$ are the sides of a $△ABC,$ and the equation $x^2+\sqrt{2}x+1=0$ have a common root, then $\angle C=$

If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral is :

Maximise Z
= 3x + 2y

subject
to.

If the new coordinates of the point (1,2,3) when the origin shifts from (0,0,0) to (3,4,6) is (l,m,n) then find the value of -(l+m+n)

If $\tan A=\frac{x\sin B}{1-x\cos B}$ and $\tan B=\frac{y\sin A}{1-y\cos A}$, then the value of $\frac{\sin A}{\sin B}$ for all permissible values of $A,B$ is

Let the length of the latus rectum of an ellipse with its major-axis along $x$-axis and centre at the origin, be $8$. If the distance between the foci of this ellipse is equal to the length of its minor axis, then which one of the following points lies on it?

Consider the quadratic equation $y=a{x}^2+bx+c$. The possible graph for the equation if $a>0$ and $D=0$ is/are ?