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The differential equation of the family of curves represented by the equation $x^2+y^2=a^2$ is

What are the points on the y-axis whose distance from the line
is
4 units.

In a G.P, it is being given that $T_1=3$, $T_n=96$ and $S_n=189$. Then the value of $n$ is

(where $T_n$ and $S_n$ denote the $n^{th}$ term and sum upto $n^{th}$ term repectively)

If x sin (a + y) + sin a cos (a + y) = 0, then the value of $\frac{\mathrm{dy}}{\mathrm{dx}}$ is

The value of $\underset{0}{\overset{10\pi }{\int }}|\sin x|dx$ is

Suppose f(x) = $\{\begin{array}{ccc}a+bx& x<1& \\ 4& x=1& \text{and if}\\ b-ax& x>1& \end{array}$
$\underset{x\to 1}{\text{lim}}=f\left(1\right)$,
what are possible values of a and b?

The range of $p$ for which $6$ lies between the roots of $x^2+2(p-3)x+9=0$ is

1. 0.014

(i) How many terms of the sequence $18,16,14,...$ should be taken so that their sum is zero?
(ii) How many terms are there in the A.P. whose first and fifth terms are $-14$ and $2$ respectively and the sum of the terms is 40?
(iii) How many terms of the A.P., $9,17,25,...$ must be taken so that their sum is $636$?
(iv) How many terms of the A.P., $63,60,57,...$ must be taken so that their sum is $693$?
(v) How many terms of the A.P., $27,24,\mathrm{21...}$ should be taken so that their sum is zero?
(vi) How many terms of the A.P., $45,39,\mathrm{33...}$must be taken so that their sum is $180$?

The radius of the circle $Re\left(\frac{iz+1}{iz-1}\right)=2$ is

Number of $4$ digit numbers using digits $0,1,2,3,4,5$ which are divisble by $9$, when each digit used at most once

Slope of normal to the curve $y=x^2-\frac{1}{x^2}$ at $(-1,0)$​ is ​

A natural number is selected at random from $1$ to $1000.$ Then the probability that non-zero digits appear at most once is

Let $A=\left[\begin{array}{cc}1& 2\\ -1& 4\end{array}\right].$ If $A^{-1}=\alpha I+\beta A,\alpha ,\beta \in R,I$ is $2\times 2$ identity matrix, then $4(\alpha -\beta )$ is

${\text{Derivative of sin}}^{-1}xw.r.t.co{s}^{-1}\sqrt{1-x^2}is$

The number of ways in which the letters of the word ARRANGE can be arranged such that both R do not come together is

The direction cosines of the line whose direction ratios are 6, - 6, 3 are:

Let $f$ be a twice differentiable function on $(1,6)$. If $f\left(2\right)=8,f^{\prime }\left(2\right)=5,f^{\prime }\left(x\right)\ge 1$ and $f^{\prime \prime }\left(x\right)\ge 4,$ for all $x\in (1,6),$ then

Let the system of linear equations

$4x+\lambda y+2z=0$

$2x-y+z=0$

$\mu +2y+3z=0,\lambda ,\mu \in R$

has a non-trivial solution. Then which of the following is true?

Find out the value of K_c
for each of the following equilibria from the value of K_p:

Foot of the perpendicular drawn from the origin to the plane $2x-3y+4z=29$ is

If $a(\frac{1}{b}+\frac{1}{c}),b(\frac{1}{c}+\frac{1}{a}),c(\frac{1}{a}+\frac{1}{b})$ are in A.P., prove that a, b, c are in A.P.

I want all formulas related to sequence and series

That is related to Harmonic progression , AritmArith progression , Geometric progression and special progression

The lateral edge of a regular hexagonal pyramid is 1 cm. If the volume is maximum, then its height is

The greatest value of the function $f\left(x\right)={\tan }^{-1}x-\frac{1}{2}\ln x$ in $[\frac{1}{\sqrt{3}},\sqrt{3}]$ is

Find the
scalar components and magnitude of the vector joining the points

.

If $\cos \alpha +2\cos \beta +3\cos \gamma =\sin \alpha +2\sin \beta +3\sin \gamma =0$, then the value of $\sin 3\alpha +8\sin 3\beta +27\sin 3\gamma$ is

If $u+iv=(x+iy{)}^3$ then $\frac{u}{x}+\frac{v}{y}=$

Find the sum to n terms of the series

If $x=\frac{72!}{(36!{)}^2}-1$, then x is

Let $P$ be a variable point on the parabola $y=4x^2+1.$ Then, the locus of the mid-point of the point $P$ and the foot of the perpendicular drawn from the point $P$ to the line $y=x$ is: