If \(1, \omega, \omega^2\) are the cube roots of unity then the value of \((x+y)^2+\left(x \omega+y \omega^2\right)^2+\left(x \omega^2+y \omega\right)^2\) is

The number of elements in the set \(S=\{x \in \mathbb{Z}\) : \(x^2-7 x+6 \leq 0\) and \(\left.x^2-3 x>0\right\}\) is

The rank of the matrix \(A=\left[\begin{array}{cccc}1 & -1 & 0 & -2 \\ -4 & 4 & 0 & 8 \\ -2 & 1 & 2 & 4\end{array}\right]\) is

The sum of the real roots of the equation \(x^4-2 x^3+x-380=0\) is

If the mean of the data \(7,8,9,7,8,7, \lambda, 8\) is 8 then variance of the data

If the mean deviation from the mean of the observations \(\{1+K \alpha\}\), where \(K=0,1,2, \ldots, 100\) and \(\alpha>0\) is 255 then \(\alpha=\)

A line L passing through the point \((2,0)\) makes an angle \(60^{\circ}\) with the line \(2 x-y+3=0\). If L makes an acute angle with the positive X -axis in the anticlockwise direction. then the Y -intercept of the line L is

If the volume of a block of metal changes by $0.12\%$ when heated through $20°\mathrm{C}$, then find its coefficient of linear expansion.

If a Bernoulli trial is conducted \(\mathrm{n}\) times, then Which one of the following is not suitable to use Poisson distribution?
(i) Each trial results in two mutually exclusive outcomes namely success, failure
(ii) The number ' \(n\) ' of such trials is sufficiently large.
(iii) The trails are independent of each other.
(iv) The probability ' \(p\) ' of success in each trial is very large.

If the normal drawn to the hyperbola \(x y=16\) at \((8,2)\) meets the hyperbola again at a point \((\alpha, \beta)\), then \(|\beta|+\frac{1}{|\alpha|}=\)

An AC generator consists of a coil of $100$ turns and is of cross-sectional area $3{ \mathrm{m}}^2$. It is rotating at a constant angular speed of $60 \mathrm{rad} {\mathrm{s}}^{-1}$ in a uniform magnetic field of $0.04 \mathrm{T}$. Resistance of the coil is $360 \mathrm{\Omega }$. What is the maximum power dissipation in the coil?

The sum of first \(n\) terms of the series \(\frac{3}{5}+\frac{21}{25}+\frac{117}{125}+\ldots\) is

In the triangle with vertices at \(A(6,3), B(-6,3)\) and \(C(-6,-3)\), the median through \(A\) meets
\(B C\) at \(P\), the line \(A C\) meets the \(x\)-axis at \(Q\), while \(R\) and \(S\) respectively denote the orthocentre and centroid of the triangle. Then the correct matching of the coordinates of points in List-I to List-II is
\(\begin{array}{llll} & \text { List-I } & & \text { List-II } \\ \text { (i) } & P & \text { (A) } & (0,0) \\ \text { (ii) } & Q & \text { (B) } & (6,0) \\ \text { (iii) } & R & \text { (C) } & (-2,1) \\ \text { (iv) } & S & \text { (D) }(-6,0) \\ & & \text { (E) }(-6,-3) \\ & & \text { (F) }(-6,3)\end{array}\)
(i)
(ii)
(iii)
(iv)