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Who must be in the same group as H?

Show that the ratio of the sum of first
n terms of a G.P. to the sum of terms from
.

A line divides a plane into 2 regions. Two lines divide the plane into maximum 4 regions. If $L_n$ is the maximum number of regions divided by $n$ lines then the following is/are true?

Find the equation for the ellipse that satisfies the given conditions: Ends of major axis (±3, 0), ends of minor axis (0, ±2)

A ball is shot vertically upward from the ground. It loses $\frac{2}{3}$rd of initial speed after rising up for 4 seconds, then total time of upward journey will be

1. 0.6

The mean of a set of observation is $\overline{x}$ .If each observation is divided by $\alpha \alpha \ne 0$, and then is increased by 10,

then the mean of the new set is

Find the equation of the line passing through the point (-3, 5) and perpendicular to the line joining (2, 5) and (-3, 6).

Let $A=\left[\begin{array}{cc}1& 1\\ 0& 1\end{array}\right]$ and $P=\left[\begin{array}{cc}\cos \frac{\pi }{6}& \sin \frac{\pi }{6}\\ -\sin \frac{\pi }{6}& \cos \frac{\pi }{6}\end{array}\right]$ and $Q=P{AP}^T,$ then $P^T{Q}^{2021}P$ is equal to

The integral $\int (1+x-\frac{1}{x})e^{x+\frac{1}{x}}dx$ is equal to:

The locus of the foot of perpendiculars drawn from the vertex on a variable tangent to the parabola $y^2=4x$ is

Which of the following statements(s) is/are true?

The mean and standard deviation of marks of $10$ students in a class test of $10$ marks is $7$ and $1$ respectively. The marks of $A$ is not known and the standard deviation of the remaining $9$ students is $0$. If $A$ does not score full marks, then the marks of $A$ is

Show that Sec² x - tan⁶x= 1 +3sec²x tan²x

The probability that $k$ number of vehicles arrive (i.e., cross a predefined line) in time $t$ is given as $(\lambda t{)}^k{e}^{-\lambda t}/k!$ where $\lambda$ is the average vehicle arrival rate. What is the probability that the time headway is greater than or equal to time $t_1$ ?

The value of integral $\int \frac{e^x(x+1)}{\sqrt{x^2{e}^{2x}-1}}dx$ is

(where $C$ is constant of integration)

If a circle whose one end of the diameter is focus of the parabola $y^2=4x$ and other end is a point on parabola, then which of the following line will always be a tangent to the given circle?

If,
then,
if the value of α is

A.
B.

C.
π D.

The value of $\underset{n\to \infty }{lim}[\frac{1}{na}+\frac{1}{na+1}+\frac{1}{na+2}+\cdots +\frac{1}{nb}]$ where $a,b>0$ and $a\ne b$ is:

Given $f^{\prime }\left(1\right)=1$ and $f\left(2x\right)=f\left(x\right),\forall x>0$. If $f^{\prime }\left(x\right)$ is differentiable, then there exists a number $c\in (2,4)$ such that $f^{\prime \prime }\left(c\right)$ is equal to:

Find the value of a, if the 2 is one root of the equation $a^2$$x^2$ - 4ax + 4 = 0

Sketch the graph of the following functions:
y=tan 2x, y=tan x

If $10$ objects are distributed at random among $10$ persons, then the probability that at least one of them will not get anything is