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The sum to 'n' terms of the series
$ta{n}^{-1}\left(\frac{1}{2}\right)+ta{n}^{-1}\left(\frac{2}{9}\right)+ta{n}^{-1}\left(\frac{1}{8}\right)+ta{n}^{-1}\left(\frac{2}{25}\right)+ta{n}^{-1}\left(\frac{1}{18}\right)+.....\infty$ terms

The differential equation of the family of curves $y=acos(x+b)$ is

[MP PET 1993]

The curve with parametric equations $x=1+4cos\theta ,y=2+3$ sin $\theta$ is

Find the image of P(-3, 5) about the line x - y + 2 = 0

The equation of the perpendicular bisector of the line segment joining the points (1, 4) and (3, 6) is

The order and degree of the differential equation are

[AIEEE 2002]

Find the value of x for which the product of the follwing matrices equals an identity matrix.
$\left(\begin{array}{ccc}2& 0& 7\\ 0& 1& 0\\ 1& -2& 1\end{array}\right]\times \left(\begin{array}{ccc}-x& 14x& 7x\\ 0& 1& 0\\ x& -4x& -2x\end{array}\right]$

The solution of the differential equation $\frac{dy}{dx}=\frac{1+y^2}{1+x^2}$ is

[SCRA 1986]

Calculate mean, variance and standard deviation of the following distribution :

$\begin{array}{ccccccc}\text{Class :}& 1-10& 10-20& 20-30& 30-40& 40-50& 50-60\\ \text{Frequency:}& 11& 29& 18& 4& 5& 3\end{array}$

Let $f:(-1,1)\to B$, be a function defined by $f\left(x\right)=ta{n}^{-1}\frac{2x}{1-x^2}$, then f is both one - one and onto when B is the interval

Find the p values of the following questions:
$ta{n}^{-1}\left(1\right)+co{s}^{-1}(-\frac{1}{2})+si{n}^{-1}(-\frac{1}{2})$
Given expression is not a standard identity, so we separately find the value of $ta{n}^{-1}\left(1\right),co{s}^{-1}(-\frac{1}{2}),si{n}^{-1}(-\frac{1}{2})$ and simplify it.

If $f"\left(x\right)>0\forall xϵR$ then for any two real numbers $x_{1}and{x}_2,(x_1\ne x_2)$

A plane meets the coordinate axes in A, B, C such that the centroid of the triangle ABC is the point (a, a, a).
Then the equation of the plane is x + y + z = p, where p is

Let $S_n$ denote the sum of first n terms of an A.P. If $S_{2n}=3S_n$, then $S_{3n}:S_n$ is equal to

The length of the chord of the circle $x^2+y^2+3x+2y–8=0$ intercepted by the y-axis is

The base of an equilateral triangle with side 2a lies along the y-axis such that the mid-point of the base is at the origin.Find the vertices of the trianlge.

If $\alpha =\underset{n\to \infty }{lim}(\frac{1}{n^3+1}+\frac{4}{n^3+1}+\frac{9}{n^3+1}+\cdots +\frac{n^2}{n^3+1})$ and $\beta =\underset{x\to 0}{lim}\frac{\sin 2x}{\sin 8x},$ then a quadratic equation whose roots are $\alpha$ and $\beta$ is

If $(m_i,\frac{1}{m_i})$, i = 1, 2, 3, 4 are con - cyclic points, then the value of $m_1,m_2,m_3,m_4$ is

How many numbers of six digits can be formed from the digits 0, 1, 3, 5, 7 and 9 when no digit is repeated? How many of them are divisible by 10?

If sets A and B are defined as
$A=\left\{\right(x,y)|y=\frac{1}{x},x\ne 0,xϵR\},B=\left\{\right(x,y)|y=-x,xϵR\}$, then

$\int \frac{x^2+1}{x^4+1}dx$ will be equal to which of the following

The length of tangent from an external point to the circle $x^2+y^2-2x-2y-7=0$ is 4 units. What is the distance of this point to the farthest point in the circle?

The sum of all $4$-digit even numbers formed by the digits $0,1,2,3,5,7$ (without repetition) is

The point where the line $\frac{x-1}{2}=\frac{y-2}{-3}=\frac{z+3}{4}$ meets the plane 2x + 4y - z = 1, is [DSSE 1981]

The equation of the circle which intersects circles $x^2+y^2+x+2y+3=0,x^2+y^2+2x+4y+5=0$ and

$x^2+y^2-7x-8y-9=0$ at right angle, will be

If the curve $y=a{x}^{\frac{1}{2}}+bx$ passes through the point (1, 2) and lies above the x-axis in $0\le x\le 9$ and the area enclosed by the curve, the x axis and the line x = 4 is 8 sq. units. Then

The sum of three numbers in G.P. is 14, If the first two terms are each increased by 1 and the third term decreased by 1, the resulting numbers are in A.P. Find the numbers.

If y = - sin2x. Find the values of x at which the tangents drawn to the graph of this function is parallel to the x- axis.

If the reduction formula for $I_n=\int \frac{\sin \mathrm{nx}}{\cos x}\mathrm{dx}$ is given by
$I_n+I_{n-2}=-\frac{2\cos \left\{\right(n-1\left)x\right\}}{n-1}$, then $\int \frac{\sin 3x}{\cos x}\mathrm{dx}$ is.

If some three consecutive coefficients in the binomial expansion of $(x+1{)}^n$ in powers of $x$ are in the ratio $2:15:70$, then the average of these three coefficients is :

1+cos thita - sin thita/ cos thita -1+ sin thita = cosec thita + cot thita

If then equals

If a, b, c are the roots of the equation $x^3+2x^2+1=0$ . Find the equation whose roots are b + c - a,c + a - b, a + b - c.

If $f\left(x\right)=sinx+cosx,g\left(x\right)=x^2-1$ then $g\left(f\right(x\left)\right)$ in invertible in the Domain

$\int e^x$ (sin x + cos x)dx is equal to -

Negation of ‘Azra is in class X or Diya is in class XII’ is ___.

The angle between the pair of tangents drawn from a point P to the circle $x^2+y^2+4x-6y+9$$si{n}^2\alpha +13co{s}^2\alpha =0$ is $2\alpha$. Then the equation of the locus of the point P is

Let $a={\log }_3{\log }_{3}2$. An integer $k$ satisfying $1<2^{(3^{-a}-k)}<2$ is

A pie chart is to be drawn for representing the following data
$\begin{array}{cc}\text{Items of expenditure}& \text{Number of families}\\ \text{Education}& 150\\ \text{Food and clothing}& 400\\ \text{House rent}& 40\\ \text{Electricity}& 250\\ \text{Miscellaneous}& 160\end{array}$
The value of the central angle for food and clothing would be

If $\frac{1}{x-2}>0$, then $x$ lies in

If $\overrightarrow{a}=4\hat{i}+6\hat{j}$ and $\overrightarrow{b}=3\overrightarrow{j}+4\overrightarrow{k}$ then the vector form of component of $\overrightarrow{a}$ along $\overrightarrow{b}$ is

If the vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ are perpendicular to each other, then a vector $\overrightarrow{v}$ in terms of $\overrightarrow{a}$ and $\overrightarrow{b}$ satisfying the equations
$\overrightarrow{v}.\overrightarrow{a}=0,\overrightarrow{v}.\overrightarrow{b}=1and\left[\overrightarrow{v}\overrightarrow{a}\overrightarrow{b}\right]=1$ is

The number of triangles that can be formed by 5 points in a line and 3 points on a parallel line is

If ${}^n{C}_4,{}^n{C}_5,{}^n{C}_6$ are in A.P., then the value(s) of $n$ is/are

For each $nϵN$ the correct statement is