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The sum and sum of squares corresponding to length $x$ (in cm) and weight $y$ (in gm) of 50 plant products are given below :

${\sum }_{i=1}^{50}{x}_i=212,{\sum }_{i=1}^{50}{x}_i^2=902.8,{\sum }_{i=1}^{50}{y}_i=261,{\sum }_{i=1}^{50}{y}_i^2=1457.6$

Which is more varying, the length or the weight ?

The differential equation of the family of curves where A and B are arbitrary constants, is

[MNR 1988]

Let $f\left(x\right)=A\sin \left(\frac{\pi x}{2}\right)+B,f^{\prime }\left(\frac{1}{2}\right)=\sqrt{2}$ and $\underset{0}{\overset{1}{\int }}f\left(x\right)dx=\frac{2A}{\pi }$, then $A$ and $B$ are

Solve the given inequality for real x:

Let the plane passing through the point $(-1,0,-2)$ and perpendicular to each of the planes $2x+y-z=2$ and $x-y-z=3$ be $ax+by+cz+8=0$. Then the value of $a+b+c$ is equal to

The ratio between the sum of n terms of two A.P.'s is (7n+1):(4n+27). Find the ratio of their 11th terms.

Let $\Delta ABC$ be an isosceles right-angled triangle where $AB\perp BC$, if the equation of hypotenuse is $2x+3y=4$, then the sum of slopes of $AB$ and $AC$ can be equal to

The integrating factor of the differential equation $\frac{dy}{dx}\left(x{\log }_{e}x\right)+y=2{\log }_{e}x$ is given by

The number of $5$ digits palindrome numbers is

1. 5

Figure shows a relation between set P and Q. Write the relation R

Choose the correct answer in Question
The planes 2x - y + 4z = 5 and 5x - 2.5y + 10z = 6 are
(a) perpendicular
(b) parallel
(c) intersect along Y-axis
(d) passes through $(0,0,\frac{5}{4})$

The value of determinant $\left|\begin{array}{ccc}{y}^2& -xy& x^2\\ a& b& c\\ a^{\prime }& b^{\prime }& c^{\prime }\end{array}\right|$ is equal to

The integral value(s) of $x$ satisfying $|x^2-9|+|x^2-4|=5$ is/are

The transformed equation of $\frac{dy}{dx}+x\sin 2y=x^3{\cos }^{2}y$ is

The solution of the differential equation $(x^2+y^2)dy=xydx$ is $y=y\left(x\right).$ If $y\left(1\right)=1$ and $y\left(x_0\right)=e,$ then $x_0$ is

The equation of plane passing through $(-1,0,1)$ and parallel to the plane $2x-3y+z+1=0,$ is

Which of the following function is an onto function-

The equation of the line passing through the points $(1,–2,3)$ and parallel to the planes $x-y+2z-5=0$ and $3x+y+z-6=0$ is

Statement:The school authority decided to rent out the school premises during weekends and holidays for organising various functions to augment its resources to meet the growing needs of the school.

Assumptions:
I.The parents of the school students may protest against the decision of the school authority.
II.There may not be enough demand for hiring the school premises for organising function.

Solve the system of equations Re ($z^2$)=0, |z| = 2.

If $\left[\sin x\right]+\left[\sqrt{2}\cos x\right]=-3,x\in [0,2\pi ]$, (where $[.]$ represents the greatest integer function), then the range of $x$ is

Solve the following system of equations in R.

x+5>2(x+1),2-x<3(x+2)

The mean and standard deviation of $20$ observations were calculated as $10$ and $2.5$ respectively. It was found that by mistake one data value was taken as $25$ instead of $35.$ If $\alpha$ and$\sqrt{\beta }$ are the mean and standard deviation respectively for correct data, then $(\alpha ,\beta )$ is

Let $f:R\to R$ be defined as

$f\left(x\right)=\{\begin{array}{cc}-\frac{4}{3}{x}^3+2x^2+3x,& x>0\\ 3x{e}^x,& x\le 0\end{array}$

Then $f$ is increasing function in the interval:

If $n$ is even positive integer, then the condition that the greatest term in the expansion of $(1+x{)}^n$ may also have the greatest coefficient is

Let $C_n=\underset{\frac{1}{n+1}}{\overset{\frac{1}{n}}{\int }}\frac{{\tan }^{-1}\left(nx\right)}{{\sin }^{-1}\left(nx\right)}dx.$ Then $\underset{n\to \infty }{lim}{n}^2.C_n$ equals

If $A$ and $B$ are two mutually exclusive events, then the relation between $P\left(\overline{A}\right)$ and $P\left(B\right)$ is

If $\int \frac{3+2\cos x}{(2+3\cos x{)}^2}dx=\frac{f\left(x\right)}{2+3\cos x}+C$, where $C$ is a constant of integration, then $f\left(x\right)$ is